<P> Four thermodynamic variables which may describe the system include temperature (T), pressure (p), mole fraction of component 1 (toluene) in the liquid phase (x), and mole fraction of component 1 in the vapour phase (x). However, since two phases are in equilibrium, only two of these variables can be independent (F = 2). This is because the four variables are constrained by two relations: the equality of the chemical potentials of liquid toluene and toluene vapour, and the corresponding equality for benzene . </P> <P> For given T and p, there will be two phases at equilibrium when the overall composition of the system (system point) lies in between the two curves . A horizontal line (isotherm or tie line) can be drawn through any such system point, and intersects the curve for each phase at its equilibrium composition . The quantity of each phase is given by the lever rule (expressed in the variable corresponding to the x-axis, here mole fraction). </P> <P> For the analysis of fractional distillation, the two independent variables are instead considered to be liquid - phase composition (x) and pressure . In that case the phase rule implies that the equilibrium temperature (boiling point) and vapour - phase composition are determined . </P> <P> Liquid--vapour phase diagrams for other systems may have azeotropes (maxima or minima) in the composition curves, but the application of the phase rule is unchanged . The only difference is that the compositions of the two phases are equal exactly at the azeotropic composition . </P>

Application of phase rule in day to day life