Property Changes of Mixing for Ideal Gases

The ideal gas provides the reference state for the vapor phase. To set up our discussion of reference states for the liquid phase, we will review the property changes of mixing for an ideal gas as discussed in Section 6.3. Recall that a property change of mixing is defined as the difference between the total solution property and the sum of the pure species properties apportioned by the amount each species present in the mixture  

We wish to determine Aomix. mix As ix. Ag ix for an ideal gas. We will represent this case with the superscript ideal. Under the ideal gas approximation, the species occupy no volume, and we have no intermolecular forces. Therefore, 

However, there will be a positive entropy change of mixing, since the ideal gas mixture has more possible configurations (i.e., is more random) than the separated pure species. The expression for the entropy change of mixing of an ideal gas is given by Equation 

See Example 6.11 for the development of this expression for a binary mixture. To find the Gibbs energy of mixing, we apply the definition of this thermodynamic property. At constant temperature. 

From the definition of a property change of mixing, we have  

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