The chemical potential of a substance in a mixture is defined as the change in the Gibbs free energy of the system when one mole of the substance is added, keeping temperature, pressure, and the number of moles of other substances constant.
Mathematically,
\[
\mu_i = \left( \frac{\partial G}{\partial n_i} \right)_{T,P,n_{j \ne i}}
\]
This definition indicates that chemical potential is the partial molar Gibbs free energy, which means it is a partial molar property.
It tells us how the free energy changes with the addition of infinitesimal amounts of a component and is crucial in understanding phase equilibrium, solution chemistry, and thermodynamics.