Minimum Solvent and Countercurrent Extraction of Acetone. An aqueous feed solution of 1000 kg/h containing 23.5 wt % acetone and 76.5 wt % water is being extracted in a countercurrent multistage extraction system using pure methylisobutyl ketone solvent at 298–299 K. The outlet water raffinate will contain 2.5 wt % acetone. Use equilibrium data from Appendix A.3.

a. Calculate the minimum solvent that can be used. [Hint: In this case, the tie line through the feed L₀ represents the condition for minimum solvent flow rate. This gives V_1min. Then, draw lines L_NV_1min and L₀V_N+1 to give the mixture point M_min and the coordinate x_AMmin. Using Eq. (27.4-4), solve for VN+_1min, the minimum value of the solvent flow rate V_N+1.]

b. Using a solvent flow rate of 1.5 times the minimum, calculate the number of theoretical stages.