Solubility of drugs

Solubility of Drugs
Dr. Prashant L. Pingale
Associate Professor-Pharmaceutics
GES’s Sir Dr. M. S. Gosavi College of Pharm. Edu. & Research, Nashik

✓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 & three component systems, ternary
phase diagram,
✓Critical solution temperature and applications).
✓Distribution law, its limitations and applications.
2

After completion of this chapter, the learner should be able to:
✓Define solubility, various terms related to solubility and factors influencing solubility,
✓Understand the solubility of gas, solid and liquid in liquid.
✓Understand Raoult’s law and real solutions,
✓Understand various concept and their applications including Partially miscible liquids,
phase diagram, Critical solution temperature, Distribution law
3

Solubility
• 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 such as complexation,
particle size, surface properties, solid-state modification, or solubilization enhancing
formulation strategies.
• 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.
4

Importance of studying the phenomenon of solubility
Understanding the phenomenon of solubility helps the pharmacist to:
✓Select the best solvent for a drug or a mixture of drugs.
✓Overcome problems arising during preparation of pharmaceutical solutions.
✓Have information about the structure and intermolecular forces of the drug.
✓Many drugs are formulated as solutions, or added as powder or solution forms to liquids.
✓Drugs with low aqueous solubility often present problems related to their formulation
and bioavailability.
5

Related Terms
✓Solution: is a mixture of two or more components that form a
homogenous Mixture. The components are referred to the solute
and/or solutes & the Solvent and/or solvents .
✓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.
✓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.
6

Solubility
✓A supersaturated solution: contains more of the dissolved solute
than it would normally contain in a saturated state at a definite
temperature.
✓Solubility:
✓ In a quantitative way: it is the concentration of solute in a saturated
solution at a certain temperature.
✓ In a qualitative way: it is the spontaneous interaction of two or more
substances (solute & solvent) to form a homogeneous molecular
dispersion.
7

Degree of saturation
✓Unsaturated, saturated or supersaturated?
✓How much solute can be dissolved in a solution?
8

Solubility Curve
✓Any solution can be made saturated, unsaturated, or supersaturated by changing the
temperature.
9

Thermodynamic solubility of drugs
✓The thermodynamic solubility of a drug in a solvent is the maximum amount of the most
stable crystalline form that remains in solution in a given volume of the solvent at a given
temperature and pressure under equilibrium conditions.
✓The equilibrium involves a balance of the energy of three interactions against each other:
✓ (1) solvent with solvent
✓ (2) solute with solute
✓ (3) solvent and solute
10

Process of Solubilization
✓Steps of solid going into solution.
1. Step 1: hole open in the solvent
2. Step 2: one molecule of the solid breaks
away from the bulk
3. Step 3: the solid molecule is enter into the
hole in the solvent
11

Solubility process
✓A mechanistic perspective of solubilization process for organic solute in water involves
the following steps:
1. Break up of solute-solute intermolecular bonds
2. Break up of solvent-solvent intermolecular bonds
3. Formation of cavity in solvent phase large enough to accommodate solute molecule
4. Transfer of solute into the cavity of solvent phase
5. Formation of solute-solvent intermolecular bonds
12

Tree types of interaction in the solution process
1. Solvent – solvent interaction
2. Solute – solute interaction
3. Solvent – solute interaction
13
ΔH sol = ΔH 1 + ΔH 2 + ΔH 3
✓ Solubility depends on chemical, electrical & structural effects that
lead to mutual interactions between the solute and the solvent.
✓ In pre or early formulation, selection of the most suitable solvent
is based on the principle of “like dissolves like”.
✓ Polar solutes dissolve in polar solvents. Ex. Salts & sugar dissolve
in water .
✓ Non polar solutes dissolve in non polar solvents. Ex. Naphtalene
dissolves in benzene.

Enthalpy
✓The enthalpy change of solution refers to the overall amount of heat which is released or
absorbed during the dissolving process (at constant pressure).
✓The enthalpy of solution can either be positive (endothermic reaction) or negative
(exothermic reaction).
✓The enthalpy of solution is commonly referred to as ΔH solution.
14

Ideal solubility parameters
✓A logical starting point for approaching formulation development is “ideal
solubility”, defined as the solubility of a solute in the perfect solvent for which there
is no energy penalty associated with the dissolution process.
✓The ideal solubility depends only on the energy penalty needed to break the
crystalline structure of the API – the API has to “melt” before it can dissolve.
✓If the enthalpy of fusion, the melting point, and heat capacities are known, the ideal
solubility can be calculated.
16

Solubility and major factors influencing
✓Solubility is the maximum amount of a substance that will dissolve in a given amount
of solvent at a specific temperature. There are two direct factors that affect solubility:
temperature and pressure.
✓Temperature affects the solubility of both solids and gases, but pressure only affects
the solubility of gases.
✓Surface area does not affect how much of a solute will be dissolved, but it is a factor in
how quickly or slowly the substance will dissolve.
17

The Effect of Temperature on Solubility
✓Temperature has a direct effect on solubility.
✓For the majority of ionic solids, increasing the temperature increases how quickly the
solution can be made.
✓As the temperature increases, the particles of the solid move faster, which increases the
chances that they will interact with more of the solvent particles.
✓This results in increasing the rate at which a solution occurs.
✓Temperature can also increase the amount of solute that can be dissolved in a solvent.
Generally speaking, as the temperature is increased, more solute particles will be dissolved.
18

