![Introduction to Geochemistry: Principles and Applications, First Edition. Kula C. Misra.
© 2012 Kula C. Misra. Published 2012 by Blackwell Publishing Ltd.
I knew of [Heisenberg’s) theory, of course, but I felt discouraged, not to say repelled, by the methods of transcendental algebra, which
appeared difficult to me, and by the lack of visualizability (Edwin Schrödinger, 1926).
The more I think about the physical portion of Schrödinger’s theory, the more repulsive I find it…. What Schrödinger writes about
the visualizability of his theory is probably not quite right, in other words it’s crap (Werner Heisenberg, 1926).
[Extracted from the worldwide web]
2 Atomic Structure
The three major physical states in which a system (part of the
universe that we have chosen for consideration) occurs are
solid, liquid, and gaseous. Although we commonly think of
distinctions among the three states in terms of physical prop-
erties such as bounding surface, hardness, viscosity, etc., the
fundamental difference lies in the arrangement of atoms in the
three states. Crystalline solids, which can occur spontaneously
in a form bounded by planar surfaces, are characterized by
long-range order, a regularity in the arrangement of atoms or
molecules that is repeated along parallel lines. Amorphous
solids consist of extremely small solid units with a very small
number of atoms per unit, so that “the forces which lead to the
planar surfaces of solids and their internal order are destroyed
by the enormous number of atoms in surface position” (Fyfe,
1964). Gases have no unique volume or boundaries, except
those imposed by the chosen container; they lack ordering of
their atoms or molecules. The liquid state may be viewed as
being somewhere in between the solid and gaseous states. The
atoms and molecules of liquids show only short-range order,
i.e., ordering of the atoms and molecules extend only over a
few molecular diameters. From the atomic perspective, glass
may be regarded as a very viscous fluid. Our focus here is on
crystalline solids because minerals, the main constituents of
rocks, are by definition crystalline solids. We begin with a
discussion of the general features of atomic structures because
the physical and chemical properties of minerals are determined
by the structure and arrangement of their constituent atoms.
2.1 Historical development
2.1.1 Discovery of the electron
The Greek philosopher Democritus (5th century bc) believed
in the existence of four elementary substances – air, water,
stone, and fire – all formed by a very large number of very
small particles called atoms, the word for “indivisibles” in
Greek (Gamow, 1961). Our understanding of the atom was
not much better until about the beginning of the 20th century.
Sir Isaac Newton (1642–1727) described atoms as “solid,
massy, hard, impenetrable, moveable particles” and this was
the generally accepted view throughout the 19th century.
In 1897, the British scientist J. J. Thompson (1856–1940),
one of the pioneers in the investigation of atomic structure,
proved by direct experiments that atoms are complex systems
composed of positively and negatively charged parts. The
experimental set-up, a primitive version of the modern televi-
sion tube, was rather simple. It consisted of a glass tube con-
taining highly rarified gas with a cathode (−) placed at one
end, an anode (+) in the middle part, and a fluorescent screen
at the other end (Fig. 2.1).When an electric current was passed
through the gas in the tube, the fluorescent screen became
luminous because of bombardment by fast moving particles
resulting from the gas. When a piece of metal was placed in
the path of the moving particles, it cast a shadow on the fluo-
rescent screen, indicating a straight-line path for the particles
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![2.2 The working model 15
The principal quantum number n, which is analogous to
Bohr’s principal quantum number, determines the size of the
orbital and also governs the allowed energy levels in the atom;
we may view n as defining the “shell” in which the orbitals
will occur. The value of n must be an integer (e.g., 1, 2, 3,
4, …) and the corresponding shells, from the nucleus outward,
are sometimes designated as K, L, M, N, …. A shell of princi-
pal quantum number n can accommodate a maximum of 2n2
electrons. Thus, the innermost or K shell (n=1) can hold
2 electrons, the L shell (n=2) 8 electrons, the M shell (n=3) 18
electrons, and so on. Not all electrons in a given shell, however,
are identical because those in a shell of principal quantum
number n are distributed over n“subshells”of different energy
levels characterized by an azimuthal quantum number l. The
azimuthal quantum number l determines the shape of the sub-
shell, and for a given value of n may assume any of the values
0, 1, 2, 3, 4, 5, …, n − 1 (the maximum possible value), and the
corresponding sub-shells are designated as s, p, d, f, g, h, …
(Table 2.2). Thus, an electron corresponding to n=1 and l=0
is symbolized as 1s, one corresponding to n =3 and l=1 as 3p,
one corresponding to n = 3 and l=2 as 3d, and so on. Further,
the number of electrons in a sub-shell may be indicated by a
superscript attached to the symbol for the sub-shell. For exam-
ple, 1s2
represents 2 electrons in the s sub-shell of the K shell,
2p6
represents 6 electrons in the p sub-shell of the L shell, and
3d5
represents 5 electrons in the d sub-shell of the M shell.
This scheme provides a convenient way to represent the elec-
tronic configuration of an atom. For example, the electronic
configurationofNi(Z=28)iswrittenas1s2
2s2
2p6
3s2
3p6
3d8
4s2
.
The electrons in each sub-shell are distributed in one or
more atomic orbitals (AOs), the number of orbitals being
determined by the magnetic quantum number ml
, which has
no effect on the size or shape of the orbitals but is related to
the orientation of an orbital in space. For a given n and l, there
are 2l+1 different possible values of ml
: −l, 0, +l (although the
actual numerical values allowed for ml
are not important for
our purpose).
Now let us consider how the quantum number l determines
the distribution of electron clouds around the nucleus
(Fig. 2.6). For l=0, the number of possible values of ml
is 1 for
all values of n, and the corresponding orbitals are s orbitals
such as 1s, 2s, 3s, etc. Electron clouds in s orbitals have a
spherical symmetry in the sense that there is the same
probability of finding an electron at a given distance from the
nucleus in any direction in space, and the sphere gets larger as
Table 2.2 Some principal quantum numbers and corresponding electron orbitals.
Principal quantum
number, n
Maximum
permissible electrons
for given n (2n2
)
Azimuthal
quantum number, l
(l=0, 1, 2, 3, … n − 1)
Names of
sub-shells
Magnetic quantum number,
ml
(maximum number of
orbitals=1, 3, 5, 7, …2l+1)
Designation of atomic
orbitals for electrons
(see Fig. 2.6)
1 (K shell) 2 0 1s 0 [1] 1s
2 (L shell) 8 0 2s 0 [1] 2s
1 2p −1, 0, +1 [3] 2px
, 2py
, 2pz
3 (M shell) 18 0 3s 0 [1] 3s
1 3p −1, 0, +1 [3] 3px
, 3py
, 3pz
2 3d −2, −1, 0, +1, +2 [5] 2
3
z
d , 2 2
–
3
x y
d , 3dxy
, 3dxz
, 3dyz
X
y
z
s
(a) 3s orbital
X
z
y
px X
y
z
py X
z
y
pz
(b) 3p orbitals
X
z
y
dxy
X
y
z
dyz
X
y
z
dxz
X
z
y
dx
2
– y
2 X
y
z
dz
2
(c) 3d orbitals
Fig. 2.6 Representation of the “shapes” of electron clouds for various
types of atomic orbitals for n (principal quantum number)=3:
(a) 3s orbital with spherical symmetry; (b) threefold degenerate 3p
orbitals; and (c) fivefold degenerate 3d orbitals. Note that the boundary
surfaces represent the regions likely to contain most (perhaps 95%) of
the electrons (meaning that there is a 95% probability of finding the
electrons within the region) and that the electron density is not the
same everywhere within a given orbital lobe.
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![18 Atomic Structure
2.3.2 The Periodic Table
The Periodic Table reflects an attempt at a systematic
organization of the elements from the perspective of their
atomic structures. In 1869, two very similar arrangements of
the known elements, much like the modern Periodic Table
(Fig. 2.8), were published independently, one by the Russian
chemist Dimitri Ivanovich Mendeleev (1834–1907) and the
other by the German chemist Lothar Meyer (1830–1895). Both
were based on regular periodic repetition of properties with
increasing atomic weight of the elements, Mendeleev’s largely
on chemical properties and Meyer’s on physical properties.The
modern version of the Periodic Table is organized on the basis
of atomic number of the elements,a concept that was developed
some 50 years later than Mendeleev’s work and is more
fundamental to the identity of each element.
The vertical columns in the Periodic Table are referred to as
groups, and the horizontal rows are referred to as periods,
which are numbered in accordance with the first quantum
number of the orbitals that are being filled with increasing
atomic number. For example, electrons fill the 1s orbital in
elements belonging to the 1st period, 2s and 2p orbitals in
elements of the 2nd period, and 3s and 3p orbitals in elements
of the 3rd period.The electron distribution in elements included
in the 4th to 7th periods becomes more complicated because of
filling of d and f orbitals (3d, 4d, 5d, 6d, 4f, 5f) as illustrated in
Fig. 2.8. Elements within a period have properties that change
progressively with increasing atomic number because of
addition of electrons. In contrast, elements in any group have
similar physical and chemical properties because of similar
electronic configuration. The groups are either designated as A
and B, and numbered from left to right in accordance with the
highest possible positive valence of the elements in that group
(American system) or numbered continuously from left to right
as 1 through 18 (International system). Some of the groups are
commonly referred to by special names: alkali metals (Group
IA, except H); alkaline earth metals (Group IIA); halogens
(Group VIIA), and noble (or inert) gases (Group VIIIA).
The Periodic Table can also be viewed as a systematic
representation of the electronic configurations of the elements.
The elements are arranged in blocks based on the kinds of
atomic orbitals (s, p, d, or f) being filled.The A groups comprise
elements in which s and p orbitals are being filled.The B groups
include elements in which the s orbital of the outermost
occupied shell contains one or two electrons (e.g., 5s1
and 5s2
for 37
Rb and 38
Sr, respectively), and the d orbitals, one shell
smaller, are being filled. The electronic configurations of the A
group elements, including the noble gases (Group VIIIA), are
quite systematic and can be predicted from their positions in
the Periodic Table, but some pronounced irregularities exist
for elements of the B group and of the 5th and higher periods.
2.3.3 Transition elements
Application of the guidelines discussed earlier to the filling of
successiveatomicorbitalswithelectronsisquitestraightforward
for atoms from 2
He(1s2
) to 18
Ar (1s2
2s2
2p6
3s2
3p6
), as illustrated
in Table 2.3.The M-shell, which can contain up to 18 electrons,
has room for 10 more electrons in the five 3d orbitals, but in
19
K [(Ar core)18
4s1
] and 20
Ca [(Ar core)18
4s2
], the additional
electrons are accommodated in the energetically more favorable
4s orbital of the N-shell compared with the 3d orbital (Fig. 2.7).
After 20
Ca, the 3d orbital is more stable than the 4s orbital, so
that from 21
Sc to 30
Zn, electrons enter the 3d orbital of the
M-shell in preference to the 4p orbital of the N-shell. The 3d
orbitals become completely filled in30
Zn, and filling of the 4p
orbitals starts with the element 31
Ga and continues progressively
to the element 36
Kr. The elements from 21
Sc to 30
Zn are called
the 3d transition elements or the first transition series.
Analogous schemes of filling the d orbitals give rise to 4d
transition series (39
Y through 48
Cd), 5d transition series (57
La
and 72
Hf through 80
Hg), and 6d transition series (89
Ac and 104
Rf
through element 112) (see Fig. 2.8). The elements of these four
transition series are all metals, and they contain electrons in
both ns and (n − 1)d orbitals, but not in the np orbitals. Two
additional transition series exist between groups IIIB and IVB
of the Periodic Table: the 4f transition series (58
Ce through 71
Li)
and the 5f transition series (90
Th through 103
Lr).These transition
elements are also metals, and are characterized by the
progressive filling of 4f and 5f orbitals, respectively (Fig. 2.8).
2.4 Chemical behavior of elements
The chemical behavior of an element is governed by its
electronic configuration because the energy level of the atom
is determined by the spatial distribution of its electron cloud.
It is only the most loosely bound electrons in the outermost
orbitals that take part in chemical interaction with other
atoms. For example, the alkali elements (group IA of the
Periodic Table), all of which have one electron in the outermost
orbital, exhibit similar chemical properties; so do the alkaline
earth metals (group IIA of the Periodic Table), all of which
have two electrons in the outermost orbital.
2.4.1 Ionization potential and electron affinity
Two concepts are useful in predicting the chemical behavior
of elements: ionization potential (or ionization energy); and
electron affinity. Ions are produced by the removal of
electron(s) from or the addition of electron(s) to a neutral
atom. The energy that must be supplied to a neutral atom (M)
in the gas phase to remove an electron to an infinite distance is
called the ionization potential (I). In other words, the
ionization potential is the difference in potential between the
initial state, in which the electron is bound, and the final state,
in which it is at rest at infinity; the lower the ionization
potential, the easier it is to convert the atom into a cation.
This is the reason why the ionization potential generally
increases from left to right in a given period and from top to
bottom within a given group of the Periodic Table (Fig. 2.9).
The first ionization potential (I1
) refers to the energy required
to remove the first (the least tightly bound) electron, the
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![22 Atomic Structure
Ground state
Hund’s rule
Ionization potential
Inert elements
Isobars
Isotones
Isotopes
Magnetic quantum number
Metalloids (semimetals)
Molar mass
Mole
Nodal plane
Octet rule
Pauli’s exclusion principle
Periodic Table
Principal quantum number
Schrödinger equation
Screening effect
Spin quantum number
Standard temperature and pressure (STP)
Transition elements
Valence electrons
Computation techniques
● The atomic weight (in amu) of an element from the data on
the abundances of its isotopes.
● Ionization potential, electron affinity.
2.7 Questions
1. Show that 1amu=1.6606×10−24
g
[Hint: 1amu=1/12 of the mass of a 12
6
C atom; 1 mole of
12
6
C contains 6.022×1023
atoms.]
2. Calculate the atomic weights (in amu) of the elements U
and Pb from the abundances of their isotopes given below:
3. A saturated solution of AgCl in water contains 1.3×10−5
mole of AgCl per liter of the solution at 25°C tempera-
ture and 1atm pressure. Calculate the mass of dissolved
AgCl in 1L of the solution. Gram atomic weights of the
elements: Ag=107.87; Cl=35.453.
4. Calculate the number of H2
O molecules that will evapo-
rate per second, given that one drop of water weighing
0.05gevaporatesin1h.Avogadro’snumber=6.022×1023
.
5. A geologist has identified two iron deposits. One of them
contains 100 million tons of magnetite (Fe3
O4
), and the
other contains 20 million tons of magnetite (Fe3
O4
), and
80 million tons of hematite (Fe2
O3
). Based on the iron
content alone, which of the two deposits should be rec-
ommended for mining? Gram atomic weights of the ele-
ments: Fe=55.85; O=16.00.
6. What is the maximum number of electrons that can be
accommodated in the following atomic orbitals?
(a) all the 6g orbitals; (b) all the 7s orbitals;
(c) all the 8f orbitals; and (d) all the orbitals with n=5
7. Write down the ground–state electronic configuration of
the following elements:
Fe (Z=26); Rubidium (Z=37); Xenon (Z=54); and
Uranium (Z=92).
8. Using the same format as for Table 2.3, prepare a table
illustrating the gradual filling with electrons of the
atomic orbitals of the 4d transition series.
9. Light near the middle of the ultraviolet region of the
electromagnetic radiation spectrum has a frequency of
2.73×1016
s−1
, whereas yellow light within the visible
spectrum has a frequency of 5.26×1014
s−1
.
(a) Calculate the wavelength corresponding to each of
these two frequencies of light.
(b) Calculate how much more is the energy associated
with a photon of ultraviolet light compared to that of
yellow light.
10. What is the wavelength associated with a neutron of
mass 1.675×10−24
g moving with a speed of 2360m s−1
.
U Pb
Isotope Mass (amu)
Abundance
(atom %) Isotope Mass (amu)
Abundance
(atom%)
234
U 234.0409468 0.0055 204
Pb 203.973020 1.4
234
U 235.0439242 0.7200 204
Pb 205.974440 24.1
234
U 238.0507847 99.2745 204
Pb 206.975872 22.1
204
Pb 207.976627 52.4
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Introduction to Geochemistry Principles and Applications 1st Edition Kula C. Misra
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- 5. Introduction to Geochemistry Principles and Applications 1st Edition Kula C. Misra Digital Instant Download Author(s): Kula C. Misra ISBN(s): 9781444350951, 1444350951 Edition: 1 File Details: PDF, 21.44 MB Year: 2012 Language: english
- 6. This book is intended to serve as a text for an introductory course in geochemistry for undergraduate/ graduate students with at least an elementary-level background in earth sciences, chemistry, and mathematics. The text, containing 83 tables and 181 figures, covers a wide variety of topics – ranging from atomic structure to chemical and isotopic equilibria to modern biogeochemical cycles – which are divided into four interrelated parts: Crystal Chemistry; Chemical Reactions (and biochemical reactions involving bacteria); Isotope Geochemistry (radiogenic and stable isotopes); and The Earth Supersystem, which includes discussions pertinent to the evolution of the solid Earth, the atmosphere, and the hydrosphere. In keeping with the modern trend in the field of geochemistry, the book emphasizes computational techniques by developing appropriate mathematical relations, solving a variety of problems to illustrate application of the mathematical relations, and leaving a set of questions at the end of each chapter to be solved by students. However, so as not to interrupt the flow of the text, involved chemical concepts and mathematical derivations are separated in the form of boxes. Supplementary materials are packaged into ten appendixes that include a standard-state (298.15 K, 1 bar) thermodynamic data table and a listing of answers to selected chapter-end questions. KULA C. MISRA is a Professor of Geology (Emeritus) at the University of Tennessee where he has taught geochemistry, economic geology, and environmental geology for more than 30 years. He received a M.Tech degree in Applied Geology from the Indian Institute of Technology (Kharagpur) and, after working for about ten years as a field geologist, a Ph.D. degree in Geology from the University of Western Ontario (Canada). His research papers have been published in several professional journals, and he is the author of the textbook Understanding Mineral Deposits published in the year 2000. He is a member of several professional organizations and has served as a consultant to corporations and government agencies on subjects related to mineral deposits and environmental geochemistry. Cover image: Lava flowing into the ocean; Puu Oo vent, Mount Kilauea, Hawaii Volcano National Park, 1991. Mark Newman/Science Photo Library. Cover design by Design Deluxe This book has a companion website www.wiley.com/go/misra/geochemistry with Figures and Tables from the book for downloading. Geochemistry INTRODUCTION TO MISRA INTRODUCTION TO Principles and Applications KULA C. MISRA Geochemistry
- 7. Misra_cover 2.indd 1 Misra_cover 2.indd 1 2/3/2012 5:51:09 PM 2/3/2012 5:51:09 PM
- 8. Misra_cover 1.indd 1 Misra_cover 1.indd 1 2/3/2012 5:50:40 PM 2/3/2012 5:50:40 PM
- 9. Misra_ffirs.indd ii Misra_ffirs.indd ii 1/31/2012 10:32:28 AM 1/31/2012 10:32:28 AM
- 10. INTRODUCTION TO GEOCHEMISTRY Misra_ffirs.indd i Misra_ffirs.indd i 1/31/2012 10:32:27 AM 1/31/2012 10:32:27 AM
- 11. Misra_ffirs.indd ii Misra_ffirs.indd ii 1/31/2012 10:32:28 AM 1/31/2012 10:32:28 AM
- 12. Introduction to Geochemistry Principles and Applications Kula C. Misra Emeritus Professor, Department of Earth and Planetary Sciences, The University of Tennessee, Knoxville, Tennessee, USA A John Wiley & Sons, Ltd., Publication Misra_ffirs.indd iii Misra_ffirs.indd iii 1/31/2012 10:32:28 AM 1/31/2012 10:32:28 AM
- 13. This edition first published 2012 © 2012 by Kula C. Misra Blackwell Publishing was acquired by John Wiley & Sons in February 2007. Blackwell’s publishing program has been merged with Wiley’s global Scientific, Technical and Medical business to form Wiley-Blackwell. Registered Office John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial Offices 9600 Garsington Road, Oxford, OX4 2DQ, UK The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK 111 River Street, Hoboken, NJ 07030-5774, USA For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com/wiley-blackwell. The right of the author to be identified as the author of this work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Misra, Kula C. Introduction to geochemistry : principles and applications / by Kula C. Misra. p. cm. Includes bibliographical references and index. ISBN 978-1-4443-5095-1 (cloth) – ISBN 978-1-4051-2142-2 (pbk.) 1. Geochemistry–Textbooks. I. Title. QE515.M567 2012 551.9–dc23 2011046009 A catalogue record for this book is available from the British Library. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books Set in 9.5/11.5pt Sabon by SPi Publisher Services, Pondicherry, India 1 2012 Misra_ffirs.indd iv Misra_ffirs.indd iv 1/31/2012 10:32:28 AM 1/31/2012 10:32:28 AM
- 14. To Anand, Lolly, and Tom Misra_ffirs.indd v Misra_ffirs.indd v 1/31/2012 10:32:28 AM 1/31/2012 10:32:28 AM
- 15. Misra_ffirs.indd vi Misra_ffirs.indd vi 1/31/2012 10:32:28 AM 1/31/2012 10:32:28 AM
- 16. Brief Contents Preface, xiii 1 Introduction, 1 PART I CRYSTAL CHEMISTRY, 7 2 Atomic Structure, 9 3 Chemical Bonding, 23 PART II CHEMICAL REACTIONS, 49 4 Basic Thermodynamic Concepts, 51 5 Thermodynamics of Solutions, 79 6 Geothermometry and Geobarometry, 107 7 Reactions Involving Aqueous Solutions, 134 8 Oxidation–Reduction Reactions, 167 9 Kinetics of Chemical Reactions, 197 PART III ISOTOPE GEOCHEMISTRY, 223 10 Radiogenic Isotopes, 225 11 Stable Isotopes, 253 PART IV THE EARTH SUPERSYSTEM, 281 12 The Core–Mantle–Crust System, 283 13 The Crust–Hydrosphere–Atmosphere System, 326 APPENDIX 1 Units of measurement and physical constants, 372 APPENDIX 2 Electronic configurations of elements in ground state, 374 APPENDIX 3 First ionization potential, electron affinity, electronegativity (Pauling scale), and coordination numbers of selected elements, 377 APPENDIX 4 Thermodynamic symbols, 379 APPENDIX 5 Standard state (298.15K, 105 Pa) thermodynamic data for selected elements, ionic species, and compounds, 382 APPENDIX 6 Fugacities of H2 O and CO2 in the range 0.5–10.0 kbar and 200–1000°C, 396 APPENDIX 7 Equations for activity coefficients in multicomponent regular solid solutions, 398 APPENDIX 8 Some commonly used computer codes for modeling of geochemical processes in aqueous solutions, 400 APPENDIX 9 Solar system abundances of the elements in units of number of atoms per 106 silicon atoms, 402 APPENDIX 10 Answers to selected chapter–end questions, 403 References, 406 Index, 431 Misra_ftoc.indd vii Misra_ftoc.indd vii 2/3/2012 1:02:22 PM 2/3/2012 1:02:22 PM
