For an ideal solution: \[H = x_AH_A + x_BH_B\] where \(H\) is the enthalpy (kJ/mol) of the binary solution, \(x_A\) and \(x_B\) are mole fractions of the two components, and \(H_A\) and \(H_B\) are the molar enthalpies (kJ/mol) of the pure components at the same temperature as the enthalpy of the solution.

A non-ideal solution can be represented as: \[H = x_AH_A + x_BH_B + \alpha x_Ax_B\] where \(\alpha\) is a non ideal parameter. \[\Delta H_{mix} = H – x_AH_A – x_BH_B = \alpha x_Ax_B\] where \(\Delta H_{mix}\) is the heat of mixing at constant temperature. \[\Delta H_{mix} = H^E\] where \(H^E\) is the excess enthalpy.

Modified Raoult’s Law: \[x_i\gamma_iP_i^{sat} = y_iP\] where \(x_i\) is the liquid phase mole fraction of component \(i\), 

\(\gamma_i\) is the activity coefficient of component \(i\), 

\(P_i^{sat}\) is the saturation pressure of component \(i\), 

\(y_i\) is the vapor phase mole fraction of component \(i\), and 

\(P\) is pressure.