Linear partitioning in binary solutions

In a continuous binary solution, the partition coefficient, expressed as a ratio of mole fractions of one component in two phases, is linear against the composition of one of the phases (the numerator phase) if the exchange coefficient K D is constant. Linearity is found in some distilling liquids, many silicate and metal alloy melts, and many mineral pairs at high pressure. Its presence facilitates the determination and analysis of phase diagrams, calculations of Rayleigh fractionation, and applications ranging from criteria for explosive volcanism to phase equilibria in the deep interior of the Earth. The rules for linear partitioning are completely mathematical. When empirically found, linearity shows the constancy of K D and permits the inference of some thermodynamic properties of the solutions. Ideality of solutions contributes strongly to linearity, but some nonideal solutions, notably azeotropes, are routinely found to be linear. This presentation is devoted to empirical examples of linear and nonlinear partitioning, and an exploration of their causes and effects. The reasons for linearity in nonideal solutions are poorly understood.