Phase Rule and Phase Phase Rule and Phase EquilibriaEquilibria

Phase (p):Phase (p): A form of matter that is A form of matter that is homogeneous in in

chemical composition and and physical state. . Typical phases are solid, liquid and gas. , Two Typical phases are solid, liquid and gas. , Two immiscible liquids separated by a distinct liquids separated by a distinct boundary are counted as two different phases. boundary are counted as two different phases.

Homogeneous phasesHomogeneous phases: : pure liquids or solutions pure liquids or solutions

Two phases systemsTwo phases systems: : immiscible liquids (or immiscible liquids (or solutions) , since there is a definite boundary between solutions) , since there is a definite boundary between them.them.

One phase systemOne phase system: : a mixture of gases, because the a mixture of gases, because the mixture is homogeneous and there are no bounding mixture is homogeneous and there are no bounding surfaces between the different gases in the mixture.surfaces between the different gases in the mixture.

One phase systemTwo phase systeTwo phase systemm

Number of components of a Number of components of a system (C)system (C)::

Is the smallest number of constituents by Is the smallest number of constituents by which the composition of each phase in the which the composition of each phase in the system at equilibrium can be expressed in the system at equilibrium can be expressed in the form form of of a chemical formula or equationa chemical formula or equation..

Ice , water , water vapor (3-phase system) the Ice , water , water vapor (3-phase system) the

number of components is 1 (formula is H number of components is 1 (formula is H22O). O). A mixture of salt and water is a two component A mixture of salt and water is a two component

system since both chemical species are system since both chemical species are independent & different independent & different . .

Phase Equilibria and the Phase Phase Equilibria and the Phase RuleRuleThe Phase Rule:

Relation between the effect of the least number of independent variables (temperature, pressure and concentration). upon

various phases (solid, Liquid and gaseous) that exist in an equilibrium system.

F = C – P + 2

Number of component

Degree of freedom or the

number of independent

variables

The number of phases

2 variables (temperature and pressure)

Degrees of freedom ( f )Degrees of freedom ( f )::

Number of degrees of freedom is the number Number of degrees of freedom is the number of variable conditions i.e. (temperature, of variable conditions i.e. (temperature, pressure & concentration) that must be pressure & concentration) that must be known, so that the condition of the system known, so that the condition of the system at equilibrium may be completely defined.at equilibrium may be completely defined.

The relationship between the number of The relationship between the number of phases (P), components (C) and degrees of phases (P), components (C) and degrees of freedom (F) for equilibria that are freedom (F) for equilibria that are influenced only by temperature, pressure and influenced only by temperature, pressure and concentration is given by equation (the phase concentration is given by equation (the phase rule):rule):

FF == CC -- PP + + 22 The application depends on the The application depends on the

number of components present in separate number of components present in separate systems. systems.

Phase diagramsPhase diagrams::

Represent the effects of temperature, pressure Represent the effects of temperature, pressure and composition on the phase equilibria , and composition on the phase equilibria , showing the variation of transition showing the variation of transition temperature such as boiling or melting point temperature such as boiling or melting point with pressure or compression. with pressure or compression.

Representation of the effect of three variables Representation of the effect of three variables would require three axes. This can be achieved would require three axes. This can be achieved with three-dimensional models but if one with three-dimensional models but if one variable is fixed the resulting planar diagram variable is fixed the resulting planar diagram can be regarded as a section through such a can be regarded as a section through such a model. model.

Systems containing one componentSystems containing one component

Systems containing two liquid Systems containing two liquid components.components.

Systems containing two components Systems containing two components (liquid & solid).(liquid & solid).

Systems containing three Systems containing three components.components.

Systems Containing One ComponentSystems Containing One Component

The difficulties associated with the representation The difficulties associated with the representation of 3 variables do not arise in systems containing of 3 variables do not arise in systems containing one C. one C.

