Solubility of drugs by Dr. Atish Mundada

Solubility of DrugsSolubility of Drugs
Solubility of drugs: Solubility expressions, mechanisms of solute solvent
interactions, ideal solubility parameters, solvation & association, quantitative
approach to the factors influencing solubility of drugs, diffusion principles in
biological systems.
Solubility of gas in liquids, solubility of liquids in liquids, Solubility of Solids in
liquids (Binary solutions, ideal solutions with respect to their colligative
properties) Raoult’s law, real solutions. Partially miscible liquids(Phase
equilibria, Phase rule, One , two and three component systems, ternary
phase diagram, Critical solution temperature and applications).
Distribution law, its limitations and applications
Dr. Atish S. Mundada,Dr. Atish S. Mundada,
Associate Professor (Pharmaceutics)Associate Professor (Pharmaceutics)
SSDJ College of Pharmacy, ChandwadSSDJ College of Pharmacy, Chandwad

General Principles:General Principles:
• Solubility is defined in quantitative terms as the
concentration of solute in a saturated solution at a certain
temperature, and in a qualitative way, it can be defined as
the spontaneous interaction of two or more substances to
form a homogeneous molecular dispersion.
• Solubility is an intrinsic material property that can be altered
only by chemical modification of the molecule.
• In contrast to this, dissolution is an extrinsic material
property that can be influenced by various chemical,
physical, or crystallographic means.
• The solubility of a compound depends on the physical and
chemical properties of the solute and the solvent as well as
on such factors as temperature, pressure, the pH of the
solution, and, to a lesser extent, the state of subdivision of
the solute.

• Equilibrium solubility: is the concentration of compound in
a saturated solution when excess solid is present, and
solution and solid are at equilibrium.
• It can be measured by the classical shake-flask method, and
while this method is accurate when performed to a high
standard, it is slow.
• Kinetic solubility: is the solubility at the time when an
induced precipitate first appears in a solution.
• The kinetic solubilities obtained are often much higher than
measured equilibrium solubilities.
• Intrinsic solubility: is the true solubility and it is the
solubility of a fully un-ionized drug. In another way it can be
defined as the solubility of free acid or free base form of an
ionizable drug at a pH where it is fully uniozied.

Solubility Expressions:Solubility Expressions:
• The solubility of a drug may
be expressed in a number of
ways.
• The United States
Pharmacopeia (USP)
describes the solubility of
drugs as parts of solvent
required for one part solute.
• The USP describes solubility
using the seven groups listed
in Table.
• Solubility is also
quantitatively expressed in
terms of molality, molarity,
and percentage.

Ways of expressing Concentration:Ways of expressing Concentration:
• There are several ways of expressing concentration of a
solution :
– (a) Per cent by weight:- It is the weight of the solute as a
per cent of the total weight of the solution.
– (b) Mole fraction:- It is the ratio of the number of moles
of solute and the total number of moles of solute and
solvent.
Thus, Mole fraction is unitless and Xsolute + Xsolvent = 1.
– (c) Molarity:- The number of moles of solute per liter of
solution.
– (d) Molality:- The number of moles of solute per
kilogram of solvent.
– (e) Normality:- number of equivalents of solute per liter
of the solution.

Solute Solvent interaction:Solute Solvent interaction:
• The pharmacist knows that water is a good solvent for salts,
sugars, and similar compounds, whereas mineral oil is often
a solvent for substances that are normally only slightly
soluble in water.
• There are three steps to the dissolving process:
– The solvent particles must move apart to make room for solute
particles. This process requires energy to overcome forces of
attraction between solvent particles. This step is endothermic.
– The solute particles must separate from their neighbours. This
process also requires energy to overcome the forces of attraction
between the solute particles. This step is endothermic.
– When the solute particles move between the solvent particles,
the intermolecular forces of attraction between solute and
solvent take hold and the particles "snap" back and move closer.
This process releases energy. This final step is exothermic.

• The dissolving process involves a consideration of the
relative strength of three intermolecular attractive forces.
• The type of forces between solute-solute molecules and
solvent-solvent molecules must be considered. These
intermolecular attractions must be broken before new
solute-solvent attractive forces can become effective.
• A solute will dissolve in a solvent if the solute-solvent forces
of attraction are great enough to overcome the solute-solute
and solvent-solvent forces of attraction.
• A solute will not dissolve if the solute-solvent forces of
attraction are weaker than individual solute and solvent
intermolecular attractions.
• Generally, if all three of the intermolecular forces of
attraction are roughly equal, the substances will be soluble
in each other.

Solubility Parameter and its determination:Solubility Parameter and its determination:
• The solubility parameter is a numerical value that indicates the
relative solvency behavior of a specific solvent.
• The various scales available to determine the solubility parameter
are: Kauri-Butanol number, solubility grade, aromatic character,
aniline cloud point, wax number, heptane number, and Hildebrand
solubility parameter.
• The Hildebrand solubility parameter is applicable for almost all
systems and hence is the most widely used.
• Sometimes only numerical values for these terms are encountered,
while at other times values are presented in the form of two or
three dimensional graphs and a triangular graph called a Teas
graph. It is used because of its accuracy and clarity.

The Hildebrand Solubility Parameter:
• The solubility behavior of an unknown substance often gives us a
clue to its identification, and the change in solubility of a known
material can provide essential information about its ageing
characteristics.
• Our choice of solvent in a particular situation involves many
factors, including evaporation rate, solution viscosity, or
environmental and health concerns, and often the effectiveness of
a solvent depends on its ability to adequately dissolve material.
• It should be noted that these systems relate to non-ionic liquid
interactions that are extended to polymer interactions; water
based systems and those systems involving acid-base reactions
cannot be evaluated by simple solubility parameter systems alone.
• It is the van der Waals force, which is reflected in the simplest
solubility value: the Hildebrand solubility parameter.

