Solutions to diffusion equation.

a$.$ Fick's First Law, Steady$-$State Diffusion. Purification of hydrogen from a gas mixture will be an important process if we are to realize the benefits of a hydrogen economy. The textbook briefly mentions that thin sheets of palladium $($Pd$)$ can be used as membranes to purify hydrogen gas from a mixture in which it is present with other gas species such as nitrogen, oxygen and water vapor. A schematic of the situation is shown in Figure $2,$ reproduced from Fig. $6\mathrm{.}4$ of the textbook. Assuming that the Pd sheet has a thickness of $5mm$ and a cross$-$sectional area of $0\mathrm{.}5m^2,$ compute the number of $kg$ of hydrogen per hour that would pass through the palladium membrane, assuming that the concentration on this high and low pressure sides are $C_A=2\mathrm{.}0k\frac{g}{m^3}$ and $C_B=0\mathrm{.}4k\frac{g}{m^3},$ respectively, and that the diffusivity for hydrogen is $D=1\mathrm{.}7{10}^{-8}\frac{m^2}{s}.$

Figure $2$: $($a$)$ Steady$-$state diffusion across a thin plate. $($b$)$ A linear concentration profile for the diffusion situation in $($a$).$ Reproduced from Fig. $6\mathrm{.}4$ in the textbook.