Solubility and distribution phenomena

Mrs. Supriya Nikam
(Pharmaceutics department)

 solution:
 A homogeneous mixture in which one substance is said to dissolve in the other.
 In quantitative terms:
 The concentration of solute in a saturated solution at a certain temperature.
 In Qualitatively terms:
 A spontaneous interaction of two or more substance to form a homogeneous
molecular dispersion
 Solute:
 is the dissolved agent . (less abundant part of the solution )
 Solvent :
 is the component in which the solute is dissolved (more abundant part of the
solution).

 A saturated solution:
 is one in which an equilibrium is established between
dissolved and undissolved solute at a definite
temperature. Or
 A solution that contains the maximum amount of solute at
a definite temperature
 An unsaturated solution: or subsaturated solution:
 is one containing the dissolved solute in a concentration
below that necessary for complete saturation at a definite
temperature.

 A supersaturated solution:
 contains more of the dissolved solute than it
would normally contain in a saturated state at
a definite temperature.
 Applied for crystallization process.

 Unsaturated, Saturated or Supersaturated?
 How much solute can be dissolved in a
solution?

 Any solution can be made saturated, unsaturated,
or supersaturated by changing the temperature.

 The USP lists the solubility of drugs as: the number of ml of
solvent in which 1g of solute will dissolve.
 E.g. 1g of boric acid dissolves in 18 mL of water, and in 4 mL
of glycerin.
 Substances whose solubility values are not known are
described by the following terms:

 BCS is a scientific framework for classifying
Drug substances according to their aqueous
solubility and their intestinal permeability

Solubility and distribution phenomena

Three steps:
1. Removal of a molecule form the solute
phase at a definite temp.
2. Creation of hole in solvent just large
enough to accept the solute molecule
3. Solute molecule is finally placed in the hole
in the solvent and gain in or decrease of
potential energy,

 Ammonia Dissolves in Water:
 Polar ammonia molecules dissolve in polar
water molecules.
 These molecules mix readily because both
types of molecules engage in hydrogen
bonding.

 Alcohol Dissolves in Water:
 The -OH group on alcohol is polar and mixes
with the polar water through the formation of
hydrogen bonds.
 A wide variety of solutions are in this
category such as sugar in water, alcohol in
water, acetic and hydrochloric acids.

 1. Polar solvents
 2. Non polar solvents
 3. Semi polar solvents

Solutions of pharmaceutical importance include:
Gases in liquids
Liquids in liquids
Solids in liquids

 Pharmaceutical solution of gases include HCL,
ammonia water and effervescent preparation
containing CO2
 Aerosol
 The solubility of gas in a liquid is expressed as
conc. Of the dissolved gas, when it is in
equilibrium with the pure gas above the solution.

 Application:
1. Preparation of reagents: conc. Reagents
prepared by passing gases into water
2. Carbonated beverages: soda water
3. Solubility of oxygen in blood:

 Effect of pressure:
 Changes solubility of dissolved gas in
equilibrium with it
 When the pressure is increased over the
SOLVENT, the solubility of the gas is
increased.
 Why? –
 pressure increases as gas molecules strike
the surface to enter solution is increased

 Henry’s Law:
 The concentration of dissolved gas is directly
proportional to the partial pressure of the gas
above the solution at equilibrium, in very dilute
solution at constant temperature.
 C2∝ P
 C2 = δP
 c= concentration of the dissolved gas mol/lit
 p= partial pressure of gas above the solution
 δ = Solubility coefficient mol/1.kPa

 Appropriate to use: Mole fraction solubility
Ration of moles of solute to total moles of
solute+ solvent
 Pressure on gas Solubility of gas
 Double pressure: twice as much of gas
dissolved in same volume
 Pressure Solubility gas escapes

 Mixture of gases:
 Partial pressure of individual gases determine solubility of each
gas.
 Solubility of each gas is proportional to its partial pressure.
 Application:
 Carbonated beverages
 Limitation:
1. Temp maintain constant
2. Gas does not involve in chemical reaction with solvent
3. Gas is slightly soluble in liquids

 Temp Solubility
 Why?
 1. Tendency of gas to expand
 2. Increase in pressure at elevated temp
 Application:
 1. dissolved gases are removed by heating
 2. Distilled water is maintained at 80ºC for parental use (gas not
dissolved)
 3. Dissolved air influences the boiling of liquid
 Disadvantage:
 1. handing of gaseous solution container in warm conditions, containers
should be immersed in ice or cold water for some time
 e,g: ammonia solution, liquid bromine & chlorine water

 Addition of other substances lowers the solubility of
a gas in solution.
 E.g. salt added to carbonated solution, gas escapes
from solution
 Salt establish greater attraction with water molecules
 Weaken gas –solvent interaction
 E.g Nacl, sucrose
 Protection of Liable to oxidation Substance: Higher
sugar conc. Decrease solubility of oxygen, less
oxidation.