• It is derived from the cohesive energy density of the solvent,
which in turn is derived from the heat of vaporization.
• The relationship between vaporization, van der Waals forces and
solubility will help us to clarify this.
1. Vaporization:
• When a liquid is heated to its boiling point, energy (in the form of
heat) is added to the liquid, resulting in an increase in the
temperature of the liquid. Once the liquid reaches its boiling point,
however, the further addition of heat does not cause a further
increase in temperature.
• The energy that is added is entirely used to separate the molecules
of the liquid and boil them away into a gas. Only when the liquid
has been completely vaporized will the temperature of the system
again begin to rise.
• If we measure the amount of energy (in calories) that was added
from the onset of boiling to the point when all the liquid has boiled
away, we will have a direct indication of the amount of energy
required to separate the liquid into a gas, and thus the amount of
van der Waals forces that held the molecules of the liquid together.

2. COHESIVE ENERGY DENSITY:
• From the heat of vaporization, in calories per cubic centimeter of
liquid, we can derive the cohesive energy density (c) by the
following expression
• Where:
C=Cohesive energy density
Δh=Heat of vaporization
R=Gas constant
T=Temperature
Vm=Molar volume
• In other words, the cohesive energy density of a liquid is a
numerical value that indicates the energy of vaporization in
calories per cubic centimeter, and is a direct reflection of the
degree of van der Waals forces holding the molecules of the liquid
together.

3. SOLUBILITY PARAMETER:
• In 1936 Joel H. Hildebrand (who laid the foundation for
solubility theory in his classic work on the solubility of non-
electrolytes in 1916) proposed the square root of the cohesive
energy density as a numerical value indicating the solvency
behavior of a specific solvent.

Solvation and Association:Solvation and Association:
• The term solvation refers to the surrounding of each dissolved
molecule or ion by a shell of more or less tightly bound solvent
molecules.
• This solvent shell is a result of intermolecular forces between
solute and solvent. For aqueous solutions, the term used is
hydration.
• Intermolecular interaction between solvent molecules and ions
are particularly important in solution of electrolytes, since ions
exert specially strong forces on solvent molecules.
• The free energy of solvation ΔGsolv, is a measure of solvation ability
of a particular solvent.
• The dissolution of a substance requires that not only the
interaction energy of solute molecules for solutes the lattice
energy) be overcome but also the interaction energy between the
solvent molecules themselves.
• This is compensated by the gain in free energy of solvation; ΔGsolv.

• The free energy of solvation Δgsolv is the result of superimposition
of four principle components of different nature:
a) The cavitation energy linked with the hole which the dissolved
molecule or ion produces in the solvent;
b) The orientation energy corresponding to the phenomenon of
partial orientation of dipolar solvent molecules caused by the
presence of the solvated molecules or ion;
c) The isotropic interaction energy corresponding to the unspecific
intermolecular forces with a long radius of activation (i.e.
electrostatic, polarization and dispersion energy);
d) The anisotropic interaction energy resulting from the specific
formation of hydrogen bonds or electron pair donor/electron pair
acceptor bonds at well localized points in the dissolved
molecules.

• The heat of solution of a compound can be formulated as the
difference between the lattice energy and solvation energy.
• If the liberated energy is higher than lattice energy, then the
overall process is exothermic.
• In opposite case the system uses up the energy and the process is
endothermic.

• Solvation of a Sodium Cation in Water

CoCo--ordination and solvation number:ordination and solvation number:
• It reflects the simple idea that the solvation of ions or molecules
consists of a co-ordination of solute and solvent molecules.
• The co-ordination number is defined as the number of solvent
molecules in the first co-ordination sphere of an ion in solution.
• The solvation number is defined as the number of solvent
molecules per ion that remain attached to a given ion long
enough to experience its translational movements.
• The solvation number of an ion in a solvent depends upon the
reference ion as well as the method of measurement. Smaller
the anion or cation more is its solvation and greater is its
solvation number and solvation energy.

Association:Association:
• ion association is a chemical reaction whereby ions of opposite
electrical charge come together in solution to form a distinct
chemical entity.
• Knowledge of the state of association of electrolytes in solution
and of their interaction with the solvent molecules is essential for a
proper understanding of their behavior in solution.
• Ion pairs are formed when a cation and anion, which are present in
a solution of an ionizable substance, come together to form a
discrete chemical species.
• There are three distinct types of ion pairs according to the nature
of the interaction as contact, solvent-shared or solvent-separated.

• With fully solvated and solvent-shared ion pairs the interaction is
primarily electrostatic, but in a contact ion pair some covalent
character in the bond between cation and anion is also present.
• Ions of opposite charge are naturally attracted to each other. This is
described by Coulomb's law:
F = q1* q2/ ϵ*r2
• where F is the force of attraction, q1 and q2 are the magnitudes of
the electrical charges, ε is the dielectric constant of the medium
and r is the distance between the ions.
• Some general conclusions can be inferred about Ion association
and is found to increase as:
– the magnitude(s) of the electrical charge(s) q1 and q2 increase,
– the magnitude of the dielectric constant ε decreases, (Solvents
with a dielectric constant in the range, roughly, 20–40, show
extensive ion-pair formation.)
– the size of the ions decreases so that the distance r between
cation and anion decreases.

Solubility of Common Compounds:Solubility of Common Compounds:

General Solubility Guidelines:General Solubility Guidelines:

Determination of Solubility:Determination of Solubility:
• The solubility of a substance is determined by preparing
its saturated solution and then finding the concentration
by evaporation or a suitable chemical method.
• Saturated solution of a solid substance may be prepared
by shaking excess of it with the solvent in a vessel placed
in a constant temperature bath and filtering the clear
solution.
• A known volume of this saturated solution is evaporated in
a china dish and from the weight of the residue the
solubility can easily be calculated.
• This method though simple, does not yield accurate
results. During filtration, cooling would take place and
thus some solid may be deposited on the filter paper or in
the stem of the funnel. However, this method is quite
good for the determination of solubility at room
temperature.

Solubility Curves:Solubility Curves:
• A curve drawn between solubility and temperature is
termed Solubility Curve. It shows the effect of
temperature on the solubility of a substance.
• The solubility curves of substances like calcium acetate
and calcium chromate show decrease in solubility with
increase of temperature while there are others like
those of Potassium nitrate and Potassium chloride
which show a considerable increase of solubility with
temperature.
• The solubility curve of sodium chloride shows very little
rise with increase of temperature.
• In general, the solubility curves are of two types :
(1) Continuous solubility curves
(2) Discontinuous solubility curves

• Solubility curves of calcium salts of
fatty acids, potassium chlorate, lead
nitrate and sodium chloride are
Continuous solubility curves as they
show no sharp breaks anywhere.
• Sometimes the solubility curves
exhibit sudden changes of direction
and these curves are, therefore,
called Discontinuous solubility
curves.
• The popular examples of substances
which show discontinuous solubility
curves are sodium sulphate, calcium
chloride, ammonium nitrate etc.

