$[25]$ A distillation column is used to separate a methanol $(MeOH)-$water $(H_{2}O)$ mixture into a pre$-$

dominantly methanol stream and a waste stream bf mostly water. The column feed is $500k\frac{g}{h}r$ of a

liquid with $60\%$ methanol and the rest water. The product streams leave at the top and bottom of the

distillation column. The composition of the top product $($distillate$)$ is $0\mathrm{.}9$ mass fraction methanol and

the rest water. The bottoms product flow rate is $275k\frac{g}{h},$ with unknown composition.

$($a$)[15]$ Draw the flowchart with labeling, including units, on a chosen basis.

$($b$)[10]$ Show that all mass flow rates and$/$or mass fractions can be calculated by a DOF analysis.

$($c$)[15]$ Write down the applicable material balance equations.

$($d$)[10]$ What percent of methanol in feed is lost in the bottoms product?