A method used to calculate the variance of a heterogeneous equilibrium of a non-reactive system or process, and to establish the number of independent variables. It is calculated from:
where F is the number of thermodynamic degrees of freedom, C is the number of components, and Π is the number of phases. Detail of phase equilibria is important in mass transfer and problems are analysed in terms of the phase rule. If insufficient degrees of freedom are fixed, then the problem will be under-specified. If too many are chosen, the problem will be over-specified. For problems involving two components with two phases such as in binary distillation, then F = 2. If the pressure is fixed then only one variable remains that can be changed independently, such as temperature. The concentration of the liquid and vapour phases are then fixed. The phase rule does not apply to systems involving chemical reactions. It was deduced by American physicist Josiah Willard Gibbsv (1839–1903). A modified Gibbs’ phase rule is used for reacting species:
where n is the number of components and r is the number of independent chemical reactions. For example, in a gas reaction involving three components in which only two react (e.g. fuel with air), then there are three independent variables such as T, P, and y1, which fixes y2 and y3.