Phase Equilibria

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Phase Equilibria

• Lecture Note 14
• Physical Chemistry II, 2008
• KAIST

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Phase equilibria from phase diagrams

• Relation between phase and T, P
• T, P and Gibbs energy
• Given T,P, phase with lower G stable
• Pressure dependence of transition T
• Chemical potential
• Component flows from high potential to low
  potential
• Statistical thermodynamics expression of the
  chemical potential (in terms of q)

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23-1. Phase diagram solid-liquid-gas behavior
A point of given T, P 1) within a region one
phase, 2) on a line two phase (vapor pressure
or melting point) 3) On a point two or more
phases (triple point or critical point)
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At triple points, solid-liquid-gas coexist
Vapor pressure pressure of the gas phase in
equilibrium with solid and/or liquid phases (?)
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For a pure substance, f 3 p f degree of
freedom, p number of phases
Coexistence curve gives pressure dependence of
melting and boiling points
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A piece of cake?
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At P lower than the triple point P, solid
sublimes.At P, T higher than the critical point,
liquid and gas are not distinguishable. (fluid)
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Water is special, but not unique
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Orthobaric densities and molar entropy of
vaporization (beyond the critical T, liquid and
gas become the same phase no more boiling)
Near critical point, large fluctuation of density
due to rapid change between gas and liquid phase
critical opalescence Path can be devised to go
from gas to liquid avoiding any phase transition
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No critical points for liquid-solidMany
different solid phases possible
(I) Is normal ice, other ice phases are stable at
higher pressures
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23-2. Gibbs energy and phase diagram are related
H(solid) lt H(liquid) lt H(gas) GH-TS, at higher
T, S dominant
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Plot corresponds to a vertical path at a given T
near triple point
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The phase with a lower molar G is a stable phase
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23-3. Chemical potentials are equal for
coexisting phases of a pure substance
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Transition proceeds in the direction of
dGlt0 sign of (µg µl) and dng opposite
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Chemical potential is an intensive quantity
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Clapeyron equation slope of the two-phase curve
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Use of the Clapeyron equation
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Melting point of ice decreases with increasing
pressure
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Neglecting molar volume of liquid and applying
ideal gas assumption,
Vapor pressure P2 can be obtained given all
others in (23.13)
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Use of Clausius-Claperyon equation
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Using
Nonlinear part present
Slope is the average value in that interval
Vapor pressure of solid ammonia 146 K 195 K
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H state function
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AU-TS
N to n using
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Chemical potential from a partition function for
an ideal gas
Relative to the standard state
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Use of
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On the choice of 0 for the chemical potential

• Set the ground state energy of the electronic
  state as energy 0
• Then
• For a diatomic molecule with the usual molar and
  standard state condition
• Factor
  omitted from q of (18.39)

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