 Henry’s Law
 Applies to Gases that does not involve in
chemical reaction with solvent
 Gases that are slightly soluble in solvent
 Hydrogen chloride, ammonia and carbon
dioxide show deviation as result of chemical
reaction between gas and solvent result of
increase in solubility
 Hydrogen chloride is about 10,000 times more
soluble in water than oxygen.

 Liquid-liquid mixture are of three types:
 Miscible liquid
 Partially Miscible liquid
 Immiscible liquid

Miscible liquid
Miscible in all proportion
E.g. ethyl alcohol and water
Partially Miscible liquid
Miscible only at a certain proportion
e.g. phenol & water
Immiscible liquid
Completely immiscible regardless of the
relative amount

 Partial miscibility
 Partial miscibility results when: Cohesive
forces of the constituents of a mixture are
quite different, e.g. water (A) and hexane (B).
A-A » B-B.
 When certain amounts of water and ether or
water and phenol are mixed, two liquid layers
are formed, each containing some of the
other liquid in the dissolved state.

 Mutual solubilities of
partially miscible liquids are
influenced by temp
 E.g.
 1. Phenol- water system
 Mutual solubilities of the
two conjugate phases
increase with temp until at
the critical solution temp.
 Composition became
identical
 Homogenous or single
phase system is formed

 Tie line, binodal curve: to
calculate both the composition
of each component in the two
conjugate phase and the
amount of one phase relative to
the other.
 2. Triethylamine water system:
 Some liquid pairs: solubility
as temp
 Below : two members are
soluble in all proportions
 Above: two separate layers
form

 3. Nicotine and water
system:
 Both upper and lower
consulate temp.
 with an intermediate
temp region in which
two liquids are only
partially miscible

4. Ethyl ether and water
No Critical solution
temp.
Neither an upper nor a
lower consulate temp.
and shows partial
miscibility over entire
temp range at which the
mixture exist.

 One in which there is no change in the
properties of the components other than
dilution, when they are mixed to form
solution.
 Heat Neither absorbed nor evolved during
mixing
 No shrinkage or expansion after mixing

 consider two liquids A and B, and mix them.
The formed solution will experience several
intermolecular forces of attractions inside it,
which will be:
 A – A intermolecular forces of attraction
 B – B intermolecular forces of attraction
 A – B intermolecular forces of attraction

 The solution is said to be an ideal solution,
only when the intermolecular forces of
attraction between A – A, B – B and A – B are
nearly equal.


 When the Vapour is assumed to be nearly
ideal, the internal pressure in cal/cm3 is
obtained by using equation
 Pi = Δ Hv -RT
V
Δ Hv = Heat of vaporization
V= molar volume of the liquid at temperature T

 Internal pressures or cohesive forces of the
constituents of a mixture are quite different and the
molecules of one constituent cannot mingle with
those of the other and partial solubility result
 Polar liquid: high cohesive forces : large internal
pressures: they are solvent for compounds of
similar nature
 Nonpolar substance with low internal pressures are
“Squeezed out” by powerful attractive force existing
between the molecules of the polar liquid.

 The vapour pressure of liquid serve as
quantitative expression for describing the
escaping tendencies of molecule.

 Mixture of miscible liquid A & B
 Partial vapour pressure exerted by liquid A= pA Kpa
 Partial vapour pressure exerted by liquid B= pB Kpa
 vapour pressure exerted by pure liquid A= pAº Kpa
 vapour pressure exerted by pure liquid B= pBº Kpa
 Mole fraction concentration of A in liquid=XA
 Mole fraction concentration of B in liquid=XB
 Partial vapour pressure of liquid=Vapour pressure of
pure liquid* mole fraction of liquid
 pA = pAºxA
 pB = pBºxB

 Two liquid are mixed, vapour pressure of
each one is reduced by the presence of other
 E.g. benzene and toluene
 N-hexane and n-heptane

 Dalton’s Law of Partial pressure states that the
total pressure exerted by mixture of ideal gases
may be considered as sum of the partial vapour
pressures exerted by each gas, if alone were
present and occupied the total volume.
 Total pressure= partial vapour pressure of A +
partial vapour pressure of B
P=pA + pB
P= pAºxA + pBºxB

 The mixture is said to be ideal when both
components of a binary solution obey Raoult’s law
over the whole range of composition.
 Some times these mixture show varying degree of
deviation from Raoult’s law depending on the liquids
and temperature.
 Deviation because of
 solute-solute,
 solute-solvent and
 solvent-solvent interactions are unequal.
 E.g. carbon tetrachloride and cyclohexane,
chloroform and acetone

 Modification: concentration replace by effective concentration
(thermodynamic activity)
 pA = pAºaA
 pB = pBºaB
 aA and aB activities of components A and B, respectively.
 Applicable for both ideal & no ideal solution.
 Ideal solution: a=X
 Non-ideal solution: a≠X
 Activity/concentration: termed as activity coefficient: measure
of deviations from ideality (ratio=1)
 Mutual interaction leads to either lowering or enhancing of the
vapour pressure

