Answer to Question #157687 in Physical Chemistry for Raana

Question

Derivation of Gibbs free energy

Answer 1

The source of Gibbs free energy is the Legendre transformation. The essence of it is that we have a function Z(X₁,X₂,...,X_n) and we want to shift to a new function that would have different dependent variables. Such a function is Ψ(Y₁,Y₂,...,Y_n), where Ψ = Z - X₁*(dZ/dX₁)X_i≠1 - X₂*(dZ/dX₂)X_i≠2 - ...

So we have an equation for inner energy dU = TdS - pdV. Here Z = U.

We apply this transformation and get Ψ = U - S*(dU/dS)V,n - V*(dU/dV)S,n = U - TS + pV = H - TS = G. Here Ψ is indeed Gibbs free energy. Gibbs free energy is much easier to operate and estimate ecause the new dependent variables can be measured in an experiment.