$(20$ points$)$ A thin layer of palladium metal is highly permeable to fydrogen but not to other gases such as nitrogen. Thus, hydrogen can be separated from a mixture of $50$ mole percent hydrogen $($A$)$ in nitrogen $($B$)$ by passing the mixture over a palladium surface. On the other side of the palladium the hydrogen pressure is adjusted so that at the surface of the palladium next to the mixture $y_A=0\mathrm{.}20.$ If resistance to mass transfer is represented by a stagnant film $0\mathrm{.}001m$ thick, calculate theflux of hydrogen through the palladium in kgmo$\frac{l}{m^2}-s.$ The process takes place at $20C$ and $101\mathrm{.}325$kPa. The diffusivity $D_{AB}$ is $0\mathrm{.}784{10}^4\frac{m^2}{s}.$