- 17. Contents Preface, xiii 1 Introduction, 1 1.1 Units of measurement, 1 1.1.1 The SI system of units, 1 1.1.2 Concentration units for solutions, 3 1.2 The Geologic Time Scale, 3 1.3 Recapitulation, 5 1.4 Questions, 5 PART I CRYSTAL CHEMISTRY, 7 2 Atomic Structure, 9 2.1 Historical development, 9 2.1.1 Discovery of the electron, 9 2.1.2 The Rutherford–Bohr atom, 10 2.1.3 Wave mechanics, 12 2.2 The working model, 13 2.2.1 Quantum numbers, 14 2.2.2 Energy levels of the atomic orbitals, 16 2.3 The ground state electron configuration of elements, 17 2.3.1 Filling atomic orbitals with electrons: the Aufbau principle, 17 2.3.2 The Periodic Table, 18 2.3.3 Transition elements, 18 2.4 Chemical behavior of elements, 18 2.4.1 Ionization potential and electron affinity, 18 2.4.2 Classification of elements, 20 2.5 Summary, 21 2.6 Recapitulation, 21 2.7 Questions, 22 3 Chemical Bonding, 23 3.1 Ionic bonding, 24 3.1.1 Ionic radii, 24 3.1.2 Coordination number and radius ratio, 25 3.1.3 Lattice energy of ideal ionic crystals, 28 3.2 Crystal structures of silicate minerals, 31 3.3 Ionic substitution in crystals, 31 3.3.1 Goldschmidt’s rules, 31 3.3.2 Ringwood’s rule, 32 3.4 Crystal-field theory, 33 3.4.1 Crystal-field stabilization energy, 33 3.4.2 Nickel enrichment in early-formed magmatic olivine, 35 3.4.3 Colors of transition-metal complexes, 35 3.5 Isomorphism, polymorphism, and solid solutions, 36 3.5.1 Isomorphism, 36 3.5.2 Polymorphism, 36 3.5.3 Solid solutions, 36 3.6 Covalent bonding, 37 3.6.1 Valence bond theory versus molecular orbital theory, 37 3.6.2 Covalent radii, 38 3.6.3 Hybridization of atomic orbitals, 38 3.6.4 Sigma (s), pi (p ), and delta (d) molecular orbitals, 39 3.6.5 The degree of ionic character of a chemical bond: Electronegativity, 40 3.7 Metallic bonds, 43 3.8 Van der Waals bonds, 44 3.9 Hydrogen bond, 44 3.10 Comparison of bond types, 45 3.11 Goldschmidt’s classification of elements, 45 3.12 Summary, 47 3.13 Recapitulation, 48 3.14 Questions, 48 PART II CHEMICAL REACTIONS, 49 4 Basic Thermodynamic Concepts, 51 4.1 Chemical equilibrium, 51 4.1.1 Law of Mass Action – equilibrium constant (Keq ), 51 4.1.2 Le Chatelier’s principle, 54 4.2 Thermodynamic systems, 54 4.2.1 Attributes of a thermodynamic system, 54 4.2.2 State functions, 56 Misra_ftoc.indd viii Misra_ftoc.indd viii 2/3/2012 1:02:22 PM 2/3/2012 1:02:22 PM
- 18. Contents ix 4.2.3 The Gibbs phase rule, 56 4.2.4 Equations of state, 57 4.2.5 Kinds of thermodynamic systems and processes, 58 4.3 Laws of thermodynamics, 58 4.3.1 The first law: conservation of energy, 58 4.3.2 The second law: the concept and definition of entropy (S), 59 4.3.3 The fundamental equation: the first and second laws combined, 60 4.3.4 The third law: the entropy scale, 60 4.4 Auxiliary thermodynamic functions, 61 4.4.1 Enthalpy (H), 61 4.4.2 Heat capacity (Cp , Cv ), 61 4.4.3 Gibbs free energy (G), 63 4.4.4 Computation of the molar free energy of a substance at T and P ( ) P T G , 64 4.5 Free energy change of a reaction at T and P ( ) , P T G Δ r , 67 4.5.1 Computation of 1 , r T G Δ , 67 4.5.2 Evaluation of the volume integral, 68 4.5.3 General equation for , P r T G Δ , 68 4.6 Conditions for thermodynamic equilibrium and spontaneity in a closed system, 68 4.7 Metastability, 71 4.8 Computation of simple P–T phase diagrams, 71 4.8.1 Procedure, 71 4.8.2 The Clapeyron equation, 72 4.9 Thermodynamic data tables, 74 4.10 Summary, 75 4.11 Recapitulation, 76 4.12 Questions, 76 5 Thermodynamics of Solutions, 79 5.1 Chemical potential, 80 5.1.1 Partial molar properties, 80 5.1.2 Definition of chemical potential (m), 81 5.1.3 Expression for free energy in terms of chemical potentials, 81 5.1.4 Criteria for equilibrium and spontaneous change among phases of variable composition, 82 5.1.5 Criteria for equilibrium and spontaneous change for a reaction, 83 5.1.6 The Gibbs–Duhem equation, 83 5.2 Variation of chemical potential ( i α μ ) with temperature, pressure, and composition, 84 5.2.1 Temperature dependence of chemical potential, 84 5.2.2 Pressure dependence of chemical potential, 84 5.2.3 Dependence of chemical potential on composition: the concept of activity, 84 5.3 Relationship between Gibbs free energy change and equilibrium constant for a reaction, 86 5.4 Gases, 87 5.4.1 Pure ideal gases and ideal gas mixtures, 87 5.4.2 Pure nonideal gases: fugacity and fugacity coefficient, 88 5.4.3 Nonideal gas mixtures, 89 5.5 Ideal solutions involving condensed phases, 92 5.5.1 Mixing properties of ideal solutions, 92 5.5.2 Raoult’s Law, 93 5.5.3 Henry’s Law, 95 5.5.4 The Lewis Fugacity Rule, 96 5.5.5 Activities of constituents in ideal solutions, 96 5.6 Nonideal solutions involving condensed phases, 97 5.7 Excess functions, 98 5.8 Ideal crystalline solutions, 98 5.8.1 Application of the mixing-on-sites model to some silicate minerals, 98 5.8.2 Application of the local charge balance model to some silicate minerals, 100 5.9 Nonideal crystalline solutions, 101 5.9.1 General expressions, 101 5.9.2 Regular solution, 102 5.10 Summary, 103 5.11 Recapitulation, 104 5.12 Questions, 104 6 Geothermometry and Geobarometry, 107 6.1 Tools for geothermobarometry, 107 6.2 Selection of reactions for thermobarometry, 110 6.3 Dependence of equilibrium constant on temperature and pressure, 111 6.4 Univariant reactions and displaced equilibria, 114 6.4.1 Al2 SiO5 polymorphs, 114 6.4.2 Garnet–rutile–Al2 SiO5 polymorph–ilmenite– quartz (GRAIL) barometry, 115 6.4.3 Garnet–plagioclase–pyroxene–quartz (GAPES and GADS) barometry, 116 6.5 Exchange reactions, 118 6.5.1 Garnet–clinopyroxene thermometry, 119 6.5.2 Garnet–biotite (GABI) thermometry, 120 6.5.3 Magnetite–ilmenite thermometry and oxygen barometry, 122 6.6 Solvus equilibria, 126 6.7 Uncertainties in thermobarometric estimates, 127 6.8 Fluid inclusion thermobarometry, 128 6.9 Summary, 130 6.10 Recapitulation, 131 6.11 Questions, 131 7 Reactions Involving Aqueous Solutions, 134 7.1 Water as a solvent, 134 7.2 Activity–concentration relationships in aqueous electrolyte solutions, 135 Misra_ftoc.indd ix Misra_ftoc.indd ix 2/3/2012 1:02:22 PM 2/3/2012 1:02:22 PM
- 19. x Contents 7.2.1 Activity coefficient of a solute, 135 7.2.2 Standard state of an aqueous solute, 135 7.2.3 Estimation of activity coefficients of solutes, 136 7.3 Dissociation of acids and bases, 139 7.4 Solubility of salts, 140 7.4.1 The concept of solubility, 140 7.4.2 Solubility product, 141 7.4.3 Saturation index, 144 7.4.4 Ion pairs, 145 7.4.5 Aqueous complexes of ore metals, 146 7.5 Dissociation of H2 CO3 acid – the carbonic acid system, 146 7.5.1 Open system, 147 7.5.2 Closed system, 147 7.6 Acidity and alkalinity of a solution, 149 7.7 pH buffers, 150 7.8 Dissolution and precipitation of calcium carbonate, 151 7.8.1 Solubility of calcite in pure water, 151 7.8.2 Carbonate equilibria in the CaCO3 –CO2 –H2 O system, 151 7.8.3 Factors affecting calcite solubility, 153 7.8.4 Abiological precipitation of calcium carbonate in the oceans, 154 7.8.5 Biological precipitation of calcium carbonate in the oceans, 156 7.8.6 Carbonate compensation depth, 157 7.9 Chemical weathering of silicate minerals, 158 7.9.1 Mechanisms of chemical weathering, 158 7.9.2 Solubility of Silica, 159 7.9.3 Equilibria in the system K2 O–Al2 O3 –SiO2 – H2 O, 161 7.10 Summary, 164 7.11 Recapitulation, 165 7.12 Questions, 165 8 Oxidation–Reduction Reactions, 167 8.1 Definitions, 167 8.2 Voltaic cells, 168 8.2.1 Zinc–hydrogen cell, 168 8.2.2 Standard hydrogen electrode and standard electrode potential, 170 8.2.3 Zinc–copper cell, 170 8.2.4 Electromotive series, 171 8.2.5 Hydrogen–oxygen fuel cell, 172 8.3 Relationship between free energy change (ΔGr ) and electrode potential (E) – the Nernst equation, 173 8.4 Oxidation potential (Eh), 174 8.5 The variable pe, 175 8.6 Eh–pH stability diagrams, 176 8.6.1 Stability limits of surface water, 176 8.6.2 Procedure for construction of Eh–pH diagrams, 179 8.6.3 Geochemical classification of sedimentary redox environments, 182 8.7 Role of microorganisms in oxidation–reduction reactions, 182 8.7.1 Geochemically important microorganisms, 182 8.7.2 Examples of oxidation–reduction reactions mediated by microorganism, 184 8.8 Oxidation of sulfide minerals, 186 8.8.1 Mediation by microorganisms, 186 8.8.2 Oxidation of pyrite, 186 8.8.3 Acid mine drainage, 187 8.8.4 Bioleaching, 188 8.8.5 Biooxidation, 190 8.8.6 Biofiltration, 190 8.9 Oxygen fugacity, 191 8.9.1 Oxygen buffers, 191 8.9.2 Oxygen fugacity–sulfur fugacity diagrams, 192 8.10 Summary, 193 8.11 Recapitulation, 194 8.12 Questions, 194 9 Kinetics of Chemical Reactions, 197 9.1 Rates of chemical reactions (ℜ): basic principles, 197 9.1.1 Elementary and overall reactions, 197 9.1.2 Rate–law expression, 198 9.1.3 Integrated rate equations for elementary reactions, 199 9.1.4 Principle of detailed balancing, 201 9.1.5 Sequential elementary reactions, 202 9.1.6 Parallel elementary reactions, 203 9.2 Temperature dependence of rate constants, 204 9.2.1 The Arrhenius equation – activation energy, 204 9.2.2 Transition states, 206 9.3 Relationship between rate and free energy change of an elementary reaction (ΔGr ), 208 9.4 Catalysts, 209 9.4.1 Homogeneous catalysis, 209 9.4.2 Heterogeneous catalysis, 209 9.5 Mass transfer in aqueous solutions, 210 9.5.1 Advection–diffusion equation, 210 9.5.2 The temperature dependence of diffusion coefficient, 212 9.6 Kinetics of geochemical processes – some examples, 212 9.6.1 Diffusion-controlled and surface-controlled reaction mechanisms, 212 9.6.2 Dissolution and precipitation of calcite in aqueous solutions, 213 9.6.3 Dissolution of silicate minerals, 216 9.7 Summary, 218 9.8 Recapitulation, 219 9.9 Questions, 220 Misra_ftoc.indd x Misra_ftoc.indd x 2/3/2012 1:02:58 PM 2/3/2012 1:02:58 PM
- 20. Contents xi PART III ISOTOPE GEOCHEMISTRY, 223 10 Radiogenic Isotopes, 225 10.1 Radioactive decay, 225 10.1.1 Abundance and stability of nuclides, 225 10.1.2 Mechanisms of radioactive decay, 226 10.2 Principles of radiometric geochronology, 227 10.2.1 Decay of a parent radionuclide to a stable daughter, 227 10.2.2 Basic equation for radiometric age determination, 228 10.2.3 Decay series, 230 10.3 Selected methods of geochronology, 230 10.3.1 Rubidium–strontium system, 230 10.3.2 Samarium–neodymium system, 232 10.3.3 Uranium–thorium–lead system, 233 10.3.4 Rhenium–osmium system, 240 10.3.5 Potassium (40 K)–argon (40 Ar) method, 241 10.3.6 Argon (40 Ar)–argon (39 Ar) method, 243 10.3.7 Carbon-14 method, 244 10.4 Isotope ratios as petrogenetic indicators, 245 10.4.1 Strontium isotope ratios, 246 10.4.2 Neodymium isotope ratios, 246 10.4.3 Combination of strontium and neodymium isotope ratios, 247 10.4.4 Osmium isotope ratios, 248 10.5 Summary, 249 10.6 Recapitulation, 250 10.7 Questions, 250 11 Stable Isotopes, 253 11.1 Isotopic fractionation, 254 11.1.1 Causes of isotopic fractionation, 254 11.1.2 Mechanisms of isotopic fractionation, 255 11.1.3 Fractionation factor, 255 11.1.4 The delta (d) notation, 256 11.1.5 Calculation of the fractionation factor from d values, 256 11.2 Types of isotopic fractionation, 258 11.2.1 Equilibrium isotope effects, 258 11.2.2 Kinetic isotope effects, 259 11.3 Stable isotope geothermometry, 259 11.3.1 Oxygen isotope geothermometry, 260 11.3.2 Sulfur isotope geothermometry, 262 11.4 Evaporation and condensation processes, 262 11.4.1 Evaporation of ocean water, 262 11.4.2 Condensation of water vapor, 263 11.4.3 Meteoric water line, 265 11.5 Source(s) of water in hydrothermal fluids, 265 11.6 Estimation of water: rock ratios from oxygen isotope ratios, 267 11.7 Sulfur isotopes in sedimentary systems, 268 11.7.1 Bacterial sulfate reduction (BSR), 269 11.7.2 Thermochemical sulfate reduction (TSR), 270 11.7.3 Sulfur isotopic composition of seawater sulfate through geologic time, 270 11.7.4 Open versus closed sedimentary systems with respect to sulfate and sulfide, 271 11.7.5 Sulfur isotope ratios of sulfides in marine sediments, 272 11.8 Mass-independent fractionation (MIF) of sulfur isotopes, 273 11.9 Iron isotopes: geochemical applications, 275 11.9.1 Fractionation of iron isotopes, 275 11.9.2 Abiotic versus biotic precipitation of Fe minerals in banded iron formations, 276 11.10 Summary, 277 11.11 Recapitulation, 278 11.12 Questions, 278 PART IV THE EARTH SUPERSYSTEM, 281 12 The Core–Mantle–Crust System, 283 12.1 Cosmic perspective, 283 12.1.1 The Big Bang: the beginning of the universe, 283 12.1.2 Nucleosynthesis: creation of the elements, 285 12.1.3 The Solar System, 290 12.1.4 Meteorites, 292 12.1.5 Solar System abundances of the elements, 294 12.1.6 Origin of the Solar System: the planetesimal model, 295 12.2 Evolution of the Earth, 296 12.2.1 The internal structure of the Earth, 296 12.2.2 Bulk Earth composition, 299 12.2.3 The primary geochemical differentiation of the proto-Earth: formation of the Earth’s core and mantle, 301 12.2.4 Formation and growth of the Earth’s crust, 306 12.3 Generation and crystallization of magmas, 310 12.3.1 Geochemical characteristics of primary magmas, 310 12.3.2 Behavior of trace elements during partial melting of source rocks, 311 12.3.3 Behavior of trace elements during magmatic crystallization, 316 12.3.4 Chemical variation diagrams, 318 12.3.5 Rare earth elements, 318 12.4 Geochemical discrimination of paleotectonic settings of mafic volcanic suites, 319 12.4.1 Tectonomagmatic discrimination diagrams, 319 12.4.2 Spider diagrams, 321 Misra_ftoc.indd xi Misra_ftoc.indd xi 2/3/2012 1:02:58 PM 2/3/2012 1:02:58 PM
- 21. xii Contents 12.5 Summary, 323 12.6 Recapitulation, 324 12.7 Questions, 324 13 The Crust–Hydrosphere–Atmosphere System, 326 13.1 The present atmosphere, 326 13.1.1 Temperature and pressure distribution in the atmosphere, 326 13.1.2 Photochemical reactions in the atmosphere, 329 13.1.3 The Ozone layer in the stratosphere, 329 13.1.4 Composition of the atmosphere, 331 13.2 Evolution of the Earth’s atmosphere over geologic time, 333 13.2.1 Origin of the atmosphere, 333 13.2.2 A warm Archean Earth: the roles of carbon dioxide and methane, 335 13.2.3 Oxygenation of the atmosphere, 336 13.2.4 The Great Oxidation Event (GOE), 337 13.2.5 A model for the evolution of the atmosphere, 342 13.2.6 The Phanerozoic atmosphere, 343 13.3 Air pollution: processes and consequences, 344 13.3.1 Depletion of stratospheric ozone – the “ozone hole”, 344 13.3.2 Smogs, 347 13.3.3 Acid deposition, 350 13.3.4 Greenhouse gases and global warming, 351 13.4 The hydrosphere, 354 13.4.1 Composition of modern seawater, 354 13.4.2 Mass balance of dissolved constituents in seawater, 356 13.5 Evolution of the oceans over geologic time, 357 13.5.1 Origin of the oceans, 357 13.5.2 Oxidation state of the oceans, 360 13.5.3 Composition of the oceans, 361 13.6 Geosphere–hydrosphere–atmosphere–biosphere interaction: global biogeochemical cycles, 362 13.6.1 The carbon cycle, 363 13.6.2 The oxygen cycle, 365 13.6.3 The nitrogen cycle, 366 13.6.4 The sulfur cycle, 367 13.6.5 The phosphorus cycle, 368 13.7 Summary, 368 13.8 Recapitulation, 369 13.9 Questions, 370 APPENDIX 1 Units of measurement and physical constants, 372 APPENDIX 2 Electronic configurations of elements in ground state, 374 APPENDIX 3 First ionization potential, electron affinity, electronegativity (Pauling scale), and coordination numbers of selected elements, 377 APPENDIX 4 Thermodynamic symbols, 379 APPENDIX 5 Standard state (298.15K, 105 Pa) thermodynamic data for selected elements, ionic species, and compounds, 382 APPENDIX 6 Fugacities of H2 O and CO2 in the range 0.5–10.0 kbar and 200–1000°C, 396 APPENDIX 7 Equations for activity coefficients in multicomponent regular solid solutions, 398 APPENDIX 8 Some commonly used computer codes for modeling of geochemical processes in aqueous solutions, 400 APPENDIX 9 Solar system abundances of the elements in units of number of atoms per 106 silicon atoms, 402 APPENDIX 10 Answers to selected chapter–end questions, 403 References, 406 Index, 431 COMPANION WEBSITE This book has a companion website www.wiley.com/go/misra/geochemistry with Figures and Tables from the book for downloading. Misra_ftoc.indd xii Misra_ftoc.indd xii 2/3/2012 1:02:58 PM 2/3/2012 1:02:58 PM
- 22. Preface Geochemistry deals essentially with the processes and conse- quences of distribution of elements in minerals and rocks in different physical–chemical environments and, as such, per- meates all branches of geology to varying degrees. An ade- quate background in geochemistry is, therefore, an imperative for earth science students. This book is an attempt to cater to that need. It covers a wide variety of topics, ranging from atomic structures that determine the chemical behavior of ele- ments to modern biogeochemical cycles that control the global–scale distribution of elements. It is intended to serve as a text for an introductory undergraduate/graduate level course in geochemistry, and it should also provide the necessary background for more advanced courses in mineralogy, petrol- ogy, and geochemistry. The organization of the book is logical and quite different from the geochemistry texts in the market. Excluding the “Introduction”, the 12 chapters of the book are divided into four interrelated parts. Part I (Crystal Chemistry – Chapters 2 and 3) provides a brief review of the electronic structure of atoms and of different kinds of chemical bonds. Part II (Chemical Reactions – Chapters 4 through 9) discusses the thermodynamic basis of chemical reactions involving phases of constant and variable composition, including reactions rel- evant to aqueous systems and reactions useful for geother- mometry and geobarometry. A substantial portion of the chapter on oxidation–reduction reactions (Chapter 8) is devoted to a discussion of the role of bacteria in such reac- tions. The last chapter of Part II is a brief introduction to the kinetic aspects of chemical reactions. Part III (Isotope Geochemistry – Chapters 10 and 11) introduces the students to radiogenic and stable isotopes, and their applications to geologic problems, ranging from dating of rocks and minerals to the interpretation of an anoxic atmosphere during the Hadean and Archean eras. Part IV (The Earth Supersystem – Chapters 12 and 13) is an overview of the origin and evolu- tion of the solid Earth (core, mantle, and crust), and of the atmosphere and hydrosphere. A brief discussion of some important biogeochemical cycles provides a capstone to the introductory course. The treatment in this book recognizes the welcome fact that geochemistry has become increasingly more quantitative, and assumes that the students have taken the usual selection of elementary courses in earth sciences, chemistry, and mathe- matics. Nevertheless, most relevant chemical concepts and mathematical relations are developed from first principles. It is my experience that the derivation of an equation enhances the appreciation for its applications and limitations. To main- tain the flow of the text, however, some derivations and tan- gential material are separated from the text in the form of “boxes.” Supplementary data and explanations are presented in 10 appendixes. Quantitative aspects of geochemistry are emphasized throughout the book to the extent they are, in my judgment, appropriate at an introductory level. Each chapter in the book contains many solved examples illustrating the application of geochemistry to real-life geo- logical and environmental problems. At the end of each chap- ter is a list of computational techniques the students are expected to have learned and a set of questions to reinforce the importance of solving problems. It is an integral part of the learning process that the students solve every one of these problems. To help the students in this endeavor, answers to selected problems are included as an appendix (Appendix 10). I owe a debt of gratitude to all my peers who took the time to review selected parts of the manuscript: D. Sherman, University of Bristol; D.G. Pearson, Durham University; Hilary Downes, University College (London); Harry McSween, Jr., University of Tennessee (Knoxville); and Harold Rowe, University of Texas (Arlington). Their constructive critiques resulted in significant improvement of the book, but I take full responsibility for all shortcom- ings of the book. Thanks are also due to many of my col- leagues in the Department of Earth and Planetary Sciences, University of Tennessee – Christopher Fedo, Robert Hatcher, Linda Kah, Theodre Labotka, Colin Sumrall, and Lawrence Taylor – who in course of many discussions patiently shared with me their expertise on selected topics covered in the book. I am particularly grateful to Harry McSween for many Misra_fpref.indd xiii Misra_fpref.indd xiii 1/18/2012 4:42:12 PM 1/18/2012 4:42:12 PM
- 23. xiv Preface prolonged discussions regarding the origin and early history of the Earth, and to Ian Francis, Senior Commissioning Editor, Earth and Environmental Sciences, Wiley-Blackwell Publishers, for his sustained encouragement throughout this endeavor. I am also indebted to the many publishers and indi- viduals who have kindly allowed me to include copyrighted figures in the book. Lastly, and most importantly, this book could not have been completed without the patience of my wife, children, and grandchildren, who had to endure my preoccupation with the book for long stretches. Kula C. Misra Department of Earth and Planetary Sciences University of Tennessee Knoxville, TN 37996 May 2011 Misra_fpref.indd xiv Misra_fpref.indd xiv 1/18/2012 4:42:13 PM 1/18/2012 4:42:13 PM
- 24. Introduction to Geochemistry: Principles and Applications, First Edition. Kula C. Misra. © 2012 Kula C. Misra. Published 2012 by Blackwell Publishing Ltd. Geochemistry, as the name suggests, is the bridge between geology and chemistry and, thus, in essence encompasses the study of all chemical aspects of the Earth and their interpretation utilizing the principles of chemistry. Rankama and Sahama (1950) 1 Introduction 1.1 Units of measurement A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard or measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement. The original metric system of measurement was adopted in France in 1791. Over the years it developed into two some- what different systems of metric units: (a) the MKS system, based on the meter, kilogram, and second for length, mass, and time, respectively; and (b) the CGS system (which was introduced formally by the British Association for the Advancement of Science in 1874), based on the centimeter, gram, and second. There are other traditional differences between the two systems, for example, in the measurements of electric and magnetic fields. The recurring need for conversion from units in one of the two systems to units of the other, however, defeated the metric ideal of a universal measuring system, and a choice had to be made between the two systems for international usage. In 1954, the Tenth General Conference on Weights and Measures adopted the meter, kilogram, second, ampere, degree Kelvin, and candela as the basic units for all international weights and measures. Soon afterwards, in 1960, the Eleventh General Conference adopted the name International System of Units (abbreviated to SI from the French “Système International d’Unitès”) for this collection of units. The “degree Kelvin” was renamed the “kelvin” in 1967. 1.1.1 The SI system of units In the SI system, the modern form of the MKS system, there are seven base units from which all other units of measure- ment can be derived (Table 1.1). The International Union of Pure and Applied Chemistry (IUPAC) has recommended the use of SI units in all scientific communications. This is certainly desirable from the perspective of standardization of data, but a lot of the available chemical data were collected prior to 1960 and thus are not necessarily in SI units. It is therefore necessary for geochemists to be familiar with both SI and non-SI units. Equivalence between SI and non-SI units, and some of the commonly used physical constants are given in Appendix 1. Most chemists, physicists, and engineers now use SI system of units, but the use of CGS (centimeter–gram–second) and other non-SI units is still widespread in geologic literature. In this book we will use SI units, but with two exceptions. As pointed out by Powell (1978) and Nordstrom and Munoz (1994), the SI unit pascal (Pa) is unwieldy for reporting geological pressures. For example, many geochemical meas- urements have been done at 1 atmosphere (atm) ambient pressure (the pressure exerted by the atmosphere at sea level), which translates into 101,325 pascals or 1.01 megapascals Misra_c01.indd 1 Misra_c01.indd 1 1/19/2012 6:11:14 PM 1/19/2012 6:11:14 PM
