What defines the chemical potential in terms of partial molar Gibbs energy?

The chemical potential is defined as the change in Gibbs energy of a system when an infinitesimal amount of substance is added, while keeping the pressure and temperature constant. The correct expression for this definition links the chemical potential to the partial molar Gibbs energy by showing how the Gibbs energy, G, changes with respect to the amount of substance n_J of component J.

In the provided expression, μ_J = (∂G/∂n_J)_p,T,n′, the notation indicates that we are considering the partial derivative of the Gibbs energy with respect to the number of moles of component J, while keeping the pressure, temperature, and the amounts of all other components constant (denoted by n′). This clearly shows that the chemical potential μ_J quantifies how the Gibbs energy changes with the addition of more of component J—essentially capturing the contribution of component J to the overall Gibbs energy of the system.

This fundamental definition is critical in thermodynamics and physical chemistry as it provides insight into how components interact in thermodynamic mixtures. The other choices do not accurately represent the definition of chemical potential in relation to the total Gibbs energy of a system.