We’re being asked to calculate **molar mass of gas Y** if it **effuse****s half as fast as**** O_{2}**.

Recall that ** Graham's Law of Effusion** allows us to compare the rate of effusion of two gases. Graham's Law states that the rate of effusion of a gas is inversely proportional to its molar mass.

$\mathbf{rate}\mathbf{=}\frac{\mathbf{1}}{\sqrt{{\mathbf{MM}}_{\mathbf{gas}}}}$

This means that when comparing two gases:

$\overline{)\frac{{\mathbf{rate}}_{\mathbf{gas}\mathbf{}\mathbf{1}}}{{\mathbf{rate}}_{\mathbf{gas}\mathbf{}\mathbf{2}}}{\mathbf{=}}\sqrt{\frac{{\mathbf{MM}}_{\mathbf{gas}\mathbf{}\mathbf{2}}}{{\mathbf{MM}}_{\mathbf{gas}\mathbf{}\mathbf{1}}}}}$

Let's designate O_{2} as gas 2 and the gas Y as gas 1.

**rate gas Y = 0.5 (rate O _{2})**

- $\frac{{\mathbf{rate}}_{\mathbf{gas}\mathbf{}\mathbf{1}}}{{\mathbf{rate}}_{\mathbf{gas}\mathbf{}\mathbf{2}}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5}$

The molar mass of O_{2} is:

O_{2}**2** O × 16 g/mol O = __32 g/mol __

** Sum = ****32 g/mol**

Gas Y effuses half as fast as O2. What is the molar mass of gas Y?