Factors affecting Solubility:Factors affecting Solubility:
• Common ion effect:
– Temperature:
– Pressure:
• pH:
• Solvents:
• Particle size:

Dissolution and Drug release:Dissolution and Drug release:
• Drug release is the process by which a drug leaves a drug product
and is subjected to absorption, distribution, metabolism, and
excretion, eventually becoming available for pharmacologic action.
• Once drug is released from the formulation in discrete particle
form, it becomes available for dissolution in the biological fluid
which in turn become available for absorption.
• Immediate release refers to the instantaneous availability of drug
for absorption or pharmacologic action.
• Modified release dosage forms include both delayed and
extended release drug products.
• In case of Immediate release dosage forms dissolution is the rate
limiting step whereas in case of modified release dosage form
drug release from dosage form is the rate limiting step.

Theories of Dissolution:Theories of Dissolution:
• Three theories are there which explain the dissolution process
from solid dosage form viz.
– Diffusion layer model/ film theory
• Dankwert’s Model/ Surface
renewal theory
– Interfacial barrier model/
Limited solvation theory
Noyes Whitney’s Equation:
dm/dt = AD(Cs – C) / h

• Oral drug absorption process occurs mainly in small intestinal
regions, which includes passive transcellular diffusion, carrier-
mediated transport processes, paracellular transport, and
endocytosis.
• In general, lipophilic compounds are usually absorbed by passive
diffusion through the intestinal epithelium.
• Many hydrophilic compounds are absorbed through a carrier-
mediated process, while some small hydrophilic compounds may
be transported through the paracellular junction.
• Two fundamental parameters govern drug absorption: drug
solubility and gastrointestinal permeability.
Diffusion Principles in Biological systems:Diffusion Principles in Biological systems:

32
Types of Intestinal Membrane Transport:Types of Intestinal Membrane Transport:
• Intestinal membrane transport include paracellular and
transcellular transport
• Transcellular transport can be further divided into passive
diffusion, endocytosis, and carrier-mediated transport.
• Paracellular transport refers to the passage of solute without
passage through the epithelium cells.

33
• Although different mechanisms of oral drug absorption have
been shown in small intestinal regions, under physiological
conditions, several routes may contribute to drug absorption at
the same time.
• Usually, the fastest route dominates the absorption of a
particular compound.
• In general, passive diffusion is the main mechanism for
absorption of many lipophilic compounds, while the carrier-
mediated process governs the absorption of transporter
substrates.
• In some cases, paracellular junction is the route for the
absorption of some small hydrophilic compounds with
molecular weight less than 300.

Solution and its types:Solution and its types:
• A solution is a homogeneous mixture of two or more
substances on molecular level.
• The constituent of the mixture present in a smaller amount
is called the Solute and the one present in a larger amount is
called the Solvent.
• A saturated solution is one in which the solute in solution is
in equilibrium with the solid phase.
• A supersaturated solution is one that contains more of the
dissolved solute than it would normally contain at a definite
temperature, were the undissolved solute present.
• The common solutions that we come across are those where
the solute is a solid and the solvent is a liquid. In fact,
substance in any three states of matter (solid, liquid, gas) can
act as solute or solvent.

Solubility of Gases in Liquids:Solubility of Gases in Liquids:
• The solubility of a gas in a solvent depends on the
pressure and the temperature.
• When a gas is enclosed over its saturated solution, the
following equilibrium exists.
gas ↔ gas in solution
• If pressure is increased on the system, the equilibrium
will move in the direction which will reduce the
pressure (Le Chatelier Principle).
• The pressure can be reduced by more gas dissolving in
solvent. Thus solubility or concentration of a gas in a
given solvent is increased with increase of pressure.

Henry’s Law:Henry’s Law:
• The relationship between pressure and solubility of a
gas in a particular solvent was investigated by William
Henry (1803).
• The generalization he gave is known as Henry’s Law
which may be stated as : for a gas in contact with a
solvent at constant temperature, concentration of the
gas that dissolves in the solvent is directly proportional
to the pressure of the gas.
• Mathematically, Henry’s Law may be expressed as
C ∝ P or C = kP
where P = pressure of the gas; C = concentration of the
gas in solution; and k = proportionality constant known
as Henry’s Law Constant.
• The value of k depends on the nature of the gas and
solvent, and the units of P and C used.

Limitations of Henry’s Law:Limitations of Henry’s Law:
• It applies closely to gases with nearly ideal behaviour.
(1) at moderate temperature and pressure.
(2) if the solubility of the gas in the solvent is low.
(3) the gas does not react with the solvent to form a
new species.
Thus ammonia (or HCl) which react with water do not
obey Henry’s Law.
NH3 + H2O ↔ NH4
+ + OH–
(4) the gas does not associate or dissociate on
dissolving in the solvent.

Solubility of Liquids in Liquids:Solubility of Liquids in Liquids:
• Frequently two or more liquids are mixed together in the
preparation of pharmaceutical solutions.
• Alcohol is added to water to form hydroalcoholic
solutions of various concentrations; volatile oils are
mixed with water to form dilute solutions known as
aromatic waters; volatile oils are added to alcohol to
yield spirits and elixirs; ether and alcohol are combined
in collodions; and various fixed oils are blended into
lotions, sprays, and medicated oils.
• Liquid–liquid systems can be divided into two categories
according to the solubility in one another:
– (a) complete miscibility and
– (b) partial miscibility.

