Answer
a) See Solution
b) $J=4.35\times10^{-17}\frac{mol}{s}$
c) $t=0.6s$
Work Step by Step
a) $\frac{n}{V}=\frac{P}{RT}=\frac{21278.3Pa}{(8.314\frac{J}{mol\cdot K})(20^oC+273K)}=8.7\frac{mol}{m^3}$
$P=0.21\times101325Pa=21278.3Pa$
b) $J=DA\frac{C_1-C_2}{\Delta x}=(1.0\times10^{-5}\frac{m^2}{s})(2\times10^{-9}m^2)\frac{8.7\frac{mol}{m^3}-4.35\frac{mol}{m^3}}{2\times10^{-3}m}$
$=4.35\times10^{-17}\frac{mol}{s}$
c) $t=\frac{\bar{C}}{\Delta C}\frac{(\Delta x)^2}{D}$
$t=\frac{\frac{8.7\frac{mol}{m^3}-4.35\frac{mol}{m^3}}{2}}{8.7\frac{mol}{m^3}-4.35\frac{mol}{m^3}}\frac{(2\times10^{-3})^2}{(1.0\times10^{-5}\frac{m^2}{s})}=0.6s$