PHASE EQUILIBRIA & THE PHASE RULE: DEFINITIONS , COMPONENTS , DEGREES OF FREEDOM

1. STATES OF MATTER
PHYSICAL PHARMACY I
LEC 1 PART 2
ASSISTANT LECTURER
DR AHMAD A YOSEF
MSC PHARMACEUTICAL SCIENCES
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2. PHASE EQUILIBRIA & THE PHASE RULE
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3. Phase
diagram –
Water
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4.  Phase Equilibrium: A stable phase structure with lowest free-energy
(internal energy) of a system, and also randomness or disorder of the
atoms or molecules (entropy).
 Any change in Temperature, Composition, and Pressure causes an
increase in free energy and away from Equilibrium thus forcing a move to
another ‘state’
PHASE EQUILIBRIA & THE PHASE RULE:
DEFINITIONS
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5.  A phase is defined as any homogeneous and physically distinct part of a system
which is separated from other parts of the system by interfaces.
 A part of a system is homogeneous if it has identical physical properties and
chemical
composition throughout the part.
A phase may be gas, liquid or solid.
A gas or a gaseous mixture is a single phase.
Totally 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.
PHASE DEFINITION
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6. • Examples
1. Liquid water, pieces of ice and water vapour are present together.
The number of phases is 3 as each form is a separate phase. Ice in the system is a single
phase even if it is present as a number of pieces.
2.Calcium carbonate undergoes thermal
decomposition. The chemical reaction is: CaCO3(s) 
CaO(s) + CO2 (g)
Number of phases = 3 : This system consists of 2 solid phases, CaCO3 and CaO and one
gaseous phase, that of CO2.
3. Ammonium chloride undergoes thermal decomposition. The chemical reaction is:
 NH4Cl(s) NH3 (g) + HCl (g) Number of phases = 2
 This system has two phases, one solid, NH4Cl and one gaseous, a mixture of NH3 and
HCl.
4. A solution of NaCl in water Number of phases =1
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7.  The number of components of a system at equilibrium is the
smallest number of independently varying chemical
constituents using which the composition of each and every
phase in the system can be expressed.
COMPONENTS
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8. • Examples
 Counting the number of components
1. The sulphur system is a one component system. All the
phases, monoclinic, rhombic, liquid and vapour – can be
expressed in terms of the single constituent – sulphur.
2. A mixture of ethanol and water is an example of a two
component system. We need both ethanol and water to
express its composition.
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9. An example of a system in which a reaction occurs and an equilibrium is
established is the thermal decomposition of solid
CaCO3.
In this system, there are three distinct phases:
Solid CaCO3
Solid CaO
Gaseous CO2
Though there are 3 species present, the number of components is only two, because of the
equilibrium:
 CaCO3 (s)  CaO(s) + CO2(g)
 Any two of the three constituents may be chosen as the components.
 If CaO and CO2 are chosen, then the composition of the phase CaCO3 is expressed as
one mole of component CO2 plus one mole of component CaO.
 If, on the other hand, CaCO3 and CO2 were chosen, then the composition of the phase
CaO would be described as one mole of CaCO3 minus one mole of CO2.
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10. DEGREES OF FREEDOM (OR VARIANCE)
 The degreesof freedom or varianceof a systemis defined as
the minimum number of variables such as:
temperature
pressure
concentration
which must be fixed in order to define the system completely.
F = C  P + 2
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11. • Examples
1. A gaseous mixture of CO2 and N2.
Three variables: pressure, temperature and composition are required to define this
system. This is, hence, a trivariant system.
2. A system having only liquid water has two degrees of freedom or is bivariant.
Both
temperature and pressure need to be mentioned in order to define the system.
3. If to the system containing liquid water, pieces of ice and gas are added and
this system with 3 phases is allowed to come to equilibrium, then it is an
invariant system.
Only one variable, either temperature or pressure need to be specified in order to
define
the system.
If the pressure on the system is maintained at 1 atm, then the temperature of the
system gets automatically fixed at 0oC, the normal melting point of ice. 11

