Question

Prove that if the chemical potential of a substance at point 1 is μ1, and the chemical potential of the same substance is μ2 at point 2, then at constant temperature and pressure the substance will spontaneous move from point 1 to point 2 if μ1 > μ2.

Answer 1

Particles tend to move from higher chemical potential to lower chemical potential. When a ball rolls down a hill, it is moving from a higher gravitational potential (higher elevation) to a lower gravitational potential (lower elevation). In the same way, as molecules move, react, dissolve, melt, etc., they will always tend naturally to go from a higher chemical potential to a lower one, changing the particle number, which is conjugate variable to chemical potential.

At constant temperature and pressure the substance will spontaneously move from point A to point B if μA > μB and this can be explained using Gibbs–Duhem equation.This equation is useful because it relates individual chemical potentials. For example, in a binary mixture, at constant temperature and pressure, the chemical potentials of the two participants are related by