 When, the vapour pressure is greater than the sum of the
partial pressure of the individual components.
 Occurs when:
 1. components differ n their polarity
 2. length of hydrocarbon chain
 3. degree of association
 Weakening the cohesive force

C6H6 CH3CH2OH Escaping tendencies
Benzene Ethyl alcohol increase
Semipolar Polar Vapour pressure
Weakening the cohesive force Increases

 The total vapour
pressure shows a
maximum at one
perticular composition. i.
e aA> XA
and aB> XB
 Known as max vapour
pressure and min
boiling point solution.
Degree of deviation as
temp
 Difference are reduced
at higher temperature
Temp , miscibility of
two components : leads
to phase sepeartion

 When, the vapour pressure is less than the sum of the partial
pressure of the individual components.
 Chloroform & acetone, pyridine & acetic acid, water & nitric acid.
 Occurs when: hydrogen bounding, salt formation & hydration
 Adhesive attraction (A-B) > cohesive attraction (A-A & B-B)

 Vapour pressure of
each component is
lowered than ideal
behavior
 aA< XA
aB< XB
 Min vapour pressure
or max boiling point
solution
(Weak attraction in liquid phase)
Hydrogen bounding
Cl3 C-H ------O=C(CH3)2
Chloroform Acetone
Weak compound
Escaping tendencies
Decrease
Vapour pressure
Decrease

 Addition of substance to binary liquid system produces a
ternary system (3 components)
 Added material is soluble in only one of the two component
or
 Its solubility in two liquid are markedly different
 Mutual solubility of the liquid pair decreases

Original binary
mixture
Upper critical
solution
temperature
Temp
raises
lower critical
solution
temperature
Temp lower by
addition of 3rd
component

 The increase in mutual solubility of two partially miscible
solvent by another agent is referred to as blending.
 The solubility in water of a non polar liquid is increases by a
micelle forming surface active agent, called as micellar
solubilization
3rd substance
soluble in
both liquid
(same extent)
Mutual
solubility of
liquid pair
increase
UCT lowered
LCT raised

 Application:
1. Solubility of drug in water & hydro-alchohlic solution: liquid orals (syrup & elixir)
2. IV, IM & SC injections
3. Solubility of drug in GI fluid (dissolution) : imp for better absorption
Aq. Solubility > 1 % in pH range of 1-7 at 37 ºC : no absorption problem
 < 1% potential problem occur
 >1 mg/ml : need of a soluble salt
4. Release & absorption from an ointment or an intra muscular injection: degree of
saturation of drug in solvent
5. Action of drug: limited by poor aq. Solubility
Side effect: poor solubility
7. Solubility: information about intermolecular forces of interaction
8. Saturated solution theory: crystallization of drug from solvent
9. Physicochemical properties
10.Difference in solubility in various solvent: separating 1 component from other &
purification: extraction & recrystallization

Solubility of solid in an ideal
solution depends on
 temp,
 M.P. of solid
 molar heat of fusion (ΔHf i.e heat
of absorbed when solid melts)
 In an ideal solution:
 Heat of solution = heat of fusion
 Assumed to be constant
independent of temp
 Ideal solubility is not affected by
nature of solvent

 Equation for an ideal solution of solid in liquid is:
 -logXi
2 = (△Hf/2.303 R) {T0-T/(TT0)}
 Xi
2= ideal solubility of the solute expressed in mole fraction
 i = an ideal solution
 2= mole fraction of solute
 T0= melting point of solute in absolute degree
 T= absolute temp of solution
 0 °C (freezing point of water) = 273.15 K
 25 °C (room temperature) = 298.15 K
 absolute temp = temp (°C) + 273.15K

 Above M.P: solute in liquid state
 Ideal solution: liquid solute miscible in all
proportions with solvent
 T> T0 , equation no longer applies
 Also below M.P (T0). , △Hf no longer used
 Mole fraction converted to molalilty
 m= 1000 X2/M1(1-X2)
 -logXi
2 = (△Hf/2.303 R) 1/T +constant
 Y=mx+c
 Plot of log of solubility (in mole fraction)
against reciprocal of absolute temp :
straight line ,
 slope: △Hf/2.303 R

 The concept of activity can be used whenever there is a difference between ideal
and observed properties as a function of concentration
 Activity of solute: "effective concentration" of a species in a mixture
 Activity of solute: concentration * activity coefficient,
 An activity coefficient:
 is a factor used in thermodynamics to account for deviations from ideal behavior in a
mixture of chemical substances.
 Concentration given in mole fraction
 a2 = X2 Ƴ 2
 Ƴ 2= rational activity coefficient
 Convert to log
 Log a2 = Log X2 + Log Ƴ 2
 Ideal solution, a2 =Xi
2, Since Ƴ 2= 1