Ideal Solution:Ideal Solution:
• Ideal solutions are formed by mixing substances with
similar properties.
• Ideal solution is the solution in which there is no
change in the properties of the components, other than
dilution, when they are mixed to form the solution.
• Ideality in solution means complete uniformity of
attractive forces (i.e. cohesive forces between A
molecules are similar to cohesive forces between B
molecules; both of which are similar to the adhesive
forces between A and B molecules).
• In ideal solution, no heat is evolved or absorbed during
the mixing process, and the final volume of the solution
represents an additive property of the individual
constituents. No shrinkage or expansion occurs when
substances are mixed together (e.g. a solution of
methanol and ethanol).

Real (nonReal (non--ideal) solutions:ideal) solutions:
• Few solution pairs are known in which cohesive
attraction of A for A and B for B exceeds adhesive
attraction existing between A&B and this may occur
even though liquids are miscible in all proportions.
These mixtures are known as real or non-ideal solution.
(Eg. Solution of chloroform and EtOH, Chloroform and
Acetone, Benzene and Ethyl alcohol)
• In real solutions, Raoult’s law does NOT apply over the
entire concentration range. It can only be applicable
for a substance with high concentration (i.e. solvents
in real solutions).
• A solution which shows deviations from Raoult’s law is
called a Non-ideal or Real solution.

Escaping TendencyEscaping Tendency
• When two bodies are in contact with each other and
one is heated to a higher temperature than the other,
heat will flow from the hotter to the colder body until
the bodies are in thermal equilibrium. This process is
termed the escaping tendency.
• The hotter body has a greater escaping tendency until
the temperature of both bodies is the same.
• Temperature is a quantitative measure of escaping
tendency of heat.
• Free energy is a quantitative measure of escaping
tendencies of substances undergoing physical and
chemical transformations – for a pure substance, it is
the molar free energy, for a solution, it is the partial
molar free energy.

Raoult’s Law:Raoult’s Law:
• Raoult (1886) gave an empirical relation connecting the
relative lowering of vapour pressure and the
concentration of the solute in solution. This is now
referred to as the Raoult’s Law.
• It states that : the relative lowering of the vapour
pressure of a dilute solution is equal to the mole
fraction of the solute present in dilute solution.
• Raoult’s Law can be expressed mathematically in the
form :
where, n = number of moles or molecules of solute N =
number of moles or molecules of solvent.

Lowering ofLowering of VapourVapour Pressure:Pressure:
• The vapour pressure of a pure solvent is decreased
when a non-volatile solute is dissolved in it.
• If p is the vapour pressure of the solvent and ps that of
the solution, the lowering of vapour pressure is (p – ps).
• This lowering of vapour pressure relative to the vapour
pressure of the pure solvent is termed the Relative
lowering of Vapour pressure.

Lowering ofLowering of VapourVapour PressurePressure--Colligative Property:Colligative Property:
• The vapour pressure of the pure solvent is caused by
the number of molecules evaporating from its surface.
• When a nonvolatile solute is dissolved in solution, the
presence of solute molecules on the surface blocks a
fraction of the surface where no evaporation can take
place. This causes the lowering of the vapour pressure.
• The vapour pressure of the solution is, therefore,
determined by the number of molecules of the solvent
present at any time in the surface which is proportional
to the mole fraction.
Where, N is moles of solvent and n is moles of solute.

• In case of pure solvent n = 0 and hence Mole fraction of
solvent is 1.
• Now from above equation, the vapour pressure p = k,
Therefore the equation assumes the form-
• This is Raoult’s Law.
k being proportionality factor.

Ethylen
Chloride
XA= 1
Benzene
XB= 1
Mole fraction of Ethylen
Chloride
PA°= 236
PB°= 268
PB°XB
PA°XA
Total vapor pressure
Vaporpressure(mmHg)
Raoult’s LawRaoult’s Law-- Ideal solutionsIdeal solutions

Deviations from Raoult’s Law:Deviations from Raoult’s Law:
• A solution which obeys Raoult’s law strictly is called an
Ideal solution.
• A solution which shows deviations from Raoult’s law is
called a Nonideal or Real solution.
• Suppose the molecules of the solvent and solute are
represented by A and B respectively.
• Now let γAB be the attractive force between A and B,
and γAA between A and A.
If γAB = γAA the solution will show the same
vapour pressure as predicted by Raoult’s law and it is an
ideal solution.

However,
if γAB > γAA molecule A will
escape less readily and the
vapour pressure will be less
than that predicted.
Negative deviation:
• When“adhesive” attractions
between molecules of
different species exceed the
“cohesive” attractions
between like molecules, the
vapor pressure of the
solution is less than
expected from Raoult’s
ideal law, and negative
deviation occurs.
Example: Chloroform and
Acetone-due to formation of
hydrogen bonds reduces the
escaping tendency of eachother.

• On the other hand,
if γAB < γAA A molecule will
escape from the solution surface
more readily and the vapour
pressure of the solution will be
higher than predicted
Positive deviation- When interaction
between A and B molecules is less
than that of the pure constituents,
the presence of B molecules
reduce the interaction of A
molecules, and vice versa
greater escaping tendency of A
and B molecules  partial vapor
pressure of the constituents is
greater than that expected.
Examples: carbon
tetrachloride and methyl
alcohol, benzene and ethyl
alcohol, carbon disulfide and
acetone, chloroform and EtOH,

Partial Miscibility:Partial Miscibility:
• A large number of liquids are known which dissolve in
one another only to a limited extent.
• 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.
• Since their mutual solubilities are limited, they are only
partially miscible. These two solutions are referred to as
conjugate solutions.
• The temperature at which the two conjugate solutions
(or layers) merge into one another to from one layer, is
called the Critical Solution Temperature (CST).
• This is characteristic of a particular system and is
influenced very much by the presence of impurities.

TwoTwo––component Systems containing Liquidcomponent Systems containing Liquid
phases:phases:
• We know from experience
that ethyl alcohol and water
are miscible in all
proportions, whereas water
and mercury are, for all
practical purposes,
completely immiscible
regardless of the relative
amounts of each present.
• Between these two extremes
lies a whole range of systems
that exhibit partial miscibility
(or immiscibility).

• The curve gbhci shows the limits of temperature and
concentration within which two liquid phases exist in
equilibrium. The region outside this curve contains
systems having but one liquid phase.
• Starting at the point a, equivalent to a system containing
100% water (i.e., pure water) at 50°C, adding known
increments of phenol to a fixed weight of water, the
whole being maintained at 50°C, will result in the
formation of a single liquid phase until the point b is
reached, at which point a minute amount of a second
phase appears.
• The concentration of phenol and water at which this
occurs is 11% by weight of phenol in water.

