It is desired to enrich the partial pressure of hydrogen in a hydrogen$-$nitrogen gas mixture for which the partial pressures of both gases are $0\mathrm{.}1013$MPa$(1$atm$).$ It has been proposed to accomplish this by passing both gases through a thin sheet of some metal at an elevated temperature; inasmuch as hydrogen diffuses through the plate at a higher rate than does nitrogen, the partial pressure of hydrogen will be higher on the exit side of the sheet. The design calls for partial pressures of $0\mathrm{.}0709$MPa$(0\mathrm{.}7$atm$)$ and $0\mathrm{.}02026$MPa$(0\mathrm{.}2$atm$),$ respectively, for hydrogen and nitrogen. The concentrations of hydrogen and nitrogen and $C_N,$ in $mo\frac{l}{m^3})$ in this metal are functions of gas partial pressures and $p_2,$ in MPa $)$ and absolute temperature and are given by the following expressions:

Furthermore, the diffusion coefficients for the diffusion of these gases in this metal are functions of the absolute temperature as follows:

$D_H(\frac{m^2}{s})=1\mathrm{.}4{10}^{-7}$exp$(-\frac{13\mathrm{.}4\frac{kJ}{m}ol}{RT})$

$D_N(\frac{m^2}{s})=3\mathrm{.}0{10}^{-7}$exp$(-\frac{76\mathrm{.}15\frac{kJ}{m}ol}{RT})$

Is it possible to purify hydrogen gas in this manner? If so$,$ specify a temperature at which the process may be carried out, and also the thickness of metal sheet that would be required. If this procedure is not possible, then state the reason$($s$)$ why. You can compare the flux by using the equation:

$J_H=\sqrt[\phantom{2}]{3\mathrm{.}5}{J}_N$