Polar molecules interact more strongly at large distances than do nonpolar molecules, and generally form nonideal solutions.

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Polar molecules interact more strongly at large distances than do nonpolar molecules, and generally form nonideal solutions. One model for solution nonidealities in a binary mixture consisting of a nonpolar species, which we denote by A, and a polar substance, designated by the symbol B, is based on the supposition that the polar substance partially dimerizes,

2B BThus, although the mixture is considered to be a binary mixture with mole fractions 

NA NA + NB and B NB NA + NB

where N°A and N°B are the initial number of moles of A and B, respectively, it is, according to the supposition, really a ternary mixture with mole fractions

No NA + NB + NB and XB2 XB = = NB NA + NB + NB2 where, by conservation of B molecules, NB NA + NB + NB2 NB =

It is further assumed that the ternary mixture is ideal, and that the apparent nonidealities in mixture properties result from considering the A-B solution to be a binary mixture with mole fractions xi, rather than a ternary mixture with true fractions xi . Show that the apparent activity coefficients for the binary mixture that result from this model are 

7B =  = 2k/6 2 (-xA + (x + 2kxAXB + kx3)1/2) (z) +

and 8 = (2k - 1)*A + k + (x +2kxXB+ kx) / B

where k = 4Ka + 1, and Ka is the equilibrium constant for the dimerization reaction.

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