$11\mathrm{.}8$ Nitrogen dioxide, $N{O}_2,$ produced by a thermal process for fixation of nitrogen is to be removed

from a dilute mixture with air by adsorption on silica gel in a continuous countercurrent adsorber.

The gas entering the adsorber at the rate of $0\mathrm{.}126k\frac{g}{s}$ contains $1\mathrm{.}5\%N{O}_2$ by volume, and $90\%$ of

the $N{O}_2$ is to be removed. Operation is to be isothermal at $25C,1$ std atm. The entering gel will be

free of $N{O}_2.$ The equilibrium adsorption isotherm at this temperature is given by the following data

$[$Foster and Daniels, Ind. Eng. Chem., $43,986(1951)]$;

$($a$)$ Calculate the minimum weight of gel required per hour.

$($b$)$ For twice the minimum gel rate, calculate the number of transfer units required.

$($c$)$ A superficial air rate of $0\mathrm{.}407k\frac{g}{m^2}*s$ is to be used. Assume that the characteristics of the

gel are the same as those described in Illustration $11\mathrm{.}6.$ Modify the gas mass$-$transfer coefficient of

Illustration $11\mathrm{.}6$ so that it will apply to the transfer of $N{O}_2$ rather than water. Modify the solid$-$phase

mass$-$transfer coefficient to apply for $N{O}_2$ on the assumption that the transfer in the pores of the

solid is by molecular diffusion through the gas filling the pores. The diffusivity of $N{O}_2$ in air is

estimated to be $1\mathrm{.}36{10}^{-5}\frac{m^2}{s}$ at $25C,1$ std atm.

Estimate the value of $H_{\text{i}\text{O}\text{G}},$ and calculate the corresponding height of the adsorber.

Ams: $3m.$