The Effect of Pressure on Solubility
✓ The second factor, pressure, affects the solubility of a gas in a liquid but never of a solid dissolving in a liquid.
✓ When pressure is applied to a gas that is above the surface of a solvent, the gas will move into the solvent
and occupy some of the spaces between the particles of the solvent.
✓ A good example is carbonated soda.
✓ Pressure is applied to force the CO2 molecules into the soda.
✓ The opposite is also true.
✓ When the gas pressure is decreased, the solubility of that gas is also decreased.
✓ When you open a can of carbonated beverage, the pressure in the soda is lowered, so the gas immediately
starts leaving the solution.
✓ The carbon dioxide stored in the soda is released, and you can see the fizzing on the surface of the liquid.
✓ If you leave an open can of soda out for a period of time, you may notice the beverage becoming flat because
of the loss of carbon dioxide.
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Solvation & Association
✓Solvation describes the interaction of solvent with dissolved molecules.
✓Both ionized and uncharged molecules interact strongly with solvent, and the strength and
nature of this interaction influence many properties of the solute, including solubility, reactivity,
and color, as well as influencing the properties of the solvent such as the viscosity and density.
✓In the process of solvation, ions are surrounded by a concentric shell of solvent.
✓Solvation is the process of reorganizing solvent and solute molecules into solvation complexes.
✓Solvation involves bond formation, hydrogen bonding, and van der Waals forces. Solvation of a
solute by water is called hydration.
✓Solvation is commonly known as dissolution.
20

Solvation
✓ Solvation is an interaction of a solute with the solvent, which leads to stabilization of the solute species in
the solution.
✓ In the solvated state, an ion in a solution is surrounded or complexed by solvent molecules.
✓ Solvated species can often be described by coordination number, and the complex stability constants.
✓ The concept of the solvation interaction can also be applied to an insoluble material, for example, solvation of
functional groups on a surface of ion-exchange resin.
✓ Solvation is, in concept, distinct from solubility. Solvation or dissolution is a kinetic process and is quantified by its
rate.
✓ Solubility quantifies the dynamic equilibrium state achieved when the rate of dissolution equals the rate
of precipitation.
✓ The consideration of the units makes the distinction clearer.
✓ The typical unit for dissolution rate is mol/s.
✓ The units for solubility express a concentration: mass per volume (mg/mL), molarity (mol/L), etc
21

Association
✓The concept was introduced by Niels Bjerrum.
✓The assembling of separate molecular entities into any aggregate, especially of oppositely charged
free ions into ion pairs or larger and not necessarily well-defined clusters of ions held together by
electrostatic attraction.
✓The term signifies the reverse of dissociation, but is not commonly used for the formation of definite
adducts by colligation or coordination.
✓Association is a chemical reaction whereby ions of opposite electrical charge come together
in solution to form a distinct chemical entity.
22

Quantitative approach to the factors influencing
solubility of drugs
✓Solubility of solids in liquids
✓Solubility of liquids in liquids
✓Solubility of gases in liquids
23

Solubility of solids in liquids
Temperature:
✓Most solids dissolve with absorption of heat and the solubility of such solids increases as the
temperature increases, e.g., solubility of NaCl, NaNO3, KNO3 in water increases with
temperature.
✓For solids which dissolve with the evolution of heat, increase in temperature causes a decrease in
solubility, e.g., solubility of Ca(OH)2 in water.
✓Effect of temperature on the solubility of solids can be represented by the use of ‘solubility curve’.
24

Solubility Curves:
✓Solubility curves are the curves drawn between the
solubility and temperature.
✓It shows the effect of temperature on the solubility of
substances.
✓The solubility curves of substances like calcium acetate
and calcium chromate shows decrease in solubility, while
those of sodium nitrate, lead nitrate shows a considerable
increase of solubility with increase in temperature.
25

✓ Many drugs behave as weak acid or weak base, so their solubility is affected by the pH of the aqueous
solvents.
✓ The ionized form of acidic or basic drug is considered as soluble whereas unionized from as insoluble.
✓ A weakly basic drug is more soluble in acidic medium and an acidic drug is more soluble in basic medium
because these can ionize properly and are insoluble in their relevant medium due to poor ionization (due to
common H+ or common OH- ).
✓ A weakly acidic drug such as Acetyl salicylic acid (Aspirin) will be more soluble in alkaline medium, since it
may ionize properly or secondly it may be converted to more soluble salt such as sodium salicylate.
✓ On the contrary, acetyl salicylic acid may be precipitated if some strong acid is added to aqueous solution of
Acetyl salicylic acid (due to common H+ ions → common ion effect).
✓ Similarly basic drug such as sulphonamide (Antibiotic) will be more soluble in acidic medium.
✓ Basic drug will be precipitated from aqueous solution, if the pH of solution is raised by the addition of strong
base (due to common OH- ions → common ion effect).
26

Particle size:
✓The particle size of the solids also affects its solubility in a given solvent.
✓Generally, a decrease in the particle size causes an increase in the solubility.
✓This is because a decrease in particle size results in increase in surface area and surface free
energy which increases solubility.
27

Molecular structure Modifications:
✓Slight modification in the molecular structure of solids may lead to marked changes in their
solubility in the given solvent.
✓For example, if a weak acid ( CH3COOH weak electrolyte, → poor soluble) is converted into
its salt (CH3COONa), its ionic dissociation in water increases markedly leading to an
increase in the interaction between the solute and the solvent which ultimately leads to an
increase in the solubility.
28

