$4\mathrm{.}30.($safety$)$ A garment to protect the wearer from toxic agents may be made of a fabric that contains an adsorbent, such as activated carbon. In a test of such a fabric, a gas stream containing $7\mathrm{.}76m\frac{g}{L}$ of carbon tetrachloride $(CCl4)$ was passed through a $7\mathrm{.}71-g$ sample of the fabric at a rate of $1\mathrm{.}0\frac{L}{m}in,$ and the concentration of $CCl4$ in the gas leaving the fabric was monitored. The run was continued for $15\mathrm{.}5$min with no $CCl4$ being detected, after which the $CCl4$ concentration began to rise.

$($a$)$ How much CCl$4$ was fed to the system during the first $15\mathrm{.}5$min of the run? How much was adsorbed? Using this information as a guide, sketch the expected concentration of $CCl4$ in the exit gas as a function of time, showing the curve from $t=0$ to $t15\mathrm{.}5$min.

$1$

$($b$)$ Assuming a linear relationship between amount of $CCl4$ adsorbed and mass of fabric, what fabric mass would be required if the feed concentration is $5m\frac{g}{L},$ the feed rate $1\mathrm{.}4\frac{L}{m}in,$ and it is desired that no CCl$4$ leave the fabric earlier than $30$min $?$