• Analysis of the second phase, which separates out on the
bottom, shows it to contain 63% by weight of phenol in
water. This phenol-rich phase is denoted by the point c on
the phase diagram.
• As we prepare mixtures containing increasing quantities of
phenol, that is, as we proceed across the diagram from
point b to point c, we form systems in which the amount of
the phenol-rich phase (B) continually increases, as
denoted by the test tubes drawn in Figure.
• At the same time, the amount of the water-rich phase (A)
decreases.
• Once the total concentration of phenol exceeds 63% at
50°C, a single phenol-rich liquid phase is formed.
• The maximum temperature at which two phases exists is
termed Critical solution temperature.
• In case of Phenol-Water system it is 66.80C

Phase Equilibria:Phase Equilibria:
• A phase may be defined as : any homogeneous part of a
system having all physical and chemical properties the
same throughout.
• A system may consist of one phase or more than one
phases.
(1) A system containing only liquid water is one-phase or
1-phase system (P = 1)
(2) A system containing liquid water and water vapor (a
gas) is a two-phase or 2-phase system (P = 2).
(3) A system containing liquid water, water vapor and solid
ice is a three-phase or 3-phase system.
• A system consisting of one phase only is called a
homogeneous system. A system consisting of two or
more phases is called a heterogeneous system.

• Ordinarily three states of matter-gas, liquid, and solid are
known as phases. However in phase rule, a uniform part
of a system in equilibrium is termed a ‘phase’. Thus a
liquid or a solid mixture could have two or more phases.
It must be remembered that a phase may or may not be
continuous.
• Any mixture of gases is a 1-phase system. A mixture of
two non-miscible liquids on standing forms two separate
layers, Hence constitutes a 2-phase system. Mixture of
two allotropes is a 2-phase system. A saturated solution
of sodium chloride in contact with excess solid sodium
chloride is a 2-phase system.
• The term component may be defined as : the least
number of independent chemical constituents in terms
of which the composition of every phase can be
expressed by means of a chemical equation.

VARIABLES that define the STATE of a System:
• Extensive – dependent on the quantity of the system –
volume, mass, moles, ...
• Intensive – properties of the phases of a system that
are independent of quantities (temperature, pressure,
density, molecular proportions, elemental ratios, ...)
• Note that ratios of extensive variables become
intensive (V/m = density, V/moles=molar volume)

The Phase Rule:The Phase Rule:
• The phase Rule is an important generalization dealing
with the behaviour of heterogeneous systems.
• In general it may be said that with the application of
phase rule it is possible to predict qualitatively by means
of a diagram the effect of changing pressure, temp. and
concentration on a heterogeneous system in equilibrium.
• This relationship governing all heterogeneous equilibria
was first discovered as early as 1874 by an American
physicist J. Willard Gibbs.
• Gibb’s Phase Rule is free from flaws and limitations
which are a common feature of all other generalizations
of Physical Chemistry based on hypothetical assumptions
as to the nature of the constitution of matter.

• It may be stated mathematically as follows :
F = C – P + 2
where F is the number of degrees of freedom, C is the
number of components and P is the number of phases of
the system.
• The term Degree of Freedom represented by F in the
phase Rule equation is defined as follows: the least
number of INTENSIVE variable which must be specified
so that the remaining variables are fixed automatically
and the system is completely defined.
• A system with F = 0 is known as nonvariant or having no
degree of freedom.
• A system with F = 1 is known as univariant or having one
degree of freedom.
• A system with F = 2 is known as bivariant or having two
degrees of freedom.

• Suppose we cool liquid water and its vapor until a third
phase (ice) separates out.
• Under these conditions, the state of the three-phase
ice–water–vapor system is completely defined, and the
rule gives F = 1 - 3 + 2 = 0; in other words, there are no
degrees of freedom.
• If we attempt to vary particular condition of temperature
or pressure necessary to maintain this system, we will
lose a phase.
• Thus if we wish to prepare three phase system of ice-
water-vapor we have no choices as to temperature or
pressure at which we will work; the combination is fixed
and unique. This is known as critical point.

Application:Application:
•A gas, e.g. water vapour confined to a particular volume.
Apply phase rule: F=1-1+2=2.
•This means that two intensive variables (temperature and
pressure, temperature and concentration) must be
known to duplicate this system exactly. Such a system is
usually described as bivariant.
•A liquid such as water in equilibrium with its vapour (we
have 2 phase system)
F=1-2+2=1.
•By stating temperature, the system is completely defined
because the pressure under which liquid and vapour can
coexist is also fixed.
•If we decide to work under a particular pressure, then the
temperature of the system is automatically defined.

• When we have a liquid water, vapor and ice- F= 1-3+2=0
There are no degrees of freedom, if we attempt to vary the
conditions of temperature or pressure necessary to maintain
the system, we will lose a phase. The combination is fixed
and unique.
The system is invariant.
• As the number of components increases, so do the required
degrees of freedom needed to define the system.
Consequently, as the system becomes more complex, it
becomes necessary to fix more variables to define the
system.
• As the number of phases in equilibrium increases, the
number of the required degrees of freedom becomes less.
Liquid water+vapor F=1-2+2=1
ethyl alcohol+vapor F=1-2+2=1
liquid water+liquid ethanol+vapor F=2-2+2=2

Phase diagrams :Phase diagrams :
• The number of phases that exist in equilibrium
depends upon the conditions of temperature and
pressure or temperature and composition, pressure
being constant.
• These conditions are determined experimentally and
interdependence of values of the variables can be
shown graphically using appropriates coordinates.
These diagrams are termed phase diagram.
• A phase diagram is the sum total of the description of
the behaviour of the phases under equilibrium.
• It is very easy to describe the phase behaviour of a
system by such diagrams and to investigate the
conditions in which various phases will constitute the
system .