12. PHASE EQUILIBRIA & THE
PHASE RULE
 A phase diagram (Equilibrium Phase Diagram)
summarizes the conditions at which a substance exists as a
solid, liquid, or gas.
 OR : It isa “map” of the information about the control of
phase structure of a particular material system.
 Therelationships between temperature and the compositions
and the quantities of phases present at equilibrium are
represented.
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13. F = C  P + 2The phase rule
THE PHASE RULE
 J.W. Gibbs formulated the phase rule, which is a general
relation between the variance, F, the number of component,
C, and the number of phases P, at equilibrium , for a system
of any composition:
 For a system in
equilibrium
 F : degree of freedom, the least number of intensive variable
that must be fixed (known) to describe the system completely
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14.  Phase Rule relation to determine the least number of intensive
variable, that can be changed without changing the equilibrium
state of the system, or, alternately,
The least number required to define the state of the system,
which is called degree of freedom F.
 Intensive variable independent variable that do not depend on
the volume or the size, e.g.Temp., pressure
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15.  Independent chemical species which comprise the
system: These could be: Elements, Ions,
Compounds
E.g. Au-Cu system : Components → Au,
Cu Ice-water system : Component
→ H2O
Al2O3 – Cr2O3 system : Components → Al2O3, Cr2O3
 Component the smallest number of constituent by which the
composition of each phase in the system at equilibrium can be
expressed in form of chemical formula or equation
PHASE EQUILIBRIA & THE PHASE RULE
Components of a system
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16. THE NUMBER OF PHASES IN A SYSTEM IS DENOTED P
(a) A gas, or a gaseous mixture is a single phase. P=1
(b)For a solid system, an alloy of two metals is a two-phase system (P=2) if the metals
are immiscible, but a single-phase system (P=1) if they are miscible---a homogeneous
mixture of the two substances---is uniform on a molecular scale.
(c)For a liquid system, according to the solubility to decide whether a system consists of
one phase or of two.
For example, a solution of sodium chloride in water is a single phase.
A pair of liquids that are partially miscible or immiscible is a two-phase system(P=2)
Oil in water
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17. Degrees of Freedom = What you can control What the system controls
F = C + 2 P
Can control the no. of
components added and P & T
System decided how many
phases to produce given the
conditions
A WAY OF UNDERSTANDING THE GIBBS PHASE RULE:
THE DEGREES OF FREEDOM CAN BE THOUGHT OF AS THE DIFFERENCE BETWEEN
WHAT YOU (CAN) CONTROL AND
what the system controls
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18.  F : degree of freedom, the least number of intensive variable that must be
fixed (known) to describe the system completely
 Degree of freedom (or variance) F is the number of variables (T, p,
and/or composition) that can be changed independently without changing
the phases of the system
a) At the triple point:
P = 3 (solid, liquid, and
gas)
C= (water)
F=1-3+2
F = 0 (no degree of
freedom)
b) liquid-solid
curve
P=2
C=1
F= 1-2+2
F=1
One variable (T or P) can be
changed
c) Liquid
P =1 C=1
So F =1-1+2
F=2
Two variables (T and P) can be varied independently
and the system will remains a single phase 18

19. ONE-COMPONENT SYSTEMS
Phase diagram of
water
P(atm)
Critical point
374
1
=100=0O--Triple point
0.006
218
Curve O -C
Sublimatio
n
Deposition
Curve O-A
Vaporization
Condensation
Curve O -B
Melting
Freezing
F = C  P + 2
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20. F = C  P + 2
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21. PHASE DIAGRAM OF CARBON DIOXIDE
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22.  Condensed system: System in which the vapor phase is ignored
and only the solid and/or liquid phases are considered.
Two component system
 For two component system F can be 3, (3D model is needed), e.g. T,
p and concentration , usually we fix p = 1atm , the vapor phase is
neglected, and F is reduced to 2
 For three component system the pressure and temperature are fixed
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24. Phenol water phase diagram
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25. e.g. for point d (24%)
TWO COMPONENT SYSTEM CONTAINING
LIQUID PHASE
 Tie Line : bc line: The line at which the
system at equilibrium will separate into
phases of constant composition, termed
‘conjugate phases’
 Lever Rule: a way to calculate the proportions of
each phase present on a phase diagram in a two
phase field (at a given temperature and
composition).
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26. E.G. FOR POINT D (24%)
For every 10 g of liquid system
in equilibrium in point d
7.5 g phase A
2.5 g phase B
Example:
Mixed 24g phenol +76g water , T 50°C,
equilibrium
75 g phase A 25 g phase B
11% phenol 63 % phenol
0.11× 75 g=8.25 g
phenol
0.63× 25 g=15.75 g
phenol
water rich phase
contains water+ phenol11%)
Phenol rich phase
contains Phenol (63%)+ water
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27. 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.
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28. A :salol B: thymol
53%
TWO COMPONENT SYSTEM CONTAINING SOLID AND
LIQUID PHASE (EUTECTIC MIXTURES)
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