 Log a2 = Log X2 + Log Ƴ 2
 Ideal solution, a2 =Xi
2, Since Ƴ 2= 1
 Log a2= log Xi
2 = (△Hf/2.303 RT) {T0-T/(T0)}
 Combining both equation
 Mole fraction solubility of solute in nonideal solution express in log form
-logX2 = (△Hf/2.303 R) {T0-T/(TT0)} +logƳ 2
Mole fraction solubility in various solvent expressed as sum of two terms:
1. Solubility in an ideal solution
2. Logarithm of activity coefficient of solute

 Solution of strong electrolyte:
 Behavior of strong electrolyte
influenced by electrostatic
attraction between ions
 Large no. of oppositely charged
ions of electrolyte influences one
another through interionic
attraction
 Dilute solution: negligible
 Moderate Conc.: appreciable

 Solution of weak electrolyte:
 No. of ions is small
 interionic attraction: negligible
 Movement of ions interfered by:
 1. atmosphere of oppositely charged ions
 2. association of ions at high concentration into group. (ion pairs)

 low dielectric constant solvent: higher orders of association
of ions: force of attraction of oppositely charged ions is large
 Moderately conc solution of strong electrolyte: Due to
electrostatic attraction & ion association : freezing point
depression & other colligative properties are less
 (Freezing-point depression is the decrease of the freezing
point of a solvent on addition of a non-volatile solute)

 Conc. Of solute in solution: effective concentration or activity
(a)
 Activity < actual conc, because of strong electrolyte is partly
ionized & some ions effectively ‘taken out of play’ by
electrostatic forces of interaction.
 Infinite dilution: Ions widely separated : do not interact with one
another
 Activity (a) of ion = conc (molality or molarity)
 Molal basis at infinite dilution:
 a=m ………… (1)
 Or, a/m =1 ………….(2)

 As conc increased ratio: less than unity
 Effective concentration or activity become less than molal
concentration (a/m =1)
 Ratio known as practical activity coefficient (ˠm)
 a/m= ˠm …………………(3)
 a= ˠm m………………(4)
 Molarity scale: a= ˠc C……………(5)
 Mole fraction scale: rational activity coefficient:
 a= ˠs X …………………(6)
 These coefficient are proportionality constants relating to
molality, molarity and mole fraction respectivey.


 Activity coefficient=1, infinitely dilute
solution
 Coefficient decrease as conc increased
 Real solution become more ideal
 Log ˠ2 approaches unity

 Solid is placed in contact with liquid:
 particle leave the surface of solid
 Pass into liquid
 Blocks of few molecules molecules & ions

 First step:
Removal of molecule from solute phase at a
definite temp:
removing a molecule 2w22
from a solute vapour state
(Work done for breaking of bonds
between adjacent molecule)
2w22: interaction between solute molecules

Solute
molecule
Liberated
solute
molecule
Molecule escape
from solute phase
Hole created closed
½ energy is regained
(W22)
Hole created

 Second step:
 Creation of hole in solvent
 Large: to accept solute molecule
 W11: energy of interaction between solvent molecule
W11

 Third step:
 Solute molecule place in hole of solvent
-W12
-W12 : gain in work or decrease of potential energy
12: interaction energy of solute with solvent
Hole in solvent is now closed & additional decrease in energy -W12
Net work in final step is =(-W12+ -W12)= -2w12

 Total work done
 W22 + W11- -2W12

 Easy numerical method of rapidly predicting the extent of interaction
between material, particularly liquid with liquid & solid.
 Useful in formulating blends of solvents.
 Hildebrand solubility parameter
 It is total van der Waals forces, which is reflected in the simplest
solubility value.
 Numerical value that indicates the relative solvency behavior of a
specific solvent

1) Heat of vaporization
 B.P. reach
Energy added (heat) Increase in temp
Energy added No further increase in temp
Used to separate molecules of liquid
Boil , liquid convert to gas
Liquid completely vaporized Temp of system begin to rise
Liquid heated

 Heat of vaporization
 The amount of energy (in calories) that was added from the onset of
boiling to point when all the liquid has boiled away is a direct indication
of amount of energy requried to separate the liquid into gas
 = van der waals forces that held molecules of liquid together
Van der waals forces that
held molecules together
B.P.
Amount of heat added to
separate molecule is imp
Low B.P ?
High B.P?
Heat of vaporization:
Energy required to vaporize the liquid
Liquid vaporized readily:
less intermolecular stickiness
Than liquid that requires considerable
addition of heat to vaporize

 2) Cohesive Energy Density
 The cohesive energy density is the amount of energy needed to
completely remove unit volume of molecules from their neighbors.
 A numerical value that indicate the energy of vaporization in calories per
cubic centimetre
 This is equal to the heat of vaporization of the compound divided by
its molar volume in the condensed phase.
 In order for a material to dissolve, these same interactions need to be
overcome as the molecules are separated from each other and
surrounded by the solvent.
 C= ΔH-RT
 Vm
 C= Cohesive Energy Density (J/m3)
 ΔH= Heat of vaporization
 R= Gas constant
 T= temp (K)
 Vm= Molar volume

