This document discusses phase equilibria and phase diagrams. It begins by defining key concepts like phases, intensive variables, and the phase rule. It then examines systems with one, two, and three components and the possible phase diagrams. For single component systems, it describes the typical temperature-pressure phase diagram and key points like the triple point. For two-component systems, it discusses liquid-liquid mixtures and solid-liquid eutectic mixtures. It finishes by briefly discussing ternary systems and how the number of degrees of freedom changes with additional components and phases present.

1. Khalid T Maaroof
MSc. Pharmaceutical sciences
School of pharmacy – Pharmaceutics department
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Online access: bit.ly/physicalpharmacy
Phase equilibria
Physical Pharmacy
10/31/2015

2. What was equilibrium?
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3. 3

4. 4

5. Phase rule
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 Coexistence of phases can only occur over a limited
range.
 phase rule is a relationship for determining the least
number of intensive variables that can be changed
without changing the equilibrium state of the system.
 P is the number of phases present
 F is termed the number of degrees of freedom
 C in represents the number of components in the system
What is intensive variable???

6. 6
 The number of degrees of freedom: is the least
number of intensive variables that must be
fixed/known to describe the system completely.
 Examples of intensive variables are: temperature,
pressure, concentration….

7. Systems Containing One Component
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8. This is the phase diagram for a typical pure substance.
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9. at higher pressure, the melting temperature would be
higher because the line between the solid and liquid
areas slopes slightly forward.
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10. Increasing pressure at constant temperature
changes liquid to solid and vice versa
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11. The same explanation for liquid vapour
boundary
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12. The point labelled as C in the phase diagrams is critical
temperature.
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 Note the process of
sublimation as shown on
the graph; below the point
T.
 Point T is called triple
point.
 Where all three lines meet,
you must have a unique
combination of temperature
and pressure where all
three phases are in

13. Normal melting and boiling points
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14. The phase diagram for water
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 In the case of water, the
melting point gets lower at
higher pressures. Why?

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16. Imagine lowering the pressure on liquid
water along the line in the diagram below.
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17. Systems Containing more than one
Component
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18. CONDENSED SYSTEMS
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 a maximum of three degrees of freedom is possible in
a two-component system.
 More components more degrees of freedom
 In two component one phase system (maximum no of
variables) F = 2 – 1 + 2 = 3
 E.g. temperature, pressure, and concentration
 we frequently choose to disregard the vapor phase
and work under normal conditions of 1 atm pressure.
 Now we can use planar figures instead of three
dimensional (this will be easier)
 condensed systems: When we only consider solid
and liquid phases

19. Two-Component Systems Containing Liquid
Phases
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The maximum
temperature at which
the two-phase region
exists is termed the
critical solution or
(upper consolute
temperature).

20. Upper and lower consulate temperatures
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21. Two-Component Systems Containing Solid
and Liquid Phases: Eutectic Mixtures
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 two components are completely miscible in the liquid
state and completely immiscible as solids,

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23. Eutectic composition
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 “contact melting”: lowest melting temperature over
a composition range.
 eutectic composition is the composition of two or
more compounds that exhibits a melting temperature
lower than that of any other mixture of the
compounds
 The primary criterion for eutectic formation is the
mutual solubility of the components in the liquid or
melt phase.
 Lidocaine and prilocaine, two local anesthetic
agents, form a 1:1 mixture having a eutectic
temperature of 18◦C

24. Phase Equilibria in Three-Component Systems
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 In systems containing three components but only one
phase.
 four degrees of freedom are temperature, pressure,
and the concentrations of two of the three
components.
 Only two concentration terms are required because the
sum of these subtracted from the total will give the
concentration of the third component.
 Temperature and pressure are considered to be

25. 25
Triangular
Diagram

26. Ternary Systems with One Pair of Partially Miscible
Liquids
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e.g. Water and
benzene + alchohol
• Alchohol provide
solvation
• binodal curve

27. Alterations of the binodal curves with
changes in temperature.
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28. Ternary Systems with Two Pairs of Partially
Miscible Liquids
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29. Ternary Systems with Three Pairs of Partially
Miscible Liquids
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F=0 Why???

30. Questions !
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