✓Solubility can also be decreased by modifications such as esterification.
Esterification
✓Chloramphenicol (antibiotic) ----------------------- → Chloramphenicol palmitate
Soluble Poor Soluble
✓Such a decrease in solubility is sometimes beneficial in pharmaceutical practice since this decrease
in solubility helps in taste masking of certain drugs such as chloramphenicol (very bitter) to
chloramphenicol palmitate (tasteless).
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Common ion effect:
• “The process in which solubility of a weak electrolyte is reduced by the addition of a strong electrolyte
which has common ion to that of weak electrolyte”.
• Ionization of sodium chloride in water can be represented by equilibrium constant expression as:
NaCl (Solid) ↔ Na+ (aq ) + Cl- (aq)
Kc = [Na+] [Cl-] / [NaCl]
HCl ionizes in water as:
HCl ↔ H+(aq) + Cl- (aq)
• On passing HCl gas through aqueous solution of NaCl , concentration of Cl- ions is increased, therefore
some of the NaCl is precipitated out to maintain the constant value of the equilibrium constant.
• This is called as common ion effect which reduces solubility.
30

Effect of complex formation:
• The apparent solubility of some solutes in a liquid may be increased or decreased by the addition of a
substance that forms a complex which is either more or less soluble.
• Solubility of iodine in water is increased by the addition of potassium iodide which forms a soluble
complex (KI3).
I2 + KI ---------------------------------→ KI3
Insoluble Soluble
• On the other hand, solubility of tetracycline is reduced when it forms complex with calcium.
Tetracycline ( antibiotic) + Ca diet ----------- → Ca-tetracycline (a complex)
Soluble Poor soluble
31

Effect of surfactants (solubilising agent):
• Solubility of poor soluble drugs may be enhanced by a technique known as micellar
solubilization, which involves the use of surfactants for increasing the solubility.
• When a surfactant having a hydro-philic (water loving) and a lipo-philic (or hydrophobic
water hating) portion is added to a liquid, it re-arranges itself to from a spherical aggregate
known as micelle.
32

• In aqueous medium, the surfactant molecule orientate in such a manner that their
hydrophilic portion faces the water and the lipophilic portion (hydrophobic) resides in the
micellar interior.
• An insoluble compound added to the surfactant liquid, enters the micelle interior and gets
solubilised.
33

• Similarly, In non- aqueous medium (e.g. oil), the surfactant molecule orientate in such a
manner that their hydrophobic portion faces the non-aqueous liquid and the hydrophilic
portion resides in the micellar interior.
• An insoluble compound ( such as water) added to the surfactant liquid, enters the micelle
interior and gets solubilised.
34

Effect of non-electrolytes on the solubility of electrolytes:
• The solubility of electrolytes in water primarily depends on the dissociation of the dissolved
molecules into ions. The ease with which the electrolyte dissociates depends on the dielectric
effect (ability of solvent to produce charge separation between positive and negative ions of an
electrolyte and keep them ionized) of the solvent, which depends on the polar nature of the
solvent.
• Addition of a water soluble non-electrolyte such as alcohol to an aqueous solution of a sparingly
soluble salt decreases the solubility of sparingly soluble electrolyte i.e. salt. This effect is due to
lowering of the dielectric effect (charge separation ability) of the solvent by the non-electrolyte,
and this in turn reduces dissociation of the salt.
35

✓Ideal solubility parameters: Temperature, pressure and surface
area
✓Solvation & Association
✓Quantitative approach to the factors influencing solubility of drugs
✓ Solubility of solids in liquids
✓ Solubility of liquids in liquids
✓ Solubility of gases in liquids
36

Solubility of liquids in liquids
• Liquid – liquid system may be divided into the following categories according to the
solution of liquids in one another.
• Completely miscible
• Practically immiscible or insoluble
• Partially miscible
• The term ‘miscible’ refers to the solubility of the components in liquid – liquid systems.
37

Complete miscibility
• In this system, liquids are completely miscible (soluble) when they are mixed in any
proportions.
• For example, polar and polar solvents such as water – alcohol, alcohol –glycerin,
water – glycerin etc. are said to be completely miscible since they mix in all
proportions.
• Similarly, non-polar and non – polar solvents are also completely miscible such as
CCl4 and Benzene.
38

Practically immiscible (insoluble):
• These liquids do not mix in any proportion.
• If they are shaken vigorously, they mix but soon form the layers on standing.
• These liquids are entirely different from each other chemically as well as polarity wise.
• For example, castor oil (organic & nonpolar) is completely immiscible with water (inorganic
& polar).
39

Partially miscible:
• These liquids are miscible to each other but to a limited extent i.e. partially.
• These liquids mix but form two layers.
• Each layer is a solution of one liquid into the other.
• Some liquid ‘A’ is dissolved into ‘B’ and some liquid ‘B’ is dissolved into liquid ‘A’.
• Both of these layers (i.e. solutions) are known as conjugate solutions.
• If such a mixture is heated, the two layers disappear and form one layer.
• The temperature at which two partially miscible liquids become completely miscible is called “critical
solution temperature or upper consulate temperature”.
40

• For example, when water and phenol are mixed
in equal quantities, they form two layers at 25OC.
• The upper layer contains solution of 95% water
+ 5% phenol, and lower layer contains solution
of 70% phenol + 30 % water.
• But at 68.4OC (critical solution temperature), two
layers disappear to form one phenol-water
solution.
41
Other examples of partially miscible liquids include;
Aniline – water, nicotine – water, triethylamine – water etc.

