Phase Diagrams

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Chapter 8

• Phase Diagrams

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Definitions

• Phase signifies a state of matter that is uniform
  throughout, not only in chemical composition but
  also in physical state.
• The number of phases in a system is denoted P.
• In a solution, atoms of A are surrounded by atoms
  of A and B, and any sample cut from it, however
  small. Is representative of the composition of
  the whole.
• A dispersion is uniform in the macroscopic scale
  but not on a microscopic scale, for it consists
  of grains or droplets of one substance in a
  matrix of the other.
• The ability to control the microstructure
  resulting from phase equilbria makes it possible
  to tailor the mechanical properties of the
  materials to a particular application.

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Definitions

• A constituent of a system is a chemical species
  that is present.
• A component is a chemically independent
  constituent of a system.
• The number of components, C, in a system is the
  min. of independent species necessary to define
  the composition of all phases present in the
  system.
• The variance, F, of a system is the number of
  intensive variables that can be changed
  independently without disturbing the number of
  phases in equilibrium.
• F is also the degrees of freedom for a system.
• Gibbs phase rule F C P 2

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One-component Systems

• For a one-component system (e.g. pure water), F
  3 - P.
• If there is only one phase, F 2 and both p and
  T can be varied independently without changing
  the number of phases.
• If two phases are present in equilibrium F 1,
  which means p is not freely variable if T is set,
  in fact, a liquid has a characteristic vapour
  pressure at a given T.
• When three phases are in equilibrium F 0 and
  the system is invariant.
• This special condition can only be established by
  a definite temperature and pressure that is
  characteristic of the substance and outside our
  control. (Triple point)

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Two-component Systems

• C 2 and F 4 P.
• If T is kept constant, the other remaining F are
  p and xA.
• Hence, one form of the phase diagram is a map of
  pressures and compositions at which each phase is
  stable.
• The other form is when pressure is kept constant.
  Then, the phase diagram is a map of temperatures
  and compositions at which each phase is stable.

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Vapour pressure Diagrams
For the partial pressures of the components of an
ideal solution The total vapour pressure at
some fixed temperature changes linearly with the
composition from pB to pAas xA changes from 0
to 1.
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Composition of the Vapour
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Phase Diagrams
Level Ruler la a2 lb a2
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Temperature-composition Diagrams

• Distillation of mixtures (compound A more
  volatile than compound B)

Fractional distillation The efficiency is
expressed in terms of theoretical plates. The
closer the vapour pressures of two substances,
the higher the number of theoretical plates.
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Azeotropes
Mixture is destabilized relative to the ideal
solution, A-B interactions are unfavourable. GE
is , so there may be contributions form both
enthalpy and entropy. Distillation cannot occur
after point b. e.g. Water / ethanol Boils
unchanged when the water content is 4 by mass
and the T 35 oC
Favourable interactions between A-B molecules
stabilize the liquid. GE is -. e.g. Hydrochloric
acid / water Boils unchanged when the water is
80 and T 108.6 oC.
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Immiscible Liquids

• At equilibrium, there is a tiny amount of A
  dissolved in B, and similarly a tiny amount of B
  dissolved in A.
• Total vapour pressure of the mixture is close to
  p pA pB. If the T is raised until p pex,
  boiling starts and the dissolved substances are
  purged from their solution.
• This boiling results in a vigorous agitation of
  the mixture.
• Each component is kept saturated in the other
  component.
• Purging continues as the very dilute solutions
  are replenished.

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Liquid-Liquid Phase Diagrams

• Partially-miscible liquids Liquids that do not
  mix in all proportions at all temperatures.

• A is pure, B is added slowly. Its one phase.
• At some mole fraction of B, the two liquids
  become immiscible.
• Two phases are in equilibrium with each other.
• The most abundant one consisting of A saturated
  with B.
• The minor one a trace of B saturated with A.
• The relative abundances of the two phases are
  given by the lever rule.

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Critical Solution Temperatures

• The upper critical solution temperature, Tuc, is
  the highest temperature at which phase separation
  occurs.
• Greater thermal motion overcomes any potential
  energy advantage in molecules of one type being
  close together.
• Lower critical solution temperature, Tlc, is the
  lowest temperature below which they mix in all
  proportions and above which they form two phases.
• At low temperatures two components form weak
  complexes which get disrupted at higher
  temperatures.
• Some systems may have both Tuc and Tlc.

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Distillation of Partially-miscible Liquids

• Consider a pair of liquids that are partially
  miscible and form a low-boiling azeotrope.
• This is common as both properties reflect the
  tendency of the two kinds molecules to avoid each
  other.

Tuc lt Tb at all compositions

• Distillation of a mixture of composition a1 leads
  to a vapour of composition b1.
• b1 condenses to 1F b2.
• Phase separates only if T is lowered to b3.

b1
a2
vapour
Temperature, T
b2
1F liquid
a1
2F liquid
Mole fraction of A, zA
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• Boiling occurs before two liquids are miscible.
• There is no Tuc.
• System at e1 forms 2F which persist up to boiling
  at e2.
• The vapour of this mixture is the same as the
  liquid.
• Condensing a vapour of composition e3 gives a 2F
  liquid of the same overall composition.
• At a fixed T, the mixture vaporizes and condenses
  like a single substance!

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Liquid-solid Phase Diagrams

• a1 to a2 System enters 2F region, liquid B
• Pure solid B begins to come out of solution and
  the remaining liquid becomes richer in A.
• a2 to a3 More of the solid forms. Relative
  amounts are given by the lever rule.
• a3 to a4 There is less liquid than at a3, and
  its composition is given by e. This liquid now
  freezes to give a 2F system of pure B and pure A.

• A liquid with eutectic composition freezes at a
  single temperature, without previously depositing
  solid A or solid B.
• A solid with eutectic composition melts, without
  change of composition, at the lowest T of any
  mixture.

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Reacting Systems

• A B C and C forms eutectic mixtures with
  species A and B.
• Excess B is mixed with A to form C. In the end a
  binary mixture of B and C remains.
• The only difference in the phase diagram is that
  the whole phase diagram is squeezed into
  compositions of equal amounts of A and B.