Relations Among Partial Molar Quantities H=U+PV We can also find relations for the partial molar Gibbs Energy analogous to the Maxwell relations: Phase Equilibria: Problem Formulation For example, consider the total solution enthalpy: Since the pressure is constant: Likewise:
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Relations Among Partial Molar Quantities
H=U+PV
We can also find relations for the partial molar Gibbs Energy analogous to the Maxwell
relations:
Phase E
quili
bria:
Pro
ble
m F
orm
ula
tion
For example, consider the total solution enthalpy:
Since the pressure is constant:
Likewise:
Reduction of multicomponent phase equilibrium problem P
hase E
quili
bria:
Pro
ble
m F
orm
ula
tion
?
?
?
Multicomponent Phase Equilibria
Criterion for Chemical Equilibria:
Phase E
quili
bria:
Pro
ble
m F
orm
ula
tion
The Chemical Potential -The Criteria for Chemical Equilibrium
(See slide 24)
Multicomponent Phase Equilibria
Criterion for Chemical Equilibria:
Criterion for Thermal Equilibrium and Mechanical Equilibrium:
Chemical Potential
(Synonymous of Partial Molar Gibbs Energy)
Phase E
quili
bria:
Pro
ble
m F
orm
ula
tion
The Chemical Potential -The Criteria for Chemical Equilibrium
(See slide 24)
Closed System
For this to be true,
Similar equation applies to m species in the
system, thus, there are m different equations
like this
This is analogous to the pure species relation presented earlier:
Phase E
quili
bria:
Pro
ble
m F
orm
ula
tion
The Chemical Potential -The Criteria for Chemical Equilibrium
The Chemical Potential is an abstract concept that cannot be measured.
Driving Force
Chemical Potential
Temperature
Pressure
Identical
Relations
Mass Transport
Energy Transport
Momentum Transport
Phase E
quili
bria:
Pro
ble
m F
orm
ula
tion
The Chemical Potential -The Criteria for Chemical Equilibrium
The Chemical Potential is an abstract concept that cannot be measured.
Driving Force
Chemical Potential
Temperature
Pressure
Identical
Relations
Mass Transport
Energy Transport
Momentum Transport
T high
α Energy
Transfer T low
β
α β
T final equal for both
systems
µi high
α Mass
Transfer
of species i,
Diffusion
µi low β
Mixture
µmixture=µiα=µi
β
Phase E
quili
bria:
Pro
ble
m F
orm
ula
tion
The Chemical Potential -The Criteria for Chemical Equilibrium
Temperature and Pressure Dependence of µi
Valid for two
phases
Vapor-Liquid
Equilibrium
Liquid-Ideal
Gas Mixture
Equilibrium
Phase E
quili
bria:
Pro
ble
m F
orm
ula
tion
Exercise
Tired of studying Thermo, you come up with the idea of becoming
rich by manufacturing diamond from graphite.
To do this process at 25oC requires increasing the pressure until