Final answer:
To derive the entropy of mixing from the Gibbs free energy of mixing, differentiate G with respect to temperature at constant pressure.
Step-by-step explanation:
The entropy of mix can be derived from the Gibbs free energy of mix by taking the partial derivative of the Gibbs free energy with respect to temperature. This is because Gibbs free energy, represented as G, is defined by the equation G = H - TS, where H is enthalpy, T is temperature, and S is entropy. At constant pressure and for a small temperature change, the change in Gibbs free energy (ΔG) can be related to the change in entropy (ΔS) by the equation ΔG = ΔH - TΔS. Rearranging for ΔS gives us ΔS = (ΔH - ΔG)/T. Thus, to find the entropy of mixing from the Gibbs free energy of mixing, we differentiate G with respect to temperature while holding pressure constant.
In order to derive the entropy of mix from the Gibbs free energy of mix, you would need to differentiate the Gibbs free energy with respect to temperature. This means that the correct answer is A) By taking the derivative of the Gibbs free energy with respect to temperature.