Relations Among Partial Molar Quantities

H=U+PV

We can also find relations for the partial molar Gibbs Energy analogous to the Maxwell

relations:

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For example, consider the total solution enthalpy:

Since the pressure is constant:

Likewise:

Reduction of multicomponent phase equilibrium problem P

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?

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Multicomponent Phase Equilibria

Criterion for Chemical Equilibria:

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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)

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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:

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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

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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

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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

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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

graphite and diamond are in equilibrium.

The following data are available at 25oC:

Δg(25oC, 1 atm) = gdiamond – ggraphite = 2866 [J/mol]

densitydiamond= 3.51 [g/cm3]

densitygraphite= 2.26 [g/cm3]

Estimate the pressure at which these two forms of carbon are in

equilibrium at 25 oC.

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Exercise

You wish to know the melting temperature of aluminum at 100 bar.

You find that at atmospheric pressure, Al melts at 933.45 K and the

enthalpy of fusion is:

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Δhfusion = 10711 [J/mol]

Heat Capacity data are given by:

Cpl=31.748 [J/(mol K)], Cps=20.068 +0.0138T [J/(mol K)]

Take the density of solid aluminum to be 2700 [kg/m3] and liquid to

be 2300 [kg/m3].

At what temperature does Aluminum melt at 100 bar?

Consider a system at temperature T and pressure P with c species present in p phases. How

many measurable properties need to be determined (e.g., T, P, and xi) to constrain the state

of the entire system?

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Application: The Phase Rule for Nonreacting Systems

Consider a system at temperature T and pressure P with c species present in p phases. How

many measurable properties need to be determined (e.g., T, P, and xi) to constrain the state

of the entire system?

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Application: The Phase Rule for Nonreacting Systems

.

.

.

Consider a system at temperature T and pressure P with c species present in p phases. How

many measurable properties need to be determined (e.g., T, P, and xi) to constrain the state

of the entire system?

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Measurable properties (degrees of freedom) to

be determined:

This yields one constraint for each phase; the

total degrees of freedom is:

Application: The Phase Rule for Nonreacting Systems

.

.

.

Consider a system at temperature T and pressure P with c species present in p phases. How

many measurable properties need to be determined (e.g., T, P, and xi) to constrain the state

of the entire system?

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We are assuming equilibrium among all components; therefore, each component has (p-1)

restrictions due to the equality of chemical potentials.

For c components, the number of additional constraints is c(p-1)

Thus, 𝕵 = p (c - 1) + 2 – c (p - 1) = c – p + 2 Gibbs Phase Rule

Measurable properties (degrees of freedom) to

be determined:

This yields one constraint for each phase; the

total degrees of freedom is:

Application: The Phase Rule for Nonreacting Systems

.

.

.

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Homework #1 due on January 17, 2013

*Follow Dropbox Instructions *

Problems from Engineering and Chemical Thermodynamics, Milo Koretsky

Chapter 6 Problems

6.9 6.12 6.14 6.20 6.22 6.39

I will make available through Moodle: 1. Chapter #6 of Engineering and Chemical Thermodynamics, Milo

Koretsky 2. Appendices A-C