 Reflect degree of vander waals forces holding molecules of liquid
together
 Vander waals forces: Vaporization : solubility
 Same intermolecular attractive forces=vaporization= solvation
=

 Two material with similar Inter molecular attractive forces :Soluble
 Similar Cohesive Energy Density miscible
C
m

 Significance:
1. Solvent spectrum:
 Ranking of solvent according to solubility parameter.
 Solvents occupying position in proximity to other solvents of
comparable strength
 Solute A soluble in acetone
May be soluble in neighboring solvents, (Diacetone
alcohol/methyl ethyl ketone)
 Solvent having similar internal energy
 Some materials will dissolve in a large range of solvents, while
other might be soluble in only a few

2. Solvent Mixture:
 Hilderbrand value of solvent mixture can be determined by Averaging
the hildebrand values of the individual solvents by volume
 Mixture of toluene + acetone: (2:1)
 Hildebrand value of mixture = (18.3*2/3 + 19.7 *1/3)
=18.7
 Same as chloroform
 2:1 toluene/acetone mixture should have solubility behavior similar
to chloroform
 If, for example, a resin was soluble in one, it would probably be
soluble in the other.
 What is attractive about this system is that it attempts to predict the
properties of a mixture using only the properties of its components
(given the solubility parameters of the polymer and the liquids); no
information on the mixture is required.

Solvent (SI)
n-Pentane (7.0) 14.4
n-Hexane 7.24 14.9
Freon® TF 7.25
n-Heptane (7.4) 15.3
Diethyl ether 7.62 15.4
1,1,1
Trichloroethan
e
8.57 15.8
n-Dodecane 16.0
White spirit 16.1
Turpentine 16.6
Cyclohexane 8.18 16.8
Amyl acetate (8.5) 17.1
Carbon
tetrachloride
8.65 18.0
Xylene 8.85 18.2
Ethyl acetate 9.10 18.2
Toluene 8.91 18.3
Tetrahydrofur
an
9.52 18.5
Benzene 9.15 18.7
Chloroform 9.21 18.7
Trichloroethylene 9.28 18.7
Cellosolve® acetate 9.60 19.1
Methyl ethyl ketone 9.27 19.3
Acetone 9.77 19.7
Diacetone alcohol 10.18 20.0
Ethylene dichloride 9.76 20.2
Methylene chloride 9.93 20.2
Butyl Cellosolve® 10.24 20.2
Pyridine 10.61 21.7
Cellosolve® 11.88 21.9
Morpholine 10.52 22.1
Dimethylformamide 12.14 24.7
n-Propyl alcohol 11.97 24.9
Ethyl alcohol 12.92 26.2
Dimethyl
sulphoxide
12.93 26.4
n-Butyl alcohol 11.30 28.7
Methyl alcohol 14.28 29.7
Propylene glycol 14.80 30.7
Ethylene glycol 16.30 34.9
Glycerol 21.10 36.2
Water 23.5 48.0

3. Selection of solvents for maximum solubility
 More alike values of δ of two components, greater the mutual solubility of
pair
 Phenanthrene δ = 9.80
 Carbon disulphide δ=10.0
 Hexane δ= 7.3
 Phenanthrene more soluble in Carbon disulphide than hexane
4. Chemical kinetics:
 Kinetics of chemical reaction related to solubility parameters of solvents,
reactants and products
 Polar solvent with high internal pressure increase rate of reaction product
having higher internal energy
 If product less polar than reactant, less polar solvent accelerate reaction &
facilitate to produce less polar product

 Solvation
 Heat must be absorbed when
solute is mixed with solvent
 (δ1- δ2)2= + value
 If 2W12> W11+W22
 ΔH become negative
 Negative deviation from
Raoult’s law
 Hydrogen bounding between
solute & solvent
 Such specific combinations
of solvent with solute are
known as Solvation
• Association
•When interaction occurs between
like molecules of one of the
components in a solution is referred
as association
• Dimerization
• Positive heat of solution (+ΔH) &
positive deviation from Raoult’s law
• Association of water molecule is
reflected in a large W11 , when water
is mixed with nonpolar solute
•W11 >>> W22
• W12 is small
Leads to low solubility

 Solubility is depend on temp
 Solubility for non electrolyte, weak electrolyte or strong electrolyte calculated
using heat of solution instead of heat of fusion
 For non electrolyte, weak electrolyte
 For strong electrolyte, R replaced by uR, u =no. of ions produced in
dissociation of electrolyte
 C”&C’= conc such as molar, molal, molar fraction, gm/lit, %
 T’&T”= Kelvin temp
 ΔHsol = Heat of solution in cal/mole
 R= universal gas constant
 Application:
 solubility of solute in particular solvent can be determine at one temp if heat
of solution and solubility at another temp are known
In (C”/C’)= ΔHsol/R (T”-T’)/(T’T”)

