A gas diffuses four times as quickly as oxygen. The molecular weight of the gas is

The molar mass of oxygen ${\mathrm{M}}_2=32$

The molar mass of unknown gas is ${\mathrm{M}}_1$

The rate of diffusion of unknown gas is ${\mathrm{r}}_1$

The rate of diffusion of oxygen is ${\mathrm{r}}_2$

but ${\mathrm{r}}_1=4{\mathrm{r}}_2$

The rate law of diffusion,

$\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{M_2}{M_1}}$

$\frac{4{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{32}{M_1}}$

Square on both sides the above equation, we will get

$16=\frac{32}{{\mathrm{M}}_1}\Rightarrow {\mathrm{M}}_1=\frac{32}{16}$

$\therefore {\mathrm{M}}_1=2$

Therefore the molecular weight of unknown gas is 2g.