\[\Delta G^{is} = RT\sum x_ilnx_i\] where \(\Delta G^{is}\) is the change in Gibbs free energy when two components are mixed to form an ideal solution
\(R\) = ideal gas constant
\(T\) = absolute temperature
\(x_i\) = mole fraction of component \(i\)

Excess Gibbs free energy \(G^E\) \[G^E = RT\sum x_iln\gamma_i\] where \(\gamma_i\) = activity coefficient for component \(i\)

Gibbs free energy of mixing \[\Delta G_{mix} = \Delta G^{is} + G^E\] where \(\Delta G_{mix}\) = Gibbs free energy of mixing (Gibbs free energy changes when two components are mixed)