The areas each correspond to a single P. The no. of The areas each correspond to a single P. The no. of degrees of F is therefore given from the equation :degrees of F is therefore given from the equation :

F =F = 1 - 1 + 2 = 2 1 - 1 + 2 = 2

((2) means that temperature & pressure can be 2) means that temperature & pressure can be varied independently within these areas. (bi-varied independently within these areas. (bi-variant)variant)

Standard phase diagram for one component system

Critical point

A

C

O

B

Vapor region

tt

tt t1t1 C tC t

System corresponding to a point that System corresponding to a point that

lies on one of the lines AO , BO, or COlies on one of the lines AO , BO, or CO,,

The number of degrees of freedom is reduced because from equation (1)

F = 1 - 2 + 2 = 1

This means that a single variable exists when equilibrium is established between 2 phases. (univariant)

Melting Point: (M.P)

The boundary BO represents the coexistence of liquid water in solid ice at various temperature and pressures.

BO therefore indicates the effect of pressure on M.P of ice

(-ve slope of BO) the M.P as the pressure .

To maintain equilibrium conditions between the two phases, the temperature & pressure must not be varied independently of each other.

Boiling PointsBoiling Points:: AO vapor pressure curve,

represents the coexistence of liquid water and water vapor under various conditions.

The T & P again cannot be varied independently.

Two phase system One phase system.

The critical temperature (374oC)(upper limit of the vapor pressure) This temperature above which it

is impossible to liquefy water vapor even if you increase the pressure.

Triple PointTriple Point: :

Point Point OO , which is the only point in , which is the only point in

the diagram where three phases maythe diagram where three phases may

coexist in equilibrium. coexist in equilibrium.

F = 1 - 3 + 2 = 0F = 1 - 3 + 2 = 0

The system is therefore invariant , The system is therefore invariant ,

i.e. any change in pressure i.e. any change in pressure

or temperature will result in an alterationor temperature will result in an alteration

of the number of phases that are present.of the number of phases that are present.

Sublimation and Sublimation Drying Sublimation and Sublimation Drying (Freeze Drying)(Freeze Drying)::

CO the sublimation pressure

curve for ice (coexistence of vapor and

solid phases in equilibrium).

A mass of ice water vapor by

heating on condition pressure is

< triple point pressure.

Important in drying compounds that are sensitive to the higher temperature usually associated with drying techniques.

Lyophilization, Gelsiccation, Freeze drying

1-It is drying by sublimation from the frozen condition , i.e. (drying of blood plasma, blood serum and penicillin).

2-Freezing the solution of the material (-l0o C to -30o C ) in suitable containers connected to a high vacuum system (0.1 - 0.3 mm Hg).

3-A partial pressure of water vapor, less than that of the material being dried, is attained .

4-water sublimes from the frozen mass until the material is desiccated.

Standard phase diagram for carbon dioxide (CO2)

Two Component Systems Containing Two Component Systems Containing Liquid PhasesLiquid Phases::

miscible partially miscible immiscible

ethyl alcohol and water water and mercuryphenol and water

Phenol and water system:

miscible Partially miscible

Two factors affecting misciblity: 1- Concentration

of phenol in

water.

2 -Temperature.

Two component systemsTwo component systems : :

Phenol

Phenol / water

water

The curve g b h c i shows limits of temperature and concentration within which two liquid phases exist in

equilibrium.

1 phase

10 % phenol 11 % phenol 24% phenol

> 63 % phenol 1 phase

Point A100% water

2 phases

water rich phasecontains water+ phenol(11%)

Phenol rich phasecontains Phenol (63%)+ water

PhenolPhenol

Point A100% water (pure water)

Point B (11 % phenol)2 phases

water rich phase& phenol rich phase

More PhenolMore Phenol

Point C ( >63% phenol) 1 phase

Completely miscible

The curve g b h c i shows limits of temperature & concentration within which two liquid phases exist in equilibrium.

The Tie LineThe Tie Line

It is always parallel to the base line It is always parallel to the base line in two component systemsin two component systems . .

All systems prepared on a tie lineAll systems prepared on a tie line,, at equilibrium, will separate into at equilibrium, will separate into

phases of constant phases of constant composition. known as composition. known as conjugate phasesconjugate phases . .

