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Chemistry
The Molecular Nature of Matter and Change
Seventh Edition
Martin S. Silberberg and Patricia G. Amateis

©McGraw-Hill Education.
Chapter 1: Keys to the Study of Chemistry
• 1.1 Some Fundamental Definitions
• 1.2 Chemical Arts and the Origins of Modern Chemistry
• 1.3 The Scientific Approach: Developing a Model
• 1.4 Measurement and Chemical Problem Solving
• 1.5 Uncertainty in Measurement: Significant Figures

Chemistry
• Chemistry is the study of matter, its properties, the changes
that matter undergoes, and the energy associated with these
changes.

Definitions
• Matter: anything that has both mass and volume – the “stuff”
of the universe: books, planets, trees, professors, students
• Composition: the types and amounts of simpler substances
that make up a sample of matter
• Properties: the characteristics that give each substance a
unique identity

The States of Matter
• A solid has a fixed shape and volume. Solids may be hard or
soft, rigid or flexible.
• A liquid has a varying shape that conforms to the shape of the
container, but a fixed volume. A liquid has an upper surface.
• A gas has no fixed shape or volume and therefore does not
have a surface.

The Physical States of Matter
• Fig 1.1

Physical and Chemical Properties
• Physical Properties
– properties a substance shows by itself without interacting with
another substance
– color, melting point, boiling point, density
• Chemical Properties
– properties a substance shows as it interacts with, or transforms into,
other substances
– flammability, corrosiveness

The Distinction Between Physical and Chemical
Change
(A) © Paul Morrell/Stone/Getty Images; (B) © McGraw-Hill Education/Stephen Frisch, photographer
• Fig 1.2

Sample Problem 1.1 – Problem and Plan
Visualizing Change on the Atomic Scale
• PROBLEM: The scenes below represent an atomic-scale view
of substance A undergoing two different changes. Decide
whether each scene shows a physical or a chemical change.
• PLAN: We need to determine what change is taking place. The
numbers and colors of the little spheres that represent each
particle tell its “composition”. If the composition does not
change, the change is physical, whereas a chemical change
results in a change of composition.

Sample Problem 1.1 – Solution
• SOLUTION: Each particle of substance A is composed of one
blue and two red spheres. Sample B is composed of two
different types of particles – some have two red spheres
while some have one red and one blue. As A changes to B, the
chemical composition has changed. A  B is a chemical
change.

Sample Problem 1.1 – Solution, Cont’d
• SOLUTION: Each particle of C is still composed of one blue
and two red spheres, but the particles are closer together and
are more organized. The composition remains unchanged, but
the physical form is different. A  C is a physical change.

Temperature and Change of State
• A change of state is a physical change.
– Physical form changes, composition does not.
• Changes in physical state are reversible
– by changing the temperature.
• A chemical change cannot simply be reversed by a change in
temperature.

Some Characteristic Properties of Copper
(copper) © McGraw-Hill Education/Mark Dierker, photographer; (candlestick) © Ruth Melnick; (copper carbonate, copper reacting with acid, copper and ammonia)
© McGraw-Hill Education/Stephen Frisch, photographer
• Table 1.1

Distinguishing Between Physical and Chemical Change
• PROBLEM: Decide whether each of the following processes is
primarily a physical or a chemical change, and explain briefly:
(a) Frost forms as the temperature drops on a humid winter
night.
(b) A cornstalk grows from a seed that is watered and
fertilized.
(c) A match ignites to form ash and a mixture of gases.
(d) Perspiration evaporates when you relax after jogging.
(e) A silver fork tarnishes slowly in air.
• PLAN: “Does the substance change composition or just
change form?”

Sample Problem 1.2 – Solution
• (a) Frost forms as the temperature drops on a humid winter
night – physical change
• (b) A cornstalk grows from a seed that is watered and
fertilized – chemical change
• (c) A match ignites to form ash and a mixture of gases –
chemical change
• (d) Perspiration evaporates when you relax after jogging –
physical change
• (e) A silver fork tarnishes slowly in air – chemical change

Energy in Chemistry
• Energy is the ability to do work.
• Potential Energy is energy due to the position of an object.
• Kinetic Energy is energy due to the movement of an object.
Total Energy = Potential Energy + Kinetic Energy

Energy Changes
• Lower energy states are more stable and are favored over
higher energy states.
• Energy is neither created nor destroyed
– it is conserved
– and can be converted from one form to another

Potential Energy is Converted to Kinetic Energy
• A gravitational system. The potential energy gained when a
weight is lifted is converted to kinetic energy as the weight
falls.
• A lower energy state is more stable.
• Fig 1.3

