# Thermodynamic Phases

Okay Sir Chet Got it

Sir Chet here in this example it says ,For n moles of a constant composition mixture and integration is at constant composition. Does that mean we cant use this equation of fugacity coefficient for a system where there is change in composition occurring ?

Also, We know that Partial molar Gibbs energy for species i in solution is equal to RT times the
##ln\hat {\mathbf \phi_i } ## , and according to equation of partial molar property , partial molar property of a species i varies with the changes in composition of species i , hence ##ln\hat {\mathbf \phi_i } ## should also change with change in composition, But then this attached example talks about constant composition . I know Im missing something here, would you please help me out with this?

Chestermiller
Mentor
View attachment 267758

Sir Chet here in this example it says ,For n moles of a constant composition mixture and integration is at constant composition. Does that mean we cant use this equation of fugacity coefficient for a system where there is change in composition occurring ?
No. It means that this equation applies at any specified composition.
Also, We know that Partial molar Gibbs energy for species i in solution is equal to RT times the
##ln\hat {\mathbf \phi_i } ## , and according to equation of partial molar property , partial molar property of a species i varies with the changes in composition of species i , hence ##ln\hat {\mathbf \phi_i } ## should also change with change in composition, But then this attached example talks about constant composition . I know Im missing something here, would you please help me out with this?
As I said, this equation applies at any specific composition of the gas mixture. But, of course, it would give different values of the fugacity coefficient of a species for different mixture concentrations, temperatures, and pressures. Do you understand how it would be used in practice?

I would love to see an example , if you could tell me or just provide me a reference/link .

Chestermiller
Mentor
I would love to see an example , if you could tell me or just provide me a reference/link .
Suppose you have a mixture of gases, with specified mole fractions of these species, and you want to experimentally determine the fugacity coefficient for one of these species at the temperature and pressure of the mixture. Can you devise an experimental way of doing that using this equation?

I tried , but cannot think of any experimental way . I guess my domain of knowledge is restricted to theoretical part .

Chestermiller
Mentor
I tried , but cannot think of any experimental way . I guess my domain of knowledge is restricted to theoretical part .
What you would do is prepare 2 samples of the gas with n moles total in each. The number of moles of species i in each sample would then be ##n_{i}=nx_{i}##. In one of these samples you would then add a small amount of species i so ##n_{i}=nx_{i}+\delta##. You would then compress each of these samples at temperature T from low pressure to pressure P, and measure ##nZ_{i}=\frac{PV}{RT}## at each intermediate pressure along the way. Then, from the two samples at each pressure along the way, you would evaluate ##\bar{Z_i}=\frac{\Delta nZ_{i}}{\delta}## between the two samples. Then you would use these values to evaluate the integral.

Rahulx084