In Ex. 15.2 a plausibility argument was developed from the LLE equilibrium equations to demonstrate that positive deviations from ideal-solution behavior are conducive to liquid/liquid phase splitting.

(a) Use one of the binary stability criteria to reach this same conclusion.

(b) Is it possible in principle for a system exhibiting negative deviations from ideality to form two liquid phases?

Example 15.2

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For the case described, to a good approximation, of - 1 Substitution into the equilibrium equations, Eqs. (15.6), gives: xfr - xf and 1- xf = (1- xf) r and solution for the mole fractions yields the approximate expressions: Alternatively, solution for the infinite-dilution activity coefficients gives: 1-xf (C) (D) 1- x Equations (A) and (B) provide order-of-magnitude estimates of equilibrium com- positions from two-parameter expressions for GF/RT, where the y° are usually related to the parameters in a simple way. Equations (C) and (D) serve the opposite function; they provide simple explicit expressions for y in relation to measurable equilibrium compositions. Equations (C) and (D) show that positive deviations from ideal-solution behavior promote LLE: 1 y° ->1 and y The extreme example of binary LLE is that of complete immiscibility of the two species. When xf = = 0, y and y are unity, and Eqs. (15.6) therefore require: Yf = r = 0 Strictly speaking, no two liquids are completely immiscible. However, actual solu- bilities may be so small (e.g., for some hydrocarbon/water systems) that the ideal- izations xf = x = 0 provide suitable approximations for practical calculations (Ex. 15.7).