The stability condition of phase equilibrium for various concentration variables

The stability conditions of phase equilibrium for various concentration variables are educed according to thermodynamic principle. When a system with k components arrives at stable equilibrium, if the mole number n_i or the mole fraction y_i(=n_i/n_k) or molality m_i= n_i/(n_kM_k)] of component i(i = 1,2,...,k − 1) are elected as concentration variables, thermodynamic theory is able to confirm that the sign of every order determinant composed of the second-order partial differential of chemical potential with respect to these concentration variables is positive; if the mole fraction x_i(= n_i/n) or mass fraction w_i(= n_iM_i/W are elected as the concentration variables, thermodynamic theory is only able to confirm that the sign of (k−1) order determinant is positive; if molarity c_i(= n_i/V are elected as the concentration variables, thermodynamic theory is not able to confirm the sign of every order determinant.