Final answer:
To derive the entropy of mixing from the Gibbs free energy of mixing, the formula ΔG = ΔH - TΔS is used. By rearranging to solve for ΔS, entropy change can be determined if the enthalpy change of mixing and Gibbs free energy are known.
Step-by-step explanation:
To derive the entropy of mixing from the Gibbs free energy of mixing, one can use the thermodynamic relationship at constant temperature, where the change in Gibbs free energy (ΔG) is related to the change in entropy (ΔS) and change in enthalpy (ΔH) through the equation ΔG = ΔH - TΔS. To find the entropy of mixing, rearrange the equation to solve for ΔS as ΔS = (ΔH - ΔG)/T. This requires knowledge of the enthalpy change of mixing and the Gibbs free energy change of mixing, which at equilibrium is equal to zero, representing a maximum entropy state. Standard free energy of formation and standard entropy values for reactants and products are often used in these calculations.
If the temperature is known and the Gibbs free energy of mixing can be computed or obtained, the entropy change associated with the process can thus be determined. This is important as it can predict the spontaneity of a chemical reaction or mixing process, where a negative ΔG implies a spontaneous process, and hence an increase in entropy.