Recap on calculating the equilibrium constants using statistical thermodynamics

Recap on calculating the equilibrium constants using statistical thermodynamics 

The reactions which we have encountered, with the exception of the inter-phase reactions, take place in the solid phase, so all the components in the reaction are components of the same solid solution. 

For such a solution, the variation in volume due to the reaction is negligible, and therefore we will have  

We can express the Helmholtz energy using statistical thermodynamics, remembering that the molecules of solid are considered to be discernible molecules. If we have a population of Nj molecules of the species / which each have a molecular partition function z , then the Helmholtz energy of that species / is written as  

In this expression, the solution is taken to be perfect, because no account is taken of an enthalpy of mixing. 

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