An algebraic formulation for an equal area rule to determine phase compositions in simple reactive systems

Equal area rules are fundamental constructs in thermodynamics for determining conditions of equilibrium. The Maxwell equal area rule (MEAR) provides saturated volumes when the two-phase isotherm/isobar cuts the van der Waals loops such that the areas above and below are equal. Another equal area rule exists for determining the phase compositions in a binary mixture when plotting the derivative of the total Gibbs energy against the composition. In this work, we show that in the determination of phase compositions in reactive systems, an equal area rule exists under the correct transformation of the mole fractions.