OneOne––component System:component System:
Application of Gibbs Phase Rule to One Component
System:
F = C – P + 2
When C = 1, P = 1 F = 1-1+2 = 2
• Hence, all one component systems can be completely
described graphically by stating only two variables,
pressure and temperature on appropriate axis.
The Water System :
• It is a one component system. Water exists in three
possible phases viz. ice (solid) , water (liquid), and
vapour (gas).
• These three single phases may form four possible
equilibria.

Phase Diagram of water system:Phase Diagram of water system:

• There are three lines or curves separating the regions or
areas. These curves show the conditions of equilibrium
between any two of the three phases.
(a) Solid/liquid line (OC) which represents the equilibrium
Solid ↔ Liquid, is referred to as the Melting curve or
Fusion curve. The fact that OC slopes to the left indicates
that the melting point of ice decreases with increase of
pressure.
(b) Liquid/vapour line (OA) which represents the
equilibrium Liquid ↔ Vapour, is referred to as the
Vapour Pressure curve. The curve OA terminates at A,
the critical point (218 atm, temp. 374⁰C)
(c) Solid/vapour line (OB), which represents the
equilibrium Solid ↔ Vapour, is referred to as the
Sublimation curve. Curve OB terminates at absolute zero
(–273⁰C) where no vapour exists.

• Triple Point: The three boundary lines enclosing the
three areas on the phase diagram intersect at a common
point called the Triple point. A triple point shows the
conditions under which all the three phases (solid,
liquid, vapour) can coexist in equilibrium.
• Thus the system at the triple point may be represented
as : Solid ↔ Liquid ↔ Vapour
• Applying the phase rule equation, we have
F = C – P + 2 = 1 – 3 + 2 = 0
which predicts that the system has no degree of
freedom.
• At the triple point both pressure and temperature on the
diagram are fixed and, therefore, the system is
nonvariant.

• This implies that if we try to change temperature or
pressure, the equilibrium will be disturbed.
• For example, if we lower the pressure on the system,
all the liquid will vaporise, leaving only two phases.
• In case of water system, the temperature and
pressure for the triple point are 0.0098⁰ and 4.58
mm Hg respectively.

TwoTwo––component Systemscomponent Systems--Eutectic Mixture:Eutectic Mixture:
• When a single phase is present in a two-component
system, the degree of freedom is three, F = 2 – 1 + 2 = 3
This means that three variables must be specified in
order to describe the condition of the phase.
• Thus in such a system, in addition to pressure and temp.,
the conc. of one of the components has also to be given.
• For the sake of having simple plane diagrams we
generally consider only two variables, the third one being
a constant.
• Thus when a two-component system consists of solid and
liquid phases only, the effect of pressure may be ignored.
Then it is necessary to take into account the remaining
variables viz., temperature and concentration. Such a
solid/liquid system with the gas phase absent is called a
condensed system.

• The experimental measurements of temperature and
concentration in condensed systems are usually carried
out under atmospheric pressure.
• Since the degree of freedom in such a case is reduced by
one, we may write the Reduced Phase rule as
F' = C – P + 1
where F' gives the remaining degrees of freedom of the
system.
• The reduced phase rule is more convenient to apply to
solid/liquid two-component condensed system.
• Since the only variables for two-component solid/liquid
systems are temperature and composition, the phase
diagrams for such systems consist of Temperature-
Concentration graphs (TC graphs).

Simple Eutectic Systems:Simple Eutectic Systems:
• The general form of the phase diagram of such a 2-
component condensed system is shown in Fig.
• Here the two components A and B are completely
miscible in the liquid state, and these solutions on
cooling yield only pure A or pure B as solid phases.

• Curve AC; the Freezing point curve of A. The point A
represents the freezing point of A. The curve AC shows
that the freezing point of A falls by the addition of B to A.
Thus along this curve, the solid A is in equilibrium with
the liquid solution of B in A.
• Curve BC; the Freezing point curve of B. The point B
shows the freezing point of B. The curve BC exhibits the
fall of freezing point by the addition of A to B. Along this
curve, the solid B is in equilibrium with the liquid
solution of A in B.
• Applying the reduced phase rule equation to the
equilibria represented by the curve AC and CB i.e., solid
A/solution and solid B/solution respectively, we have
F = C – P + 1 = 2 – 2 + 1 = 1 The degree of
freedom is one i.e., both equilibria are monovariant.

• The Eutectic point C. The two curves AC and BC meet at
the point C. Here both the solids A and B must be in
equilibrium with the solution phase (solution of A and B).
The number of phases is 3. By applying the reduced phase
rule equation, we have F' = C – P + 1 = 2 – 3 + 1 = 0
• Thus the system represented by the point C is nonvariant.
In other words, both the temperature and composition of
the system solid A/solid B/solution are fixed.
• The mixture of components A and B as at point C melts at
the lowest temperature TE indicated on the graph. The
point C is therefore, called the Eutectic point (Greek
eutectos = easy melting).
• The corresponding composition (CE) and temperature (TE)
are known as the eutectic composition and the eutectic
temperature respectively of the system.

Phase Equilibria in ThreePhase Equilibria in Three--Component Systems:Component Systems:
• In systems containing three components but only one
phase, F = 3 - 1 + 2 = 4 for a non-condensed system.
• The four degrees of freedom are temperature, pressure,
and the concentrations of two of the three components.
Only two concentration terms are required because the
sum of these subtracted from the total will give the
concentration of the third component.
• If we regard the system as condensed and hold the
temperature constant, then F = 2, and we can again use
a planar diagram to illustrate the phase equilibria.
• Because we are dealing with a three-component system,
it is more convenient to use triangular coordinate
graphs.

Advantages of Phase Rule :Advantages of Phase Rule :
(i) It provides a simple method of classifying equilibrium states
of systems.
(ii) The phase rule confirms that the different systems having the
same number of degrees of freedom behave in same
manner.
(iii) It predicts the behaviour of systems with changes in the
variables that govern the system in equilibrium.
(iv) It predicts under given conditions whether a number of
substances taken together would remain in equilibrium as
such or would involve interconversion or elimination of some
of them.
(v) It takes no account of nature of the reactants or products in
phase reactions.
(vi) It finds extensive use in the study of many heterogenous
systems. In particular it has been found extremely useful in
the extraction of metals.