Potential Energy is Converted to Kinetic Energy (2)
• A system of two balls attached by a spring. The potential
energy gained by a stretched spring is converted to kinetic
energy when the moving balls are released.
• Energy is conserved when it is transformed.
• Fig 1.3

Potential Energy is Converted to Kinetic Energy,
Cont’d
• A system of oppositely charged particles. The potential
energy gained when the charges are separated is converted to
kinetic energy as the attraction pulls these charges together.
• Fig 1.3

Potential Energy is Converted to Kinetic Energy,
Further Cont’d
• A system of fuel and exhaust. A fuel is higher in chemical
potential energy than the exhaust. As the fuel burns, some of
its potential energy is converted to the kinetic energy of the
moving car.
• Fig 1.3

Chemical Arts and the Origins of Modern
Chemistry
• Alchemy, medicine, and technology placed little emphasis on
objective experimentation, focusing instead on mystical
explanations or practical experience, but these traditions
contributed some apparatus and methods that are still
important.
• Lavoisier overthrew the phlogiston theory by showing,
through quantitative, reproducible measurements, that
oxygen, a component of air, is required for combustion and
combines with a burning substance.

The Scientific Approach to Understanding
Nature
• Fig 1.6

SI Base Units
• Table 1.2

Common Decimal Prefixes Used With SI Units
• Table 1.3

Common SI-English Equivalent Quantities
• Table 1.4

Some Volume Relationships in SI
• Fig 1.7

Common Laboratory Volumetric Glassware
• Fig 1.8

• Fig 1.9
Quantities of Length (A), Volume (B), and Mass
(C)

Chemical Problem Solving
• All measured quantities consist of
– a number and a unit.
• Units are manipulated like numbers:
3ft × 4ft = 12ft2
350 m𝑖
7 h
=
50 mi
1 h
or 50 mi ∙ h−1

Conversion Factors
• A conversion factor is a ratio of equivalent quantities used to
express a quantity in different units.
• The relationship 1 mi = 5280 ft gives us the conversion factor:
1 mi
5280 ft
=
5280 ft
5280 ft
= 1

Conversion Factor Problem
• A conversion factor is chosen and set up so that all units
cancel except those required for the answer.
• PROBLEM: The height of the Angel Falls is 3212 ft. Express this
quantity in miles (mi) if 1 mi = 5280 ft.
• PLAN: Set up the conversion factor so that ft will cancel and
the answer will be in mi.
• SOLUTION: 3212 ft ×
1 mi
5280 ft
= 0.6083 mi

Systematic Approach to Solving Chemistry
Problems
• State Problem
• Plan
– Clarify the known and unknown.
– Suggest steps from known to unknown.
– Prepare a visual summary of steps that includes conversion factors,
equations, known variables.
• Solution
• Check
• Comment
• Follow-up Problem

Converting Units of Length
• PROBLEM: To wire your stereo
equipment, you need 325
centimeters (cm) of speaker wire
that sells for $0.15/ft. What is the
price of the wire?
• PLAN: We know the length (in cm)
of wire and cost per length ($/ft).
We have to convert cm to inches
and inches to feet. Then we can find
the cost for the length in feet.

Sample Problem 1.3 - Solution
• SOLUTION:
Length (in) = length (cm) x conversion factor
= 325 cm ×
1 in
2.54 cm
= 128 in
Length (ft) = length (in) x conversion factor
= 128 in ×
1 ft
12 in
= 10.7 ft
Price ($) = length (ft) x conversion factor
= 10.7 ft ×
$0.15
1 ft
= $𝟏. 𝟔𝟎

Converting Units of Volume
• PROBLEM: A graduated cylinder
contains 19.9 mL of water. When a
small piece of galena, an ore of
lead, is added, it sinks and the
volume increases to 24.5 mL. What
is the volume of the piece of galena
in cm3 and in L?
• PLAN: The volume of the galena is
equal to the difference in the
volume of the water before and
after the addition.

• SOLUTION
24.5 − 19.9 mL = volume of galena = 4.6 mL
4.6 mL ×
1 cm3
1 mL
= 𝟒. 𝟔 𝐜𝐦𝟑
4.6 mL ×
10−3L
1 mL
= 𝟒. 𝟔 × 𝟏𝟎−𝟑 𝐋

Converting Units of Mass
• PROBLEM: Many international
computer communications are
carried out by optical fibers in cables
laid along the ocean floor. If one
strand of optical fiber weighs 1.19 x
10-3 lb/m, what is the mass (in kg) of
a cable made of six strands of optical
fiber, each long enough to link New
York and Paris (a distance of 8.94 x
103 km)?
• PLAN: The sequence of steps may
vary but essentially we need to find
the length of the entire cable and
convert it to mass.

