$3\mathrm{.}19b.$ Material balances: adsorption of benzene vapor on activated carbon; cocurrent operation

If the adsorption process described in Problem $3\mathrm{.}17$ took place cocurrently, calculate the minimum flow rate of activated carbon required.

Answer: $0\mathrm{.}543k\frac{g}{s}$

$3\mathrm{.}17{?}^b.$ Material balances: adsorption of benzene vapor on activated carbon

Activated carbon is used to recover benzene from a nitrogenbenzene vapor mixture. The mixture, at $306K$ and $1$atm containing $1\mathrm{.}0\%$ benzene by volume, is to be passed countercurrently at the rate of $1\mathrm{.}0\frac{m^3}{s}$ to a moving stream of activated carbon so as to remove $85\%$ of the benzene from the gas in a continuous process. The entering activated carbon contains $15c{m}^3$ of benzene vapor $($at STP$)$ adsorbed per gram of the carbon. The temperature and total pressure are maintained at $306K$ and $1$atm. Nitrogen is not adsorbed.

a$.$ Plot the equilibrium data given in the table below as $x^{\text{'}}=kg$ benzene $\frac{?}{kg}$ dry carbon, $Y^{\text{'}}=kg$ benzene $\frac{?}{kg}$ nitrogen for a total pressure of $1$atm.

b$.$ Calculate the minimum flow rate required of the entering carbon $($remember that the entering carbon contains some adsorbed benzene$).$

Answer: $0\mathrm{.}096kg$ of activated carbon$/$s

c$.$ If the carbon flow is $20\%$ above the minimum, what will be the concentrationof benzene adsorbed on the carbon leaving the process?

Answer: $0\mathrm{.}295kg$ benzene$/$kg activated carbon

d$.$ For the conditions of part $($c$),$ calculate the number of ideal stages required.

Answer: $3\mathrm{.}32$ stages

$\backslash$table$[[\backslash$table$[[$Benzene vapor adsorbed,$],[c{m}^3($STP$)/$g of carbon$]],\backslash$table$[[$mm Hg$],[($STial pressure of benzene,$]]],[15,0\mathrm{.}55],[25,0\mathrm{.}95],[40,1\mathrm{.}63],[50,2\mathrm{.}18],[65,3\mathrm{.}26],[80,4\mathrm{.}88],[100,6\mathrm{.}22]]$

The equilibrium adsorption of benzene on this activated carbon at the temperature of $306K$ is reported as follows: