A liquid mixture containing $40$ mol$\%$ benzene $($B$)$ and $60\%$ toluene $($T$)$ isseparated in a distillation column. The vapor leaving the top of thecolumn, which contains $95\%$benzene, is condensed and split into two equal fractions: One is takenoff as the overhead productstream, and the other $($the reflux$)$ is recycled to the top of the column.The overhead product stream contains $90\%$ of the benzene fed to thecolumn. The liquid leavingthe bottom of the column is fed to a partial reboiler, in which $45\%$ ofthe liquid is vaporized. Thevapor generated in the reboiler is returned to the bottom of thecolumn, and the residual liquid istaken off as the bottom product stream $($see flow chart diagram ofProblem $4\mathrm{.}42$ in your textbook$).$The compositions of the stream leaving the reboiler are governed bythe relation:$11=2\mathrm{.}25$where yB and xB are the mole fractions of benzene in the vapor andliquid streams, respectively.For a basis of $100$ moles fed to the column, calculate the molar flowrate of the overhead productstream, and the molar flow rates and mole fractions of benzene in thebottom product stream, thevapor stream recycled to the column from the reboiler, and the liquidstream leaving the bottom ofthe column.