The entropy change to form an ideal gas mixture

When pure ideal gases mix at constant T and p to form an ideal gas mixture, the molar entropy change A5 (mix) = -R yt In (Eq. 11.1.9) is positive. 

Consider a pure ideal-gas phase. Entropy is an extensive property, so if we divide this phase into two subsystems with an internal partition, the total entropy remains unchanged. The reverse process, the removal of the partition, must also have zero entropy change. Despite the fact that the latter process allows the molecules in the two subsystems to intermingle without a change in T or / , it cannot be considered mixing because the entropy does not increase. The essential point is that the same substance is present in both of the subsystems, so there is no macroscopic change of state when the partition is removed. 

From these considerations, one might conclude that the fundamental reason the entropy increases when pure ideal gases mix is that different substances become intermingled. This conclusion would be mistaken, as we will now see. 

The partial molar entropy of constituent i of an ideal gas mixture is related to its partial pressure pi by Eq. 9.3.6  

Thermodynamics and Chemistry, second e6i6on,veis on 3 20 by Howard DeVoe. Latest version www.chem.umd.edu/themobook 

---