A fresh feed stream contains liquid mixture containing $35\mathrm{.}0$mol$\%$ toluene $(T),27\mathrm{.}0$mol$\%$ xylene $($X$),$ and the remainder benzene $($B$)$ is fed to a distillation column. The fresh feed molar flow rate is $100$kmo$\frac{l}{h}.$ The bottom product contains $97\mathrm{.}0$mol$\%x$ and no $B,$ and $93\mathrm{.}0\%$ of the xylene in the feed is recovered in this stream. The overhead product is fed to a second column. The overhead product from the second column contains $5\mathrm{.}0$mol$\%T$ and no $x,$ and $96\mathrm{.}0\%$ of the benzene fed to the system is recovered in this stream. Draw and completely label a flow sheet of the process. Calculate $($i$)$ the composition of the bottoms stream from the second column, and $($ii$)$ the percentage of toluene contained in the process feed that emerges in the bottom product from the second column. $[$Bottoms stream from the second column: $n=35\mathrm{.}71$ kmo$\frac{l}{h}$;$x_{\text{B}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}=0\mathrm{.}043$mol Benzene $\frac{?}{\text{m}\text{o}\text{l}}$;$x_{\text{X}\text{y}\text{l}\text{e}\text{n}\text{e}}=0\mathrm{.}053$mol Xylene $\frac{?}{\text{m}\text{o}\text{l}}$; Fraction of toluene recovered in the bottom stream $=0\mathrm{.}923$

The feed to a separation process contains $50wt\%$ benzene, $30wt\%$ toluene, and $20wt\%$ xylene. The feed enters the process at a flow rate of $100k\frac{g}{h}.$ The overhead stream from the first unit contains $95wt\%$ benzene, $3wt\%$ toluene, and $2wt\%$ xylene. The overhead stream from the second unit contains $3wt\%$ benzene, $95wt\%$ toluene, and $2wt\%$ xylene. The flow rate of the overhead from the first unit is $52\%$ of the fresh feed flow rate. The amount of benzene in the overhead from the second unit is $75\%$ of the benzene that enters the second unit. $($a$)$ Determine the flow rates for all of the streams leaving both units. $[52,15,$ and $33k\frac{g}{h}$

It is proposed to separate $CaC{O}_3($solid$)$ from slurry via crystallization. The feed slurry contains equal mass fractions of $CaC{O}_3$ precipitate in a solution of NaOH and $H_{2}O.$ The slurry is washed with a dilute solution of $5wt\%$NaOH in $H_{2}O$ and of an equal flow rate as the slurry. The washed slurry, after leaving the unit, contains $2kg$ solution per $1kg$ of solid $(CaC{O}_3).$ The clear solution $($free of solid$)$ withdrawn from the unit can be assumed to have the same concentration in NaOH and water as the solution withdrawn with the solid crystals. On the basis of $100k\frac{g}{h}$ of feed slurry, draw and label the process flowchart and calculate the composition of sodium hydroxide in the clear solution. $[0\mathrm{.}23]$