Limitations:Limitations:
(i) The phase rule is applicable to heterogeneous systems in
equilibrium, so, it is therefore of no use for such systems
which are slow in attaining the equilibrium state.
(ii) It is applicable to a single equilibrium state, so it never
gives information about the other possible equilibrium in
the system.
(iii) In Gibbs phase rule, various variables are temperature,
pressure and composition. It does not take in account the
electric and magnetic influences. For consideration of
such variables, the factor 2 of the Phase rule has to be
adjusted accordingly.
(vi) All the phases in the system must be present under the
same temperature, pressure and gravitational force .
(v) No solid or liquid phases should be finely divided,
otherwise deviation occurs.

Solubility of Solids in Liquids:Solubility of Solids in Liquids:
• System of solids in liquids include the most frequent
and important type of pharmaceutical solutions.
• Most drugs belongs to the class of weak acids and
bases. They yields water soluble salts on reacting with
strong acids or bases.
• Acidic drugs are more soluble in alkaline solutions
where the ionized form is predominant.
• Basic drugs are more soluble in acidic solutions where
the ionized form of drug is predominant.
• Carboxylic acids containing more than 5 carbons are
relatively insoluble in water but it reacts with NaOH
and carbonate to form soluble salts whereas fatty acids
form soluble soaps with alkali metals and insoluble
soaps with other metal ions.

• Substitution also influences the solubility by affecting
the solute molecule cohesion and its interaction with
water molecule.
• Polar groups such as –OH are capable of hydrogen
bonding leading to high solubility to the substance.
• Non polar groups such as –CH3 and –Cl are hydrophobic
and results in low solubility.
• The position of the substituent on the moelcule can
affect the solubility. The aqueous solubility of o-, m- and
P-Hydroxybenzenes are 4,9 and 0.6 mol/L respectively.
• Symmetric particles can be less soluble than asymmetic
ones because they form compact crystals while
asymmetric particles pack less efficiently in crystals.

• Complexation can increase or decrease the solubility
of drugs.
• Cyclodextrin can form water soluble complexes with
most drugs whereas tetracycline form water insoluble
complexes with various metal cations.
• The aqueous solubility of substance decreases with
increasing the boiling and melting point which is
contributed to the stronger interactions between the
molecules in the pure state.
• Solubility can also be increased with decreasing the
particle size.

• The solutes (whether gases, liquids, or solids) are
divided into two main classes: nonelectrolytes and
electroytes.
• Nonelectrolytes are substances that do not yield ions
when dissolved in water and therefore do not conduct
an electric current through the solution.
• Examples of noneletrolytes are sucrose, glycerin,
naphthalene, and urea.
• Electrolytes are substances that form ions in solutions,
conduct the electric current.
• Examples of electrolytes are hydrochloric acid, sodium
sulfate, ephedrine, and phenobarbital.
• Electrolytes may be subdivided further into strong
electroytes (hydrochloric acid, sodium sulphate) and
weak electrolytes (ephedrine, phenobarbital).

Solution properties:Solution properties:
• The macroscopic or bulk properties of a system (volume,
pressure, mass, etc.) can be divided into two classes :
(a) Intensive properties & (b) Extensive properties
• Intensive Properties:
A property which does not depend on the quantity of
matter present in the system, is known as Intensive
Property.
• Some examples of intensive properties are pressure,
temperature, density, and surface tension.
• Extensive Properties:
A property that does depend on the quantity of matter
present in the system, is called an Extensive Property.
• Some examples of extensive properties are volume, number
of moles, enthalpy, entropy, and Gibbs’ free energy.

• Electrolytes are electrovalent substances that form ions
in solution which conduct an electric current.
• Sodium chloride, copper sulphate, potassium nitrate are
examples of electrolytes.
• Nonelectrolytes, on the other hand, are covalent
substances which furnish neutral molecules in solution.
Their water-solutions do not conduct an electric current.
Sugar, alcohol and glycerol are typical nonelectrolytes.
• An electrolyte invariably undergoes chemical
decomposition as a result of the passage of electric
current through its solution.
• The phenomenon of decomposition of an electrolyte by
passing electric current through its solution is termed
Electrolysis (lyo = breaking).
Electrolytes:Electrolytes:

• What would make a good electrolyte?
– Ionic compounds – the positive and negative ions
separate from each other in solution and are free to
move making it possible for an electric current to
pass through the solution
– Polar covalent molecules
• The strength of an electrolyte depends on the ability of
a substance to form ions, or the degree of ionization.
 Strong elctrolytes: Ex. Strong acids (HCl, HNO3),
Strong bases (NaOH)
 Weak Electrolytes: Ex. Weak Acids (Acetic Acid),
Weak Bases (ammonium hydroxide)

Conductance of Electrolytes:Conductance of Electrolytes:
• The power of electrolytes to conduct electric currents is
termed conductivity or conductance. Like metallic
conductors, electrolytes obey Ohm’s law.
• According to this law, the current I flowing through a
metallic conductor is given by the relation.
where E is the potential difference at two ends (in
volts); and R is the resistance measured in ohms (or Ω).
• The resistance R of a conductor is directly proportional
to its length, l, and inversely proportional to the area of
its cross-section, A.
where ρ “rho” is a proportionality constant and is called
resistivity or specific resistance.

Specific Conductance:Specific Conductance:
• It is evident that a substance which offers very little
resistance to the flow of current allows more current to
pass through it. Thus the power of a substance to
conduct electricity or conductivity is the converse of
resistance.
• The reciprocal of specific resistance is termed Specific
conductance or Specific conductivity.
• It is defined as : the conductance of one centimeter
cube (cc) of a solution of an electrolyte.
• The specific conductance is denoted by the symbol κ
(kappa). Thus
• Specific conductance is generally expressed in
reciprocal ohms (r.o) or mhos or ohm–1.

Equivalent Conductance:Equivalent Conductance:
• It is defined as the conductance of an electrolyte
obtained by dissolving one gram-equivalent of it in
Vcc of water.
• The equivalent conductance is denoted by Λ .
• It is equal to the product of the specific conductance, κ
and the volume V in cc containing one gram-equivalent
of the electrolyte.
• In general, if an electrolyte solution contains N gram-
equivalents in 1000 cc of the solution, the volume of
the solution containing 1 gram-equivalent will be
1000/N. Thus,
• The unit of equivalent conductance is ohm–1 cm2 eqvt-1
.

