Question

Effusion is the process of a gas escaping into an empty container (in other words, a vacuum). Graham's law of effusion relates the relative rates of effusion for two gases to their molar masses. The rate at which a gas effuses is a measure of the root mean square velocity of the molecules.
If the average velocity of methane molecules, $C{H}_4$, is $5.00\times {10}^4{}_{\frac{cm}{8}}$ at a particular temperature and pressure, what is the average velocity of helium atoms at the same temperature and pressure?

• A. $2.50\times {10}^4{}_{\frac{cm}{8}}$
• B. $5.00\times {10}^4{}_{\frac{cm}{8}}$
• C. $1.25\times {10}^4{}_{\frac{cm}{8}}$
• D. $10.0\times {10}^4{}_{\frac{cm}{8}}$

Answer 1

The correct option is D $10.0\times {10}^4{}_{\frac{cm}{8}}$

$\frac{\text{rate of effusion of A}}{\text{rate of effusion of B}}=\frac{M_B}{M_A}$

$\frac{5.00\times {10}^{4}cm/8}{\text{rate of effusion of B}}=\sqrt{\frac{4}{16}}$

$\text{rate of effusion of B}=10\times {10}^{4}cm/8$