Solubility of gases in liquids
Effect of pressure:
• The pressure of the gas above the solution is important in gaseous solutions since this significantly affects the
solubility of the dissolved gas. Greater the pressure of the gas above the solution, greater will be the solubility of
the gas in the solution and vice versa.
• The effect of the pressure of the gas is given by the Henry ‘s law which states that ‘ in a dilute solution, the mass
of a gas which dissolves in a given volume of a liquid at a constant temperature is directly proportional to the
partial pressure of the gas.
• According to Henry’s law:
C = δ P
• Where, C is the concentration of the dissolved gas in grams per litre of the solvent, P is the partial pressure in
mm of Hg of the undissolved gas above the solution and can be obtained by subtracting the vapor pressure of the
solvent from the total pressure of the solution, δ is the proportionality constant and is referred as solubility
coefficient.
• The solubility of gases generally increase with increase in pressure and on the release of pressure, the solubility
decreases and the gas escape.
42

Effect of temperature
• Temperature also has a marked influence on the solubility of a gas in a liquid. As
the temperature increases, the solubility of most of the gases decreases owing to
the greater tendency of the gas to expand in comparison to the solvent.
• It is therefore essential that caution must be exercised when opening the container
containing the gaseous solution under elevated temperature.
43

Salting out:
• “Process in which solubility of a non - electrolyte is reduced by the addition of an electrolyte having
more affinity to the solvent than that of non-electrolyte”.
• Gases (non-electrolyte) are often liberated from the solution when an electrolyte such as sodium
chloride is added.
• It can be demonstrated by adding a small amount of sodium chloride to a carbonated solution (cold
drinks).
• The liberation of the gas is due to the attraction of salt ions to the water molecules which reduces the
availability of solvent molecules for the gas molecules due its greater affinity for water than that of
gas molecules.
44

Effect of chemical reaction:
• Chemical reaction if any between a gas and a solvent greatly increases the
solubility of the gas in the solvent.
• For example, when ammonia and Sulphur dioxide dissolve into water,
following reaction takes place.
NH3(g)+ H2O(L) ↔NH4OH(aq.) ↔NH4
+
(aq.) + OH-
(aq.)
SO2(g)+ H2O(L) ↔H2SO3 (aq.) ↔ H+
(aq.) + HSO3
-
(aq.)
45

Ideal Solutions
▪ A solution that obeys Raoult’s law for all concentrations is an ideal solution.
▪ The solution which obeys Raoult’s law over the entire range of concentration are known as
ideal solution.
▪ 2 important properties of Ideal Solution:
▪ The enthalpy of mixing of the pure components to form the solution is zero and volume of
mixing is also zero.
Δmix H = 0
Δmix V = 0
▪ It means that no heat is observed or evolved when components are mixed.
▪ Volume of Solution would be the equal to the sum of the volumes of two components mixed.
46

Ideal Solutions
▪ The solute-solute interaction and solvent-solvent interaction
is nearly equal to solute-solvent interaction
▪ Perfectly ideal solutions are rare in nature, only some
solutions show some ideal behavior.
▪ Examples of Ideal Solutions
▪ n-hexane and n-heptane
▪ Bromoethane and Chloroethane
▪ Benzene and Toluene
▪ CCl4 and SiCl4
▪ Chlorobenzene and Bromobenzene
▪ Ethyl Bromide and Ethyl Iodide
▪ n-Butyl Chloride and n-Butyl Bromide
47

Non-Ideal / Real Solutions
▪ The solutions which don’t obey Raoult’s law at every
range of concentration and at all temperatures are
called Non-Ideal Solutions.
▪ Non-ideal solutions deviate from ideal solutions and
are also known as Non-Ideal Solutions.
48

▪ The solute-solute and solvent-solvent interaction is different from that of solute-solvent
interaction
▪ The enthalpy of mixing that is, Δmix H ≠ 0, which means that heat might have released if
enthalpy of mixing is negative (Δmix H < 0) or the heat might have observed if enthalpy of
mixing is positive (Δmix H > 0)
▪ The volume of mixing that is, Δmix V ≠ 0, which depicts that there will be some expansion or
contraction in dissolution of liquids
▪ Non-ideal solutions are of two types:
▪ Non-ideal solutions showing positive deviation from Raoult’s Law
▪ Non-ideal solutions showing negative deviation from Raoult’s Law
Non-ideal solutions- characteristics
49

Positive Deviation from Raoult’s Law
• Positive Deviation from Raoult’s Law occurs when the vapour
pressure of component is greater than what is expected in Raoult’s
Law.
• For Example, consider two components A and B to form non-ideal
solutions. Let the vapour pressure, pure vapour pressure and mole
fraction of component A be PA , PA
0 and xA respectively and that of
component B be PB , PB
0 and xB respectively. These liquids will show
positive deviation when Raoult’s Law when:
• PA > PA
0 xA and PB > P0
B xB, as the total vapour pressure (PA
0 xA + P0
B xB) is
greater than what it should be according to Raoult’s Law.
• The solute-solvent forces of attraction is weaker than solute-solute and
solvent-solvent interaction that is, A – B < A – A or B – B
• The enthalpy of mixing is positive that is, Δmix H > 0 because the heat
absorbed to form new molecular interaction is less than the heat
released on breaking of original molecular interaction
• The volume of mixing is positive that is, Δmix V > 0 as the volume expands
on dissolution of components A and B.
50