- 25. 2 Introduction (Mpa), a rather cumbersome number to use. Most geochemists prefer to use bar as the unit of pressure, which can easily be converted into pascals (1 bar=105 pascals or 0.1MPa) and which is close enough to pressure expressed in atmosphere (1 bar=0.987atm) for the difference to be ignored in most cases without introducing significant error. A similar problem exists in the use of the SI unit joule (J), instead of the more familiar non-SI unit calorie (cal). The calorie, defined as the quantity of heat required to raise 1 gram (g) of water from 14.5 to 15.5°C, has a physical meaning that is easy to under- stand. Moreover, tables of thermodynamic data, especially the older ones, use calories instead of joules. Thus, we may use calories in the calculations and report the final results in joules (1cal=4.184J). The familiar scale of temperature is the Celsius scale (°C), which is based on two reference points for temperature: the ice point, the temperature at which ice is in equilibrium with liquid water at 1 atm pressure; and the steam point, the temperature at which steam is in equilibrium with liquid water at 1 atm pressure. The Celsius scale arbitrarily assigns a temperature of zero to the ice point and a temperature of 100 to the steam point. The SI unit of temperature is kelvin (K), which is the temperature used in all thermodynamic calculations. If pressure–temperature (°C) plots at different volumes are constructed for any gas, the extrapolated lines all intersect at a point representing zero pressure at a temperature around −273°C (Fig. 1.1). This temperature, which is not physically attainable (although it has been approached very closely), is called the absolute zero of temperature. It is the temperature at which the molecules of a gas have no translational, rotational, or vibrational motion and therefore no thermal energy. The temperature scale with absolute zero as the starting point is the kelvin temperature scale and the unit of temperature on this scale is kelvin (K, not °K), so named after Lord Kelvin who proposed it in 1848. The kelvin unit of temperature is defined as the 1/273.16 fraction of the so-called triple point for H2 O (the temperature at which ice, liquid water, and steam coexist in equilibrium at 1 atm pressure), which is 0.01 K greater than the ice point. Thus, the ice point, which is defined as 0°C, corresponds to 273.15 K (see Fig. 4.3) and the relationship between kelvin and Celsius scales of temperature is given by: T (K)=t (°C)+273.15 (1.1) Temperature (°C) V1 V2 V3 V4 100 –273 0 200 Pressure (bar) Absolute zero of temperature Fig. 1.1 The definition of absolute zero of temperature. The lines V1 –V4 show the variation of different volumes of a gas as a function of temperature and pressure. When extrapolated, the lines intersect at a point representing zero pressure at a temperature around −273°C. This temperature, which is not physically attainable, is called the absolute zero of temperature. Table 1.1 The SI base units and examples of SI derived units. SI base units Examples of SI derived units Physical quantity Name Symbol Physical quantity Name Symbol Definition in terms of the SI base units Length Meter m Force Newton N m kg s−2 Mass Kilogram kg Pressure Pascal Pa m−1 kg s−2 =Nm−2 Time Second s Energy, work, heat Joule J m2 kg s−2 =Nm Temperature Kelvin K Electric charge Coulomb C sA Amount of substance Mole mol Electric potential difference Volt V m2 kg s−3 A−1 Electric current Ampere A Volume Liter L m3 10−3 Luminous intensity Candela cd Electric conductance Siemens S m−2 kg−1 s3 A2 Newton=the force that will accelerate a mass of 1kg by 1m s−2 . Pascal=the pressure exerted when a force of 1N acts uniformly over an area of 1m2 . Joule=work done when a force of 1N produces a displacement of 1m in the direction of the force. Misra_c01.indd 2 Misra_c01.indd 2 1/19/2012 6:11:15 PM 1/19/2012 6:11:15 PM
- 26. 1.2 The Geologic Time Scale 3 Evidently, the steam point (100°C) corresponds to 373.15K. It follows from equation (1.1) that the degree Celsius is equal in magnitude to the kelvin, which in turn implies that the numer- ical value of a given temperature difference or temperature interval is the same whether it is expressed in the unit degree Celsius (°C) or in the unit kelvin. (In the USA, temperatures are often measured in the Fahrenheit scale (F). The expression relating temperatures in the Celsius and Fahrenheit scales is: F=9/5°C+32.) 1.1.2 Concentration units for solutions Concentrations of solutes (dissolved substances) in solutions (solids, liquids, or gases) are commonly expressed either as mass concentrations (parts per million, or milligrams per liter, or equivalent weights per liter) or as molar concentrations (molality, molarity, or mole fraction; Table 1.2). To obtain the number of moles (abbreviated mol) of a sub- stance, the amount of the substance (in grams) is divided by its gram-molecular weight; to obtain the mole fraction of a sub- stance, the number of moles of the substance is divided by the total number of moles in the solution (see section 2.2 for fur- ther elaboration). For example, the mole fraction of NaCl (gram-molecular weight=58.44) in a solution of 100g of NaCl in 2kg of H2 O (gram-molecular weight=18.0) can be calculated as follows: Number of moles of NaCl=100/58.44=1.7112 Number of moles of H2 O=2 (1000)/18.0=111.1111 Total number of moles in the solution= 1.7112 + 111.1111 = 112.8223 Mole fraction of NaCl in solution=1.7112 /112.8223=0.0152 Note that the mole fraction of a pure substance (solid, liquid, or gas) is unity. The concentration units mg/L and ppm, as well as molality and molarity, are related through the density of the solution (r): ρ − − = 1 1 concentration of solute (g L ) concentration (ppm) (g mL ) (1.2) 1 weight of solution (g) weight of solution (g) total weight of solutes (g) 1 (g mL ) m M ρ − ⎛ ⎞ = ⎜ ⎟ − ⎝ ⎠ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (1.3) Concentrations expressed in molality or mole fraction have the advantage that their values are independent of temperature and pressure; molarity, on the other hand, is dependent on the volume of the solution, which varies with temperature and pressure. The advantage of using molarity is that it is often easier to measure the volume of a liquid than its weight. For dilute aqueous solutions at 25°C, however, the density of the solution is very close to that of pure water, r=(1kg)/(l L), so that little error is introduced if the difference between mg/L and ppm or molality and molarity is ignored for such a solution. The strength of an acid or a base is commonly expressed in terms of normality, the number of equivalent weights of the acid or base per liter of the solution, the equivalent weight being defined as the gram-molecular weight per number of Hs or OHs in the formula unit. For example, the equivalent weight of H2 SO4 (gram-molecular weight=98) is 98/2=49, and the normality of a solution of 45g of H2 SO4 in 2L of solution is 45/(49×2)=0.46. 1.2 The Geologic Time Scale Discussions of events require a timeframe for reference. The Geologic Time Scale provides such a reference for past geologic events. Forerunners of the current version of the time scale were developed in small increments during the 19th century, long before the advent of radiometric dating, using techniques applicable to determining the relative order of events. These techniques are based on the principles of original horizontality (sediments are deposited in horizontal layers), superposition (in a normal sequence of sedimentary rocks or lava flows, the layer above is younger than the layer below), and faunal succession (fossil assemblages occur in rocks in a definite and determinable order). Although the time scale evolved haphazardly, with units being added or modified in different parts of the world at different times, it has been organized into a universally accepted workable scheme of classification of geologic time. The Geologic Time Scale spans the entire interval from the birth of the Earth (t=4.55Ga, i.e., 4.55 billion years before the present) to the present (t=0), and is broken up into a hierar- chical set of relative time units based on the occurrence of distinguishing geologic events. Generally accepted divisions for increasingly smaller units of time are eon, era, period, and epoch (Fig. 1.2). Different spans of time on the time scale are usually delimited by major tectonic or paleontological events Table 1.2 Concentration units for a solute. Concentration unit Definition Milligrams per liter (mg/L) Mass of solute (mg) / volume of solution (L) Parts per million (ppm) Mass of solute (mg) / mass of solution (kg) Mole fraction (X) Moles of solute / total moles of solution1 Molarity (M) Moles of solute / volume of solution (L) Molality (m) Moles of solute / mass of solvent (kg) Normality (N) Equivalent weight of solute (g) / volume of solution (L) 1 Moles of a substance=weight of the substance (g)/gram-molecular weight of the substance. Misra_c01.indd 3 Misra_c01.indd 3 1/19/2012 6:11:15 PM 1/19/2012 6:11:15 PM
- 27. 4 Introduction such as orogenesis (mountain–building activity) or mass extinctions. For example, the Cretaceous–Tertiary boundary is defined by a major mass extinction event that marked the disappearance of dinosaurs and many marine species. Absolute dates for the boundaries between the divisions were added later on, after the development of techniques for dating rocks using radioactive isotopes (see Chapter 10).The time scale shown in Fig. 1.2 includes these dates, producing an integrated Holocene Pleistocene Pliocene Miocene Oligocene Eocene Paleocene Cretaceous Jurassic Triassic Permian Pennsylvanian Mississippian Devonian Silurian Ordovician Cambrian PRECAMBRIAN PALEOZOIC Carboniferous MESOZOIC CENOZOIC Tertiary Quaternary Millions of years ago Era Period Epoch HADEAN ARCHEAN PHANEROZOIC PRECAMBRIAN PROTEROZOIC 251 65 544 1000 1600 2500 3000 3400 3800 LATE MESO- PROTEROZOIC NEO- PROTEROZOIC PALEO- PROTEROZOIC PALEOZOIC MESOZOIC CENOZOIC MIDDLE EARLY Eon 4550 Era 144 206 251 286 325 0.01 2.6 5.3 23.8 33.7 54.8 360 410 440 505 544 Millions of years ago Fig. 1.2 The Geologic Time Scale. The age of the Earth, based on the age of meteorites, is 4.55 ± 0.05Ga according to Patterson (1956) and 4.55–4.57Ga according to Allègre et al. (1995). Misra_c01.indd 4 Misra_c01.indd 4 1/19/2012 6:11:20 PM 1/19/2012 6:11:20 PM
- 28. 1.4 Questions 5 geologic time scale.Time units that are older than the Cambrian Period (that is, units in the Precambrian Eon) pre-date reliable fossil records and are defined by absolute dates. 1.3 Recapitulation Terms and concepts Absolute zero of temperature Celsius scale (temperature) CGS system of units Eon Epoch Era Equivalent weight Fahrenheit scale (temperature) Faunal succession Geologic Time Scale Fahrenheit scale (temperature) Geologic time scale Gram–molecular weight Kelvin scale (temperature) Mass concentration Mass extinction MKS system of units Molality Molarity Mole Mole fraction Original horizontality Period SI units Superposition Computation techniques ● Conversion of SI units to non-SI units. ● Conversion of °C to °F and K. ● Calculations of number of moles, mole fraction, molarity, molality, ppm. 1.4 Questions Gram atomic weights: H=1.0; C=12.01; O=16.00; Na=22.99; Al=26.98; Si=28.09; S=32.07; Cl=35.45; K=39.10; Ca=40.08. 1. The gas constant, R, has the value 1.987cal K−1 mol−1 . Show that R=8.317 Joules K−1 mol−1 =8.317×107 ergs K−1 mol−1 =83.176cm3 bar K−1 mol−1 2. Show that (a) 1 calorie bar−1 =41.84cm3 , and (b) 1m3 = 1 joule pascal−1 3. What is the molarity of one molal NaCl solution (at 25°C and 1 bar)? Density of the NaCl solution (at 25°C and 1 bar) is 1.0405kg L−1 . 4. What are the mole fractions of C2 H5 OH (ethanol) and H2 O (water) in a solution prepared by mixing 70.0g of ethanol with 30.0g of water? 5. What are the mole fractions of C2 H5 OH (ethanol) and H2 O (water) in a solution prepared by mixing 70.0mL of ethanol with 30.0mL of water at 25°C? The density of ethanol is 0.789g mL−1 , and that of water is 1.00g mL−1 . 6. When dissolved in water, NaCl dissociates into Na+ and Cl− ions (NaCl=Na+ +Cl− ). What is the molality of Na+ in a solution of 1.35g of NaCl dissolved in 2.4kg of water? What is the concentration of Na+ the solution in ppm? 7. The density of an aqueous solution containing 12.5g K2 SO4 in 100.00g solution is 1.083g mL−1 . Calculate the concentration of K2 SO4 in the solution in terms of molal- ity and molarity. What is the mole fraction of the solvent in the solution? 8. The ideal chemical formula of the mineral albite is NaAlSi3 O8 . How many moles of NaAlSi3 O8 do 5g of the mineral contain? How many moles of Si? 9. A solution made by dissolving 16.0g of CaCl2 in 64.0g of water has a density of 1.180g mL−1 at 25°C. Express the concentration of Ca in the solution in terms of molality and molarity. Misra_c01.indd 5 Misra_c01.indd 5 1/19/2012 6:11:21 PM 1/19/2012 6:11:21 PM
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- 30. The task of crystal chemistry is to find systematic relationships between the chemical composition and physical properties of crystalline substances, and in particular to find how crystal structure, i.e., the arrangement of atoms or ions in crystals, depend on chemical composition. Goldschmidt (1954) Part I Crystal Chemistry Misra_p01.indd 7 Misra_p01.indd 7 1/18/2012 5:06:14 PM 1/18/2012 5:06:14 PM
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- 32. Introduction to Geochemistry: Principles and Applications, First Edition. Kula C. Misra. © 2012 Kula C. Misra. Published 2012 by Blackwell Publishing Ltd. I knew of [Heisenberg’s) theory, of course, but I felt discouraged, not to say repelled, by the methods of transcendental algebra, which appeared difficult to me, and by the lack of visualizability (Edwin Schrödinger, 1926). The more I think about the physical portion of Schrödinger’s theory, the more repulsive I find it…. What Schrödinger writes about the visualizability of his theory is probably not quite right, in other words it’s crap (Werner Heisenberg, 1926). [Extracted from the worldwide web] 2 Atomic Structure The three major physical states in which a system (part of the universe that we have chosen for consideration) occurs are solid, liquid, and gaseous. Although we commonly think of distinctions among the three states in terms of physical prop- erties such as bounding surface, hardness, viscosity, etc., the fundamental difference lies in the arrangement of atoms in the three states. Crystalline solids, which can occur spontaneously in a form bounded by planar surfaces, are characterized by long-range order, a regularity in the arrangement of atoms or molecules that is repeated along parallel lines. Amorphous solids consist of extremely small solid units with a very small number of atoms per unit, so that “the forces which lead to the planar surfaces of solids and their internal order are destroyed by the enormous number of atoms in surface position” (Fyfe, 1964). Gases have no unique volume or boundaries, except those imposed by the chosen container; they lack ordering of their atoms or molecules. The liquid state may be viewed as being somewhere in between the solid and gaseous states. The atoms and molecules of liquids show only short-range order, i.e., ordering of the atoms and molecules extend only over a few molecular diameters. From the atomic perspective, glass may be regarded as a very viscous fluid. Our focus here is on crystalline solids because minerals, the main constituents of rocks, are by definition crystalline solids. We begin with a discussion of the general features of atomic structures because the physical and chemical properties of minerals are determined by the structure and arrangement of their constituent atoms. 2.1 Historical development 2.1.1 Discovery of the electron The Greek philosopher Democritus (5th century bc) believed in the existence of four elementary substances – air, water, stone, and fire – all formed by a very large number of very small particles called atoms, the word for “indivisibles” in Greek (Gamow, 1961). Our understanding of the atom was not much better until about the beginning of the 20th century. Sir Isaac Newton (1642–1727) described atoms as “solid, massy, hard, impenetrable, moveable particles” and this was the generally accepted view throughout the 19th century. In 1897, the British scientist J. J. Thompson (1856–1940), one of the pioneers in the investigation of atomic structure, proved by direct experiments that atoms are complex systems composed of positively and negatively charged parts. The experimental set-up, a primitive version of the modern televi- sion tube, was rather simple. It consisted of a glass tube con- taining highly rarified gas with a cathode (−) placed at one end, an anode (+) in the middle part, and a fluorescent screen at the other end (Fig. 2.1).When an electric current was passed through the gas in the tube, the fluorescent screen became luminous because of bombardment by fast moving particles resulting from the gas. When a piece of metal was placed in the path of the moving particles, it cast a shadow on the fluo- rescent screen, indicating a straight-line path for the particles Misra_c02.indd 9 Misra_c02.indd 9 1/19/2012 6:22:28 PM 1/19/2012 6:22:28 PM
- 33. 10 Atomic Structure in question, similar to light rays. Thompson visualized the atom as a complex system consisting of a positively charged substance (positive electric fluid) distributed uniformly over the entire body of the atom, with negatively charged particles (electrons) embedded in this continuously positive charge like seeds in a watermelon (Gamow, 1961). The model, however, was soon found to be unsatisfactory as the theoretically calcu- lated optical line spectra (a set of characteristic light frequencies emitted by an“excited”atom) of different elements based on this model could not be matched with the observed optical spectra. Thompson also conducted experiments to determine the charge : mass ratio (e/m) of an electron (1.76×10−8 coulomb g−1 ). A few years later, Robert A. Millikan experimentally measured the charge of an electron (1.602×10−19 coulomb) and com- puted its mass (about 9.109×10−28 g−1 ). 2.1.2 The Rutherford–Bohr atom In 1911, Ernest Rutherford (1871–1937), a New Zealand– born physicist, advanced the concept that the mass of an atom is concentrated at its center, which he named the nucleus. The experimental set-up that led to this discovery was quite simple (Fig. 2.2). A small amount of radioactive material emitting α-particles (positively charged helium ions that are ejected from the nucleus of an atom if it undergoes radioactive decay) was put on a pinhead and placed at a certain distance from a thin foil made from the metal to be investigated. The beam of α-particles was collimated by passing it through a lead dia- phragm. A fluorescent screen was placed behind the foil to record the α-particles that would pass through the foil, each α-particle producing a little spark (scintillation) on the screen at the point of impact that could be viewed with the help of a microscope. In his experiments, Rutherford noticed that the majority of the α-particles passed through the foil almost without deflection, but some were deflected considerably and in a few cases (with a somewhat different experimental arrangement) some α-particles bounced back toward the source. Rutherford reasoned that collisions between the α-particles of the beam and the atoms of the target could not possibly deflect the incident particles by more than a few degrees; the observed large deflections required strong electro- static repulsion between the positive charge of the bombarded atom and the positive charge of the incident α-particles. He concluded that the positive charge of the atom (associated with most of its mass) was not distributed throughout its body, as Thompson had envisaged, but had to be concentrated in a small central region of the atom, which he called the “atomic nucleus.” It followed that the rest of the atom must be composed of a bunch of negatively charged electrons, rotating around the nucleus at high velocities so as not to fall into the positively charged nucleus because of electrostatic attraction. The positive charge of the nucleus was attributed to suba- tomic particles called protons. Rutherford speculated that the nucleus might also contain electrically neutral particles, although such elementary particles, called neutrons, were discovered only in 1932. Thus, the atomic model proposed by Rutherford consisted of negatively charged, light electrons whirling at very high velocities in circular paths around a positively charged, heavy nucleus at the center, so that the outward centrifugal force associated with such a motion would balance the electrostatic attraction between the electrons and the nucleus. Rutherford’s model,however,faced a serious problem because of the inherent instability of an electron orbiting around a positively charged nucleus. According to the laws of classical physics, such an electron would lose energy by emitting an electromagnetic wave, resulting in an increase in the velocity of the electron and a decrease in the radius of its orbit until the electron falls into the nucleus. Consider the hydrogen atom consisting of a bare proton and a single electron of mass me and charge e orbiting the nucleus of circular path of radius r at velocity ve (Fig. 2.3). For this system, the energy of the atom (Eatom ) is inversely proportional to the radius of the orbit (see Box 2.1): 2 2 atom e e 1 1 – 2 2 e E m v r ⎛ ⎞ = = − ⎜ ⎟ ⎝ ⎠ (2.1) + + + + Neutral gas molecules Positive ions Negative electrons Cathode Anode Fluorescent screen Fig. 2.1 Thompson’s experimental set-up to study the effect of electric current on rarefied gas. α α α α Metal foil Diaphragm * * * * * * * * * Fluorescent screen α α α Radioactive material Fig. 2.2 Rutherford’s experimental set-up for studying the scattering of α-particles emitted from a radioactive source. Misra_c02.indd 10 Misra_c02.indd 10 1/19/2012 6:22:28 PM 1/19/2012 6:22:28 PM