 If ΔHsol is negative:
 increasing temp of the solvent will decrease the solubility of solute :
 heat must be released for solute to dissolve :
 further increase in temp:
 add more heat:
 less solute will dissolve at higher temp
 If ΔHsol is positive:
 increase in temp:
 more solubility
 Rise in temp, increase solubility of solid that absorbs heat (endothermic)
when it dissolves

 Le chatelier principle:
 A system tends to adjust itself in a manner so as to counteract stress such as
increase in temp.
 Exothermic process: Heat is evolved, temp of sol raises & container warm
 E.g.
 Sodium sulfate: hydrated form (Na2So4.10 H2O)
 Up to 32°C:
 solution process (dissolution) endothermic (solubility increase with temp)
 Above 32°C:
 Compound as anhydrous salt (Na2So4), dissolution is exothermic (solubility
decreases with temp)
 Nacl: not absorb or evolve an appreciable heat when dissolve in water:
solubility not alter by changing temp: heat of solution is approximately Zero

 Partial or differential heat of solution (ΔH):
 The heat absorbed per mole when a small quantity of solute is added to a large
quantity of solution.
 Rate of change of the heat of solution per mole of solute in a solution of any
specified concentration.
 Total or integral heat of solution:
 Heat absorbed when 1 mole of solute is dissolved in enough solvent to produce a
solution of specified concentration

 Heat of solution of crystalline substance=
heat of sublimation of solid (crystal lattice energy)+heat of hydration/solvation
 ΔHsol=ΔHsubl + Δhhyd
Lattice energy: energy required to separate 1 mole
of a crystal into it ions in gaseous sate or to vaporize
the solid
NaCl solid Na+
gas + Cl-
gas
Heat of hydration:
Heat librated when the gaseous ions are hydrated.
Influenced by radius of ion
Smaller ionic radius :
grater electrostatic field surrounding ion:
larger heat of hydration
Na+
gas + Cl-
gas Na+
aq + Cl-
aq

How Water Dissolves Salt - YouTube (360p).mp4

 If heat of hydration (heat librated when ions are hydrated) is
sufficient to provide the energy needed to overcome the lattice
forces
 Pull ions from crystal & salt will soluble
 IN ideal solution:
 No hydration
 Heat absorbed required to transform
the crystal to liquid state
Only heat of fusion is included in ideal
solubility equation

 ΔH (heat of solution) positive: Absorption of heat
 ΔH (heat of solution) negative: heat evolved
 Heat of hydration & lattice energy of NaCl so similar that process
is only slightly endothermic
 Temp has little effect on the solubility

 When slightly soluble electrolyte are dissolved to form saturated
solution, the solubility is described by a special constant known
as solubility product Ksp
 E.g. Silver chloride
 slightly soluble salt
 Excess solid in equilibrium with ions in saturated solution at a
specific temp
 AgCl(solid) Ag+
(aq)+Cl-
(aq)
 Silver chloride is so insoluble in water (0.002 g/L) that a
saturated solution contains only about 1.3 x 10-5 moles of AgCl
per liter of water.
solid

 Since the solution is saturated, the concentration of unionised
molecules of the electrolyte is constant at a particular
temperature.
 Conc of solid phase is essentially constant
 Ksp = [Ag+][Cl-]
 This equation is only for sparingly soluble salt or in presence of
other salt
 Not for salt that are freely soluble in water
 Conc of each ion is raised to power equal to the number of ions
appearing in formula
 Al (OH3)solid Al3+ +3OH-
 (Al3+) (OH-)3 = Ksp
 If an ion is common, equilibrium is altered

 the solubility of a sparingly soluble ionic substance is
markedly decreased in a solution of another ionic compound
when the two substances have an ion in common. This is just
what would be expected on the basis of the LeChâtelier
Principle; whenever the process
 CaF2(s) Ca2+ + 2 F–
 is in equilibrium, addition of more fluoride ion (in the form of
highly soluble NaF) will shift the composition to the left,
reducing the concentration of Ca2+, and thus effectively
reducing the solubility of the solid.