Any system represented by a point Any system represented by a point on the line bc , at 50on the line bc , at 50ooC. C. separates to give a pair of separates to give a pair of conjugate phases whose conjugate phases whose composition is composition is 11% phenol11% phenol

in water rich phase (A)in water rich phase (A) & & 63 % 63 % phenolphenol in phenol rich phase in phenol rich phase..

Importance of Tie lineImportance of Tie line::

Calculation of the composition of Calculation of the composition of each phase. each phase.

Determination of the weight of each Determination of the weight of each phases. (calculation of the phases. (calculation of the distribution of phenol (or water) distribution of phenol (or water) throughout the system as a whole. throughout the system as a whole.

bd

dc

Length

Length

B Phase ofWeight

A Phase ofWeight

• The relative weights of the two phases can be calculated using the tie line using the following formula:

The use of Tie line in calculationsThe use of Tie line in calculations::

As an example, let us suppose that we mixed 24 g As an example, let us suppose that we mixed 24 g of phenol with 76 g of water, warmed the mixture of phenol with 76 g of water, warmed the mixture to 50to 50ooC, and allowed it to reach equilibrium at this C, and allowed it to reach equilibrium at this temperature.temperature.

Weight phase A = dc = 63-24 = 39 = 3Weight phase A = dc = 63-24 = 39 = 3

weight of phase B bd 24 -11 13 1weight of phase B bd 24 -11 13 1 Weight of A= Weight of A= ¾¾ x 100= 75, wt. of B = x 100= 75, wt. of B = ¼¼ x 100= x 100=

2525 Phase A=75 gm , phase B =25 gm.Phase A=75 gm , phase B =25 gm. Amount of phenol in A=75 x 11/100= 8.25 gmAmount of phenol in A=75 x 11/100= 8.25 gm Amount of phenol in B= 25 x 63/100= 15.75 gmAmount of phenol in B= 25 x 63/100= 15.75 gm

24 gm24 gm

Application of Tie lineApplication of Tie line::

To formulate systems containing more To formulate systems containing more than one component where it may be than one component where it may be advantageous to achieve a single-phase advantageous to achieve a single-phase product. product.

Handling of solid phenol, a necrotic agent Handling of solid phenol, a necrotic agent (caustic agent), is facilitated in the (caustic agent), is facilitated in the pharmacy if a solution of phenol and water pharmacy if a solution of phenol and water is used. The most convenient formulation is used. The most convenient formulation of a single liquid phase solution was 80% of a single liquid phase solution was 80% w /v, equivalent to about 76% w / w. This w /v, equivalent to about 76% w / w. This mixture has a freezing point of about 3.5mixture has a freezing point of about 3.5ooC C

The Critical Solution Temperature: The Critical Solution Temperature: CSTCST Is the maximum temperature at which the Is the maximum temperature at which the

2-phase region exists (or upper consolute 2-phase region exists (or upper consolute temperature). In the case of the phenol-temperature). In the case of the phenol-water system, this is 66.8water system, this is 66.8ooC (point h)C (point h)

All combinations of phenol and water > All combinations of phenol and water > CST are completely miscible and yield 1-CST are completely miscible and yield 1-phase liquid systems.phase liquid systems.

Systems Showing a Decrease in Systems Showing a Decrease in Miscibility with Rise in Miscibility with Rise in TemperatureTemperature::

A few mixtures, exhibit a lower A few mixtures, exhibit a lower critical solution temperature critical solution temperature (low CST), e.g. triethylamine (low CST), e.g. triethylamine plus water. The miscibility plus water. The miscibility with in temperature. with in temperature.

In the preparation of paraldehyde In the preparation of paraldehyde enemas, (consist of a solution of enemas, (consist of a solution of paraldehyde in normal saline). paraldehyde in normal saline).

Cooling the mixture during Cooling the mixture during preparation allows more rapid preparation allows more rapid solution, and storage of enema in solution, and storage of enema in a cool place is recommended. a cool place is recommended.