Negative Deviation from Raoult’s Law
• Negative Deviation occurs when the total vapour
pressure is less than what it should be according to
Raoult’s Law. Considering the same A and B
components to form a non-ideal solution, it will show
negative deviation from Raoult’s Law only when:
• PA < PA
0 xA and PB < P0
B xB as the total vapour pressure (PA
0 xA +
P0
B xB) is less than what it should be with respect to Raoult’s
Law
• The solute-solvent interaction is stronger than solute-
solute and solvent-solvent interaction that is, A – B > A – A
or B – B
• The enthalpy of mixing is negative that is, Δmix H < 0 because
more heat is released when new molecular interactions are
formed
• The volume of mixing is negative that is, Δmix V < 0 as the
volume decreases on dissolution of components A and B. 51

Examples
Positive deviation from Raoult’s Law Negative deviation from Raoult’s Law
52
✓Chloroform and Benzene
✓Chloroform and Diether
✓Acetone and Aniline
✓Nitric Acid ( HNO3) and water
✓Acetic Acid and pyridine
✓Hydrochloric Acid ( HCl) and water
✓Acetone and Carbon disulphide
✓Acetone and Benzene
✓CCl4 and Toluene or Chloroform
✓Methyl Alcohol and Water
✓Acetone and Ethanol
✓Ethanol and Water

Raoult’s law
• Raoult’s law has been named after François-Marie Raoult, a French
chemist who while conducting an experiment found out that when
substances were mixed in a solution, the vapor pressure of the
solution decreased simultaneously.
• Raoult’s law was established in the year 1887 and is also considered
as the law of thermodynamics.
53

Raoult’s law
• Raoult’s law states that a solvent’s partial vapor pressure in a solution (or mixture) is equal or
identical to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution.
• “The vapor pressure of solution (Ps) is directly proportional to the mole fraction of solvent
(Xsolvent)”.
• Mathematically, Raoult’s law equation is written as;
Psolution = XsolventP0
solvent
Where,
Psolution = vapour pressure of the solution
Xsolvent = mole fraction of the solvent
P0
solvent = vapour pressure of the pure solvent
54

Principle in Raoult’s law
• Consider a solution of volatile liquids A and B in a container.
Because A and B are both volatile, there would be both particles
of A and B in the vapor phase.
• Hence, the vapor particles of both A and B exert partial
pressure which contributes to the total pressure above the
solution.
(Raoult’s Law)
• https://youtu.be/QRYT-QfPBK4
(Vapor pressure)
• https://youtu.be/ffBusZO-TO0 55

Factors influencing Raoult’s law
• Where Psoltuion is the vapour pressure of the solution,
Xsolvent is the mole fraction of the solvent and
Po
solvent is the vapour pressure of the pure solvent.
• The law explains that when adding a solute to a solution,
the vapour pressure of the solution gradually decreases.
• However, this observation was dependent on two
variables:
• mole fraction of the dissolved solute and
• vapour pressure of the pure solvent.
56

Basic Theory in Raoult’s law
• At a given pressure for a particular solid or liquid, there is a pressure at which the vapour of
the substance is in equilibrium with the substance in solid or liquid form.
• At that temperature, the pressure above the substance is referred as vapour pressure.
• At this equilibrium, the rate of the evaporation of solid or liquid substance is equal to the
vapour that condenses back to the solid or liquid form.
• This is the basic theory behind Raoult law. However, Raoult law works for ideal solutions.
But it also works well with solvents in a very dilute state.
• For real substances (not ideal substances), the decrease in vapour pressure is practically
greater than the value we calculate from the Raoult law.
57

Vapor and Vapor Pressure
• Vapor is the liquid molecule in gas form over the liquid surface.
• Vapor Pressure: At the particular temperature, the pressure
acted over the substance( solid or liquid) at which the Vapors
are formed then that pressure is called Vapor Pressure.
• The formation of Vapor always in Dynamic Equilibrium, means:
• The rate at which the solid or liquid is evaporated is equal to the
rate at which the liquid is condensed back to its original form.
• All Solids and liquids have their own vapor pressure.
58

Vapor Pressure of Solutions
• In a closed container at constant temperature an equilibrium vapor
pressure is established.
• Here the Dynamic Equilibrium is established.
• The picture on the left indicates that vapor molecules leave a solvent
to dilute a solution.
• The solute decreases the number of solvent molecules per unit
volume lowering the tendency for the molecules to escape into vapor.
• The vapor pressure of a liquid in Solution and in Pure solvent is much
different.
• The vapor pressure of pure solvent is decreased when the nonvolatile
solute particles are dissolved in it.
• The solute decreases the number of solvent molecules per unit
volume lowering the tendency for the molecules to escape into vapor.
59

Limitations of Raoult’s law
• The Solution which obeys Raoult’s Law is called Ideal
Solution. However the Real Solution deviates from Raoult’s
Law.
• Raoult’s Law is only applicable on the Dilute or Less
Concentrated solutions.
60

Phase
✓ A phase is the part whose physical and chemical properties are completely equal and homogenous.
✓ It is separated from other parts of the system by interfaces.
✓ A system containing water and its vapor is a two-phase system.
✓ An equilibrium mixture of ice, liquid water, and water vapor is a three phase system.
✓ Phase: It is a form of matter which is uniform throughout in chemical composition and physical state.
Examples:
✓ A system containing only liquid water is one-phase system.
✓ A system containing water and water vapour (gas) is a two phase system.
✓ A system containing liquid water, water vapour and solid ice is a three phase system.
✓ Pure substances (solid, liquid, or gas) made of one chemical species only, is considered as one phase.61

Phase
✓A phase may be gas, liquid or solid.
✓A gas or a gaseous mixture is a single phase.
✓Completely miscible liquids constitute a single phase.
✓In an immiscible liquid system, each layer is counted as a separate phase.
✓Every solid constitutes a single phase except when a solid solution is formed.
✓A solid solution is considered as a single phase.
✓Each polymorphic form constitutes a separate phase.
62