- 34. 2.1 Historical development 11 Thus, the energy of the atom is negative and is inversely related to the radius of the orbit. The atom should become more stable as r decreases, and the electron should gradually fall into the nucleus. Calculations using classical physics predicted that electrons orbiting around a positively charged nucleus would lose all their energy in the form of electromagnetic waves within about one-hundred-millionth of a second and collapse into the nucleus. The Danish physicist Neils Bohr (1885–1962), who had joined Rutherford as a postdoctoral fellow after a falling out with Thompson at the Cavendish Laboratory, Cambridge, provided the answer by applying Max Planck’s revolutionary theory of quantization of electromagnetic energy. Speaking at the meeting of the German Physical Society on December 14, 1900, Max Planck (1858–1947) had proposed that light energy can exist only in the form of discrete packages, which he called “light quanta,” and that the amount of energy of a light quantum (E) is directly proportional to the frequency (J) of the radiation and inversely proportional to its wave length (l). Since wavelength and frequency for light waves are related by the equation lJ=c, we have (see section 13.1.2) hc E hϑ λ = = (2.4) where h is the proportionality constant known as the Planck’s Constant (h = 6.62517×10−34 J s), c is the speed of light “(c=3×1010 cm s−1 ), l is expressed in angstrom units (1 Å=10−8 cm), and E is in units of kiloelectron volts (keV). (Electron and X-ray energies are expressed in electron volts, 1eV being the kinetic energy gained by a single unbound elec- tron when it accelerates through an electric potential differ- ence of 1 volt.) In his first article on the Theory of Relativity in 1905, Albert Einstein (1879–1955) had also used the quantum theory to explain empirical laws of the photoelectric effect, the emission of electrons from metallic surfaces irradiated by vio- let or ultraviolet rays. Bohr reasoned that, if the electromag- netic energy is quantized – i.e., permitted to have only certain discrete values – mechanical energy must be quantized too, although perhaps in a somewhat different way. After strug- gling with the idea for almost two years, he finally published it in 1913 (Bohr, 1913a,b). Bohr retained Rutherford’s concept of electron motion in circular orbits (but rejected the classical law that moving charged particles radiate energy), and postu- lated that electrons moving around the atomic nucleus can reside only in a few permitted circular orbits or “shells,” each with a specific level of energy (En ) and a radius (rn ) given by (for a hydrogen atom, which has only one electron): 2 4 e n 2 2 2 m e E h n π = − (2.5) 2 2 n 2 4 e 4 h n r m e π = (2.6) where me is the mass of the electron, e is the magnitude of its charge, h is Planck’s Constant, and n is the principal quantum number (see section 2.2.1) that can assume only integral values (1, 2, 3, …), each value of n defining a particular energy level for the electron. Note that the closer an orbit is to the nucleus (i.e., as the value of n gets smaller), the larger is En in absolute value but actually smaller in arithmetic value because of the negative sign (an arbitrary convention for attractive forces). The smallest radius permitted by Bohr’s theory, the so- called Bohr radius (r0 ), is obtained from equation (2.6) by setting n=1. This is the radius of the orbit (r0 =0.529×10−8 cm) with the lowest permitted energy and thus represents the most r Proton Electron Fig. 2.3 Model of a hydrogen atom with a single electron moving in a circular orbit of radius r around a nucleus consisting of one proton. Box 2.1 Derivation of equation for Eatom Let us consider an electron of mass me and charge e orbiting around the nucleus of an atom in a circular path of radius r at velocity ve (Fig. 2.3). The condition of stability for such an atom is that the force of attraction between the proton and electron (e2 /r2 ) must be balanced by the centrifugal force(me ve 2 /r2 ): = 2 2 e e 2 m v e r r (2.2) The energy of the system is the sum of the kinetic energy (1/2 me ve 2 ) and potential energy (−e2 /r): 2 2 atom e e 1 = – 2 e E m v r (2.3) The potential energy term has a negative sign because the force between the proton in the nucleus and the electron is due to electrostatic attraction, which by convention is assigned a negative sign. Substituting the value of me from equation (2.2), me =e2 /rve 2 we get 2 2 2 2 atom e e 1 1 1 – – 2 2 2 e e e E m v r r r ⎛ ⎞ ⎛ ⎞ = − = = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ (2.1) Misra_c02.indd 11 Misra_c02.indd 11 1/19/2012 6:22:29 PM 1/19/2012 6:22:29 PM
- 35. 12 Atomic Structure stable state. The orbits corresponding to n=1, 2, 3, …, 7 are sometimes referred to as K, L, M, …, Q “shells”, respectively. An essential feature of the model is that an orbit of principal quantum number n can accept no more that 2n2 electrons. Bohr postulated further that an electron moving around the nucleus in a particular orbit is prohibited from emitting any electromagnetic radiation, but it does emit a quantum of mon- ochromatic radiation when it jumps from an orbit of higher energy, say E1 , to an orbit of lower energy, say E2 , according to the relation derived earlier by Einstein: E1 − E2 =ΔE=hJ (2.7) where J is the frequency of the radiation and h is the Planck’s Constant. Bohr’s model of the atom provided a convincing explanation for the emission of X-rays (which had been discovered by William Konrad Röntgen in1895) from target elements bombarded with a stream of electrons, and for the characteristic X-ray spectra of elements (Charles G. Barkla, 1911), which constitute the theoretical basis of modern elec- tron microprobe and X-ray fluorescence analytical techniques. Bohr’s notion of circular quantum orbits worked very well for the hydrogen atom, the simplest of all atoms containing a single electron. By this time, the optical line spectra for hydrogen was well known from spectroscopic studies, and the spectra predicted from Bohr’s model was a perfect match. The model, however, broke down almost completely for atoms having two or more electrons. Soon after, to allow more freedom in choosing the “permitted” orbits for multi-electron atoms, Arnold Sommerfeld (1868–1951) introduced the idea of elliptical orbits, which had different geometrical shapes but corresponded to almost the same energy levels as Bohr’s circular orbits. According to Sommerfeld’s postulate, the orbit closest to the nucleus (n=1) is circular and corresponds to the lowest energy of the electron. The next four orbits (n=2), one circular and the other three energetically equivalent but elliptical, have higher energy than that associated with the first orbit; the next nine orbits (n=3), one circular and the rest eight energetically equivalent but elliptical, correspond to a still higher level of energy, and so on (see Table 2.2 and Fig. 2.7). 2.1.3 Wave mechanics In a doctoral thesis presented in 1925, Louis Victor de Broglie (1892–1987) proposed a new interpretation of Bohr’s quan- tum orbits. He postulated that each electron moving along a given orbit is accompanied by some mysterious “pilot waves” (now known as de Broglie waves), whose propagation velocity and wavelength depend on the velocity of the electron in ques- tion. He deduced that the wavelength l of an electron of mass me and velocity ve is inversely proportional to its momentum (me ve ) and related to Planck’s Constant (h) by the equation: e e h m λ ν = (2.8) The validity of this relationship was confirmed later by exper- iments demonstrating diffraction effects for electrons similar to those of X-rays. A year later, in 1926, de Broglie’s ideas were brought into more exact mathematical form by Werner Heisenberg (1901–1976) and Edwin Schrödinger (1887– 1961). The two scientists used entirely different formulations but arrived at the same results concerning atomic structure and optical spectra. Heisenberg developed the Uncertainty Principle, which states that the position and velocity of an electron in motion, whether in a circular or in an elliptical orbit, cannot be measured simultaneously with high preci- sion. The mathematical formulation, however, was abstract and relied on matrix algebra. Most physicists of the time were slow to accept “matrix mechanics” because of its abstract nature and its unfamiliar mathematics. They gladly embraced Schrödinger’s alternative wave mechanics, since it entailed more familiar concepts and equations, and it seemed to do away with quantum jumps and discontinuities. However, Schrödinger soon published a proof that matrix mechanics and wave mechanics gave equivalent results: mathematically they were the same theory, although he argued for the superiority of wave mechanics over matrix mechanics. The recognition of the wave-like nature of the electron forced a fundamental change in ideas regarding the distribution of electrons in an atom. The concept of electrons as physical particles moving in orbits of definite geometrical form was replaced by a probability distribution of electron density (the number of electrons per unit volume) around the nucleus, rendering it possible to calculate the probability of finding the position of the electron at any point around the nucleus. From classicalequationsgoverningthebehaviorofwaves,Schrödinger developed a general equation for de Broglie waves and proved its validity for all kinds of electron motion in three-dimensional space. Schrödinger’s theory, which has now become known as wave mechanics (or quantum mechanics), explains not only all the atomic phenomena for which Bohr’s model works, but also those phenomena (such as intensities of optical spectral lines) for which Bohr’s model does not. In its most commonly used form (Fyfe, 1964), 2 2 2 2 e 2 2 2 2 8 ( – ) 0 m E V x y z h ∂ ψ ∂ ψ ∂ ψ π ψ ∂ ∂ ∂ + + + = (2.9) the Schrödinger’s wave equation, in essence, is a differential equation that relates a quantity y, the “wave function” of the system, to its total energy E and potential energy V. As defined earlier, me is the mass of the electron, h is Planck’s Constant, and n is the principal quantum number. Such an equation can be satisfied by an infinite number of values of y, which lead to separate (not continuous) values of E for a given potential V. Of greatest interest are those solutions that yield the lowest possible values of E, the stable stationary state. The signifi- cance of y for our purpose lies in the fact that the value of y2 at any point in space is a measure of the probability of finding Misra_c02.indd 12 Misra_c02.indd 12 1/19/2012 6:22:36 PM 1/19/2012 6:22:36 PM
- 36. 2.2 The working model 13 the electron in an infinitely small volume at that point; it is thus a measure of electron density. The larger the value of y2 , the greater the probability of finding the electron there (although there is also a very small but finite probability of finding the electron far away from the nucleus). A region of space in which the probability of finding an electron is high is called an (atomic) orbital (to distinguish it from “orbits” of the Bohr– Sommerfeld model). An orbital may be occupied (fully or par- tially) or empty. The probability interpretation is consistent with the idea that the electron is a particle, although described by a wave function, if we visualize an electron as a diffuse cloud of negative charge rather than a small discrete entity. The simplest solutions of Schrödinger’s equation are the ones that predict spherical probability distributions, which give the same energies as Bohr’s model for circular orbits of different principal quantum numbers. For example, let us consider the spherical solution for a hydrogen atom. The electron distribu- tion around a nucleus can be described by the radial distribution function 4pr2 y2 , which is a measure of the probability of finding the electron in an orbital at a certain distance r from the nucleus. For a hydrogen atom in ground state (the most stable state of an atom, with the lowest permitted energy), this function when plotted against r passes through a maximum (Fig. 2.4) that can be shown for a spherical solution (n=1) to be identical in mag- nitude to the radius permitted by Bohr’s model. Thus, there is a striking correlation between the results of the two treatments despite a vast difference in the physical significance. The Schrödinger equation has been solved exactly only for one-electron systems such as the hydrogen atom and the ions He+ and Li2+ . Even in a two-electron system such as helium, the repulsion between the two electrons makes the potential energy term V very complicated and requires simplifying assumptions to solve the equation. However, experimental observations justify the extrapolation of the one-orbital results to bigger, multi-orbital atoms (Companion, 1964). 2.2 The working model For our purpose, the atom (also referred to as nuclide), which is about 10−8 cm in diameter,may be considered to be composed of three elementary particles: neutron, proton, and electron. Each electron carries one unit of negative charge and has a mass so small that it can be ignored for simplicity. Each proton carries one unit of positive charge (measured in terms of the charge of the electron as the unit) and one unit of mass. Each neutron carries one unit of mass but no charge. The number of neutrons (N) in the nucleus, the neutron number, affects the atomic mass but has no direct bearing on chemical properties of the element. The atom consists of a nucleus (about 10−13 cm in diameter), which contains all its positive charge and practically all of its mass, and negatively charged electrons that orbit around the nucleus (Fig. 2.5). The atom in ground state is electrically neutral, so that the number of protons is balanced by an equal number of electrons. Each element is uniquely identified by its atomic number (Z), the number of protons in its nucleus. The mass number or atomic weight (A) of an element is defined as A=Z+N, and the chemical notation for an element includes both its Z and A numbers. In reality, the mass of a nuclide is slightly less than the combined mass of its neutrons and protons. The “missing” mass is expressed as the nuclear binding energy, which represents the amount of energy required to break up the nucleus into its constituent nucleons (protons and neutrons). The mass number is not unique in the sense that the same element may have different a1s Distance from the nucleus (r) Probability of finding the electron (4 p r 2 y 2 ) Fig. 2.4 Variation of the radial distribution function for the ground state hydrogen atom with increasing distance (r) from the nucleus. The magnitude of the function at a given value of r represents the electron density in a thin spherical orbital at distance r from the nucleus. In this case, the maximum probability occurs at a distance a1s that can be shown to be exactly the same as the radius of the smallest orbit (n=1) permitted by the Bohr model. Nucleus (3p+3n) Electron Fig. 2.5 Schematic representation of the Bohr-type model of a lithium atom (Z=3), which has a centrally located nucleus consisting of three protons (p) and three neutrons (n), and three electrons that orbit around the nucleus. Not to scale. The electronic structure of the 3 Li atom is represented as 1s2 2s1 . Misra_c02.indd 13 Misra_c02.indd 13 1/19/2012 6:22:38 PM 1/19/2012 6:22:38 PM
- 37. 14 Atomic Structure values of N, and different elements may have the same value of A. In terms of Z, N, and A, atoms are classified as isotopes, isobars, and isotones (Table 2.1). The chemical notation for an element includes both its Z and A numbers. For example, 238 92 U denotes an isotope of uranium having Z=92 and A=238, whereas 235 92 U denotes another isotope of uranium with the same Z but with A=235. Evidently, the nucleus of 238 U contains three more neutrons than that of 235 U, and the two isotopes respond quite differently in nuclear reactions involving their nuclei. The characteristic chemical properties of the isotopes of an element, however, are essentially the same because they have the same number and distribution of electrons in their atoms. This is the reason why the ratio of various isotopes in a mass of a naturally occurring element is nearly fixed. The atomic weight (or mass number) of an element is the sum of the masses of its naturally occurring isotopes weighted by the fractional abundance of each isotope, and it is expressed in atomic mass units. The atomic mass unit (amu) is defined as one-twelfth of the mass of the carbon isotope 12 6 C, which is arbitrarily fixed at 12.000, and the atomic weights of all other elements are obtained by comparison to the mass of 12 6 C. On this scale, the atomic weight of hydrogen (H) is 1.00794amu (usually approximated as 1amu), that of Na atom is 22.989768amu, and that of Mg is 24.3050amu. Thus, a Na atom has nearly 23 times the mass of an H atom, and a Mg atom has nearly 24 times the mass of an H atom. Example 2–1: Calculation of atomic weights from abundances of naturally occurring isotopes Calculate the atomic weights (in amu) of the elements K and Ar from the given data on the abundances of their isotopes: Atomic weight of K=(38.9637074×0.932581) + (39.9639992×0.0001167) + (40.9618254×0.067302)=39.0983 Atomic weight of Ar=(35.96754552×0.003365) + (37.9627325×0.000632) + (39.9623837×00.9960003)=39.9477 The gram-atomic weight of an element is numerically equal to its atomic weight expressed in grams. Similarly, the gram- molecular weight or the gram-formula weight (gfw) of a com- pound, which is the sum of the gram-atomic weights of its con- stituent atoms, is numerically equal to its molecular weight or formula weight expressed in grams. Both the gram-atomic weight and gram-molecular weight are referred to as mole (mol). In other words, the molar mass of an element (or a compound) expressed in units of (g mol−1 ) is numerically the same as the atomic weight of the element (or molecular weight of the com- pound) in amu. The mole is defined as the amount of substance that contains as many entities (atoms, molecules, ions, or other particles) as there are atoms in exactly 0.012kg of pure carbon-12 atoms.The currently accepted value is: 1 mole=6.0221367×1023 entities. This number, which is often rounded off to 6.022×1023 , is known as Avogadro’s number in honor of Amedeo Avogadro (1776–1856). It is a consequence of the hypothesis he proposed in 1811 that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. (The molar volume of an ideal gas is taken to be 22.414L per mole at stand- ard temperature and pressure, 273.15K and 1atm). The number of moles of an element or a compound in a given mass of an ele- ment (or a compound) is calculated by dividing the mass by the corresponding molar mass (see Chapter 1). 2.2.1 Quantum numbers As stated earlier, a variable that is allowed by the properties of the system to have only certain discrete values is said to be quantized. The integer that enumerates these permitted values is called a quantum number. To describe the motion of an electron in the space around the nucleus of an atom, solution of the Schrödinger equation requires three characteristic inter- related quantum numbers: the principal quantum number (n), the azimuthal (or subsidiary, or angular momentum) quantum number (l),and the magnetic quantum number (ml ) (Table 2.2). Table 2.1 Isotopes, isobars, and isotones. Relationship among Z, N, and A Examples Isotopes Same Z, different N and A 16 8 O, 17 8 O, 18 8 O (Z=8) Isobars Same A, different N and Z 12 7 N, 12 6 C, 12 5 B, 12 4 Be (A=12) Isotones Same N, different A and Z 16 6 C, 17 7 N, 18 8 O, 19 9 F (N=10) K Ar Isotope Mass (amu) Abundance (atom%) Isotope Mass (amu) Abundance (atom%) 39 K 38.9637074 93.2581 36 Ar 35.96754552 0.3365 40 K 39.9639992 0.01167 38 Ar 37.9627325 0.0632 41 K 40.9618254 6.7302 40 Ar 39.9623837 99.6003 Misra_c02.indd 14 Misra_c02.indd 14 1/19/2012 6:22:39 PM 1/19/2012 6:22:39 PM
- 38. 2.2 The working model 15 The principal quantum number n, which is analogous to Bohr’s principal quantum number, determines the size of the orbital and also governs the allowed energy levels in the atom; we may view n as defining the “shell” in which the orbitals will occur. The value of n must be an integer (e.g., 1, 2, 3, 4, …) and the corresponding shells, from the nucleus outward, are sometimes designated as K, L, M, N, …. A shell of princi- pal quantum number n can accommodate a maximum of 2n2 electrons. Thus, the innermost or K shell (n=1) can hold 2 electrons, the L shell (n=2) 8 electrons, the M shell (n=3) 18 electrons, and so on. Not all electrons in a given shell, however, are identical because those in a shell of principal quantum number n are distributed over n“subshells”of different energy levels characterized by an azimuthal quantum number l. The azimuthal quantum number l determines the shape of the sub- shell, and for a given value of n may assume any of the values 0, 1, 2, 3, 4, 5, …, n − 1 (the maximum possible value), and the corresponding sub-shells are designated as s, p, d, f, g, h, … (Table 2.2). Thus, an electron corresponding to n=1 and l=0 is symbolized as 1s, one corresponding to n =3 and l=1 as 3p, one corresponding to n = 3 and l=2 as 3d, and so on. Further, the number of electrons in a sub-shell may be indicated by a superscript attached to the symbol for the sub-shell. For exam- ple, 1s2 represents 2 electrons in the s sub-shell of the K shell, 2p6 represents 6 electrons in the p sub-shell of the L shell, and 3d5 represents 5 electrons in the d sub-shell of the M shell. This scheme provides a convenient way to represent the elec- tronic configuration of an atom. For example, the electronic configurationofNi(Z=28)iswrittenas1s2 2s2 2p6 3s2 3p6 3d8 4s2 . The electrons in each sub-shell are distributed in one or more atomic orbitals (AOs), the number of orbitals being determined by the magnetic quantum number ml , which has no effect on the size or shape of the orbitals but is related to the orientation of an orbital in space. For a given n and l, there are 2l+1 different possible values of ml : −l, 0, +l (although the actual numerical values allowed for ml are not important for our purpose). Now let us consider how the quantum number l determines the distribution of electron clouds around the nucleus (Fig. 2.6). For l=0, the number of possible values of ml is 1 for all values of n, and the corresponding orbitals are s orbitals such as 1s, 2s, 3s, etc. Electron clouds in s orbitals have a spherical symmetry in the sense that there is the same probability of finding an electron at a given distance from the nucleus in any direction in space, and the sphere gets larger as Table 2.2 Some principal quantum numbers and corresponding electron orbitals. Principal quantum number, n Maximum permissible electrons for given n (2n2 ) Azimuthal quantum number, l (l=0, 1, 2, 3, … n − 1) Names of sub-shells Magnetic quantum number, ml (maximum number of orbitals=1, 3, 5, 7, …2l+1) Designation of atomic orbitals for electrons (see Fig. 2.6) 1 (K shell) 2 0 1s 0 [1] 1s 2 (L shell) 8 0 2s 0 [1] 2s 1 2p −1, 0, +1 [3] 2px , 2py , 2pz 3 (M shell) 18 0 3s 0 [1] 3s 1 3p −1, 0, +1 [3] 3px , 3py , 3pz 2 3d −2, −1, 0, +1, +2 [5] 2 3 z d , 2 2 – 3 x y d , 3dxy , 3dxz , 3dyz X y z s (a) 3s orbital X z y px X y z py X z y pz (b) 3p orbitals X z y dxy X y z dyz X y z dxz X z y dx 2 – y 2 X y z dz 2 (c) 3d orbitals Fig. 2.6 Representation of the “shapes” of electron clouds for various types of atomic orbitals for n (principal quantum number)=3: (a) 3s orbital with spherical symmetry; (b) threefold degenerate 3p orbitals; and (c) fivefold degenerate 3d orbitals. Note that the boundary surfaces represent the regions likely to contain most (perhaps 95%) of the electrons (meaning that there is a 95% probability of finding the electrons within the region) and that the electron density is not the same everywhere within a given orbital lobe. Misra_c02.indd 15 Misra_c02.indd 15 1/19/2012 6:22:39 PM 1/19/2012 6:22:39 PM
