Which equation expresses the total Gibbs energy of a mixture?

The correct equation expressing the total Gibbs energy of a mixture is based on the summation of the chemical potentials of the individual components multiplied by their respective amounts. In this context, G represents the total Gibbs energy, n_A and n_B are the amounts (in moles) of components A and B, respectively, and μ_A and μ_B are the chemical potentials of those components.

This formulation is rooted in the foundational principles of thermodynamics, particularly in how the Gibbs energy is defined for a system of multiple components. It reflects the idea that the total Gibbs energy of a system is the sum of the contributions of each component's chemical potential multiplied by its number of moles, effectively capturing the energy landscape of the mixture.

This equation allows us to understand how changes in the composition of the mixture can affect the overall Gibbs energy, which is crucial for determining the direction of spontaneous processes and equilibrium conditions in chemical reactions and phase transitions.