• SOLUTION:
8.84 × 103 km ×
103 m
1 km
= 8.84 × 106 m
8.84 × 106 m ×
1.19 × 10−3 lb
1 m
= 1.05 × 104 lb
1.05 × 104 lb
1 fiber
×
6 fibers
1 cable
= 6.30 × 104 lb/cable
6.30 × 104
lb
1 cable
×
1 kg
2.205 lb
= 𝟐. 𝟖𝟔 × 𝟏𝟎𝟒
𝐤𝐠/𝐜𝐚𝐛𝐥𝐞

Converting Units Raised to a Power
• PROBLEM: A furniture factory needs 31.5
ft2 of fabric to upholster one chair. Its
Dutch supplier sends the fabric in bolts
that hold exactly 200 m2. How many
chairs can be upholstered with three
bolts of fabric?
• PLAN: We know the amount of fabric in
one bolt in m2; multiplying the m2 of
fabric by the number of bolts gives the
total amount of fabric available in m2. We
convert the amount of fabric from m2 to
ft2 and use the conversion factor 31.5 ft2
of fabric = 1 chair to find the number of
chairs (see the road map).

• SOLUTION:
Converting from number of bolts to amount of fabric in m2:
Amount m2
of fabric = 3 bolts ×
200 m2
1 bolt
= 600 m2
Converting the amount of fabric from m2 to ft2:
Since 0.3048 m = 1 ft, we have (0.3048)2 m2 = (1)2 ft2, so
Amount ft2 of fabric = 600 m2 ×
1 ft2
(0.3048)2 m2
= 6460 ft2
Finding the number of chairs:
Number of chairs = 6460 ft2
×
1 chair
31.5 ft2
= 𝟐𝟎𝟓 𝐜𝐡𝐚𝐢𝐫𝐬

Density
𝐝𝐞𝐧𝐬𝐢𝐭𝐲 =
𝐦𝐚𝐬𝐬
𝐯𝐨𝐥𝐮𝐦𝐞
• At a given temperature and pressure, the density of a
substance is a characteristic physical property and has a
specific value.

Densities of Some Common Substances

Calculating Density from Mass and Volume
• PROBLEM: Lithium, a soft, gray solid with the lowest density
of any metal, is a key component of advanced batteries. A slab
of lithium weighs 1.49 x 103 mg and has sides that are 20.9
mm by 11.1 mm by 11.9 mm. Find the density of lithium in
g/cm3.
• PLAN: Density is expressed in g/cm3 so we need the mass in g
and the volume in cm3.

Sample Problem 1.7 –Plan, Cont’d

• SOLUTION:
1.49 × 103 mg ×
10−3 g
1 mg
= 1.49 mg
20.9 mm ×
1 cm
10 mm
= 2.09 cm
Similarly the other sides will be 1.11 cm and 1.19 cm,
respectively.
Volume = 2.09 cm × 1.11 cm × 1.19 cm = 2.76 cm3
Density of Li =
1.49 g
2.76 cm3
= 0.540 g/cm3

Some Interesting Temperatures
• Fig 1.10

Freezing and Boiling Points of Water
• Fig 1.11

Temperature Scales
• Kelvin (K) – The “absolute temperature scale” begins at
absolute zero and has only positive values. Note that the
kelvin is not used with the degree sign (o
).
• Celsius (o
C) – The Celsius scale is based on the freezing and
boiling points of water. This is the temperature scale used
most commonly around the world. The Celsius and Kelvin
scales use the same size degree although their starting points
differ.
• Fahrenheit (o
F) – The Fahrenheit scale is commonly used in
the U.S. The Fahrenheit scale has a different degree size and
different zero points than both the Celsius and Kelvin scales.

Temperature Conversions
T in K = T in°C + 273.15
T in°C = T in K − 273.15
T in°F =
9
5
T in°C + 32
T in°C = [T in℉ − 32]
5
9

Sample Problem 1.8 – Problem, Plan and
Solution
Converting Units of Temperature
• PROBLEM: A child has a body temperature of 38.7°C, and
normal body temperature is 98.6°F. Does the child have a
fever? What is the child’s temperature in kelvins?
• PLAN: We have to convert °C to °F to find out if the child has a
fever. We can then use the °C to Kelvin relationship to find the
temperature in Kelvin.
• SOLUTION:
Converting from °C to °F:
9
5
38.7℃ + 32 = 101.7℉
Yes, the child has a fever.
Converting from °C to K 38.7℃ + 273.15 = 𝟑𝟏𝟏. 𝟖 𝐊

Extensive and Intensive Properties
• Extensive properties are dependent on the amount of
substance present; mass and volume, for example, are
extensive properties.
• Intensive properties are independent of the amount of
substance; density is an intensive property.

Significant Figures
• Every measurement includes some uncertainty. The
rightmost digit of any quantity is always estimated.
• The recorded digits, both certain and uncertain, are called
significant figures.
• The greater the number of significant figures in a quantity, the
greater its certainty.