Examples of Phase
How many phases in each of the following systems?
✓Liquid water, pieces of ice and water vapor are present together.
✓ Number of phases = 3
✓Calcium Carbonate undergoes thermal decomposition.
✓ CaCO3 (s) → CaO (s) + CO2 (g)
✓A solution of NaCl in water
✓Liquid water + water vapor
✓Liquid water + water vapor + air
63

Phase Equilibria
✓Phase equilibrium is the study of the equilibrium which exists between or within
different states of matter namely solid, liquid and gas.
✓Equilibrium is defined as a stage when chemical potential of any component present in
the system stays steady with time.
✓Phase is a region where the intermolecular interaction is spatially uniform or in other
words physical and chemical properties of the system are same throughout the region.
✓Within the same state, a component can exist in two different phases such as allotropes
of an element.
✓Two immiscible compounds in same liquid state can coexist in two phases.
64

Phase Equilibria
✓Phase equilibrium has wide range of applications in industries including
production of different allotropes of carbon, lowering of freezing point of water by
dissolving salt (brine), purification of components by distillation, usage of
emulsions in food production, pharmaceutical industry etc.
✓Solid-solid phase equilibrium has a special place in metallurgy and is used to make
alloys of different physical and chemical properties.
✓For instance, melting point of alloys of copper and silver is lower than melting point
of either copper or silver.
65

The Phase Rule
✓It was first presented by Gibbs in 1875.
✓It is very useful to understand the effect of intensive variables, such as temperature, pressure, or
concentration, on the equilibrium between phases as well as between chemical constituents.
✓It is used to deduce the number of degrees of freedom (f) for a system. Sometimes called: “the
variance of the system”.
✓For every heterogeneous system in equilibrium, the sum of number of phases and degrees of freedom
is greater than the number of components by two i.e.:
F+P=C+2
F = C-P+2
66

The Phase Rule
✓To understand and define the state of a phase, knowledge of several independent variables is
required.
✓Independent variables (also called Intensive variables) are the variables that do not depend on the
volume or size of the phase, e.g. temperature, pressure, density, boiling point and concentration.
✓It states that :
✓When the equilibrium between any number of phases is influenced only by temperature, pressure
and concentration but not influenced by gravity, or electrical or magnetic forces or by surface
action then the number of Degrees of Freedom (F) of the system is related to the number of
Components (C) and of Phases (P) by the phase rule equation:
F + P = C + 2 or F = C-P+2 67

Advantages of Phase Rule
✓Provides convenient method of classification of equilibrium states of system.
✓Predict the behavior of system with changes in the intensive variables.
✓Indicate that different systems having the same number of degrees of freedom behave in the
same manner.
✓Applicable to macroscopic system.
✓It takes no account of nature of reactant and products in phase.
✓Applicable to physical and chemical equilibria.
68

Limitation of Phase rule
✓Applicable only for the system in equilibrium.
✓Applicable to a single equilibrium statẹ
✓Considers only intensive variables.
✓Considers only number of phases not quantity of phases.
✓It requires that all the phases to be present under the same conditions of temperature and
pressure.
69

Phase Diagram
✓Phase diagram (also known as Equilibrium Diagrams)
shows the multisystem state changes with the temperature,
pressure, composition and other intensive properties.
✓The simplest phase diagrams are pressure-temperature
diagrams of a single simple substance.
✓The axes correspond to the pressure and temperature.
✓The lines in the phase diagram represent two phase
systems, while The spaces between the lines represent one
phase systems.
70

Phase Diagram
✓ It is a convenient graphical representation formed by plotting the
values of intensive variables for equilibrium conditions between
two phases.
✓ It shows the properties such as mp, bp, phase transition point and
triple point.
✓ The complex city of phase diagram increase with increase in
number of component in the system.
✓ For a simple substance (one component system) phase diagram is
two dimensional plot where P & T are independent variables.
✓ The phase diagram of a two component system is a three
dimensional plot, where third axis is for composition.
✓ Three dimensional plot can also converted into two dimensional
plot by keeping one variable constant. Isobaric Isothermal.
✓ When one of the variable kept constant then phase rule equation is
reduced to:
F=C-P+1
✓ This is known as reduced phase rule.
71

One component system: The Gibbs phase rule
✓ Consider a one component system composed of a liquid with particular volume.
✓ Using the phase rule:
F = 1 - 1 + 2 = 2
the maximum number of degree of freedom for one component system
✓ Only two independent variables are required to define the system (temperature and
pressure)
✓ For a one component system comprising a liquid and its vapor.
✓ The phase rule states that:
F = 1 - 2 + 2 = 1
✓ Only one independent variable is required to define this system (either temperature
or pressure).
✓ For a one component system composed of solid, liquid, and vapor.
✓ The phase rule states that:
F = 1 - 3 + 2 = 0
✓ There are no degrees of freedom.
✓ The ice– water–vapor system is completely defined (the temperature and pressure is
fixed at a point called the triple point).
72

One component system: The phase diagram
✓ The curve OA in the phase diagram of one component system
represents the vapor pressure curve where vapor and liquid coexist in
equilibrium.
✓ The curve OB represents the melting curve where the solid and liquid
phases coexist in equilibrium.
✓ The curve OC represents the sublimation curve where the solid and
vapor phases coexist in equilibrium.
✓ The spaces between the curves represent area of one phase system.
✓ The critical point is the point on a phase diagram that indicates the
critical temperature and pressure.
✓ While the triple point represents the temperature and pressure where
all three physical states are in equilibrium. 73

