Maggumax
Phase Equilibrium: Fugacity and Equilibrium Calculations (FEC)
Phase Equilibrium: Fugacity and Equilibrium Calculations
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Relate the fugacity and the chemical potential (or the partial molar Gibbs free energy)
Use the fugacity coefficient to calculate the vapor phase fugacity
Use the activity coefficient to calculate the liquid (or solid) phase fugacity
Identify conditions when a liquid or solid mixture would form an ideal solution
Explain when Lewis-Randall versus Henry ideal solution reference states are appropriate Use the Gibbs-Duhem equation to relate activity coefficients in a mixture
Perform bubble-point and dew point calculations using Raoult's Law using complete fugacity relations (assuming known fugacity coefficients and activity coefficients) Draw and read Txy and Pxy diagrams for VLE
Use Henry's Law to calculate VLE for gases dissolved in liquids
FEC: Definition of Fugacity
Fugacity
We have already established that all of the property relations that are used for the purespecies Gibbs free energy, , also are applicable for the partial molar Gibbs free energy.
Specifically, we are interested right now in the fact that:
If we have a closed, isothermal system then and are actually constant (rather than being held constant mathematically as in a partial differential) so that this relation becomes: This relation is useful because, in order to obtain a value for we need to calculate it relative to some other value (i.e., a reference state).
If we consider the simplest case that we can think of, that is an ideal gas, we can rearrange, substitute and integrate
where the values refer to whatever the reference state is chosen to be.
There are two issues with this:
• there is not a simple choice of what the reference state should be
• at low (zero) pressure the term goes to
To alleviate these problems, mixture equilibrium relations are not built using the partial molar Gibbs free energy (or
Phase Equilibrium: Fugacity and Equilibrium Calculations
•
•
•
•
•
•
•
◦
◦
•
•
Relate the fugacity and the chemical potential (or the partial molar Gibbs free energy)
Use the fugacity coefficient to calculate the vapor phase fugacity
Use the activity coefficient to calculate the liquid (or solid) phase fugacity
Identify conditions when a liquid or solid mixture would form an ideal solution
Explain when Lewis-Randall versus Henry ideal solution reference states are appropriate Use the Gibbs-Duhem equation to relate activity coefficients in a mixture
Perform bubble-point and dew point calculations using Raoult's Law using complete fugacity relations (assuming known fugacity coefficients and activity coefficients) Draw and read Txy and Pxy diagrams for VLE
Use Henry's Law to calculate VLE for gases dissolved in liquids
FEC: Definition of Fugacity
Fugacity
We have already established that all of the property relations that are used for the purespecies Gibbs free energy, , also are applicable for the partial molar Gibbs free energy.
Specifically, we are interested right now in the fact that:
If we have a closed, isothermal system then and are actually constant (rather than being held constant mathematically as in a partial differential) so that this relation becomes: This relation is useful because, in order to obtain a value for we need to calculate it relative to some other value (i.e., a reference state).
If we consider the simplest case that we can think of, that is an ideal gas, we can rearrange, substitute and integrate
where the values refer to whatever the reference state is chosen to be.
There are two issues with this:
• there is not a simple choice of what the reference state should be
• at low (zero) pressure the term goes to
To alleviate these problems, mixture equilibrium relations are not built using the partial molar Gibbs free energy (or