Question

How many times as fast does helium (He) effuse compared to oxygen?

Answer 1

The rate of effusion of helium is always about twice that of oxygen.

Step-by-step explanation:

Recall Graham's law of effusion:

`\displaystyle (r_1)/(r_2) = \sqrt{\frac{\mathcal{M}_2}{\mathcal{M}_1}}`

Where r are the rates of effusion and M are the respective molecular weights.

Let r₁ be the effusion rate of helium and r₂ be the effusion rate of oxygen. Hence, M₁ = 8.00 g/mol and M₂ = 32.00 g/mol.

Substitute:

`\displaystyle \begin{aligned}(r_1)/(r_2) & = \sqrt{\frac{(32.00\text{ g/mol})}{(8.00\text{ g/mol})}} \\ \\ & = √(4.00) \\ \\ & = 2.00 \end{aligned}`

Solving for r₁ yields:

`\displaystyle \begin{aligned} (r_1)/(r_2) & = 2.00\\ \\ r_1 & = 2.00r_2\end{aligned}`

Hence, the rate of effusion of helium is always about twice that of oxygen. This is expected, as helium is smaller than oxygen.