Water System and Area of Phase diagram
✓ Water exist in three possible phases: ice, water, vapors.
✓ It is a one component system so maximum degrees of freedom is two, when one phase is stable at
equilibrium.
C-P+2 = 1-1+2=2
✓ Phase diagram of water is two dimensional plot where P & T are taken as axes.
✓ Areas of Phase Diagram of Water System Phase diagram is divided into three areas:
✓ Area BOC — where ice has stable existence,
✓ Area COA — where water has stable existence,
✓ Area BOA — where water vapors has stable existence.
✓ Phase Rule for this system:
F = C-P+2 = 2
✓ Degrees of freedom is two hence bivariant system.
74

Various Curves of Phase Diagram of Water System
• Melting point Curve (Curve OC),
• Vaporization curve or vapor pressure curve (Curve OA),
• Metastable equilibrium (Curve OA’),
• Sublimation Curve (Curve OB),
• Triple point O
75

Melting point Curve
(Curve OC)
• Also known as melting point curve or
freezing point curve or fusion curve.
• Represents equilibrium between ice &
water.
• It is enough to know either T or P because
other variable gets automatically fixed.
• At atmospheric pressure, ice & water can
be in equilibrium only at one temperature
i.e. at freezing point of water.
• Thus ice- water equilibrium line (Curve
OC) has only one degree of freedom
(Univariant system).
• Phase Rule: = 1-2+2 = 1
76
Vaporization Curve
(Curve OA)
• Also known as vapor pressure curve.
• Represents the equilibrium between two phases water &
vapor.
• It enough to know either T or P because other variable
gets automatically fixed.
• At any temperature, Pressure of vapor in equilibrium is
fixed in value.
• Thus water & vapor equilibrium line OA has only one
degree of freedom so univariant system.
• Phase Rule: = 1-2+2 = 1
• At higher end, curve OA terminates at point A which is
critical temperature (374C) and Pressure (218atm.) of
water.
• At this point liquid & vapor phases become
indistinguishable & merge into single fluid phase.
• Under normal conditions terminus point is O where
water freezes to form ice.

Metastable equilibrium
(Curve OA’)
• Represents the meta-stable equilibrium.
• Under some special conditions pure water
may be cooled down much below the
freezing point without forming ice.
• Thus it is possible to extend vapor
pressure curve even below freezing point
of water.
• This equilibrium can be approached by
cooling liquid water and not by heating
ice.
• Metastable vapor pressure of super cooled
liquid is higher than the vapor pressure of
ice.
77
Sublimation Curve (Curve 0B)
• Represents the condition for equilibrium
between ice and vapors.
• Shows vapor pressure of ice at different
temperature.
• In order to describe the system along line
0B either value of T or P need to be
specified.
• Because at any temperature, value of
vapor pressure of ice is fixed.

Two component systems containing liquid phases
✓ Systems containing more than one component are best discussed as condensed systems.
✓ Condensed systems are systems in which the vapour phase is ignored and only solid and liquid phases
are considered.
✓ Systems containing liquids often are classified as:
✓ Completely immiscible (such as mercury and water) (not concern)
✓ Completely miscible in all proportions (e.g. ethanol and water), (solution)
✓ Partially miscible (e.g. diethyl ether and water), (considered)
✓ For two component systems: C = 2 F = C – P+ 2 ⟹ F = 4 – P. P = 1 at least, so F is 3 at most.
✓ Three variables are required: temperature, pressure, and composition.
✓ If the pressure is fixed: C = 2 F = C – P +1 ⟹ F = 3 – P. P = 1 at least, so F is 2 at most.
✓ Only are temperature and composition are required: 78

Two component systems containing liquid phases
✓ Phase diagrams for two component systems are
commonly constructed with temperature and
composition as the coordinates.
✓ Usually the composition is expressed as mole fraction or
as percent by weight (% w/w).
79

Two component systems containing solid and liquid
phases
✓ Two component system consisting of two solids D and E brought to a
temperature above the melting points of both (point d).
✓ A one-phase system will form consisting of a liquid solution of D and E.
✓ The points of D and E represent the melting points of D and E.
✓ When the temperature fall to point c, pure solid E will form dispersed in a
solution of D and E.
✓ At point G solid D, solid E and solution phase are in mutual equilibrium
(exist together).
✓ The solid phase at this point is a finely divided two-phase dispersion of
crystalline D and E called a eutectic, and G is the eutectic point.
✓ Eutectic melts at a lower temperature than either of its pure components.
80

Eutectic System
✓ Two component system in which both the components are completely miscible in liquid phase but do
not react chemically is called a eutectic system e.g. Ag-Pb System.
✓ Eutectic Temperature and composition: for a pure substance A, the freezing point is higher and
upon increasing the conc. of B freezing point decreases to lowest value. This is called eutectic
temperature and composition at this state is called eutectic composition.
✓ Eutectic Point: is defined as the lowest melting point attained by the mixture.
81

Three component system containing liquid phases
✓ For three component systems:
✓ C = 3, P = 1 at least
✓ F =C – P + 2
✓ F = 3 - P + 2 = 5 – P
✓ so F is 4 at most
✓ Four variables are required: temperature, pressure, and two composition.
✓ If the temperature and pressure is both fixed:
✓ C = 3 F = C - P ⟹ F = 3 - P
✓ P = 1 at least, so F is 2 at most
✓ Only two composition is required.
✓ Phase diagrams are commonly constructed on equilateral triangle with three peaks
that separately stands for pure composition A, B and C 82

