We synthisezd a new material in the lab, please design the experiments to measure $($a$)$ surface area; $($b$)$ if we measure the adsorption equlibrium conatansts for $O_2{K}_{O2}=20,$ and $K_{N2}=5,$ please calculat the adsorption selectivity of $\frac{O_2}{N_2}$ in air $($assume $20\%O_2$ and $80\%N_2$ in air$).$ Both $($a$)$ and $($b$)$ require mechanism, please show the steps in details instead of simplely giving the answers. $(25$ points$)$