1. Phase Rule and Phase Equilibria

2. Homogeneous phases: pure liquids or solutions
Phase (p):
A form of matter that is homogeneous in chemical composition and physical state. Typical phases are solid, liquid and gas. , Two immiscible liquids separated by a distinct boundary are counted as two different phases.
Homogeneous phases: pure liquids or solutions
Two phases systems: immiscible liquids (or solutions) , since there is a definite boundary between them.
One phase system: a mixture of gases, because the mixture is homogeneous and there are no bounding surfaces between the different gases in the mixture.
Two phase system
One phase system

3. Number of components of a system (C):
Is the smallest number of constituents by which the composition of each phase in the system at equilibrium can be expressed in the form of a chemical formula or equation.
Ice , water , water vapor (3-phase system) the number of components is 1 (formula is H2O).
A mixture of salt and water is a two component system since both chemical species are independent & different .

4. Phase Equilibria and the 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.

5. Phase Rule also known as Gibbs phase rule
F = C – P
Degree of freedom or the number of independent
variables
2 variables (temperature and pressure)
Number of component
The number of phases

6. Degrees of freedom ( f ):
Number of degrees of freedom is the number of variable conditions i.e. (temperature, pressure & concentration) that must be known, so that the condition of the system at equilibrium may be completely defined.
The relationship between the number of phases (P), components (C) and degrees of freedom (F) for equilibria that are influenced only by temperature, pressure and concentration is given by equation (the phase rule):
F = C - P + 2
The application depends on the number of components present in separate systems.

7. Phase diagrams:
Represent the effects of temperature, pressure and composition on the phase equilibria , showing the variation of transition temperature such as boiling or melting point with pressure or compression.
Representation of the effect of three variables would require three axes. This can be achieved with three-dimensional models but if one variable is fixed the resulting planar diagram can be regarded as a section through such a model.

8. Systems containing one component
Systems containing two liquid components.
Systems containing two components (liquid & solid).
Systems containing three components.

9. Systems Containing One Component
The difficulties associated with the representation of 3 variables do not arise in systems containing one C.
The areas each correspond to a single P. The no. of degrees of F is therefore given from the equation :
F = = 2
(2) means that temperature & pressure can be varied independently within these areas. (bi-variant)

11. B A C Standard phase diagram for one component system Critical point
Vapor region O C

12. t

13. C t t t1

14. System corresponding to a point that lies on one of the lines AO , BO, or CO,
The number of degrees of freedom is reduced because from equation (1)
F = = 1
This means that a single variable exists when equilibrium is established between 2 phases. (univariant)

15. 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.

16. Boiling 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.

17. Triple Point : Point O , which is the only point in
the diagram where three phases may
coexist in equilibrium.
F = = 0
The system is therefore invariant ,
i.e. any change in pressure
or temperature will result in an alteration
of the number of phases that are present.

18. Sublimation and Sublimation 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.

19. 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 ( 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.

20. Standard phase diagram for carbon dioxide (CO2)

21. Two Component Systems Containing Liquid Phases:
miscible
partially miscible
immiscible
ethyl alcohol and water
phenol and water
water and mercury
Phenol and water system:
Two factors affecting misciblity:
1- Concentration of
phenol in water.
2- Temperature. z
miscible
Partially miscible

22. Two component systems:
water
Phenol / water
Phenol

23. The curve g b h c i shows limits of temperature and concentration within which two liquid phases exist in equilibrium.
2 phases
1 phase
11 % phenol
Point A
100% water
10 % phenol
24% phenol
water rich phase
contains water+ phenol(11%)
> 63 % phenol
1 phase
Phenol rich phase
contains Phenol (63%)+ water

24. water rich phase& phenol rich phase
The curve g b h c i shows limits of temperature & concentration within which two liquid phases exist in equilibrium.
Point A
100% water (pure water)
Phenol
Point B (11 % phenol)
2 phases
water rich phase& phenol rich phase
More Phenol
Point C ( >63% phenol)
1 phase
Completely miscible

25. The Tie Line
It is always parallel to the base line in two component systems.
All systems prepared on a tie line,
at equilibrium, will separate into phases of constant composition. known as conjugate phases.
Any system represented by a point on the line bc , at 50oC. separates to give a pair of conjugate phases whose composition is 11% phenol
in water rich phase (A) & 63 % phenol in phenol rich phase.