 If Ag or Cl added to AgCl solution
 Addition of Nacl, increase conc of Cl-
 (Ag+) (Cl-) > Ksp
 Some AgCl ppt from solution until equilibrium
 (Ag+) (Cl-) = Ksp reestablished
 Addition of common ion, reduce solubility of a slightly soluble electrolyte, unless
common ion forms a complex with salt whereby net solubility can be increased
 Salt having no common ion with slightly soluble electrolyte produce an effect
opposite to that of common ion.
 At moderate concentration they increase rather than decrease solubility because
they lower activity coefficient
 Ksp = aAg + acl-
 Activity = conc * Activity coefficient
 Ksp= (Ag+) (Cl-) γAg + * γcl-
 = (Ag+) (Cl-) γ2
+/-
 Ksp/ γ2
+/- = (Ag+) (Cl-)
 Solubility=(Ag+) = (Cl-) = /

Ksp
γ+/-

 Solubility of weak electrolytes as influenced by pH:
 1 % solution of phenobarbital sodium is soluble at
pH high in alkaline range
 pH: Soluble ion molecular phenobarbital
 <3: drug ppt
 Atropine sulphate
 ppt as pH elevated
 For clear homogeneous solution & max therapeutic
effectiveness: Optimum pH

 Solubility of weak electrolytes as influenced by pH
 pH & Solubility:
 Principle of pH:
 pH means H ion exponent
 In term of H ion activity, pH defined as
 pH=-log10aH+ or 10-pH
= aH+
 pH equal the negative logarithm of the hydrogen ion activity
 Activity is Effective concentration of hydrogen ion in solution
 Difference between Effective and actual concentration decrease
as one move toward more dilute solution
 In which ionic interaction become progressively less important

 Solubility of weak electrolytes as influenced by pH
 pH & Solubility:
 Drug Solubility:
 Effect of pH on solubility is imp in IV admixture, TPN, aq. Liquid
dosage form, oral solution
 Solubility of weak acid & base is pH dependent
 Total quantity of monoprotic weak acid (HA) in solution at a specific
pH = conc of both free acid + salt (A-) forms
 pH of solution increases, quantity of drug in solution increases
because water-soluble ionized salt is formed.
 Monoprotic: donates only one proton or hydrogen atom per molecule
to an aqueous solution

 HA H+ + A-
 Ka = dissociation constant
 pH max : There may be a certain pH level reached
where total solubility (ST) of the drug solution is
saturated with respect to both the salt & acid form
of drug
Ka

 pH > pH max : Solution
can be saturated with
respect to salt at not
with respect to acid
 pH< pH max : Solution
can be saturated with
respect to acid, not with
respect to salt

 Adding excess free acid form
of a drug to water; we are in
the "pH<pHmax" portion of the
graph.
 Base (i.e., sodium hydroxide)
is added dropwise, and, as
the free base is converted into
a salt, the salt goes into
solution.
 At this point, we have both
free acid and the formed salt
in solution.
 Additional base is added until
all the free acid is converted
into the salt form and we are
at the "pH>pHmax" portion of
the graph.

 To calculate the total quantity of drug that will remain
dissolved in solution at a selected pH, either of two
equations can be used, depending on whether the product
is to be in a pH region above or below the pHmax. The
following equation is used in the pH range below the pHmax:
 ST = Sa (1 + Ka/[H+]) (Equation 1)
 The next equation is used in the pH range above the pHmax:
 ST = S'a (1 + Ka/[H+]) (Equation 2)
 where
Sa is the saturation solubility of the free acid and
S'a is the saturation solubility of the salt form.

 Optimum pH: necessary To ensure clear homogeneous solution &
max therapeutic effectiveness
 The solubility of weak electrolyte is strongly influenced by pH of
solution
 e.g. 1% solution of Phenobarbital sodium
 Soluble at pH high in alkaline range
 As pH lowered: Soluble ionic form is converted to molecular
Phenobarbital
 Below pH 8.3: drug begin to ppt from solution

 Influence of solvent on solubility of drug:
 pH at which drug is entirely in ionic form: behave like
strong electrolyte & solubility increases
 pH adjusted to value at which unionized molecules are
produced in sufficient conc to ppt occurs
 Mostly, solute soluble in mixture of solvent than in one
solvent
 Cosolvency


 Combined effect of pH and solvent:
 Solvent affect solubility of weak electrolyte in two ways:2
1. Addition of alcohol to buffered aqueous solution of weak
electrolyte increases solubility of unionized species by
adjusting polarity of solvent to more favorable value
2. Being less polar than water, alcohol decreases the
dissociation of a weak electrolyte and the solubility of the
drugs goes down as the dissociation constant is decreased

 If an excess of liquid or solid is added to a mixture of two
immiscible liquid. It will distribute itself between the two
phases so that each becomes saturated
 C1/C2 =K
 K=distribution ratio, distribution coefficient or partition
coefficient
 Distribution law: applicable to dilute solution
 Importance:
 Preservation of oil-water system
 Drug action at nonspecific sites
 Absorption of drug throughout the body (also distribution)

 Nernst Distribution Law
 “A dissolved substance, irrespective of its amount, distributes
itself between two on-miscible solvents in contact with each
other in such a way that at equilibrium, the ratio of conc of
substance in two layers is constant at any given temp”
 Limitation:
 Conditions to be satisfied for application of law:
1. Constant temp:
2. Same molecular state: Same molecular state in two solvent, not
applicable if association or dissociation of solute in one of solvent
3. Dilute solution:
4. Non-miscibility of solvents: non-miscible/only slightly soluble
Extent of mutual solubility of solvents remains unaltered by
addition of solute to them

 Solute exist partly or wholly as associated
molecules or dissociated into ions in either of
liquid phases.
Law applies to monomer or simple molecules
E.g. benzoic acid between oil & water phase
The general case where benzoic acid associates
in the oil phase and dissociates in the
aqueous phase is shown schematically in
Figure

Two cases:
1st case:
 benzoic acid is considered to be distributed between the two phases,
peanut oil and water.
 Although benzoic acid undergoes dimerization (association to form two
molecules) in many nonpolar solvents,
 it does not associate in peanut oil.
 It ionizes in water to a degree, however, depending on the pH of the
solution.

