Question

The rate of diffusion of Hydrogen is about
A. $\dfrac{1}{2}$ that of Helium.
B. 1.4 times that of helium.
C. Twice that of helium.
D. Four times that of helium.

Answer 1

Hint: In the process of diffusion mentioned here, there is a movement of particles from higher to lower concentration of materials.
The relationship of rate of diffusion between two gases is given by Graham's law which states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight.

Complete step by step answer:
According to Graham's law
When the temperature and pressure is kept constant, the molecules with lower mass will diffuse faster than those with higher mass.
The rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight. Mathematically:
$R \propto \dfrac{1}{{\sqrt M }}$
For the comparison of two gases, the law can be given as:
\[\dfrac{{{R_1}}}{{{R_2}}} = \sqrt {\dfrac{{{M_2}}}{{{M_1}}}} \] _________ (1)
${R_1}$ and ${M_1}$ are the rate of diffusion and molar mass of gas 1 (Hydrogen)
${R_2}$and ${M_2}$ are the rate of diffusion and molar mass of gas 2 (Helium)
Now,
${M_1}$= molar mass of Hydrogen = 2
${M_2}$= molar mass of Helium = 4
Substituting these values in (1), we get:
\[\dfrac{{{R_1}}}{{{R_2}}} = \sqrt {\dfrac{4}{2}} \\
\dfrac{{{R_1}}}{{{R_2}}} = \sqrt 2 \\
\dfrac{{{R_1}}}{{{R_2}}} = 1.4 \\
{R_1} = 1.4{R_2} \\ \]

Therefore, it can be said that the rate of diffusion of Hydrogen is about 1.4 times that of helium, option B).

Note: Helium exists as monatomic He and Hydrogen exist as diatomic molecules \[{H_2}\].
Diffusion is the movement of a substance from an area of high concentration to an area of low concentration and gas molecules undergo diffusion due to presence of kinetic energy.
At higher temperature diffusion is faster because the gas molecules have high kinetic energy.