- 39. 16 Atomic Structure n gets larger. Thus, a 1s electron is more strongly attracted by the nucleus than a 2s electron because the former spends more time closer to the nucleus. When l=1, ml (= 2l+1) has three possible values (ml =−1, 0, or +1), giving rise to three spatially distinct but equally probable p orbitals, all having the same energy, for a given n (i.e., the p solutions of y are threefold degenerate). The three p orbitals are named px , py , and pz to remind us that their dumbbell-shaped lobes of maximum electron density lie along arbitrarily defined x, y, and z orthogonal axes in space, respectively. An electron in px orbital, for example, exists (at least 95% of the time) somewhere in the dumbbell-shaped space along the x axis, with equal probability for each lobe. Unlike s orbitals, the p orbitals have a plane of zero electron density, a so-called nodal plane separating the lobes, a plane that is perpendicular to the long axis of the orbital and contains the nucleus. In the case of the pz orbital, for example, it is the xy plane. For l=2, ml has five possible values (i.e., the d solutions of y are fivefold degenerate) and, therefore, there are five spatially distinct d orbitals of equal energy for a given n: dxy , dyz , dxz , 2 2 – x y d , and 2 z d . The 2 2 – x y d orbital lies in the xy plane with its four lobes coinciding with the x and y axes; dxy also lies in the xy plane, but with its lobes pointed between the axes; dxz and dyz lie in the xz and yz planes, respectively, and like dxy have their lobes of electron density pointed between the axes. The 2 z d orbital has a very different shape; most of its electron density is concentrated around the z-axis as shown in Fig. 2.6. The more complex shapes of f, g, and higher orbitals will not be discussed here because they are not particularly important in geochemistry. For a discussion of the orbital distribution of electrons for various elements, we need to define one more quantum num- ber,the spin quantum number (ms ).Even before the Schrödinger equation came into play, experimentalists had found that a great deal of spectroscopic data could be explained if it were postulated that the electron is able to spin in one of two pos- sible directions about an arbitrary axis through its center. The spin quantum number describes the spin of an electron and the direction of the magnetic field produced by the spin. For every set of n, l, and ml values, ms can take the value of either +1/2 (a spin, commonly denoted by the symbol ↑) or −1/2 (b spin, commonly denoted by the symbol ↓) depending on the direc- tion of the spin of the electron. The existence of spin requires us to consider another postulate known as the Pauli’s exclu- sion principle, which states that any orbital (defined by a set of n, l, ml ) can accommodate a maximum of two electrons, and then only if they have spins in opposite directions (ab pair, ↑↓). Thus, the quantum numbers n, l, ml , and ms uniquely define the state of an electron in an atom; two or more electrons can- not exist in the same state at the same time. 2.2.2 Energy levels of the atomic orbitals The energy of an electron is determined by how strongly it is attracted by the nucleus (i.e., by the closeness of its orbital to the nucleus). It is, therefore, necessary to consider the relative energy levels of the different atomic orbitals (Fig. 2.7), which have been determined from a combination of the wave equa- tion and study of atomic spectra. An examination of Fig. 2.7 leads to the following general conclusions (Evans, 1966): (1) For a given n and l, the energy level is the same for all the possible atomic orbitals. Thus, for n=2, the three 2p orbitals have the same energy; for n=3, the three 3p orbitals have the same energy and so do the five 3d orbitals. (2) For a given l, the orbital energy for any value of atomic number (Z) increases with increasing n. Thus, the sequences of increasing energy are: 1s < 2s < 3s < 4s < 5s < 6s < 7s 2p < 3p < 4p < 5p < 6p 3d < 4d < 5d < 6d 4f < 5f (3) For a given n and any value of Z less than about 20, orbital energy increases with increasing l. Thus, the sequences of increasing energy are: 2s < 2p 3s < 3p < 3d 4s < 4p < 4d < 4f, etc. For Z > 20, the energy level of the 4s orbitals is lower than that of the three 3d orbitals, and the relationships between 5s and 4d orbitals and between 6s and 5d orbitals are similar. Energy (arbitrary scale) ~20 ~90 Atomic number (Z ) 1s 2s 3s 3d 4p 4d –5p 6s 5d 4f 3p 2p 4s 5s Fig. 2.7 Schematic representation of the variations in the energy levels of atomic orbitals in the ground state of atoms as a function of atomic number. (From An Introduction to Crystal Chemistry, 2nd edition, by R.C. Evans, Figure 2.02, p. 19; Copyright 1966, Cambridge University Press. Reproduced with permission of the publisher.) Misra_c02.indd 16 Misra_c02.indd 16 1/19/2012 6:22:41 PM 1/19/2012 6:22:41 PM
- 40. 2.3 The ground state electron configuration of elements 17 2.3 The ground state electron configuration of elements The ground state of an isolated atom is its quantum state of lowest permissible energy. The distribution of electrons among various electron “shells” of an atom corresponding to the quantum state of minimum energy is called the ground state electron configuration. An atom is said to be in an excited state if it has a higher energy than the ground state because of one or more of its electrons occupying one or more “shells” of higher energy compared to the ground state. 2.3.1 Filling atomic orbitals with electrons: the Aufbau principle The single electron in an H atom (Z=1) enters the orbital with the lowest energy (1s1 ). Subject to the Pauli’s exclusion princi- ple, the electronic configuration of atoms of increasing atomic number is constructed by adding appropriate number of elec- trons (depending on the atomic number) to the possible orbit- als in a way that minimizes the energy of the atom, because the lowest energy state of an atom is its most stable (or ground) state. This filling-up procedure is called the Aufbau (meaning “build-up”) principle, which is governed by the following set of guidelines (Companion, 1964; Evans, 1966): (1) Because of unsystematic variations in energy levels of atomic orbitals as a function of quantum numbers n and l (Fig. 2.7), (i) electrons are assigned to orbitals in order of increasing value of (n+l), and (ii) for subshells with the same value of (n+l), electrons are assigned first to the sub-shell with lower n. For example, the 5s orbital (n+l=5+0=5) would fill before the 4d orbital (n+l=4+2 = 6), and the 4d orbital before the 5p orbital (n+l=5 + 1=6) because 4d has a lower value of n. The sequence in which orbitals are filled is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 6d (2) No two electrons may have identical sets of the four quantum numbers (Pauli’s exclusion principle). (3) As many of the orbitals as possible are occupied by a single electron before any pairing of electrons takes place (see Table 2.3); the unpaired electrons have parallel spins, and the paired electrons have opposite spins (Hund’s rule of maximum multiplicity). This is because, even with pairing of spins, two electrons that are in the same orbital repel each other more strongly than two electrons in different orbitals. The rules listed above should be considered only as a guide to predicting electron distribution in atoms.The experimentally determined electron configurations of lowest total energy do not always match those predicted by these guidelines, especially for the B group elements of the Periodic Table (see section 2.3.2). The electronic configurations of isolated atoms in the ground state are presented in Appendix 2. Alternative elec- tronic configurations may have to be considered for atoms in excited states or when they are not isolated (e.g., when involved in chemical reactions). Table 2.3 The electronic configuration of the elements of the first three periods. K-shell (n=1) L-shell (n=2) M-shell (n=3) Notation for electronic configuration Element Z 1s 2s 2px 2py 2pz 3s 3px 3py 3pz H 1 ↑ 1s1 He 2 ↑↓ 1s2 Li 3 ↑↓ ↑ 1s2 2s1 Be 4 ↑↓ ↑ 1s2 2s2 B 5 ↑↓ ↑ ↑ 1s2 2s2 2p1 C 6 ↑↓ ↑↓ ↑ ↑ 1s2 2s2 2p2 N 7 ↑↓ ↑↓ ↑ ↑ ↑ 1s2 2s2 2p3 O 8 ↑↓ ↑↓ ↑↓ ↑ ↑ 1s2 2s2 2p4 F 9 ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s2 2s2 2p5 Ne 10 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 1s2 2s2 2p6 Na 11 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s2 2s2 2p6 3s1 Mg 12 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s2 2s2 2p6 3s2 Al 13 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ 1s2 2s2 2p6 3s2 3p1 Si 14 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ 1s2 2s2 2p6 3s2 3p2 P 15 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ ↑ 1s2 2s2 2p6 3s2 3p3 S 16 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ 1s2 2s2 2p6 3s2 3p4 Cl 17 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s2 2s2 2p6 3s2 3p5 Ar 18 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 1s2 2s2 2p6 3s2 3p6 Misra_c02.indd 17 Misra_c02.indd 17 1/19/2012 6:22:46 PM 1/19/2012 6:22:46 PM
- 41. 18 Atomic Structure 2.3.2 The Periodic Table The Periodic Table reflects an attempt at a systematic organization of the elements from the perspective of their atomic structures. In 1869, two very similar arrangements of the known elements, much like the modern Periodic Table (Fig. 2.8), were published independently, one by the Russian chemist Dimitri Ivanovich Mendeleev (1834–1907) and the other by the German chemist Lothar Meyer (1830–1895). Both were based on regular periodic repetition of properties with increasing atomic weight of the elements, Mendeleev’s largely on chemical properties and Meyer’s on physical properties.The modern version of the Periodic Table is organized on the basis of atomic number of the elements,a concept that was developed some 50 years later than Mendeleev’s work and is more fundamental to the identity of each element. The vertical columns in the Periodic Table are referred to as groups, and the horizontal rows are referred to as periods, which are numbered in accordance with the first quantum number of the orbitals that are being filled with increasing atomic number. For example, electrons fill the 1s orbital in elements belonging to the 1st period, 2s and 2p orbitals in elements of the 2nd period, and 3s and 3p orbitals in elements of the 3rd period.The electron distribution in elements included in the 4th to 7th periods becomes more complicated because of filling of d and f orbitals (3d, 4d, 5d, 6d, 4f, 5f) as illustrated in Fig. 2.8. Elements within a period have properties that change progressively with increasing atomic number because of addition of electrons. In contrast, elements in any group have similar physical and chemical properties because of similar electronic configuration. The groups are either designated as A and B, and numbered from left to right in accordance with the highest possible positive valence of the elements in that group (American system) or numbered continuously from left to right as 1 through 18 (International system). Some of the groups are commonly referred to by special names: alkali metals (Group IA, except H); alkaline earth metals (Group IIA); halogens (Group VIIA), and noble (or inert) gases (Group VIIIA). The Periodic Table can also be viewed as a systematic representation of the electronic configurations of the elements. The elements are arranged in blocks based on the kinds of atomic orbitals (s, p, d, or f) being filled.The A groups comprise elements in which s and p orbitals are being filled.The B groups include elements in which the s orbital of the outermost occupied shell contains one or two electrons (e.g., 5s1 and 5s2 for 37 Rb and 38 Sr, respectively), and the d orbitals, one shell smaller, are being filled. The electronic configurations of the A group elements, including the noble gases (Group VIIIA), are quite systematic and can be predicted from their positions in the Periodic Table, but some pronounced irregularities exist for elements of the B group and of the 5th and higher periods. 2.3.3 Transition elements Application of the guidelines discussed earlier to the filling of successiveatomicorbitalswithelectronsisquitestraightforward for atoms from 2 He(1s2 ) to 18 Ar (1s2 2s2 2p6 3s2 3p6 ), as illustrated in Table 2.3.The M-shell, which can contain up to 18 electrons, has room for 10 more electrons in the five 3d orbitals, but in 19 K [(Ar core)18 4s1 ] and 20 Ca [(Ar core)18 4s2 ], the additional electrons are accommodated in the energetically more favorable 4s orbital of the N-shell compared with the 3d orbital (Fig. 2.7). After 20 Ca, the 3d orbital is more stable than the 4s orbital, so that from 21 Sc to 30 Zn, electrons enter the 3d orbital of the M-shell in preference to the 4p orbital of the N-shell. The 3d orbitals become completely filled in30 Zn, and filling of the 4p orbitals starts with the element 31 Ga and continues progressively to the element 36 Kr. The elements from 21 Sc to 30 Zn are called the 3d transition elements or the first transition series. Analogous schemes of filling the d orbitals give rise to 4d transition series (39 Y through 48 Cd), 5d transition series (57 La and 72 Hf through 80 Hg), and 6d transition series (89 Ac and 104 Rf through element 112) (see Fig. 2.8). The elements of these four transition series are all metals, and they contain electrons in both ns and (n − 1)d orbitals, but not in the np orbitals. Two additional transition series exist between groups IIIB and IVB of the Periodic Table: the 4f transition series (58 Ce through 71 Li) and the 5f transition series (90 Th through 103 Lr).These transition elements are also metals, and are characterized by the progressive filling of 4f and 5f orbitals, respectively (Fig. 2.8). 2.4 Chemical behavior of elements The chemical behavior of an element is governed by its electronic configuration because the energy level of the atom is determined by the spatial distribution of its electron cloud. It is only the most loosely bound electrons in the outermost orbitals that take part in chemical interaction with other atoms. For example, the alkali elements (group IA of the Periodic Table), all of which have one electron in the outermost orbital, exhibit similar chemical properties; so do the alkaline earth metals (group IIA of the Periodic Table), all of which have two electrons in the outermost orbital. 2.4.1 Ionization potential and electron affinity Two concepts are useful in predicting the chemical behavior of elements: ionization potential (or ionization energy); and electron affinity. Ions are produced by the removal of electron(s) from or the addition of electron(s) to a neutral atom. The energy that must be supplied to a neutral atom (M) in the gas phase to remove an electron to an infinite distance is called the ionization potential (I). In other words, the ionization potential is the difference in potential between the initial state, in which the electron is bound, and the final state, in which it is at rest at infinity; the lower the ionization potential, the easier it is to convert the atom into a cation. This is the reason why the ionization potential generally increases from left to right in a given period and from top to bottom within a given group of the Periodic Table (Fig. 2.9). The first ionization potential (I1 ) refers to the energy required to remove the first (the least tightly bound) electron, the Misra_c02.indd 18 Misra_c02.indd 18 1/19/2012 6:22:46 PM 1/19/2012 6:22:46 PM
- 43. 20 Atomic Structure second ionization potential (I2 ) to the energy corresponding to the removal of the second electron, and so on: M ⇒ M+ +e− (I1 ) (2.10) M+ ⇒ M2+ +e− (I2 ) (2.11) Electron affinity (Eea ) is defined as the energy required for detaching an electron from a singly charged anion (Lide, 2001): M− ⇒ M+e− (Eea ) (2.12) In other words, electron affinity is the energy difference between the lowest (ground) state of a neutral atom and the lowest state of its corresponding negative ion. Note that it is not exactly the reverse of the ionization process. The sign convention for Eea is opposite to most thermodynamic quantities (see Chapter 4); a positive Eea indicates that energy is released when the electron goes from an atom to an anion. All atoms have positive values of Eea ; a high value of Eea indicates strong attraction for extra electrons. Electron affinity is a precise quantitative term like ionization potential, but it is difficult to measure. Values of I1 and Eea for selected elements are listed in Appendix 3, and how they vary with atomic number is presented graphically in Fig. 2.9. Why is there so much variation in ionization potential and electron affinity of elements? The explanation lies in the “screening effect” (or “shielding effect”) of the electrons. For example, consider the Na atom (1s2 2s2 2p6 3s1 ). The difficulty of removing the outer 3s electron of the Na atom is due to the electrostatic attraction of the positive nucleus. However, the effective nuclear charge (Zeff ) is somewhat less than what would be exerted by the 11+ nuclear charge because of the electrostatic repulsion or shielding effect (Selectron screening ) of the 10 inner-shell electrons on the 3s electron. For an atom with a known distribution of the inner electrons, it is possible to calculate (Selectron screening ) and, thus, Zeff (Zeff = Zatomic number − Selectron screening ) (Fyfe, 1964). 2.4.2 Classification of elements On the basis of first ionization potentials and electron affinities, the elements may be separated into three classes (Table 2.4): (1) Electron donors (metals), such as elements of Groups 1A and IIA in the Periodic Table, which easily lose one or more valence electrons (electrons in the outermost occupied s and p orbitals) and become positively charged ions (cations); these elements have relatively low values of I1 and Eea . For any period in the Periodic Table, the metallic character of the elements generally decreases with increasing atomic number (i.e., with progressive filling of the atomic orbitals), as the first ionization potential increases in the same direction. (2) Electron acceptors (nonmetals), such as elements of Groups VIA and VIIA in the Periodic Table, which readily acquire one or more added electrons and become negatively charged ions (anions); these elements are characterized by relatively high values of I1 and Eea . For any period, Eea generally increases with increasing atomic number. (3) Noble elements (inert gases), such as the elements of Group VIIIA in the Periodic Table, which do not easily lose or gain electrons. These elements are characterized by a complete octet of electrons in their outermost s and p orbitals (ns2 np6 ) (except for 2 He, which has only 2 electrons), very H He Li B N O Ne Na Mg Al Ar K Zn Ga Kr Rb P Xe Cs Se Cd Cl Cr Br Pd In I Lu Re Hg Tl Pb Ac Th U F First ionization potential Na Al K Ge Rb Cl H F Ne Ar Cr Zn Br Kr I Cd Xe Cs Au Hg Bi Re Electron affinity 0 0 Atomic number (z) 5 10 15 20 25 30 35 40 50 60 70 80 45 55 65 75 85 90 95 0 5 5 0 10 15 20 25 Pauling electronegativity 5 H He F Ne Cl Ar Zn Br Kr I Xe Energy (electron volts) Be Fig. 2.9 Variation of first ionization potential, electron affinity, and Pauling electronegativity (see section 3.6.5) of atoms with increasing atomic number. Note that the noble gases (He, Ne, etc.) appear at peak values of first ionization potential, reflecting their chemical inertness, whereas the alkali metals (Li, Na, K, Rb, Cs) appear at minimum values, consistent with their reactivity and ease of cation formation. The peak values of electron affinity, on the other hand, are marked by halogens (F, Cl, Br, I) and the minimum values by the noble gases. 1eV=96.48532kJ mol−1 . (Source of data: compilations in Lide, 1998.) Misra_c02.indd 20 Misra_c02.indd 20 1/19/2012 6:22:46 PM 1/19/2012 6:22:46 PM
- 44. 2.6 Recapitulation 21 high values of I1 , and near-zero values of Eea ; they do not normally occur in the ionized state. By losing or gaining electrons, the cation- and anion-forming elements achieve the stable noble element configurations characterized by 8 electrons in their outermost shells (the octet rule). To the above list, we may add a fourth class of elements (such as B, Si, Ge, As, Sb, Te, Po, and At), called metalloids (or semimetals), which show certain properties that are character- istic of metals and other properties that are characteristic of nonmetals. Many of the metalloids (especially Si and Ge) are used as semiconductors in solid-state electronic circuits. Whereas metals become less conductive with increasing temperature, semiconductors are insulators at low temper- atures, but become conductors at higher temperatures. 2.5 Summary 1. The atom consists of a nucleus (about 10−13 cm in diameter), which contains all its positive charge in the form of protons and practically all of its mass (neutrons and protons), and negatively charged electrons that orbit around the nucleus. Each element is uniquely identified by its atomic number (Z), the number of protons in its nucleus. The mass number or atomic weight (A) of an element is the sum of its protons (Z) and neutrons (N). Atoms with the same atomic number but different mass numbers are called isotopes. 2. The state of an electron in the structure of an atom can be described by four quantum numbers, not all of which can be the same for any two electrons: the principal quantum number (n), which determines the size of the orbital; the azimuthal quantum number (l), which determines the shape of the orbital for any given value of n; the magnetic quantum number (ml ), which determines the number of atomic orbitals (2l+1) accommodating the electrons of the orbital; and the spin quantum number (ms ), which can take the value of +1/2 (a spin, commonly denoted by the symbol ↑) or −1/2 (b spin, com- monly denoted by the symbol ↓) depending on the direction of the spin of the electron. An atomic orbital (defined by a set of n, l, ml ) can accommodate a maximum of two electrons, and then only if they have spins in opposite directions (ab pair, ↑↓), a postulate known as Pauli’s exclusion principle. 3. The electronic configuration of atoms of increasing atomic number is constructed by adding the appropriate number of electrons (depending on the atomic number) to the possible orbitals in a way that minimizes the energy of the atom. 4. The Periodic Table can be viewed as a systematic representation of the electronic configurations of the elements. 5. Two concepts useful in predicting the chemical behavior of elements are: ionization potential (I), the energy that must be supplied to a neutral atom (M) in the gas phase to remove an electron to an infinite distance (M ⇒ M+ +e− ); and electron affinity (Eea ), the energy required to detach an electron from a singly charged anion (M− ⇒ M+e− ). On the basis of these two parameters, the elements may be divided into three broad categories: electron donors (metals); electron acceptors (nonmetals), and noble elements (inert gases). 2.6 Recapitulation Terms and concepts Anions Aufbau principle Avogadro’s number Azimuthal quantum number Bohr radius Cations Electron affinity Electron acceptors (nonmetals) Electron donors (metals) Excited state Table 2.4 Examples of the three classes of elements in terms of ionization potentials and electron affinities. Electron distribution First ionization potential* (eV) Second ionization potential* (eV) Electron affinity1 (eV) Element type Example 1s 2s 2p 3s Electron acceptors F (Z=9) ↑↓ ↑↓ ↑↓ ↑↓ ↑ 17.42 34.97 3.40 Noble elements Ne (Z=10) ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 21.56 40.96 ∼0 Electron donors Na (Z=11) ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ 5.14 47.29 0.55 1 Source of data: Lide (1998). The values of these parameters are often expressed in molar equivalent of electronvolt (eV), which is the kinetic energy that would be gained by a mole of electrons passing through a potential difference of one volt. 1eV=96.48532kJ mol−1 . Misra_c02.indd 21 Misra_c02.indd 21 1/19/2012 6:22:47 PM 1/19/2012 6:22:47 PM
- 45. 22 Atomic Structure Ground state Hund’s rule Ionization potential Inert elements Isobars Isotones Isotopes Magnetic quantum number Metalloids (semimetals) Molar mass Mole Nodal plane Octet rule Pauli’s exclusion principle Periodic Table Principal quantum number Schrödinger equation Screening effect Spin quantum number Standard temperature and pressure (STP) Transition elements Valence electrons Computation techniques ● The atomic weight (in amu) of an element from the data on the abundances of its isotopes. ● Ionization potential, electron affinity. 2.7 Questions 1. Show that 1amu=1.6606×10−24 g [Hint: 1amu=1/12 of the mass of a 12 6 C atom; 1 mole of 12 6 C contains 6.022×1023 atoms.] 2. Calculate the atomic weights (in amu) of the elements U and Pb from the abundances of their isotopes given below: 3. A saturated solution of AgCl in water contains 1.3×10−5 mole of AgCl per liter of the solution at 25°C tempera- ture and 1atm pressure. Calculate the mass of dissolved AgCl in 1L of the solution. Gram atomic weights of the elements: Ag=107.87; Cl=35.453. 4. Calculate the number of H2 O molecules that will evapo- rate per second, given that one drop of water weighing 0.05gevaporatesin1h.Avogadro’snumber=6.022×1023 . 5. A geologist has identified two iron deposits. One of them contains 100 million tons of magnetite (Fe3 O4 ), and the other contains 20 million tons of magnetite (Fe3 O4 ), and 80 million tons of hematite (Fe2 O3 ). Based on the iron content alone, which of the two deposits should be rec- ommended for mining? Gram atomic weights of the ele- ments: Fe=55.85; O=16.00. 6. What is the maximum number of electrons that can be accommodated in the following atomic orbitals? (a) all the 6g orbitals; (b) all the 7s orbitals; (c) all the 8f orbitals; and (d) all the orbitals with n=5 7. Write down the ground–state electronic configuration of the following elements: Fe (Z=26); Rubidium (Z=37); Xenon (Z=54); and Uranium (Z=92). 8. Using the same format as for Table 2.3, prepare a table illustrating the gradual filling with electrons of the atomic orbitals of the 4d transition series. 9. Light near the middle of the ultraviolet region of the electromagnetic radiation spectrum has a frequency of 2.73×1016 s−1 , whereas yellow light within the visible spectrum has a frequency of 5.26×1014 s−1 . (a) Calculate the wavelength corresponding to each of these two frequencies of light. (b) Calculate how much more is the energy associated with a photon of ultraviolet light compared to that of yellow light. 10. What is the wavelength associated with a neutron of mass 1.675×10−24 g moving with a speed of 2360m s−1 . U Pb Isotope Mass (amu) Abundance (atom %) Isotope Mass (amu) Abundance (atom%) 234 U 234.0409468 0.0055 204 Pb 203.973020 1.4 234 U 235.0439242 0.7200 204 Pb 205.974440 24.1 234 U 238.0507847 99.2745 204 Pb 206.975872 22.1 204 Pb 207.976627 52.4 Misra_c02.indd 22 Misra_c02.indd 22 1/19/2012 6:22:47 PM 1/19/2012 6:22:47 PM