Systems Showing Upper and Systems Showing Upper and Lower CSTsLower CSTsThe miscibility with

temp. in systems having a lower CST is not indefinite.

> a certain temperature miscibility starts to again

with further in temperature.

Closed-phase diagram, i.e. nicotine-water system.

Type of CST

Solubility of additive in each

component

Effect on

CST

Effect on miscibil

ity

UpperApprox. equally

soluble in both components

Lowered

Increased

UpperReadily soluble in one

component but not in the other

RaisedDecrease

d

LowerApprox. equally

soluble in both components

Raised Increased

LowerReadily soluble in one

component but not in the other

Lowered

Decreased

The Effects of Added Substances on CST:

Added of substances on Systems with

lower CST

ExamplesExamples::

If 0.1 M naphthalene is added to a mix. of phenol and water, it dissolves only in the phenol and raises the CST about 20°C

If 0.1 M KCl is added to a phenol-water mix, it dissolvesonly in water and raises the CST approximately 8°C.

Blending :

The in miscibility of two liquids due to the addition of a third substance.

Example : the formulation of solution of cresol with soap BP 1968, which

contains 50% cresol.

Cresol is only partially miscible with water, but the soap in this

preparation decreases the upper CST and produces complete miscibility at

ordinary temperature.

Addition of substanceAddition of substance That equally miscibleThat equally miscible

In 2 phasesIn 2 phases..

Two-component Systems Two-component Systems Containing Solid and Liquid Containing Solid and Liquid PhasesPhases::

Solid- liquid mixtures in which 2 Solid- liquid mixtures in which 2 components are completely miscible components are completely miscible in the liquid state and completely in the liquid state and completely immiscible as solid. immiscible as solid.

Examples of such systems are:Examples of such systems are: Salol & thymol. Salol & thymol. Salol & camphor.Salol & camphor.

Solid thymol + solid Salol

a4 b4 X4

Increasing the % of thymol in the mixture till reaching 100 %.

100%100% thymolthymol100%100% salolsalol

The phase diagram for the salolThe phase diagram for the salol

thymol systemthymol system::

(i) Single liquid phase, (ii) Region containing solid salol and a

conjugate liquid phase,

(iii) Region in which solid thymol is in equilibrium with

a conjugate liquid phase.(iv) Region in which both components are

present as pure solid phases.

Those regions containing two phases (ii,

iii, and iv) are comparable to the two-phase region of the phenol-water system.

Solid thymol + solid Salol

a4 b4 X4

F=2-2+1=1F=2-2+1=1

System is represented by point X (60% by weight of thymol in salol) temperature (50 o C)

On cooling the system, the following sequence of the phase occurs: The system remains as a single liquid until 29oC. At 29oC a minute amount of solid thymol At 25oC, (system X1) a liquid phase, a1 (53% thymol in salol) and b1 (pure solid thymol). At 20oC, (system X2) the liquid phase is a2 (45%. by weight of thymol in salol), b2 (pure solid thymol). At 15oC, (system X3) the liquid phase a3 is 37 % thymol in salol and b1 (pure solid thymol).

Below 13 Below 13 o o C the liquid phase disappears C the liquid phase disappears altogether and the system contains two altogether and the system contains two solid phases of pure salol and pure solid phases of pure salol and pure thymol. thymol.

At 10At 10ooC (point X4), the system contains C (point X4), the system contains an equilibrium of an equilibrium of a4 & b4 (pure solid a4 & b4 (pure solid thymol + pure solid salol). thymol + pure solid salol).

The lowest temperature at which The lowest temperature at which liquid phase coexists is known as liquid phase coexists is known as eutectic point.eutectic point.

