(Solved): Problem 2: An equimolar liquid mixture of benzene and toluene is fed to a distillation column. The ...

Problem 2: An equimolar liquid mixture of benzene and toluene is fed to a distillation column. The vapor leaving the top of the column is \( 97 \% \) benzene. The vapor is completely condensed and split into 2 equal streams - the distillate and the reflux streams (reflux ratio \( =1 \) ). The recovery of benzene in the distillate stream is \( 89.2 \% \). Some of the liquid leaving the bottom of the tower is recycled back into the tower as a vapor using a partial reboiler. \( 45 \% \) of the liquid stream entering the partial reboiler is vaporized and recycled back to the column. The liquid out of the reboiler is the final liquid product stream. The composition of the liquid/vapor streams leaving the reboiler is given by the following equation: \[ \frac{\frac{y_{b v}}{\left(1-y_{b v}\right)}}{\frac{y_{b l}}{\left(1-y_{b l}\right)}}=2.25 \] Where \( y_{b v} \) is mole fraction of benzene in vapor and \( y_{b l} \) is mole fraction of benzene in liquid. If the feed to the distillation tower is \( 100 \mathrm{~mol} / \mathrm{s} \), 1. Sketch the problem (10 points) 2. Label all streams (10 points) 3. Write out the material balance table (10 points) 4. Write the general material balance (for each control volume used) (4 points) 5. Decide which terms stay, and which are zero (for each control volume used) (6 points) 6. Write out the specific balances for each control volume (10 points) 7. Degree of Freedom Analysis - Count the possible number of unknowns, number of knowns, and remaining unknowns (10 points) 8. Write down all independent equations you would need to solve for all the variables in the material balance table ( 40 points)