The feed to Column C$3$ in Figure $1\mathrm{.}8$ is given in Table $1\mathrm{.}5.$ The separation is to be altered to produce a distillate of $96$mol$\%$ pure isobutane with a recovery $($SF$)$ in the distillate of $95\%.$ Because of the sharp separation in Column C$3$ between $iC4$ and $nC4,$ assume all propane goes to the distillate and all C$5\text{'}$s go to the bottoms.

a$)$ Compute the flow rates in lbmo$\frac{l}{h}$ of each component in each of the two products leaving Column C$3.$

b$)$ What is the percent purity of the n$-$butane bottoms product?

c$)$ If the isobutane purity in the distillate is fixed at $96\%,$ what $\%$ recovery of isobutane in the distillate will maximize the $\%$ purity of normal butane in the bottoms product?

Table $1\mathrm{.}5$

bmo$\frac{l}{h}$ in Stream

$\backslash$table$[[$Component$,$Foed to C$3],[C_2{H}_6,0\mathrm{.}00],[C_3{H}_4,220],[C_4{H}_{50},175\mathrm{.}6],[n{C}_4{H}_{10},226\mathrm{.}60],[C_5{H}_{12},28\mathrm{.}10],[n_4{H}_{12},17\mathrm{.}50],[C_6,0\mathrm{.}00],[$Total$,450]]$