Question

A vessel contains an equal number of moles of helium and methane. Through a small orifice, half of gas effused out. The ratio of the number of mole of helium and methane remaining in the vessel is :

• A. 2 : 1
• B. 1 : 2
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is B 1 : 2

According to Graham's law of diffusion, the ratio of the rates of the gases is equal to the reciprocal of the ratio of the square roots of their molecular weights.

$\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}$.

This is also equal to the ratio of the number of moles of two gases that diffuse in a given time.

The molecular weight of methane (16 g/mol) is four times the molecular weight of helium (4 g/mole).

Hence, in a given time, the number of the moles of helium that diffuse in a given time is one half the number of moles of methane that diffuse at the same time.

The ratio of the number of mole of Helium and methane remaining in the vessel is $1:2$.