THEORY OF COEXISTING STATES - CALCULATION OF BINODALS

A set of differential equations is established that determine the posi tions of the tielines for phase separation at constant temperature, pr ovided the equation of state for a binary mixture is given in analytic al form. Despite the fact that a large amount of work has been done on this problem, there is little information on the general theory, exce pt for some papers that were written at the turn of the century. In mo st cases tielines ere calculated by a ''brute force'' method, i.e. aft er the problem is formulated a non-linear simultaneous equation-solvin g program is called upon, with little or no attention to the specifics of the problem on hand. It is shown that there exists a very useful r elation between the orientation of the tieline and the tangents to the binodals at each end. This relation persists near the almost pure liq uid limit despite the fact that the Helmholtz free energy is a singula r function in this case. In addition, a differential equation is given for the binodal as well as a theorem on the termination of a set of t ielines in the neighborhood of a three-phase (or triple) point. The eq uations given here are different from the Gibbs Konowalow expressions. The latter hold at constant concentration, while the equations presen ted here are at constant temperature.