Answer
$t=0.987s$
$8.1\times10^{-8}$
Work Step by Step
$t=\frac{\bar{C}}{\Delta C}\frac{(\Delta x)^2}{D}$
$\Delta C=\frac{C_1-C_2}{2}=\frac{1.00\frac{mol}{m^3}-0.50\frac{mol}{m^3}}{2}=0.25\frac{mol}{m^3}$
$t=\frac{1.5\frac{mol}{m^3}}{2\times0.50\frac{mol}{m^3}}\frac{(25\times10^{-6}m)^2}{95\times10^{-11}\frac{m^2}{s}}=0.987s$
$v_{rms}=\sqrt{\frac{3kT}{m}}=\sqrt{\frac{3(1.38\times10^{-23}\frac{J}{K})(20^oC)}{(75)(1.66\times10^{-27})}}=312.14\frac{m}{s}$
$\frac{v_D}{v_{rms}}=\frac{\frac{25\times10^{-6}m}{0.987s}}{312.14\frac{m}{s}}=8.1\times10^{-8}$