Ternary phase diagram
✓Phase diagrams are graphical representations of the
liquid, vapor, and solid phases that co-exist at various
ranges of temperature and pressure within a reservoir.
✓Ternary phase diagrams represent the phase behavior
of mixtures containing three components in a
triangular diagram.
83

Ternary phase diagram
✓A ternary diagram is a triangular coordinate system;
the edges of the triangle are the axes.
✓Ternary diagrams are used to plot three dependent
variables that always add up to a fixed value, for
example, to visualize the compositional variations of
rocks or minerals.
84

Critical solution temperature
✓The temperature at which complete miscibility is reached as the temperature
is raised or in some cases lowered, used of two liquids that are partially
miscible under ordinary conditions.
✓The temperature at which a mixture of two liquids, immiscible at ordinary
temperatures, ceases to separate into two phases.
✓Also called also consolute temperature.
85

Upper critical solution temperature
✓The upper critical solution temperature (UCST) or upper
consolute temperature is the critical temperature above which
the components of a mixture are miscible in all proportions.
✓The word upper indicates that the UCST is an upper bound to a
temperature range of partial miscibility, or miscibility for certain
compositions only.
✓For example, hexane-nitrobenzene mixtures have a UCST of 19 °C,
so that these two substances are miscible in all proportions
above 19 °C but not at lower temperatures.
86

Lower critical solution temperature
✓The lower critical solution temperature (LCST) or lower consolute
temperature is the critical temperature below which the
components of a mixture are miscible for all compositions.
✓The word lower indicates that the LCST is a lower bound to a
temperature interval of partial miscibility, or miscibility for certain
compositions only.
✓The phase behavior of polymer solutions is an important property
involved in the development and design of most polymer-related
processes. Partially miscible polymer solutions often exhibit two
solubility boundaries, the upper critical solution
temperature (UCST) and the lower critical solution temperature
(LCST), which both depend on the molar mass and the pressure. At
temperatures below LCST, the system is completely miscible in all
proportions, whereas above LCST partial liquid miscibility occurs.
87

✓The upper critical solution temperature, Tuc is the highest temperature at
which phase separation occurs.
✓Above the critical temperature the two components are fully miscible.
✓On the molecular level, this can be interpreted as the kinetic energy of each
molecule over coming molecular interactions that want molecules of one
type to come close together.
✓Some systems show a lower critical solution temperature, Tlc.
✓Below this temperature the two components mix in all proportions and
above which they form two phases.
✓An example is water and triethylamine. 88

✓Is the maximum temperature at which the two phase
region exists. In the case of the phenol-water system
this is 66.8°.
✓All combinations of phenol and water above this
temperature are completely miscible and yield one-
phase liquid systems.
89

Systems showing a decrease in miscibility with
rise in temperature
✓Triethylamine & Water:
✓ The solubility of liquid pairs may increase as the temperature is lowered.
✓ The system will exhibit a lower consolute temp.
✓ Below which the two members are soluble in all proportions
✓ Above which two separate layers are formed.
90

Systems showing upper and lower consolute
temperature
✓NICOTINE & WATER
✓Mixtures such as nicotine & water show both an
upper and a lower consolute temperature with an
intermediate temperature region in which the two
liquids are only partially miscible.
91

Systems with no critical solution temperature
✓The pair, ethyl ether and water, has neither an upper nor a lower consolute temperature and
shows partial miscibility over the entire temperature range at which the mixture exists.
92

Distribution law
• Distribution law or the Nernst's distribution law gives a generalization which governs the
distribution of a solute between two non miscible solvents.
• This law was first given by Nernst who studied the distribution of several solutes between
different appropriate pairs of solvents.
• 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 a:
C1/C2 = S1/S2 = KD
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. 93

Application of Distribution Law
• 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.
94

• Partition Chromatography: A paste of the mixture is applied at the top of a column of silica
soaked in water. Another immiscible solvent ( 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.
95

• 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 800º C,
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.
96

• 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 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.
97

• Determination of Association: When a substance is associated (or polymerized) in solvent A
and exists as simple molecules in solvent B, the Distribution law is modified as n√Ca/Cb = k
when n is the number of molecules which combine to form an associated molecule.
98

• Determination of Dissociation: Suppose a substance X is dissociated in aqueous layer and
exists as single molecules in ether. If x is the degree of dissociation (or ionization), the
distribution law is modified as C1 /C2 )(1-x) = K where C1 = concentration of X in benzene
C2 = concentration of X in aqueous layer The value of x can be determined from
conductivity measurements, while C1 and C2 are found experimentally. Thus the value of K
can be calculated. Using this value of K, the value of x for any other concentrations of X can
be determined.
99

• Determination of Solubility: Suppose the solubility of iodine in benzene is to be determined.
Iodine is shaken with water and benzene. At equilibrium concentrations of iodine in benzene
(Cb) and water (Cw) are found experimentally and the value of distribution coefficient
calculated.
Cb / Cw = KD Sb/ Sw = KD
where Sb = solubility in benzene; and
Sw = solubility in water.
100

Distribution Law: Limitations
• Dilute solutions: The concentration of solute must be low in two solvents. This law does not holds
good when concentrations are high.
• Constant temperature: Temperature should be kept constant throughout the experiment, since
solubility is dependent on temperature.
• Same molecular state: Solute must be in the same molecular state in both the solvent.
• Equilibrium concentration: This is achieved by shaking the mixture for longer time.
• Non-miscibility of solvent: The solvents are to be lowed for separation for a sufficient time.
101

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