 Co, the total concentration of
benzoic acid in the oil phase, is
equal to [HA]o,
 The monomer concentration in
the oil phase, because
association does not occur in
peanut oil.
 The species common to both the
oil and water phases are the
unassociated and undissociated
benzoic acid molecules. The
distribution is expressed as

 where K is the true distribution coefficient,
 [HA]o = Co is the molar concentration of the
simple benzoic acid molecules in the oil phase,
and
 [HA]w is the molar concentration of the
undissociated acid in the water phase.
 The total acid concentration obtained by analysis
of the aqueous phase is

 The experimentally observed or apparent
distribution coefficient is
The observed distribution coefficient depends on two
equilibria:
1. The distribution of the undissociated acid between the
immiscible phases as expressed in equation
The species distribution of the acid in the aqueous phase,
which depends on the hydrogen ion concentration [H3O + ]
and the dissociation constant Ka of the acid, where
Ka =

 Association of benzoic acid in peanut oil does
not occur, and
 Kd (the equilibrium constant for dissociation of
associated benzoic acid into monomer in the oil
phase) can be neglected in this case.
 Given these equations and the fact that the
concentration, C, of the acid in the aqueous
phase before distribution, is
 assuming equal volumes of the two phases

 one arrives at the combined result
 Above expression is a linear equation of the form y = a +
bx,
 therefore a plot of (Ka + [H3O + ])/Cw against [H3O+]
 yields a straight line with a slope b = (K + 1)/C and an
intercept a = Ka/C.
 The true distribution coefficient, K, can thus be obtained
over the range of hydrogen ion concentration considered.
 Alternatively, the true distribution constant could be
obtained according to equation

 By analysis of the oil phase and of the water phase at
a sufficiently low pH (2.0) at which the acid would
exist completely in the un-ionized form.
 One of the advantages of equation
 The oil phase need not be analyzed; only the
hydrogen ion concentration and
 Cw, the total concentration remaining in the aqueous
phase at equilibrium, need be determined.

 Second :
 When the solute is associated in the organic phase and exists as
simple molecules in the aqueous phase.
 If benzoic acid is distributed between benzene and acidified water,
 it exists mainly as associated molecules in the benzene layer
 and as undissociated molecules in the aqueous layer.
 The equilibrium between simple molecules HA and associated
molecules (HA)n is
 and the equilibrium constant expressing the dissociation of
associated molecules into simple molecules in this solvent is

Because benzoic acid exists predominantly in the form of double
molecules in benzene,
Co can replace [(HA)2],
where Co is the total molar concentration of the solute in the organic
layer.
Then equation can be written approximately as
Or

 In conformity with the distribution law as given
in equation
The true distribution coefficient is always
expressed in terms of simple species common to
both phases, that is, in terms of [HA]w and
[HA]o. In the benzene–water system, [HA]o is
given by equation and the modified distribution
constant becomes

 The results for the distribution of benzoic
acid between benzene and water

 1. Extraction
Determine the efficiency with which one
solvent can extract a compound from a second
solvent—
an operation commonly employed in analytic
chemistry and in organic chemistry.
when w represent grams of a solute is
extracted repeatedly from V1 mL of one
solvent with successive portions of V2 mL of a
second solvent, which is immiscible with the
first.

 Let w1 be the weight of the solute remaining
in the original solvent after extracting with
the first portion of the other solvent.
 Then, the concentration of solute remaining
in the first solvent is (w1/V1) g/mL and
 the concentration of the solute in the
extracting solvent is (w - w1)/V2 g/mL.
 The distribution coefficient is thus

 The process can be repeated, and after n
extractions,
By use of this equation, it can be shown that most efficient
extraction results when n is large and V2 is small, in other
words, when a large number of extractions are carried out
with small portions of extracting liquid.

1. Preservative action of weak acids in oil-water
systems:
Solution of foods, drugs & cosmetics: deterioration by
enzymes of microbes that act as catalyst
Benzoic acid: soluble salt, sodium benzoate
Preservative action due to undissociated acid & not to
ionic form
Relative ease with which unionized molecule penetrates
living membrane
Undissociated molecule consist of large non polar
portion is soluble in lipoidal membrane of microbes
Bacteria in oil-water system located in aq phase & at
oil-water interface

Solubility and distribution phenomena

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