Question

From a certain apparatus, the diffusion rate of hydrogen has an average value of $28.7$ $c{m}^3$ $s^{-1}$. The diffusion of another gas under the same conditions is measured to have an average rate of $7.2$ $c{m}^3$ $s^{-1}$. The gas is:

• A. nitrogen
• B. helium
• C. argon
• D. oxygen

Answer 1

The correct option is D oxygen

According to Graham's law of diffusion, $\frac{r_1}{r_2}=\sqrt{\frac{{\rho }_2}{{\rho }_1}}$ or $\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}$

Here, $r_1=$diffusion rate of hydrogen $=28.7c{m}^3{s}^{-1}$.

$r_2=$diffusion rate of unknown gas$=7.2c{m}^3{s}^{-1}$

$M_1=$molecular mass of hydrogen $=2$g

$\therefore \frac{28.7}{7.2}=\sqrt{\frac{M_2}{2}}$ or $M_2={\left(\frac{28.7}{7.2}\right)}^2=32$g

$32$g is molecular mass of oxygen.