The Number of Significant Figures in a
Measurement
• Fig 1.13

Determining Which Digits Are Significant
• All digits are significant
– except zeros that are used only to position the decimal
point.
• Zeros that end a number are significant
– whether they occur before or after the decimal point
– as long as a decimal point is present.
• 1.030 mL has 4 significant figures.
• 5300. L has 4 significant figures.
• If no decimal point is present
– zeros at the end of the number are not significant.
• 5300 L has only 2 significant figures.

Determining the Number of Significant Figures
• PROBLEM: For each of the following quantities, underline the
zeros that are significant figures (sf), and determine the
number of significant figures in each quantity. For (d) to (f),
express each in exponential notation first.
(a) 0.0030L (b) 0.1044g (c) 53.069L
(d) 0.00004715m (e) 57,600.s (f) 0.0000007160cm3
• PLAN: We determine the number of significant figures by
counting digits, paying particular attention to the position of
zeros in relation to the decimal point, and underline zeros that
are significant.

• SOLUTION:
(a) 0.0030 L has 2 sf
(b) 0.1044 g has 4 sf
(c) 53,069 mL has 5 sf
(d) 0.00004715 m = 4.715 x 10-5 m has 4 sf
(e) 57,600. s = 5.7600 x 104 s has 5 sf
(f) 0.0000007160 cm3 = 7.160 x 10-7 cm3 has 4 sf

Rules for Significant Figures in Calculations
• 1. For multiplication and division. The answer contains the
same number of significant figures as there are in the
measurement with the fewest significant figures.
Multiply the following numbers:
9.2 cm × 6.8 cm × 0.3744 cm = 23.4225 cm3 = 𝟐𝟑𝐜𝐦𝟑

Rules for Significant Figures in Calculations,
Cont’d
• 2. For addition and subtraction. The answer has the same
number of decimal places as there are in the measurement
with the fewest decimal places.
Example: adding two volumes
83.5 mL + 23.28 mL = 106.78 mL = 𝟏𝟎𝟔. 𝟖 𝐦𝐋
Example: subtracting two volumes
865.9 mL − 2.8121 mL = 863.0879 mL = 𝟖𝟔𝟑. 𝟏 𝐦𝐋

Rules for Rounding Off Numbers
• 1. If the digit removed is more than 5, the preceding number
increases by 1.
– 5.379 rounds to 5.38 if 3 significant figures are retained.
• 2. If the digit removed is less than 5, the preceding number is
unchanged.
– 0.2413 rounds to 0.241 if 3 significant figures are retained.
• 3. If the digit removed is 5 followed by zeros or with no
following digits, the preceding number increases by 1 if it is
odd and remains unchanged if it is even.
– 17.75 rounds to 17.8, but 17.65 rounds to 17.6.
• If the 5 is followed by other nonzero digits, rule 1 is followed:
– 17.6500 rounds to 17.6, but 17.6513 rounds to 17.7

Rules for Rounding Off Numbers, Cont’d
• 4. Be sure to carry two or more additional significant figures
through a multistep calculation and round off the final answer
only.

Significant Figures in the Lab
• The measuring device used determines the number of
significant digits possible.
• Fig 1.14

Exact Numbers
• Exact numbers have no uncertainty associated with them.
• Numbers may be exact by definition:
– 1000 mg = 1 g
– 60 min = 1 hr
– 2.54 cm = 1 in
• Numbers may be exact by count:
– exactly 26 letters in the alphabet
• Exact numbers do not limit the number of significant digits
in a calculation.

Significant Figures and Rounding
• PROBLEM: Perform the following calculations and round each
answer to the correct number of significant figures:
a
16.3521 cm2 − 1.448 cm2
7.085 cm
(b)
4.80 × 104
mg
1 g
1000 mg
11.55 cm3
PLAN: We use the rules for rounding presented in the text: (a)
We subtract before we divide. (b) We note that the unit
conversion involves an exact number.

• SOLUTION:
a
16.3521 cm2 − 1.448 cm2
7.085 cm
=
14.904 cm2
7.085 cm
= 𝟐. 𝟏𝟎𝟒 𝐜𝐦
b
4.80 × 104
mg
1 g
1000 mg
11.55 cm3
=
48.0 g
11.55 cm3
= 𝟒. 𝟏𝟔 𝐠/𝐜𝐦𝟑

Precision, Accuracy, and Error
• Precision refers to how close the measurements in a series
are to each other.
• Accuracy refers to how close each measurement is to the
actual value.
• Systematic error produces values that are either all higher or
all lower than the actual value.
– This error is part of the experimental system.
• Random error produces values that are both higher and lower
than the actual value.

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