Complete the following:

Introduction to Chemical Engineering

In$-$Class Problem

A distillation column has two feed streams $(F_1$ and $F_2)$ and three exiting streams $($Distillate $($D$),$ Side $($S$),$ and Bottoms $($B$)).F_1$ has a mass flow rate of $20,000l\frac{b}{h}r$ and contains $30wt\%$ hexane and $70wt\%$ octane. $F_2$ has a mass flow rate of $6,000l\frac{b}{h}r$ and contains $40wt\%$ hexane and $60wt\%$ octane. The Distillate mass flow rate is $2,000l\frac{b}{h}r.$ The hexane composition of the Distillate, Side, and Bottoms products are $80,30,$ and $0\mathrm{.}1wt\%,$ respectively. What are the Side and Bottoms streams mass flow rates?

Overall Mass Balance

$F_1+F_2=D+S+B$

$S=F_1+F_2-D-B$

$B=F_1+F_2-D-S$

$S=(z_1{F}_1+z_2{F}_2-y_0)-y_B(F_1+F_2-0-)$

$x_{S}S-x_{B}S=(z_1-x_B)F_1+(z_2-x_B)F_2-(x_9+x_B)D$

Component Balance of Hexame

$z_1{F}_1+z_2{F}_e=x_{0}D+x_{S}S+x_{B}B$

$S=\frac{z_1{F}_1+z_2{F}_2-x_{0}D-x_{B}B}{x_S}$

$S(x_5-x_B)=\frac{(2_1-x_B)F_1+(2_2-x_B)F_2-(x_0+x_B)D}{x_S-x_B}$

$1\frac{b}{h}r$

$F,20,000$

$F_{2}6000$

D $2000$

$S=$

$B$

$2_1,0\mathrm{.}30$

$22,0\mathrm{.}40$

$x_0,0\mathrm{.}80$

$x_S,0\mathrm{.}30$

$x_B,0\mathrm{.}001$