Two systems contain water, acetone, and methyl isobutyl ketone in equilibrium at 25°C. The first system contains equal masses of the three species, and the second one contains 9.0% acetone, 21.0% water, and 70.0% MIBK by mass Let x_a.aq and x_a.org respectively, denote the mass fractions of acetone in the aqueous phase (the phase that contains most of the water in the system) and the organic phase (the phase that contains most of the MIBK), and let and x_w,org denote the mass fractions of water in the two phases.

(a) Use Figure 6.6-1 to estimate the mass and composition (component mass fractions) of each phase of the mixtures in System 1 and in System 2.

(b) Determine the distribution coefficient of acetone in the organic phase relative to the aqueous phase in each system. Ka = x_a.org/x_a.aq. If a process is being designed to extract acetone from one of the two solvents (water and MIBK) to the other one, when would a high value of Ka be desirable and when would a low value be desirable?

(c) Determine the selectivity, of acetone relative to water in the two systems, where β_aw = (mass fraction acetone/mass fraction water) _{extract phase} / (mass fraction acetone/mass fraction water) _{extract phase} what would be the value of 485w if water and MIBK were completely immiscible?

(d) Express the selectivity, β_aw in terms of the distribution coefficients of acetone and water, K_a and K_w. [Start with the formula given in part (c).] If MIBK ‘s being used to extract acetone from an aqueous phase, under what circumstances might it be important to have a very high value of even if it means that less acetone is being extracted?