Question

For a ternary solution at constant T and P, the composition dependence of molar property M is given by: M = x1M1 + x2M2 + x3M3 + x1 x2 x3C where M1, M2, and M3 are the values of M for pure species 1, 2, and 3, and C is a parameter independent of composition. Determine expressions for M¯1,M¯2, and M¯3 by application of Eq. (10.7). As a partial check on your results, verify that they satisfy the summability relation, Eq. (10.11). For this correlating equation, what are the M¯i at infinite dilution?

Answer 1

Answer:

$M_{i} = M_{i} + C_{xjxk} (1-2x_{i})$ ...1

$M^{\alpha } = M_{i} + CX_{xjxk}$          ...2

Explanation:

The ternary constant is given by the following equation:

The symbol XiXi, where XX is an extensive property of a homogeneous mixture and the subscript ii identifies a constituent species of the mixture, denotes the partial molar quantity of species ii defined by

$M_{i} = [\frac{d(nM)}{dn_{i} }]_{P,t,n,j}$

This is the rate at which property  X  changes with the amount of species  i  added to the mixture as the temperature, the pressure, and the amounts of all other species are kept constant.  A partial molar quantity is an intensive state function.  Its value depends on the temperature, pressure, and composition of the mixture.

In a multi phase system (in this case, a ternary system), the components resolved give:

$M_{i} = M_{i} + C_{xjxk} (1-2x_{i})$

and $M^{\alpha } = M_{i} + CX_{xjxk}$