A $2$ mm thick palladium sheet of $1000 \mathrm{~mm}^{2}$ cross section is used as a diffusional membrane to purify hydrogen. The hydrogen concentration is maintained at a steady state with $\boldsymbol{c}_{\boldsymbol{h}}=1.5 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\boldsymbol{c}_{\boldsymbol{l}}=0.3 \mathrm{~kg} \mathrm{~m}^{-3}$ on the two sides of the membrane as shown in the figure below.
The rate of hydrogen purification is $\text{(in units of $\mathrm{kg} \mathrm{hr}^{-1}$ )}$ _________ $\times 10^{-6}$ $\text{(rounded off to one decimal place)}$.
Given: The diffusion coefficient of hydrogen in palladium is $1.0 \times 10^{-8} \mathrm{~m}^{2} \mathrm{~s}^{-1}$
