Beyond Margules

Similarly, we can derive the analogous equation for a ternary asymmetric solution by summing expressions (10.103) for a mixture of three asymmetric binary solutions of the same three components  

The brackets here show the original three asymmetric binary solutions we have mixed. Derivation of Equation (10.111) by series expansion shows that there is actually a seventh term on the right side, a constant, which is often arbitrarily set to zero. 

Kress (2003) uses the system CO-O2 to illustrate the problem in a striking fashion. A naive consideration of the energetics of mixing of these two gases would result in a near-zero enthalpy of mixing and an entropy of mixing based on Equation (7.15) 

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Figure 13.28. Vapor-liquid equilibria of some azeotropic and partially miscible liquids, (a) Effect of pressure on vapor-liquid equilibria of a typical homogeneous azeotropic mixture, acetone and water, (b) Uncommon behavior of the partially miscible system of methylethylketone and water whose two-phase boundary does not extend byond the y = j line, (c) x-y diagram of a partially miscible system represented by the Margules equation with the given parameters and vapor pressures P = 3,. = 1 atm the broken line is not physically significant but is represented by the equation, (d) The same as (c) but with different values of the parameters here the two-phase boundary extends beyond the y=x line.

For unsymmetrical systems beyond the capabilities of the van Laar equations, the Scatchard-Hamer equations, although less convenient, are better. If Va = Vb, they reduce to the Margules equations, while if Aab/Aba = Va/Vb, they reduce to those of van Laar. Carlson and Col-bum (5) consequently suggest that the ratio of Va/Vb may be taken as a guide as to which of the equations are applicable. For systems that cannot be handled by any of these, the more complex equations suggested by Wohl (35) may be tried. 

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