Answer to Question #112373 in General Chemistry for giselle ventura

Question

How much faster is Nitrogen gas vs Oxygen gas
Use three significant figures

Answer 1

By Graham's Law of Diffusion,

Rate of diffusion is inversely proportional to the square root of the molar mass of gas.

$r\propto\frac{1}{\sqrt{M}}$

$M_{O_2}=32 \ g,M_{N_2}=28\ g.$

$\implies \frac{r_{N_2}}{r_{O_2}}=\sqrt{\frac{M_{O_2}}{M_{N_2}}}=\sqrt{\frac{32}{28}}=1.069=1.07$ (up to $3$ significant digits)

$\implies$ $r_{N_2}=1.07\times r_{O_2}$ .

So,Nitrogen gas is $1.07$ times faster than oxygen gas.