- 46. Introduction to Geochemistry: Principles and Applications, First Edition. Kula C. Misra. © 2012 Kula C. Misra. Published 2012 by Blackwell Publishing Ltd. The forces responsible for chemical combination of atoms are of two main types. There are those forces which arise between electri- cally charged species, repulsive if the charges are similar, attractive if dissimilar. … The second type of force may be called an exchange force and these can be described in terms of the Schrödinger wave equation…. A little reflection will reveal that we under- stand neither – all we have is two ways of describing different situations, and in all probability the origin of both forces is the same. Fyfe (1964) 3 Chemical Bonding Chemical compounds are formed by the combination of two or more atoms (or ions), and the formation of a stable compound occurs when the combination results in a lower energy than the total energy of the separated atoms (or ions). Interatomic (or interionic) net attractive forces that hold atoms (or ions) in solids together are called chemical bonds. Chemical bonds usually involve only the valence electrons (s and p electrons in the outermost orbitals) of an atom. Physical and chemical properties of all substances depend on the character of the chemical bonds that hold them together. Much of the bonding in solids of geochemical interest can be described in terms of two end-member types: (i) ionic (or electrovalent) bonds that exist because of electrostatic attrac- tion between cations and anions formed by transfer of one or more electrons between atoms; and (ii) covalent bonds that arise because of sharing of electrons between atoms that results from overlap of orbitals from the two atoms. For example, the ionic bonding in NaCl results from the electro- static attraction between a Na+ cation formed by the loss of a valence electron from the 3s orbital of the Na atom (1s2 2s2 2p6 3s1 ) and a Cl− anion formed by incorporation of thatelectronintothe3porbitaloftheClatom(1s2 2s2 2p6 3s2 3p5 ) (Fig. 3.1a): Na (1s2 2s2 2p6 3s1 ) ⇒ Na+ (1s2 2s2 2p6 ) + e− Cl (1s2 2s2 2p6 3s2 3p5 ) + e− ⇒ Cl− (1s2 2s2 2p6 3s2 3p6 ) 2Na(s) + Cl2(g) ⇒ 2Na+ Cl− (s) The NaCl molecule itself is electrically neutral because its structure contains a Na+ cation for every Cl− anion. Sodium and chlorine atoms combine readily because of the large dif- ference in their first ionization potential and electron affinity (see section 2.4). Covalent bonding, on the other hand, arises from sharing of electrons. The covalent bonding in Cl2 , for example, may be viewed as resulting from the sharing of a pair of electrons between two Cl atoms, each of which contributes one electron to the shared pair (Fig. 3.1b). Atoms can share one, two, or three electron pairs, forming, respectively, single, double, and triple covalent bonds. All bonds between atoms of different elements have some degree of both ionic and cova- lent character. Compounds containing predominantly ionic bonding are called ionic compounds, and those that are held together mainly by covalent bonds are called covalent compounds. This difference in bonding accounts for the differences in some properties associated with simple ionic and covalent compounds (Table 3.1). Other types of bonds that will be dis- cussed briefly in this chapter include metallic bonds, Van der Waals bonds, and hydrogen bonds. Misra_c03.indd 23 Misra_c03.indd 23 1/19/2012 8:56:27 PM 1/19/2012 8:56:27 PM
- 47. 24 Chemical Bonding 3.1 Ionic bonding 3.1.1 Ionic radii The potential energy of a system (Ep) comprised of two oppo- sitely charged ions (e.g., Na+ and Cl− ), each with its electron cloud around the nucleus, approaching each other is given by (Fyfe, 1964): 2 2 p n e be E R R = − + (3.1) where R is the interionic distance (i.e., distance between the centers of the two ions, which are assumed to be hard spheres), b is a constant, and n is an integer with values between 8 and 12. The term −e2 /R represents the coulombic attraction between the opposite net charges (±e), and the term e2 /Rn arises out of the repulsion caused by interpenetration of the electron clouds and by the repulsion between the nuclei of the ions. As R gets smaller, the attraction term (which, by conven- tion, is assigned a negative sign) becomes more negative, indi- cating lower potential energy and thus increased stability. The repulsion (which, by convention, is assigned a positive sign) contributes little to Ep for large values of R, but its contribu- tion increases very rapidly when R becomes smaller than a critical value R0 , which is the equilibrium interionic distance at which the isolated ion pair is most stable (Fig. 3.2). When the two ions are separated by the distance R0 , we have a stable ionic bond formed between them. The value of R0 , the bond length, can be determined from the fact that it corresponds to the minimum value of Ep and occurs when dE/dR = 0. (When the cation is associated with more than one anion, as in a crys- tal, repulsion between the anions makes R0 somewhat larger.) The curve for Ep in Fig. 3.2 is typical of all atomic–molecular systems, and it is the basis of the concepts of interionic dis- tance and ionic radius, and the premise that to a first approxi- mation ions have a more or less constant ionic size. Strictly speaking, the electron density distribution around a nucleus does not have a spherical symmetry, as implied by the term “ionic radius.” A more appropriate term, according to Gibbs et al. (1992), is “bonded radius,” which refers to the distance between the center of one atom to the point of minimum elec- tron density in the direction between two nuclei. The outer extent of an atom in other directions is usually different because of a different distribution of electrons (i.e., the atom is not spherical). The bonded radius can be measured from electron distribution maps. However, we continue to rely on the concept of ionic radii because the approach has been quite successful in explaining most of the ionic crystal structures. Or Cl Cl Cl Cl Bonding pair Electron in the outermost shell Lone pairs (nonbonding) (a) Ionic bonding in NaCl (b) Covalent bonding in Cl2 Na Cl Na+ Cl Cl + + – Cl Fig. 3.1 Lewis dot representation of (a) ionic bonding (solid NaCl) and (b) covalent bonding (Cl2 gas). In this kind of illustration, the chemical symbol of the element includes the inner complete shells of electrons, and the valence electrons (i.e., electrons in the outermost occupied s and p orbitals) are represented by dots. The single covalent bond in Cl2 is represented by the two dots of the “bonding pair” or by a single line representing that pair; any pair of unshared electrons in the same orbital, which does not participate in the formation of covalent bonds, are referred to as a “lone pair.” Table 3.1 Some properties of ionic and covalent compounds. Property Ionic compounds Covalent compounds Participating elements Commonly between two elements with quite different electronegativities1 , usually a metal and a nonmetal Commonly between two elements with similar electronegativities1 , usually nonmetals. Homonuclear molecules (such as Cl2 comprised of only one element) are covalent Melting point They are solids with high melting points (typically > 400°C). Ionic compounds do not exist as gases in nature They are gases, liquids, or solids with low melting points (typically < 300°C) Solubility Many are soluble in polar solvents such as water, and most are insoluble in nonpolar solvents such as carbon tetrachloride (CCl4 ). Many are insoluble in polar solvents, and most are soluble in nonpolar solvents such as carbon tetrachloride (CCl4 ) Electrical conductivity Molten compounds and aqueous solutions are good conductors of electricity because they contain charged particles (ions) Due to lack of charged particles, liquid and molten compounds do not conduct electricity, and aqueous solutions are usually poor conductors of electricity 1 See section 3.6.5. Misra_c03.indd 24 Misra_c03.indd 24 1/19/2012 8:56:27 PM 1/19/2012 8:56:27 PM
- 48. 3.1 Ionic bonding 25 For the discussion below, we assume a model of pure ionic bonding arising out of a geometric framework of ions repre- sented by hard spheres of constant radius. But how do we determine the radius of each ion? Actually, it is not possible to measure the radius of individual ions in a solid, but we can measure the interionic distance between centers of two ions in a solid from its cell dimensions determined with X-ray diffrac- tion techniques, and then determine the radius of individual ions through some manipulation (Companion, 1964). For the purpose of illustration, let us suppose that Fig. 3.3 represents the packing in LiCl and KCl crystals as revealed by X-ray diffraction data. It is reasonable to expect that Li+ , with only two electrons, is a very small cation and assume that the pack- ing in LiCl be largely determined by the much larger Cl− ani- ons (each containing18 electrons) touching each other. In this case, the radius of the Cl− ion – Cl ( ) r is one-half of the measur- able interionic distance d1 . We can now determine the radius of K+ ion from the measured interionic distance d2 in a KCl crystal: + 2 – K Cl r d r = − . It turns out that the ionic radii calcu- lated by this strategy are reasonably constant from compound to compound and, carried over the entire Periodic Table, this has enabled the setting up a self-consistent set of average ionic radii (Fig. 3.4). As expected, ionic radii of cations and anions vary with atomic number. The radius of a given ion is also a function of the coordination number, the number of nearest neighbors of the ion in a crystalline structure (see section 3.1.2). Some general trends for ionic radii (expressed in Å) with octahedral (or six- fold) coordination (Fig. 3.4), the most common kind of coordi- nation for most ions in silicate minerals, are summarized below: (1) Cations are smaller than anions, the only exceptions being the five largest cations (Rb+ , Cs+ , Fr+ , Ba2+ , and Ra2+ ), which are larger than F− , the smallest anion. (2) Within an isoelectronic series – a series of ions with the same number of electrons – ionic radius decreases with increasing atomic number because of increased nuclear attraction for the electron cloud. For example, 4 3 2 Si Al Mg Na – 2– F O (0.48) (0.54) (0.72) (1.02) (1.33) (1.40) r r r r r r + + + + < < < < < (3) On the other hand, in the lanthanide (or rare-earth) series characterized by cations with 3+ charge, the ionic radius decreases with increasing atomic number, from 1.13 for La3+ to 0.94 for Lu3+ . This so-called lanthanide contrac- tion can be attributed to the influence of the increasing nuclear charge. (4) Within a family of ions, such as the alkali metals or the halogens, the ionic size increases as we go down the Periodic Table. For example, Li Na K Rb Cs Fr (0.76) (1.02) (1.38) (1.52) (1.67) (1.80) r r r r r r + + + + + + < < < < < – – – – F Cl Br I (1.33) (1.81) (1.96) (2.20) r r r r < < < This variation is a consequence of adding electrons with their most probable distance farther from the nucleus. (5) In the case of cations of the same element, ionic radius decreases with increase in ionic charge because of a decrease in the number of electrons. For example, 3 2 Fe Fe (0.73) (0.78) r r + + < 4 3 2 Mn Mn Mn (0.62) (0.73) (0.83) r r r + + + < < 4 3 2 Ti Ti Ti (0.61) (0.72) (0.87) r r r + + + < < 6 4 U U (0.81) (0.97) r r + + < The opposite is true for anions, although anions with variable charge are not common. 3.1.2 Coordination number and radius ratio How do ions fit together to produce different crystal struc- tures? The fundamental constraint is that, for a given set of ions, the most stable arrangement is the one that has the 0 Repulsion Attraction Net potential Minimum Ep at R=R0 R0 Potential energy (E p ) Interionic distance (R) Fig. 3.2 Variation of the potential energy (Ep ) of a system consisting of a singly charged cation and a singly charged anion as a function of interionic distance. The equilibrium interionic distance (R0 ) is marked by the minimum value of Ep , when dE/dR=0. For R>R0 , Ep is essentially determined by the coulombic attraction between the opposite charges and for R<R0 by the repulsion between the nuclei and the electron clouds. d 2 LiCl d1 rCl– = d1/2 Cl– rCl– d2 – = rK+ KCl Cl– Cl– Cl– Cl– Cl– Cl– Cl– Fig. 3.3 Strategy for determining ionic radii from packing of ions (assumed to be hard spheres) in LiCl and KCl. Misra_c03.indd 25 Misra_c03.indd 25 1/19/2012 8:56:29 PM 1/19/2012 8:56:29 PM
- 49. 26 Chemical Bonding lowest potential energy. The general rules that need to be observed for attaining maximum stabilization of a crystal structure are as follows: (1) The crystal structure must be electrically neutral, that is, the cation: anion ratio must be such that the posi- tive charges are exactly balanced by the negative charges. (2) The cation–anion separation must be close to the equilib- rium interionic distance (R0 in Fig. 3.2) for the compound under consideration. (3) The arrangement of the ions must be in a regular pattern, with as many cations around anions as possible and as far away from each other as possible; analogous restric- tions apply to the anions. In other words, we may treat the ions as spherical balls and pack them as closely as possible, subject to the constraints of electrical neutrality of the structure and minimum interionic distance. In a given three-dimensional close packing of spheres, the number of oppositely charged nearest neighbors sur- rounding an ion is called its coordination number (CN). If an ion A, for example, is surrounded by four ions of B, CNA = 4 (tetrahedral coordination); if A is surrounded by six ions of B, CNA = 6 (octahedral coordination), and so on. As discussed below, coordination number is an important consideration in crystal chemistry. Generally, cations are smaller than anions, so the number of anions that can be packed around the smaller cations determines crystal structures. The combined influence of cati- ons and anions on coordination number can be predicted from a consideration of the magnitudes of their radii 1 H Very small 2 He 3 Li+ 0.76 IONIC RADII (Å) (octahedral coordination) 4 Be2+ 0.27∗ 5 B3+ 0.11∗ 7 N5+ 0.13 8 O2– 1.40 9 F– 1.33 10 Ne 11 Na+ 1.02 12 Mg2+ 0.72 13 Al3+ 0.54 14 Si4+ 0.26∗ 15 P5+ 0.17∗ 16 S–2 1.84 17 Cl– 1.81 18 Ar 19 K+ 1.38 20 Ca2+ 1.00 21 Sc3+ 0.75 22 Ti4+ 0.61 23 V5+ 0.54 24 Cr3+ 0.62 25 Mn2+ 0.83 26 Fe2+ 0.78 27 Co2+ 0.75 28 Ni2+ 0.69 29 Cu2+ 0.73 30 Zn2+ 0.74 31 Ga3+ 0.62 32 Ge4+ 0.73 33 As3+ 0.58 34 Se2– 1.98 35 Br– 1.96 36 Kr 37 Rb+ 1.52 38 Sr2+ 1.18 39 Y3+ 0.90 40 Zr4+ 0.72 41 Nb5+ 0.64 42 Mo4+ 0.65 43 Te6+ 0.56 44 Ru3+ 0.76 45 Rh3+ 0.75 46 Pd2+ 0.86 47 Ag+ 0.94 48 Cd2+ 0.95 49 In3+ 0.80 50 Sn4+ 0.69 51 Sb5+ 0.60 52 Te6+ 0.56 53 I– 2.20 54 Xe 55 Cs+ 1.67 56 Ba2+ 1.35 57– 71 Lanth 72 Hf4+ 0.71 73 Ta5+ 0.64 74 W6+ 0.60 75 Re4+ 0.63 76 Os4+ 0.71 77 Ir4+ 0.71 78 Pt4+ 0.71 79 Au+ 1.37 80 Hg2+ 1.02 81 Tl3+ 0.67 82 Pb2+ 1.19 83 Bi3+ 1.03 84 Po6+ 0.67 85 At7+ 0.62 86 Rn 87 Fr+ 1.80 88 Ra2+ 1.43 89– 103 Actin 104 Rf 105 Db 106 Sg 107 Bh 108 Hs 109 Mt 110 111 112 Lanthanides 57 La3+ 1.13 58 Ce3+ 1.09 59 Pr3+ 1.08 60 Nd3+ 1.06 61 Pm3+ 1.04 62 Sm3+ 1.04 63 Eu3+ 1.03 64 Gd3+ 1.02 65 Tb3+ 1.00 66 Dy3+ 0.99 67 Ho3+ 0.98 68 Er3+ 0.97 69 Tm3+ 0.96 70 Yb3+ 0.95 71 Lu3+ 0.94 Actinides 89 Ac3+ 1.18 90 Th4+ 1.08 92 U4+ 0.97 91 Pa4+ 0.98 95 Am4+ 94 Pu4+ 0.88 93 Np4+ 0.95 97 Bk4+ 96 Cm4+ 99 Es 98 Cf4+ 100 Fm 101 Md 102 No 103 Lr ∗ Tetrahedral coordination 6 C4+ 0.15∗ Fig. 3.4 Ionic radii of ions in octahedral coordination. Å = 10−10 m. Sources of data: compilations by Krauskopf and Bird (1995), and Faure (1991). Misra_c03.indd 26 Misra_c03.indd 26 1/19/2012 8:56:38 PM 1/19/2012 8:56:38 PM
- 50. 3.1 Ionic bonding 27 expressed as the radius radio (RR). For a cation in a binary ionic solid, RR is defined as c a Radius ratio ( ) r RR r = (3.2) where rc and ra are ionic radius of the cation and the anion, respectively. Evidently, as the cation becomes larger relative to the anion, a larger number of anions may fit around the cat- ion. In other words, the CN of the cation is likely to increase as RR increases. Accepting a model based on close packing of spheres, we can easily calculate the critical radius ratios (i.e., the limiting values of the radius ratio) for different geometrical arrange- ments of the spheres. The smallest value of CN is 2, which represents the situation when the cation is so small that it is possible to pack only two anions around it if anion–cation contact is to be maintained. As the size of the cation increases relative to that of the anion, it becomes possible to place three anions in mutual contact around the cation (i.e., CN = 3) when RR reaches a critical value of 0.155 (Fig. 3.5a). With increas- ing size of the cation relative to that of the anion, the CN changes to higher values. The calculated critical radius ratios for different possible symmetries are: 0.155–0.225 for CN = 3 (trigonal coordination); 0.225–0.414 (Fig. 3.5b) for CN = 4 (tetrahedral or square planar coordination); 0.414–0.732 for CN = 6 (octahedral coordination); 0.732–1.0 for CN = 8 (body-centered cubic coordination); and > 1.0 for CN = 12 (edge-centered cubic coordination) (Fig. 3.6). Other coordina- tion numbers, such as 5, 7, 9, 10, and 11, do exist but are quite uncommon because such coordination polyhedra cannot be extended into infinite, regular three-dimensional arrays (Greenwood, 1970). In mineral structures, the most common anion is O2− , which has an ionic radius of 1.40 Å, and the ionic radii of most common cations are between 0.60 and 1.10 Å. Thus, the radius ratios with oxygen in minerals mostly lie between 0.43 and 0.79, suggesting that the most frequent coordination number in minerals is 6. This is why Fig. 3.4 lists ionic radii for octahedral coordination rather than for tetrahe- dral or cubic coordination. Examples of some ionic crystal structures characterized by different coordinations are presented in Fig. 3.7. Many cations in silicate minerals occur exclusively in a particular coordination with oxygen, but some occur in more than one coordination, to some extent controlled by the temperature and pressure of crystallization. For example, the radius ratio of Al3+ bonded to O2− is 0.54 Å/1.40 Å = 0.386, which is very close to the theoretical boundary of 0.414 between CN = 4 and CN = 6. Thus, in silicate minerals formed (a) (b) F Anion Anion Anion G C E H ranion=1/2 EF; rcation=CF – 1/2 CF=2/3 FH=2/3 EF Sin 60 rcation / ranion=0.155 Trigonal coordination (CN=3) rcation / ranion=0.414 CY=XY Sin 45 ranion= XY; rcation = CY – XY Anion Anion Anion Anion C X Y Z Square planar coordination (CN=4) Fig. 3.5 Critical radius ratios for (a) threefold (trigonal) and (b) fourfold (square planar) coordinations. Symmetry of anions around the cation Trigonal planar (Corners of an equilateral triangle) Sketch of symmetry Example Linear Tetrahedral (Corners of a tetrahedron) Square planar (Corners of a regular square) Octahedral (Corners of a regular octahedron) Body-centered cubic (corners of a cube) Critical radius ratio 0.155 – 0.225 0.155 0.225 – 0.414 0.014 – 0.732 0.014 – 0.732 0.732 – 1.00 1.00 Cation coordination number (CN) 3 2 4 4 6 8 12 Edge-centered cubic (mid–points of cube edges) HF2 CO3 2– ZnS NaCl CsCl Ni(CN)4 2– Cation Anion Fig. 3.6 The effect of critical radius ratios on coordination number and possible geometrical arrangements of ions in ionic crystals. ZnS (sphalerite) itself is not an ionic compound but its name is given to the structure because it is the most common compound in which this geometrical arrangement occurs (Evans, 1966). Misra_c03.indd 27 Misra_c03.indd 27 1/19/2012 8:56:39 PM 1/19/2012 8:56:39 PM
- 51. Another Random Scribd Document with Unrelated Content
- 52. Some of these statements you girls will have to read to your mothers. Then if prudery has blinded them to the truth, take the matter into your own hands. It is upon you, in the future, that depends the decent regulating of instruction in the public schools. The girl who goes to dances or any evening entertainment lightly clothed, low neck and short sleeves, while she is menstruating, as thousands do, will certainly land in the doctor’s hands or become one of those pitiful things, a drug fiend. And the drug habit starts from taking “some harmless thing” to ease the pains or stop the flow. That curse of the American girls, constipation, does as much if not more, to hurt the womb than a full bladder. We shall have a lot to say about this matter later on in our Chats about the skin and complexion. When the menstrual period first makes its appearance the swelling and tenderness of the breasts, the itching, a feeling of fullness in the region of the womb, are all natural and should not cause any worry. If you are in perfect health and KEEP so, these little symptoms will become less noticeable as you grow into full womanhood. So do not get frightened, do not take any medicines nor act upon the foolish advice from other girls. The flashes of heat, frequent blushing, dizziness and the frequent desire to pass your water, are all natural. There are some fortunate girls who approach and pass this first period without all these uncomfortable symptoms, but most of you will have some or all of them. The itching of the skin, pimples on the face and body, sometimes a sore throat, all these are nothing but indications of the great revolution you are going through from being a girl to becoming a glorious woman. Then there are the toilet duties to be done at this period and throughout your life which make for perfect health. Oh, yes, I shall tell you all about these matters and what to do. During the periods of the first year or so you are in a condition to catch many of the diseases all around you, such as tuberculosis—
- 53. consumption—erysipelas, tonsilitis, scarlet fever and the mumps. Remember I do not say you are liable to catch such a disease as consumption, only that you are in a condition when the germs can find lodgment better than at other times. Of course you should never sleep in a room with a consumptive or even be around one at any time, but should it happen that during your developing period anyone with the disease was liable to be brought into contact with you, keep away, away in the open air. At this period also mumps may be a serious matter for you, so if you have a little brother or sister who is suffering from this disease of childhood, you should keep out of the room and, if possible, out of the house. No matter if you did have the mumps when a little girl. If you catch the mumps during the first years of your young womanhood the affection MAY go to your ovaries. This, of course, produces a painful swelling and, if not attended to by a reputable physician, will go to destroy the usefulness of the ovaries—prevent you from ever having children. This has happened in girls who did not know—or rather their mothers did not know—what the danger was, and when the girl grew up to be married and no children came, she was blamed, often accused of being one who did not want children. Many a time when a young woman had been married several years and was childless, I have asked the mother if her daughter had the mumps when she was growing into womanhood, and if she suffered pain in the groin and back. “Why, yes, Doctor—but what has that to do with it?” “Didn’t you know that the mumps sometimes went to the ovaries and destroyed their function?” “Why, no; it can’t be possible?” “Yes, possible and probable. Your daughter can never have children because you did not tell her all about her sex organs, and when her little brother had a swelling and pain in the glands of throat and jaws, you did not know enough to send her away or keep her away from him, telling her plainly why you did so.
