Question

Are $\Delta G = RT \ln{\frac{Q}{K}}$ and $\Delta S = -\frac{RT\ln{\frac{Q}{K}}-q_p}{T}$ legitimate relations?

Answer 1

While messing around with ΔG=ΔG⊖+RTlnQΔG=ΔG⊖+RTln⁡Q and ΔG⊖=−RTlnKΔG⊖=−RTln⁡K, I found this relation:

ΔG=RTlnQKΔG=RTln⁡QK

which helped me clarify how ΔGΔG is affected by changes in QQ, but I wanted to make sure that it is actually true before I rely on it for such things.

Also, would this mean that:

ΔS=−RTlnQK−ΔHTΔS=−RTln⁡QK−ΔHT

and therefore, at constant pressure:

ΔS=−RTlnQK−qpTΔS=−RTln⁡QK−qpT

holds true? That is, that change in entropy can be increased by essentially adding product, or is that cancelled out by the heat exchange

Answer 2

Let's consider the special case of an ideal gas. If your development is valid in general, then it must work for that special case. In your equation ΔG=RTlnQKΔG=RTln⁡QK, what are the initial and final thermodynamic equilibrium states, according to your understanding....
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