Question

The rate of diffusion of hydrogen is about:
A. One half that of He
B. 1.4 times that of He
C. Twice that of He
D. Four times that of He

Answer 1

Hint- In order to deal with this question we will use the basic concept of chemistry which states that the rate of diffusion is inversely proportional to the square root of molar mass. So we will compare the rate of diffusion by the help of molar masses of hydrogen and helium.

Complete answer:
Formula used- ${\displaystyle \frac{r_{H_2}}{r_{He}}}=\sqrt{{\displaystyle \frac{M_{He}}{M_H}}}$
Hydrogen gas exists as a diatomic molecule $$H_2$$ . However, helium gas exists as monatomic He.
Let rate of diffusion of hydrogen be $R_1$ And rate of diffusion of helium be $$R_2$$
We know that, The rate of diffusion is inversely proportional to the square root of molar mass
${\displaystyle \frac{R_1}{R_2}}=\sqrt{{\displaystyle \frac{M_2}{M_1}}}$
Where M is molar mass.
So the relation between the rate of diffusion of hydrogen and helium is:
$$\begin{gathered} {\displaystyle \frac{R_1}{R_2}}={\displaystyle \frac{r_{H_2}}{r_{He}}}=\sqrt{{\displaystyle \frac{M_{He}}{M_H}}} \\ \Rightarrow {\displaystyle \frac{R_1}{R_2}}=\sqrt{{\displaystyle \frac{4}{2}}}=\sqrt{2} \\ \Rightarrow {\displaystyle \frac{R_1}{R_2}}={\displaystyle \frac{r_{H_2}}{r_{He}}}=1.414 \\ \therefore r_{H_2}=1.414\times r_{He} \end{gathered}$$
Hence, the rate of diffusion of hydrogen is about 1.4 times that of He.

Hence the correct answer is option B.

Note- Pressure difference, surface area and the constant k are multiplied together. They're divided by a diffusion barrier to determine the exact rate of diffusion. Diffusion is a measure of average speed of the molecule. The diffusion rate depends on several factors: the concentration gradient, the amount of surface area available for diffusion; and the distance the gas particles must travel.