A solution containing 30 wt. % benzene (B), 45 wt. % toluene (T) and 25 wt. % xylene (X) is fed into a distillation process as shown in the attached diagram. The overhead product from the first column contains (by wt.) 91.40 % B, 8.30% T, and 0.30 % X. The overhead product from the second column contains 4.25 % B, 91.60 % T, and 4.15 % X. One-third of the bottom product of the second column is recycled into the first column. It is also required that the benzene in the first column overhead product be 20 times that of the second column overhead product, and 2 times that of the second column bottom product. Assuming a basis of 100 kg fresh feed, carry out the following operations:
(1) Derive the simultaneous linear mass balance equations for the system using all the information provided.
(2) Solve the mass balance equations using the Excel Solver only (see example demonstrated in recitation). The formula used in each cell must be shown in the submitted work as well as the computed cell result.