Gas X has a mass of 28.02 amu and gas Y has a mass of 32 amu. Which gas will diffuse faster?

Aug 19, 2016

The two gases will almost diffuse at the same speed.

Explanation:

The root mean square velocity (${U}_{r m s}$) of a gas is found by:

${U}_{r m s} = \sqrt{\frac{3 R T}{M M}}$

where, $M M$ is the molar mass of the gas.

If you have two gases, X and Y, the ratio between their ${U}_{r m s}$ can be determined by:

$\frac{{U}_{X}}{{U}_{Y}} = \sqrt{\frac{M {M}_{Y}}{M {M}_{X}}}$

$\implies \frac{{U}_{X}}{{U}_{Y}} = \sqrt{\frac{32}{28.02}} = 1.068 \cong 1.1 \left(\text{2 significant figures}\right)$

Therefore, the two gases will almost diffuse at the same speed.