Question

The ratio of diffusion of hydrogen and helium gas is :
A. $1:1.4$
B. $1:1$
C. $1.4:1$
D. $1:2$

Answer 1

Hint: We know that Graham’s Law of diffusion states that rate of diffusion or effusion of gas is inversely proportional to the square root of the molar mass. If $r$ is rate of diffusion of a gas and $M$ is its molecular mass so this law mathematically can be represented as ; $r \propto \dfrac{1}{M}$ . It can also be used to determine the molecular mass of a gas if one gas is known.

Complete step by step solution:
Let the rate of diffusion of hydrogen gas be ${r_1}$ and the rate of diffusion of helium be ${r_2}$. We know that the ratio of the rate of diffusion of a gas is inversely proportional to the square root of the molar mass. Hence the ratio of rate of diffusion of hydrogen gas to helium gas will be; $\dfrac{{{r_1}}}{{{r_2}}} = \sqrt {\dfrac{{{m_2}}}{{{m_1}}}}$ , where ${m_1},{m_2}$ is the molar mass of hydrogen and helium respectively. (molar mass of hydrogen gas $= 2$,molar mass of helium gas $= 4$) .We know that hydrogen gas is found as a diatomic molecule while helium is an inert gas which exists as atomic helium.
Thus the ratio of diffusion,
$\Rightarrow \dfrac{{{r_1}}}{{{r_2}}} = \sqrt {\dfrac{4}{2}} = \sqrt 2$
$\Rightarrow \dfrac{{{r_1}}}{{{r_2}}} = 1.41$
So the ratio of the rate of diffusion of hydrogen gas and helium gas is $1.4:1$ ,hence option C is the correct answer to this problem.

Note: We have approached this problem with the help of Graham’s Law of effusion of gases. Graham’s law is most accurate for the calculation of diffusion of gases which involves the movement of one gas at a time through a hole. It also provides a basis for the separation of isotopes by diffusion.