- 54. “But you were never allowed to mention these things when you were a young woman—you never knew these important things? Exactly so, and this is the punishment thousands of mothers and daughters are receiving for this prudery.”
- 55. CHAPTER III THE DISORDERS OF MENSTRUATION AND GENERAL HEALTH Civilization has brought many unnatural effects upon the monthly period of women, and ignorance of how to care for the body has made matters worse. It is with these unnatural disturbances that you are mostly concerned. The inability to understand certain symptoms of your menstrual flow, the consequent neglect of these symptoms or ignorantly taking drugs and medicines for the troubles, are the causes for so many girls and women being miserable and invalids struggling on under most distressing conditions. There is always a good cause for any irregularity or stoppage of the monthly period; some reason why the flow is scanty or too profuse. These causes can readily be discovered when the girl knows herself and all that pertains to that self. In the healthy girl the flow should come and go without any marked pains or distress. Of course during four or five days there will be a feeling of weakness, lassitude, a “please-let-me-alone” attitude, and in many girls, a desire for pure love and caresses. These various feelings are natural and only go to show that you are a full-blown woman. There is nothing to be ashamed of in this feeling for love and caresses, this peculiar desire to want protection and a something that you cannot exactly explain to yourself. It is really an awakening of all your womanly desires, and these are your greatest powers over man, children and the best of everything in the world. These feelings should not be suppressed, but kept under control. They
- 56. should be carefully saved, for they are the feelings which bring future happiness, and you want to give them as little attention as possible except that attention which keeps them pure and holy. Avoid all women who scoff at motherhood, who deride the domestic life for women, who stand and shout their demands in public places instead of sweetly using their influence for a better condition for men and women so that the future babies will have a proper birthright. No discussion or knowledge which will make better fathers and mothers can be wrong, but every attempt to ignore the subject is sinful. There is nothing to be ashamed of in maternal feeling and impulses; what a girl is to be blamed for is a want of control over these natural instincts and giving way to them. The care of the company she keeps, the kind of thoughts she lets get into her mind and the way she cares for her body, are the factors which make for a good and chaste girl or otherwise. But how can we blame all those girls who accidentally go wrong? I certainly do not. They have never been told just what to do, where the danger lurks and all the consequences. Should we blame and shun the girls who have been sent out into the world amid the dangers and snares laid for them; young women who see chastity mocked, virtue a thing to bargain for, the glitter of gold pouring into the laps of those thousands who find “the easiest way” out of their poverty and struggles? Yet the truth is, hard as it may seem and as often as it has been told to you, that virtue and chastity in deeds and thoughts DO bring rich awards. These awards may be a long and tedious time in coming and the struggle is hard, but in the end all this will be proven to have been worth while. As I have told you, the monthly period should come and go without much physical pain. It should last from four to five days and be regular in recurring about every twenty-eight days. But it is seldom so normal in the average American girl, the girl who has
- 57. been left alone to solve her own mysteries and go her own way. This is equally true of the high-school girl or the working girl. And why? Because she has been brought up through her early developing days to go on and disregard all her sex functions—the greatest factor in all life. The high-school girl has been mixed up with all kinds of youths and not kept away from tantalizing and embarrassing conditions. The shop and working-girl has been forced to do her work, day in and out, standing upon her feet or working at a machine while the sensitive and full-blooded womb was trying to empty itself. Let us first consider the girl whose monthly flow is scanty or entirely absent. She has arrived at the age of sixteen years and has not “seen anything.” But every month, for a year or so, she has had headaches, felt extremely nervous, had some pains, the breasts have felt tender and sore, and altogether she has had a miserable twelve months of these symptoms, but no relief from a flow. What is the matter with such a girl? Remember I told you that the womb was pear-shaped, the small end hanging down. Here is a little opening, through which the menstrual blood flows, and then out of the body. The womb is in reality only a big bunch of muscles so arranged that it can relax and empty itself and then tightly close. In the unmarried woman, or before one has given birth to a child, this little opening is completely closed except during the period. Even then it is only very slightly opened, but open and shut it must if a girl is to be in good health. A girl may have over-exercised or injured herself when she was twelve years of age or thereabouts, and brought about a little inflammation, which at the time she knew nothing about. The womb was already getting prepared to do its monthly work, and as the weeks went on the inflammation increased. Inflammation always means some kind of an extra growth at the injured spot; like a scar, for example, after a wound has healed up. The womb itself is not a sensitive organ to the touch or to slight inflammations at the lower end, hence the little girl does not, at the
- 58. time, feel any pain. She may feel uncomfortable in that region, but as she has been brought up NEVER to mention any matters concerning her sex organs, of course she keeps silent while the injury goes on. The little inflammation heals up, but in healing what does it do? Leaves a scar, of course. Now this scar may be big enough to have CLOSED the outlet for the monthly flow—to have made the entrance of the womb grow together. It is under these circumstances a sealed bag; nothing can come away from it. The girl’s time comes, but the blood does not. All the other signs being present, she watches and worries. Sometimes, alas, too many times, she has never been told just what should happen. Backache troubles her, headaches often drives her to take some harmful drug, she becomes fretful, loses control of her temper in the simplest things and finally loses friends because she “is so horrid, says so many cutting things.” Yet she does not mean to be disagreeable; she simply cannot help it. How could she? There is a clot of blood in her womb that cannot come away; it remains and hardens and each month is added to by the banked-up blood. It is a very sad condition, and one that often continues until a tumor is formed, or some other complication makes an invalid of her in the prime of her life—or what should be her prime. This condition is frequently the cause of hysteria, of desperation, of a gradual mental failing. There is another condition which goes to ruin a girl’s health and happiness, for the effects are the same as in a closed womb. There is a membrane in all chaste girls called the hymen. This closes the entrance to the vagina. Now there should always be a little opening, or several little openings in this membrane to let out the blood. In some girls this is closed from birth; so completely closed and tough that the weight of the first monthly blood cannot break through it. Then we have all the symptoms of the stoppage we have in the closed womb, only the blood packs and hardens in the lower parts
- 59. instead of the womb. Often this produces greater distress than when the same conditions exist in the womb. Here great bloody tumors form and the state of the poor girl is certainly pitiable. From birth also the womb may be closed, grown together. Then there are some girls so nervously constituted that the least touch on the muscles of the womb will shut it up spasmodically. Such a girl’s womb is not grown together, but when the first drops of blood are trying to ooze away, the womb shuts tightly. In all these cases the results to the girl is the same as I have described. The remedy for all this misery is simple, almost painless, and will not detain you from your duties but a few days; sometimes not at all. By simply cutting or snipping apart the growth at the entrance to the organ, or opening it by a little stretching instrument, the fault is remedied; the girl cured. And all this simple knowledge could have saved thousands of suffering girls and women. No, it does not interfere with your proof of virginity. The snipping is too slight. But supposing it should? What of it, as long as you know in your own heart that your are a chaste girl? Do you want to be a miserable wreck of a woman just on account of an ancient superstition, a foolish and harmful idea of a lot of old women and medieval theologians? It is a sad condition—this closed womb—and should not be allowed to sicken a girl for one hour—IF SHE KNOWS. Alas! she has not been allowed to know these things—just allowed to suffer and be blamed. If you have reached the age of fifteen years or thereabouts and for a year or so have had all the nervous and mental symptoms of a period occurring every month and no blood comes, then go at once to a reputable physician. Be certain you go to one in good standing. Never go to one who advertises “women’s troubles,” or to one whom you do not know by the best of repute. Remember that honest and true physicians do not advertise in the papers. So whenever you see an advertisement of a doctor who says he can cure you of THAT
- 60. trouble, keep away from him. Never mind what the other girls tell you about a doctor or some medicine that cured them, probably the cause for their trouble was an entirely different one. Naturally, your mother is the first one to consult, but I fear that if you have a mother who has allowed you to suffer month after month, and constantly said, “Oh, don’t bother about such matters; it will come out all right when you get older;” such a mother will not exactly be the one to go to—go to a RELIABLE physician. Never, under any circumstances, take medicines for this trouble. Let “regulating pills” alone as you would a rattlesnake. Now that you know the cause, common-sense will tell you that pills, or any and all things of the kind, are not only useless, but harmful. “But, Doctor, how about the girl who has had several good periods and then stops for several months, or even skips a month and only flows every other month? There can be no closing of the mouth of the womb under these circumstances?” No, in such cases the cause is entirely different, or rather the causes, for there are many. Most of you can find out for yourself just what YOUR cause is for being irregular, after I point out to you some facts. Many times it is only Nature’s way of preserving your health. For instance, if you have not sufficient blood in your system to allow you to lose a certain amount every month, Nature will prevent it going to the womb to be thrown away. Some girls will have “nose bleeds” once or twice a month and this takes the place of the monthly flow. This is not a sign of good health, just a sign that something is wrong —see a good doctor, he will know and tell you what to do. If you are troubled with headaches (especially in the back of the head and neck), if your appetite is poor, if you lost too great an amount during your last flow, or if your nervousness increases, it means that you are in poor condition. Perhaps you have danced too much and lost too much sleep, been unduly excited or had some great grief; any of
- 61. these things will affect in some way your menses. Anything, in fact, which lowers the tone of your general health will affect the menses. If you are over-fat and growing fatter every day, this unhealthful condition will stop your menses. I don’t mean a plump, jolly, happy amount of fat,—this is a good state for a growing girl,—but I mean an overplus of fat with white cheeks, flabby flesh, swollen ankles and big stomach. Such a condition indicates some disease. There are many diseases which leave you in a condition of suppressed or irregular menstruation; such as typhoid fever, kidney affections, chlorosis—lack of red blood—consumption, scarlet fever. If you have gone through any one of these illnesses and your periods are irregular or scanty, don’t worry; time will put this matter right as you recover from the general effects of the disease. If you have reason to fear consumption, be grateful that Nature is preserving your blood to help you get well; for, as you know, you can get well—can completely recover from consumption—if you WILL EAT AND SLEEP IN THE OPEN AIR—LIVE IN THE OPEN AIR. Most of the causes for irregularities and scanty flows are due to your unhygienic methods of living and playing. Sleeping in rooms where fresh air only gets in through a crack, insufficient and improper food and too much tea and coffee, will soon cause irregularities and other menstrual troubles. Catching cold or getting wet feet, damp skirts flapping around thinly-clad ankles just before or during the time of your monthlies, will also bring you to some womb trouble. Then the influence of the mind upon all these matters plays a very important part in your health. Evil suggestions from girls or youths, seeing plays which you ought not to see, reading all that rotten stuff put out for young women and girls to read and dream over—I don’t mean the nasty ones, but all those which unduly excite the imagination and throw a false light upon life—the Duke, the Prince and Villain kind—the virtuous blonde maiden and the hard-working hero stuff, you all know what I mean. There is plenty of good literature, exciting stories, to be read without reading a lot of cheap
- 62. tinsel and ready-made romances which have no more to do with real life than a mask has to do with the human features. You can over-exercise, become too much excited over contests in the gymnasium, use up force to such an extent that your growing womanly functions become weakened and sometimes dried up. No girl of a nervous temperament should go into any athletic contest, team or personal. Such a girl should not play basketball, attempt any stunts on horizontal bars or flying rings; nothing, in fact, which calls for a strain upon the nervous system. The function of the womb, as well as of all the sex organs, are directly affected by the nervous system. You can never be a strong woman, complete in all that belongs to a woman and her career, if you, as a young woman, over- strain the nervous system. Hundreds of girls who are playing contests of basketball, to see which team is to be the champion of the state or the town, are going to suffer from all this excitement. Your teachers do not take into serious consideration your growing sex organs. They do not seem to know what it means for a girl to get over-excited at any time during her development, that there is nothing except alcohol which will arouse dangerous impulses more than athletic excitement. So do be careful of your exercise. On the other hand, no exercise will also produce some disturbance of the menstrual period. If you do not take some form of useful exercise, poisons accumulate in your system. This causes unnatural fat to pile up around your ovaries and kidneys; in fact, it will bring you to a sad state in middle life if you have neglected to exercise in a careful and regular manner when you are growing. The girl who works in the shop, the department store, or follows any of the numerous careers which are open to her, as a rule gets plenty of exercise. To be sure it is not the best kind of exercise by any means, but as she has to be on her feet almost all the day, for her to take any gymnasium work at night is harmful. She needs the fresh air, to eat proper food and to obtain plenty of sleep—all she can get or steal. The girl who is so situated that she can walk to and
- 63. from her place of employment, is fortunate; the girl who cannot, must get walking exercise in the open air some way if she wishes her periods and general health to be perfect. Profuse menstruation, that is, too much blood flowing and for too long a time, is always a sign that something is wrong with the womb as well as with your general health. It is not a sign that “you have too much blood in your system,” but a symptom that the womb is weak, has lost its tone and does not close up tightly at the finish as it should. The cause is one of the many I have told you about; too long standing on the feet, going to parties or dances when you should have been in bed, improper food or too little of it, undue excitement at a time when you should have been quiet. Search well your own heart, and some of the causes you will be able to discover yourself. In other words, any irregularity or little errors in your conduct will bring about irregularity in your menstrual functions. No girl should use the sewing machine when she is unwell, or do any work which involves the movement of the thighs and legs. Food, nourishment and clothing have a lot to do with all the irregularities and disturbances of the sex organs, but we shall have to chat about these important matters when dealing with the skin and complexion, so leave them here. It will save repeating. One great curse—for that is what it really is—of all American girls and women, is constipation. False modesty, ignorance and not drinking enough water are the principal causes for this injurious state. But never mind the causes, let us get at the effects. Every portion of your body, including the bones, can be in a state of good health only when constantly supplied with fresh water. Coffee, soda water, chocolate or other makeshifts do not take the place of pure water. You should get the water into you daily, by the quart. I wish I could go into this matter so thoroughly as to make you all see and understand the importance of this fact. However, I can show you in these Chats how necessary it is even to your sex
- 64. organs and what they throw off, to make you, I hope, drink plenty of water throughout all your lives. The bowels must be emptied every day. Any keeping of the cast- off material of the intestines in the bowels means an odorous skin, foul breath and other disagreeable odors, no matter how clean you may be OUTWARDLY. Then there is another very important feature of this dried-up state. As you grow older the arteries harden, they cannot expand and contract as the blood pressure demands they should, and when any strain comes upon the heart or blood vessels, these latter burst and apoplexy is the result. But before this takes place there has been a failing of the memory, perhaps of the intellect, because the proper amount of blood needed to nourish the brain cannot pass through the tiny, but important arteries of the brain. So some kind of softening of the brain follows. “She died from apoplexy” is said. No, she died because, when a young woman, she would not drink water in sufficient quantities to keep her organs flushed and clear of accumulated material. Now, if this absence of water in the system so affects the brain, its arteries and veins, just imagine what trouble the womb will have in getting enough water for all its needed blood. But there is a more important effect that the absence of plenty of water in the system has upon the girl. It is a very serious matter to her, as it affects her attractiveness and happiness, and this is what we want to get at in these Chats. You all know that at certain times girls will have more or less an odor from their skins and breaths. It is very noticeable in some girls, and in others of the most careful cleanliness and habits it will be detected. Perfumery only makes matters worse; the attempt to cover the natural odors is too marked. These odors are all caused by acids and other chemical materials which exist in the natural secretions of the body; the perspiration, breath and other secretions. The less water there is in the human
- 65. system, the more will these chemical odors pervade the atmosphere surrounding the girl. It is the lack of plenty of water that causes the skin to give forth odors. If you have exercised to the extent of bringing on profuse perspiration and have not drank plenty of water before, during and after the exercise, no amount of bathing will prevent an odor coming from the skin. If you are going out to a dance or any place where you will be in a warm room, you will not be able to disguise the chemical odors coming from the skin. But if you have filled your system with water two or three hours before going out, your skin will have a delicious, natural odor. During the menstrual period every gland in the growing girl is very active. The skin throws off an extra amount of perspiration, the glands under the arms are very, extremely, active. Then at this time the breath comes faster than usual and throws off its poisons in large quantities. All these off-castings of the body are loaded with material that must leave the body if we are to keep in good health. But here is the point. You can so saturate your system with pure water that all these fatty and acid odors become highly diluted and scarcely any of them will make their presence known to those around you. Drinking water will make you fat? Nonsense. That is some old woman’s tale—some old woman who tries to excuse herself from drinking water. Water will not make you fat nor make you lean; just keep you in the good health and state you were born to be in. Then it helps keep the bowels clean, gives a good flow to the blood and keeps the womb free from any little clots being left over from your last menstruation. How much water shall I drink? Two tumblerfuls every morning before breakfast, two between each meal and as much at meals as you want. Don’t bother yourself about the fads of drinking water, such as none at meals, for instance.
- 66. Look at a horse; he drinks when he is thirsty and he drinks all he wants. Take water away from a horse, keep it away from him as it has been kept away from girls and young women, and you would soon see his coat become dull, sticky, and the light go from his eyes. Remember that a horse’s coat of hair corresponds to your skin; it is his complexion. Deprive yourself of water and your skin becomes dull, sticky and malodorous. But we shall have a lot to say about the skin, so nothing more now. With all this good habit of drinking plenty of water must go the application of water to the outside of the body. This you must do to wash away the dried crystals of all the chemical materials sent out from the skin and glands. Warm SPONGE baths, while you are menstruating, are necessary. I know that you all have been told never to take a bath while your period was on, but you see that you must get rid of these tell-tale odors now that you are out in the world. Of course you must be careful not to take cold; you should not use any but warm water, and then jump into bed warmly covered. Use no scented soap, not even under the arms, just plain castile or a similar PURE soap. After the flow has ceased be certain to wash your external parts with a soft sponge and pure soap. You want to consider this part of your toilet just as important as washing the teeth or ears, and it should be done in the same unconcerned and unthinking manner.
- 67. CHAPTER IV THE CARE OF THE SKIN AND COMPLEXION All girls want a good complexion and a clear skin. The skin and hair are the glories of a healthy woman. Most of you can have this desired state of a clear skin and pure complexion. A good complexion merely means a perfect state of health. A clear skin does not depend on what you apply to it, but what you keep off it. The clear, satin-like skin, the skin which looks like a transparent piece of silk laid upon a soft cushion of white flesh, and that sheeny skin resembling fine velvet, seen in the pure blonde type of girls, are all the effects of the blood beneath and how that blood is treated by the emotions. Muddy and contaminating thoughts will cause a muddy skin. Clean and clear thoughts will give you a clear skin. Jealousy and anger will, in time, affect the flow of blood through your tiny skin-veins and give you the appearance of age. Any emotion which causes indigestion will do the same thing. In fact, the state of mind and the manner in which you control your thoughts and temper are reflected in the tone of the skin. It is during the first few years of menstruating that the girl who does not understand these matters commences to ruin her complexion. While your body is developing, the tiny glands in the skin are undergoing great changes. These changes cause the glands to pour out oily matter, perspiration and other material, all of which naturally bring about a muddy complexion in some girls and redness of the nose, or pimples on the face, in others. These conditions are natural to the growing girl. The skin is clearing itself of all the little girl’s activities and making ready for the
- 68. woman’s complexion. It is Springtime with the skin, and this dirt—or what looks like dirt—is the result of all this skin-cleaning. Hair is appearing on certain parts of the body; that almost invisible down which all women possess, is growing on all portions of the body and face. The monthly periods are causing congested blood vessels throughout the whole body and especially the tiny arteries of the skin. Every part of your system is really undergoing a great change and does not get into a state of perfect health until you are eighteen years of age and over. As in all things in which a decided revolution takes place, there is more or less of a disturbance. This is the time when a girl commences to worry about her complexion. She frets and becomes anxious about the little spots appearing upon her face. If she has not the proper home advice, but hears all sorts of tales and sees all sorts of things in the school or shop, she soon resorts to the drug stores for a face lotion, powder or cream. She may have been told by an older girl that, “No, I never had anything but a good complexion; you’d better take something for yours, I would,” and much more of this kind of foolish advice. Some girls go through the period of development without any marked change in their complexion; others, especially brunettes, will have a “broken-out-face,” a hot and oily skin and not infrequently pimples on some part of their bodies. Girls of nervous temperament are apt to have more or less of a spotted complexion during the first few years of menstruation. In all these girls it is more of a sign of good health than otherwise, and if the skin had been left alone,— which it has not, because you have never known the truth,—the quack advertisements of “face creams,” “skin food,” “complexion wafers,” and all the other skin poisons and complexion-destroyers, would never have been put out to swindle girls and women. Pimples most frequently show on the shoulders and upper arms, and unless the girl knows that these really mean a splendid complexion when she has grown to full womanhood, she worries herself to a point that makes her little life miserable.