26. Importance of Tie line:
Calculation of the composition of each phase.
Determination of the weight of each phases. (calculation of the distribution of phenol (or water) throughout the system as a whole.

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

29. The use of Tie line in calculations:
As an example, let us suppose that we mixed 24 g of phenol with 76 g of water, warmed the mixture to 50oC, and allowed it to reach equilibrium at this temperature.
Weight phase A = dc = = 39 = 3
weight of phase B bd
Weight of A= ¾ x 100= 75, wt. of B = ¼ x 100= 25
Phase A=75 gm , phase B =25 gm.
Amount of phenol in A=75 x 11/100= gm
Amount of phenol in B= 25 x 63/100= gm gm

30. Application of Tie line:
To formulate systems containing more than one component where it may be advantageous to achieve a single-phase product.
Handling of solid phenol, a necrotic agent (caustic agent), is facilitated in the pharmacy if a solution of phenol and water is used. The most convenient formulation of a single liquid phase solution was 80% w /v, equivalent to about 76% w / w. This mixture has a freezing point of about 3.5oC

31. The Critical Solution Temperature: CST
Is the maximum temperature at which the 2-phase region exists (or upper consolute temperature). In the case of the phenol-water system, this is 66.8oC (point h)
All combinations of phenol and water > CST are completely miscible and yield 1-phase liquid systems.

32. Systems Showing a Decrease in Miscibility with Rise in Temperature:
A few mixtures, exhibit a lower critical solution temperature (low CST), e.g. triethylamine plus water. The miscibility with in temperature.
In the preparation of paraldehyde enemas, (consist of a solution of paraldehyde in normal saline).
Cooling the mixture during preparation allows more rapid solution, and storage of enema in a cool place is recommended.

33. Systems Showing Upper and Lower CSTs
The 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.

34. Solubility of additive in each component
The Effects of Added Substances on CST:
Effect on miscibility
Effect on CST
Solubility of additive in each component
Type of CST
Increased
Lowered
Approx. equally soluble in both components
Upper
Decreased
Raised
Readily soluble in one component but not in the other
Lower

35. Added of substances on Systems with lower CST

36. Examples:
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 dissolves
only in water and raises the CST approximately 8°C.

37. 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.

38. Addition of substance
That equally miscible
In 2 phases.

39. Two-component Systems Containing Solid and Liquid Phases:
Solid- liquid mixtures in which 2 components are completely miscible in the liquid state and completely immiscible as solid.
Examples of such systems are:
Salol & thymol.
Salol & camphor.

41. 100% salol
100% thymol
Increasing the % of thymol in the mixture till reaching 100 %.

42. The phase diagram for the salol­ thymol system:
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.
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.

43. F=2-2+1=1

44. On cooling the system, the following sequence of the phase occurs:
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). z

45. Below 13 o C the liquid phase disappears altogether and the system contains two solid phases of pure salol and pure thymol.
At 10oC (point X4), the system contains an equilibrium of a4 & b4 (pure solid thymol + pure solid salol).
The lowest temperature at which liquid phase coexists is known as eutectic point.
In case of thymol / salol system the eutectic point is 13 o C ( 3 phases liquid, solid salol & solid thymol)

46. The eutectic point therefore denotes an invariant system for, in a condensed system
Substances forming eutectic mixtures (e.g., camphor, chloral hydrate, menthol, and betanaphthol).
If such combinations is dispensed as dry powder, drying may be achieved by the addition of an absorbent powder such as kaolin or light magnesium oxide.

47. Phase Equilibria in Three-Component System
In systems containing three components but only one phase,
F = = 4
For non-condensed system. The four degrees of freedom are temperature, pressure & the concentration of 2 of the 3 components.
For condensed & the temperature is kept
constant, then F = 2 . T
constant 4 P
condensed
C 1 C2

48. Ternary System with One Pair of Partially Miscible Liquids:
Water and benzene are partially miscible system
two-phase system.
benzene saturated with water
2 – phase
system
water saturated with benzene
Addition of alcohol (solvent effect)
1- phase system

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

50. 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.

51. 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.

52. 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.

53. 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.

54. Ternary Systems with Two or Three Pairs 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).

55. Systems containing three pairs of partially 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.

56. One phase
2 phases
3 phases X
A, B, C Y Z

57. Arrangement of three phases: It depends on the composition of the phases
At point D , F = 0 ??????