Kohlrausch’sKohlrausch’s Law:Law:
• From a study of the equivalent conductances of
different electrolytes at infinite dilution (Λ∞), Kohlrausch
discovered that each ion contributes to the conductance
of the solution. In 1875, he enunciated a generalization
which is called the Kohlrausch’s Law.
• It states that: the equivalent conductance of an
electrolyte at infinite dilution is equal to the sum of
the equivalent conductances of the component ions.
• The law may be expressed mathematically as :
Λ∞
= Λa+ Λc
where Λa is the equivalent conductance of the anion and
Λc that of the cation.

Solubility of Solids in Solids:Solubility of Solids in Solids:
• Solution of a solid in another solid can be prepared by
melting them together and subsequent cooling of the
mixture.
• For example, gold and silver when mixed together,
melted and cooled, yield solid solutions which are
perfectly homogeneous.
• Sometimes solid solutions may be obtained by simply
pressing together the two metals and thus establishing
better contact when one metal would diffuse into the
other.
• Solutions of gold and lead have been obtained by this
method.
• The study of solutions of solids in solids is of great
practical importance in metallurgy.

Distribution of Solutes between Immiscible Solvents:Distribution of Solutes between Immiscible Solvents:
• If we take two immiscible solvents A and B in a beaker,
they form separate layers.
• If an excess of liquid or solid (X) is added to a mixture of
two immiscible liquids, it will distribute itself between
the two phases so that each becomes saturated.
• Molecules of X pass from solvent A to B and from
solvent B to A. Finally a dynamic equilibrium is set up.
• If the substance is added to the immiscible solvents in
an amount insufficient to saturate the solutions, it will
still become distributed between the two layers in a
definite concentration ratio.

Statement of Nernst’s Distribution Law:Statement of Nernst’s Distribution Law:
• Nernst (1891) studied the distribution of several solutes
between different appropriate pairs of solvents.
• He gave a generalization which governs the distribution of a
solute between two non-miscible solvents. This is called
Nernst’s Distribution law (or Nernst’s Partition law) or
simply Distribution law or Partition law.
• If a solute X distributes itself between two immiscible
solvents A and B at constant temperature and X is in the
same molecular condition in both solvents,
• If C1 denotes the concentration of the solute in solvent A and
C2 the concentration in solvent B, Nernst’s Distribution law
can be expressed as
• The constant KD (or simply K) is called the Distribution
coefficient or Partition coefficient or Distribution ratio.

Solubilities and Distribution Law:Solubilities and Distribution Law:
• When a solute is shaken with two non-miscible
solvents, at equilibrium both the solvents are saturated
with the solute.
• Since the solubility also represents concentration, we
can write the distribution law as
where S1 and S2 are the solubilities of the solute in the
two solvents.
• Hence knowing the value of the Distribution coefficient
(KD) and the solubility of solute in one of the solvents,
the solubility of solute in the second solvent can be
calculated.

Limitations of Distribution Law:Limitations of Distribution Law:
The conditions to be satisfied for the application of the Nernst’s
Distribution law are :
1. Constant temperature- The temperature is kept constant
throughout the experiment.
2. Same molecular state- The molecular state of the solute is the
same in the two solvents. The law does not hold if there is
association or dissociation of the solute in one of the solvents.
3. Equilibrium concentrations- The concentrations of the solute are
noted after the equilibrium has been established.
4. Dilute solutions- The concentration of the solute in the two
solvents is low. The law does not hold when the concentrations
are high.
5. Non-miscibility of solvents- The two solvents are non-miscible or
only slightly soluble in each other. The extent of mutual solubility
of the solvents remains unaltered by the addition of solute to
them.

Applications of Distribution Law:Applications of Distribution Law:
• There are numerous applications of distribution law in
the laboratory as well as in industry.
(1) Solvent Extraction-
• This is the process used for the separation of organic
substances from aqueous solutions.
• The aqueous solution is shaken with an immiscible
organic solvent such as ether (or benzene) in a
separatory funnel.
• The distribution ratio being in favour of ether, most of
the organic substance passes into the ethereal layer.
• The ethereal layer is separated and ether distilled off.
Organic substance is left behind.

(2) Partition Chromatography-
• This is a modern technique of separating a mixture of
small amounts of organic materials.
• A paste of the mixture is applied at the top of a column
of silica soaked in water. Another immiscible solvent,
say hexane, is allowed to flow down the column. Each
component of the mixture is partitioned between the
stationary liquid phase (water) and the mobile liquid
phase (hexane).
• The various components of the mixture are extracted
by hexane in order of their distribution coefficients.
• Thus the component with the highest distribution
coefficient is first to move down in the flowing hexane
which is collected separately.
• Similarly, a component with a lower distribution ratio
comes down later and is received in another vessel.

(3) Desilverization of Lead (Parke’s Process)-
• When molten zinc is added to molten lead containing
silver (argentiferous lead), zinc and lead form immiscible
layers and silver is distributed between them.
• Since the distribution ratio is about 300 in favour of zinc
at 800 ºC, most of silver passes into the zinc layer. On
cooling the zinc layer, an alloy of silver and zinc
separates.
• The Ag-Zn alloy is distilled in a retort when zinc passes
over leaving silver behind.
• The lead layer still contains unextracted silver. This is
treated with fresh quantities of molten zinc to recover
most of the silver.

(4) Confirmatory Test for Bromide and Iodide-
• The salt solution is treated with chlorine water. Small
quantity of bromine or iodine is thus liberated.
• The solution is then shaken with trichloromethane
(chloroform). On standing chloroform forms the lower
layer. The free bromine or iodine being more soluble in
chloroform concentrates into the lower layer, making it
red for bromine and violet for iodine.
(5) Determination of Association-
(6) Determination of Dissociation-
(7) Determination of Solubility-
(8) Deducing the Formula of a Complex Ion (I3
-)–
(9) Distribution Indicators-

Solubility of drugs by Dr. Atish Mundada

Solubility of drugs by Dr. Atish Mundada

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