- 69. This is the point in a girl’s life where she starts in to ruin her complexion forever. She commences to fill in the openings made to let out the fatty and other substances in her skin, by powdering, applying some ointment which keeps these pores closed, or goes to bed with greasy or other injurious “skin foods” upon her face. In fact, she does just what in the end will give her a pasty complexion instead of a clear one. Of course she will later on take to the rouge and powder puffs and have to keep them in constant use until her skin becomes like that of a dried codfish. Please remember that what you need during the first years of your menstrual life is to allow full freedom for the skin to get rid of all the material your state is producing behind the outer skin. This material must come away if the skin is to be a clear and healthy one. Banking up, stopping this sweating process of the glands of the body, will ruin your complexion in time. You would not attempt to clean a room by sweeping all the dust under the carpet and not expect this dust to be always flying up and making the room dusty and ill-smelling? But you do about the same thing when you do not let all the dirt and dust come away through the spring cleaning of the skin. The period of your development is the Springtime of your life, and you must expect all kinds of disagreeable feelings and little annoyances to occur during this period. Each month, just as your menses are coming on, you will find little pimples or some redness on your face, nose or shoulders; perhaps on the arms. You should not want to go to dances or entertainments at these times; in fact you should not; but at no time during your growth into full womanhood should you wear gowns with short sleeves and low necks. For even between the menstrual periods there will be some indications upon the face or skin which tell the story. To hide these little eruptions or redness of the skin you have to apply powder to the neck, shoulders and arms. What are the consequences? The perspiration, due to the heat of the room and the exercise of dancing, keeps the inflammation active under the powder and may cause such pimples that the scars are left forever.
- 70. And right here is where you “catch cold.” Drafts, sleeping by an open window or going from a warm room to a colder one do not give you a cold. You may catch cold by doing these things, but the cause is something which has brought about a too rapid loss of heat from the body; such as any wrong way of clothing or underclothing yourself; low-neck dresses for winter; or covering the skin with powder or enamel, through which the perspiration cannot have free play and keep the temperature of the body equal; these are the reasons you “catch cold.” Those girls you occasionally see with a pitted skin on their faces and shoulders, are those who in all probability prevented the natural grease and other substances from getting out when they were in the first two or three years of their development. They have generally brought about this disagreeable complexion by attempting to dress as full-grown women and covering face, shoulders and backs with some kind of lotion, powder or cream. The girl who was noted for her fine, soft and smooth skin when she was eight or ten years of age, commences at puberty to have pimples and blackheads on her nose, cheeks and forehead. This being about the time she takes more notice of herself and others around her, these little facial blotches worry her. It is the opening of a new life and much attention is given dress, hair and complexion; to her whole appearance. She brushes and fixes her hair with great care; tries all sorts of experiments. She probably uses the brush of her older sister or one belonging to some of her family, or more frequently it is the common one at school or in the store. She does not intentionally use a dirty brush, nor will she use one which she has the least suspicion has been used by the unclean. But even the brush of her mother or sister carries germs that at this time do much injury to her skin and scalp, because the skin of the forehead is affected by the germs which get to the scalp. This germ is one which is always to be found in the glands of any person’s scalp or hairy portions of the body. These glands are known as the sebaceous glands. They are the ones which secrete the oily
- 71. substance that is necessary for the health of the skin and hair. You have enough of the oily substances in your own hair and skin, and it is usually free from germs at this time if you have used only YOUR OWN BRUSH. But the moment you use a brush belonging to some older and full-grown woman you carry to your own scalp these germs. If some of the other germs which are sometimes found upon common brushes get onto your scalp, there is another trouble for you to combat—dandruff. In the first case you simply add oily stuff to your own supply, get over-much of the oil; in the other case, dandruff is piled thick with the fatty material and then comes scalp disease. This may go on for some time and not noticeably affect you, but it may cause in a few weeks a certain form of eczema about the forehead and even the face. This is a very important matter for all girls and young women to remember. I have shown you that on the approach and for some time after puberty, all the tiny glands of the skin are enlarged and very active, so you can now see that there are hundreds of thousands of little holes for the germs to get into, and they do so from the brushes you are in the habit of using—that is, most of you. When these germs have located themselves upon the scalp, they soon commence to show the fact by giving you a muddy complexion. Sometimes you will be accused of not thoroughly washing your face, so marked is the line around your forehead and neck made by the attack of these germs. When the openings of the glands begin to gape, the effect is not agreeable to you nor to your friends. The pimples commence to irritate you on account of the increase of the oily substance, and soon you see that little creamy spot, then you or a misguided friend will squeeze it out. Often before this harmful procedure is gone through with, a formation of a little cocoon-like body is formed and then you have blackheads. This is not all dirt as is generally supposed, but a little cylinder filled with fatty stuff, water and some dirt from the skin. If these blackheads keep coming and if you go on squeezing them, if you insist upon covering the pimples with powder or lotion, a real skin disease will
- 72. be the result. This skin disease we call acne, and it is a difficult and trying one to cure. Never mind all those fetching advertisements in the papers which claim to cure acne in a few applications. Don’t touch such harmful stuff. All these advertised lotions simply COVER UP the symptoms of the disease, drive it further into the skin, and when you finally have to go to a reputable doctor, too much harm has been done for him to save you from being marked for life. Never trifle with advertised cures, go to a well-known doctor, or if you cannot afford to pay a specialist’s price, seek one at the outdoor clinics. There you will receive the same kind and careful treatment you would if you went to his office in an automobile of your own. What are we to do to keep from having all these disagreeable pimples and their after-effects? Prevent them. You understand; not cure, but prevention; for I want to put you all in a position to keep from having any trouble which needs a CURE in the medical sense. The first thing to do is to look out for your scalp as soon as you recognize the approach of puberty and for ever after. I do not mean that even a little girl should ever have her scalp neglected, but that you must, as soon as your menstrual time comes, NEVER use any other brush than your own and this must be a new one. No matter how old you are, get a new brush every few months and guard it as you would your jewels or your most precious gift. You should consider a brush for the hair as sacred as the one for your teeth. You surely would not think of brushing your teeth with any old toothbrush which happened to come along; neither should you use any other hairbrush but your own. And all this is such a simple matter, for whatever you do, wherever you go, whether you attend school, work in an office or store, you can easily carry with you your own hairbrush as you do your own toothbrush. Of course the same rule applies to comb, soap and towel. The habit some girls have of brushing and combing each other’s hair is all very well if only your brush is used upon your hair, and only upon your hair. As a rule girls take one brush and go over each
- 73. other’s scalps, thereby contaminating all the scalps; carrying oily matter from head to head. The scalp of a blonde-haired girl is not kept in good condition by the same quality or amount of secretions that a brunette requires; a woman’s scalp that has been neglected will carry to a young woman’s sensitive skin germs which will affect her scalp and complexion, but would not probably affect a middle- aged person. So let no person use your brush and allow no other person’s brush used upon you. The habit of promiscuously kissing each other that some girls at this age of puberty so often have, is a dangerous habit, because you may have placed upon your lips some of the germs which cause pimples, and then comes trouble again. Anyway, a girl is too young to be kissed and not old enough to kiss—without danger to herself. There are many, many more little things which cause a poor complexion in the girl and grown woman. First of all is that curse of American girls and women—constipation—the result of our false and injurious prudery. I warned you we should have to refer to it again and again, for it is a condition that enters into the cause of many women’s illnesses, indispositions, tumors, open sores, headaches and other avoidable troubles. Allowing any of the cast-off material of the stomach and intestines to remain in the lower bowel will most positively cause a muddy and pimpled skin. The reason is plain. This material is dead stuff meant to be cast off out of the body EVERY day. If it remains in the body it putrefies, forms gases and acids, which are REabsorbed into your system, taken up by the blood, which later on shows it in your face. Just think of it! Would you like to go around with all the signs of putrid matter being kept in your body? Of course not; yet you will outwardly show these signs if you do not keep your lower bowels always cleaned. What is the best way to keep the bowels clean? Regularity in your habits of toilet is, first of all, the most important factor. Drinking plenty of water—you see I am at it again—in the
- 74. morning, is next in importance. Your breakfast food can be so arranged that the bowels will empty themselves every morning if the habit and water drinking have been carefully looked after. Fruit, stewed or ripe, should be taken every morning. Little or no meat is needed nor advisable for you in the morning. Cereals—real cereals, not the sawdust and roasted bread crust stuff—are good for the morning meal. Plain, old-fashioned oatmeal comes first, then hominy or similar cereals. The idea that buckwheat or other breakfast cakes cause pimples is all nonsense. The same is true about syrups, butter or sugar. If you have flushed your stomach and intestines with water and fruit, you may eat all the cakes and sugar you wish. Candy does not affect your complexion, neither do cakes, pie, nor any sweets which ARE PURE AND EATEN AT THE PROPER TIME. All our grandmothers’ scare and advice about eating candy and other sweets is due to the fact that they DO harm in this way. Candy and other sweets are too often eaten between meals or early in the morning and thus cause a lack of appetite. With this loss of appetite, the body cannot get its nourishing and bowel-cleansing food. It is the loss of this nourishing food and the natural result of having nothing in the intestines which will wash these food tracts out, that does all the harm. It is living unnaturally to be in such a condition, and any unnatural way of living will bring about unhealth, and this will be shown by a poor and nasty-looking complexion, a hot skin and flabby flesh. Young women and girls often need sugar in their system and at certain times will crave it. Other girls will crave something sour— pickles, for instance. EAT PICKLES AND CANDY IF YOU CRAVE THEM. But do not forget that first you must have had a breakfast free from these substances, have thoroughly emptied your bowels and had a good noon meal. After these good meals you may eat candy, pickles, ice cream, any old thing—IF THE MATERIALS ARE PURE. This is a very important matter. Eat nothing that has been exposed to the dust of the streets or any filthy place. We shall have
- 75. something to say about “dope” drops and candies in which are brandies, cocaine and other drugs. The girl who goes out at noon and buys for her luncheon éclaires, doughnuts, cream puffs and other pastry, and makes a meal of this stuff, is positively going to have a pasty complexion, be constantly constipated and unable to do her full amount of work—school, house or office. If she has taken some good soup and eaten a little nourishing food, THEN the pastry will not harm her; perhaps do her good. I have said nothing about eggs or fish. I think most of you are glad of it and know the reason. I have had thousands of girls and young women under my charge and but few of them could eat either eggs or fish; and to many, milk was positively repulsive. At certain times these kinds of foods are nauseating to many girls and young women. Now and then a young woman will take an egg or a few bites of fish, but all through the active portion of her life she abhors a diet of such eatables. It is a case of— Jack Spratt could eat no pie, His wife could eat no fish; So betwixt them both Each had a separate dish. Do not force yourself to eat anything that you do not enjoy. In good health the body will know what it needs. If it needs sugar, it will give you a craving for sugar; if you need beef, you will want it. The cravings for sweets or sours only become unnatural when they are eaten to the exclusion of nourishing food. If you have the HABIT of eating sweets in the morning, you must break this habit. You got into the habit because you gave in to a natural desire at an unnatural time. If you are hungry before going to bed, then you will benefit by taking some nourishing and easily-digested food. Eating at night will NOT injure your complexion. It is eating indigestible food which ruins the complexion, and before bedtime you are too apt to eat those
- 76. foods which lie all night in your stomach and ferment there. This is a sure and quick way to bring on a muddy complexion and a red nose. Never drink milk with beef, pork or ham. But I do not fear this tough combination in girls or women, only it is best that you should know that such a combination will remain all night in your stomach and let you know it for a few days afterwards. I know that the majority of girls and women who are out in the selfish world, including schoolgirls, do not fully realize the great importance of proper food eaten at the proper time, that is, the bearing it has upon all their growing powers. If they did, we should not have all these patent medicines for skin, womb, stomach, headaches, and all the other doped stuff, which is ruining hundreds of thousands of those who ought to be the mothers of the future generation. I say ought to be, because unless you girls take hold at once and absorb these facts I have been telling you, and shall tell you, many, yes, most of you, will weep throughout a childless life. What shall I apply to my face? Nothing but water and pure soap. Does not washing the face in water, hot or cold, bring on wrinkles? No, never. Did you ever see wrinkles upon your canary bird? Don’t you have a bath ready for her every morning? What made the Greek and Roman maidens so beautiful in face, figure and complexion? Baths, bathing their bodies and faces daily. But they used facial ointments, powders and creams. No, not the pure maidens or matrons; only the other kind. If a woman, when young, was foolish or ignorant enough to use powder or grease upon her face and kept it up, when she gets to be thirty-five or so, she has to resort to enameling her face. If now she allowed her face to be thoroughly washed by either cold or warm water, she would have wrinkles, big, deep ones. She, of course, does not believe in water on the face and will tell you so; she has her reason. And the reason is this: For years she has been maltreating
- 77. her skin by stopping the natural oil from leaving the skin glands. As time went on she has applied the necessary powder—necessary to her—then had to use some form of facial cream, increasing the amount year by year. There has been no opportunity for the skin to stretch or relax, to work out its secretions, it remains almost immovable; consequently ridges and furrows form, and a good wash brings out the wrinkles and also her secret. There is no harm in having the face massaged when you are tired, dusty and your skin feels tightly stretched. But having it gently rubbed and washed with cold water, then protected by a veil as you go out into the fresh air, is an entirely different matter from having it rubbed by one who fills in the open pores with a “facial cream” or some “beautifier.” There is only one beautifier, and that is GOOD HEALTH. And once you get it you do not have to apply it every day. It will stand the rain and the sun, will defy heat and salt sprays, will be always by your side wherever you go and not put you in the awful condition of a well-known professional beauty I once knew. This woman was traveling and became ill. I was sent for, but when I arrived I was told by the maid that Madame could not see me at that hour. Now the case was important; the woman was suffering and in danger. Never mind, she simply COULD NOT see me for several hours. She went into a delirium and was finally taken to a hospital for mental invalids. Why wouldn’t she see me? Because her fine and notorious complexion had been left behind, and as the suffering from her pain had caused her to freely perspire, the perspiration had opened up all her wrinkles and furrows. Unless the skin of the whole body is freely washed, the neglect will show on the complexion. A bath every morning is the secret of many bright and rosy cheeks. If you are so situated that you cannot get a tub bath every morning, winter and summer, you certainly can get a big sponge and have a sponge bath in your room. Let the water run down your spine, especially down the small of your back. Give your face a good dose of cold water. A shower on the face will
- 78. keep wrinkles away until late in life. Do not stop your bathing because you are unwell, only use warm or tepid water. I know that many girls are told not to even put their hands in cold water while menstruating. This is utter nonsense, if the girl is otherwise in good health. These old ideas have done much harm and kept girls from benefiting themselves by helping Nature in all her growths. Cold baths will keep your flesh firm and hard; will take off fat if you are too fat, and put on flesh if you are too lean. Like everything in nature, the improvement comes slowly, but it certainly comes. You should commence the baths in the summer and keep them up so that when the cold weather comes the change is not very noticeable. Of course all this should be done in a warm room and you should have a warm rug to stand upon. Be sure to take a good rub with a coarse towel. This brings us to some simple form of exercise you can do at this time which will help the bowels to empty themselves by toning the muscles of the abdomen—the stomach, you call it. These exercises consist in bending the body from your waist several times, then swinging from side to side. You do this with your feet close together and with straightened knees. Bend forwards and downwards, touching the floor with the tips of your fingers without bending the knees. Keep it up until you can do it without effort. Then swing your body from side to side, twisting and turning from the hips. Nothing will give you a more graceful figure than these forms of movements. Keep up this exercise all through your active life, and with all the other advice I have and shall give you, you can be attractive even when the gray hairs have made their appearance. It is not the purpose of these Chats to advise you in purely medical matters, that is to tell you what to do in illness and what medicines to take. The purpose of these talks is to put you in possession of knowledge that will bring you to full womanhood, a strong, healthy woman to whom marriage and children will be a state of happiness for both husband and wife, or to a state of content, if you choose “single blessedness.” But in the matter of
- 79. constipation, I think it will do no harm to tell you that, if you will take once a week a tablespoonful of SODIUM PHOSPHATE, you will be benefited. This sodium phosphate should be taken before breakfast in a full glass of water. What about thin hair, split hairs, that dead-feeling hair? If this condition is found in the young woman, it is ninety-nine times out of a hundred her own fault, or due to her ignorance of what the scalp and hair need. It is because she has piled a lot of dead and often diseased hair on top of her healthy and growing hair. Put a bunch of dead matter upon live and growing matter and what is the result? Death, decay! Most of the fashions in hair and dress originate in those whose lives and age compel some artificial aid to attract attention. These foolish and freakish fashions are not for the young woman to adopt. Take the fashion of long trains, for example. The women of Paris seldom walk, they go about in automobiles or carriages. Now, sitting in these open conveyances it attracts attention to have a long folding train wrapped around the sitting figure and pulled up at the ankles to show a dainty slipper and silken hosiery. Don’t you see how ridiculous it is for a good young woman who has to walk to her daily work or school, to try to copy a fashion which is intended for an entirely different class of women? Yet, when trains were the fashion, you all did it. You are doing about the same foolish thing now with your head. Head-gear—that is the best name for it—is intended for women whose age has depleted them of much hair or whose lives have been such that their hair has become dead through bleaching or other injurious processes—these women must repair the damage. Wigs are too evident, so these women buy the hair which once graced or disgraced some other women, and pile it up in freakish forms and call it the latest fashion. The American girl and young woman immediately follow “the fashion,” and then you ask me what to do for thin hair and dead tresses!
- 80. Now, if you keep up this heathenish fashion of ruining your own beautiful hair, many of you will not only have thin hair, but become BALDHEADED. False hair, such as “puffs,” “rats,” frames, pads, “transformations,” “pin curls” and “mouse-traps,” will do the trick for you. Even the artificial means used to puff out the natural hair will ultimately injure it—injure it beyond repair. All the false hair with the appliances to keep it in shape, press on the scalp and impede the circulation of the blood, and the part of the scalp it should supply will wither and lose all life. The result of any pressure on the blood vessels of the scalp is that the roots of the hair become impoverished, and in time the hair gets so thin and weak that it drops out. Very little, if any, air can get to the scalp when you are “following the fashion,” which is just now in vogue. Stop this injurious and ridiculous wearing of false puffs, pads, and especially “transformations.” I have seen schoolgirls and typists with enough rigging of false hair and rusty wires upon their heads to give a strong man a constant headache and make him bald in a month. Your hair also falls out rapidly and constantly, but as you are blessed at the start with more luxuriant and more active growth in the scalp, it takes longer for the injury to show. But it is only a matter of time, not effect. Then there is another matter which you do not fully realize—all good and worthy men detest this ill-smelling and dead hair you pile upon your heads. You lose all your fresh appearance, all the looks of a maiden, all the proofs of innocence. Your complexion takes on the hue of the dead hair, and when the fashion passes you can never get back the shining, luxuriant tresses men so dearly admire. Men and youths may not have told you these truths, but way down in their hearts they will pick a girl for a wife or sweetheart who has not the smell of a dead Chinaman, or whose hair has been the abiding place for an old “mouse-trap” and left the mousy odors.
- 81. The best way to insure a good head of hair is to wear it loose and free, without any artificial aids and appliances. Of course you may dress it any way it pleases you, but aside from pins it should never have any other pressure upon it. The hair should be washed frequently in water with a little powdered borax, but remember you wash the hair only to clean the scalp, nothing should be applied to the hair directly. There is another fashion which has made many a girl suffer from headaches, thinned her hair and injured her complexion. This is the wearing of tight collars, neck bands, and those torturing things with points you wear stuck right up under the ears. I forget now what you call them, and I won’t tell you what I call them, for it would not sound nice to polite ears. But if you keep on wearing them a man will be able to say almost anything without you being able to hear him; for you will be deaf. The reason these tight collars do so much injury is that they compress the arteries and veins of the neck, which at this part of the body are near the surface. They are large, full-blooded vessels and bring the blood to and return it from brain and scalp. I have known girls to faint simply from the compression due to tight collars or bands around the neck. They will almost invariably cause headaches, and every one of you know of the great relief you derive from taking them off and putting on a loose wrap or dressing sack. I have known women to suffer violent pains in the head, then dizziness and final collapse, by preventing a free circulation through the brain. The same blood vessels supply the skin, and when these are stopped from nourishing the skin what do you get? A poor, pale and finally diseased skin, a starved face.
- 82. CHAPTER V NERVES AND THE NERVOUS GIRL It seems that not anything worth while in this world is gained without self-fighting and worry. The great things that are accomplished by men and women are accomplished only through will power, determination and concentration. Determination is different from will power in this respect: one may be determined to do a thing but find that she has not the nervous power to carry out the determination. In other words, the nervous force is really the basis of all will power. So all the factors which go to make for self- control and concentration upon whatever you have decided upon doing, are dependent upon a good and perfectly adjusted nervous system. Without a powerful nervous force we would be nothing but eating and sleeping animals. The men and women who do not know from any personal feeling that there is a tremendous force in a trained nervous system are those who do nothing for the world’s progress; they only eat, sleep and automatically labor. Many who have plenty of nervous force but do not know what it means, and hence cannot control it and use it for the benefit of man and themselves, are those who throw it away in dissipations, abnormal excitement and riotous living. To have a highly-sensitive nervous organization is the greatest gift a woman can have; but unless she early knows its value and how to train it, it becomes a curse to her. It will run away with all her impulses—good and bad—and finally separate her from her womanly stability. We hear a lot about “nervous women and girls;” and that the condition is increasing, due to our rapid way of living and all the
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