Gibbs free energy per mole for a pure substance is equal to the

The chemical potential is nothing but partial molar gibbs free energy (since the partial molar functions tells about the change in total molar property with change in composition(moles) we consider partial molar functions as intensive properties),
$${\mu _i} = \left( {\frac{{\partial nG}}{{\partial {n_i}}}} \right)T,P,{n_j}$$
When there is only one component ,G(total molar gibbs free energy) becomes independent of composition(intensive property ) so the equation becomes $${\mu _i} = G\left( {\frac{{\partial {n_I}}}{{\partial {n_i}}}} \right)T,P,{n_j}$$
Hence, $${\mu _i} = G$$