Application to binary and ternary systems

Application to binary and ternary systems 5.13.1. Binary systems 

The evaluation of partial molar volumes from the experimentally determined dependency of the molar volume on composition in binary systems is made generally using the method of intercepts. Let us consider a binary melt at constant temperature and pressure in which just one mole of the mixture is present. Then it holds 

if the dependency of the molar volume of the system on composition is known from the density measurement, it is possible to calculate the partial molar volumes of both the components according to Eqs. (5.13) and (5.14). In the graphic representation they are the intercepts, which for a given composition, cut the tangent of the molar volume versus composition plot on the y axes at X2 = 0 and X2 = 1. 

The partial molar volume of a component in the ternary system can be calculated in sections with constant ratio of two components. For instance, in the system A-B-C the partial molar volume of the component A can be calculated according to a relation similar to Eq. (5.14). Since (1 - xa) = xb + xc, Eq. (5.14) transforms to 

For excess molar volume in real ternary systems, the validity of the Redlich-Kister s (1948) general equation can be assumed. For the description of the composition dependency on the molar volume, the following equation is used 

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