Antoine equation for component \(i\): \[log_{10}(P_i ^{sat}) \,= \, A_i \, – \frac{B_i}{C_i+T}\] Where \(P_i^{sat}\) is the saturation pressure, \(T\) is the temperature (most often in \(^oC\)), and \(A_i, B_i,\) and \(C_i\) are constants for a given component, \(i\).

Raoult’s Law: \[x_iP_i^{sat} \, = y_iP\] for each component \(i,\) where \(x_i\) is the liquid-phase mole fraction and \(y_i\) is the vapor phase mole fraction.

Raoult’s Law and mass balances combined \[x_i\,=\,\frac{z_i}{1+\left(\frac{V}{F}\right)\left(K_i-1\right)}\]

Where \(z_i\) is the feed mole fraction of component i, \(K_i\) is the K-factor, which is \(y_i/x_i\) for component i, \(F\) is the feed molar flow rate, and \(V\) is the vapor molar flow rate out.

Overall mass balance: \[F\,=\,V\,+\,L\] where \(F\) is the feed flow rate, \(V\) is the vapor flow rate, and \(L\) is the liquid flow rate.

Component mass balance: \[z_iF\,=\,y_iV\,+\,x_iL\] where \(z_i\) is the mole fraction of component i in the feed, \(y_i\) is the vapor mole fraction of component i, and \(x_i\) is the liquid mole fraction of component i.

Mole fractions in a liquid phase: \[\sum x_i\,=\,1\]

Mole fractions in a vapor phase:\[\sum y_i,=\,1\]

Energy Balance for an adiabatic system: \[F(H_F)\,=\,L(H_L)\, +\,V(H_V)\] where \(H_F\) is the molar enthalpy of the feed (kJ/mol), \(H_L\) is the molar enthalpy of the liquid effluent (kJ/mol), and \(H_V\) is the molar enthalpy of the vapor effluent (kJ/mol).