When operation of a distillation column begins, vapor is generated at the bottom of the column, flows upward through the column, and

leaves the top of the column to be condensed in a heat exchanger.

During the startup phase, all of the condensate is allowed to flow back into the top of the column as reflux where it contacts the

upward$-$flowing vapor.

When conditions in the column begin to stabilize, a valve controlling the flow of reflux to the column is opened, and a fraction of the

condensate is allowed to leave the system as product instead of re$-$entering the column as reflux. The ratio of the flow rate of

condensate returned to the column $($reflux$)$ to the product withdrawal rate is $2\mathrm{.}75.$

A mixture of $89\mathrm{.}0$ mol $\%$ ethanol and the remainder water enters the condenser at a rate of $110\mathrm{.}0lb-mo\frac{l}{h}.$

The ethanol$-$water condensate has a density of $49\mathrm{.}9l\frac{b_m}{f}{t}^3.$ When operated at steady$-$state conditions, the tank collecting the

condensate is half full, and the mean residence time in the tank is $10\mathrm{.}0$ minutes.

Using the following figure as a guide, write a general mass balance around a system consisting of the condenser, condensate tank, and

splitter.

From the information given, determine

a$.$ the product withdrawal rate at steady state

b$.$ the volume of the tank in gallons