In case of thymol / salol system the In case of thymol / salol system the eutectic point is 13 eutectic point is 13 o o CC ( 3 phases ( 3 phases liquid, solid salol & solid thymol)liquid, solid salol & solid thymol)

The eutectic point therefore denotes an The eutectic point therefore denotes an invariant system for, in a condensed invariant system for, in a condensed system system

F = 2 - 3 + 1 = 0. F = 2 - 3 + 1 = 0. Substances forming eutectic mixtures Substances forming eutectic mixtures

(e.g., camphor, chloral hydrate, (e.g., camphor, chloral hydrate, menthol, and betanaphthol).menthol, and betanaphthol).

If such combinations is dispensed as If such combinations is dispensed as dry powder, drying may be achieved by dry powder, drying may be achieved by the addition of an absorbent powder the addition of an absorbent powder such as kaolin or light magnesium such as kaolin or light magnesium oxide.oxide.

Phase Equilibria in Three-Phase Equilibria in Three-Component SystemComponent System In systems containing three components In systems containing three components

but only one phase,but only one phase,

F = 3 - 1 + 2 = 4F = 3 - 1 + 2 = 4

For non-condensed system. The four For non-condensed system. The four degrees of freedom are temperature, degrees of freedom are temperature, pressure & the concentration of 2 of the pressure & the concentration of 2 of the 3 components. 3 components.

For condensed & the temperature is keptFor condensed & the temperature is kept

constant, then F = 2 .constant, then F = 2 .

TT

PP

C2C2C 1C 1

constantconstant

condensedcondensed44

Ternary System with One Pair of Ternary System with One Pair of Partially Miscible LiquidsPartially Miscible Liquids::

Water and benzene are partially Water and benzene are partially miscible systemmiscible system

two-phase systemtwo-phase system . .

water saturated with water saturated with benzenebenzene

benzene saturated with benzene saturated with waterwater22 – – phasephase

systemsystem

11 - -phase systemphase system

Addition of alcohol Addition of alcohol (solvent effect(solvent effect))

Mixture = 60% B, 20%A, 20% C.

A, B & C represent water, alcohol & benzene, respectively. AC binary mixture of A and C. a & c are the limits of solubility of C in A and A in C.

waterwater benzenebenzene

AlcoholAlcohol

System (g) after reaching equilibrium, will separate into two phases, (f ) and ( i).

weight of phase f /weight of phase I = gi / fg. Mixture h, mid point of the tie line, will contain equal weights of

the two phases at equilibrium.

The curve a f d e i c, a binodal curve

(the extent of the two-phase region).

The remainder of the triangle contains one liquid

phase.

The directions of the tie lines are related to the shape

of binodal, (depends on the relative solubility of 3rd

component (alcohol) in the other 2 components).

when the added component acts equally on the other

two components to bring them into solution

binodal be symmetric & the tie lines are parallel

to the base line.

Effect of Temperature:

Changes in temperature will cause the area of immiscibility, (the binodal curve) to change.

Area of the binodal as the temperature is & miscibility is

A point is reached at which complete miscibility is obtained and the binodal vanishes.

Ternary Systems with Two or Three Ternary Systems with Two or Three Pairs of Partially Miscible LiquidsPairs of Partially Miscible Liquids::

A & C , B & C show partial miscibility. A and B are completely miscible at the temperature used.

Temperature gradually leads to a reduction in the areas of the two

binodal curves & their eventual disappearance. (c) Temperature expands the binodal curves.

At a sufficiently low temperature, they meet and fuse to form a single band of immiscibility as shown in (a).

Systems containing three pairs of Systems containing three pairs of

partially miscible liquidspartially miscible liquids

3 binodal curves meet, a central region appears in which 3 conjugate liquid phases exist in equilibrium. In this region, D, which is triangular, F = 0 ( condensed system under isothermal conditions). All systems lying within this region consist of 3 phases whose composition are always given by the points x, y & z. The only quantity that varies is the relative amounts of these 3 conjugate phases.

One phaseOne phase

33 phasesphases

22 phasesphases

XX

YYZZ

A, B, C

Arrangement of three phases:Arrangement of three phases: ItIt depends on the composition of the phasesdepends on the composition of the phases

At point D , F = 0 ??????At point D , F = 0 ??????