Question

A box contains equal molecules of oxygen, hydrogen, and helium. If a fine hole is made in the box, then the gas that will leak more rapidly is _________.
1. Hydrogen only
2. All at the same rate
3. Helium only
4. Oxygen only

Answer 1

Correct Answer - Option 1 : Hydrogen only

CONCEPT:

Graham's law

• This law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of the mass of its particles.

​\(\Rightarrow r\propto \frac{1}{\sqrt{M}}\)

Where r = rate of effusion or diffusion and M = molar mass

CALCULATION:

We know that,

\(\Rightarrow M_{H}=1\) (molar mass of hydrogen)

\(\Rightarrow M_{He}=2\) (molar mass of helium)

\(\Rightarrow M_{O}=16\) (molar mass of oxygen)

• By Graham's law, we know that the effusion or diffusion of a gas is inversely proportional to the square root of the mass of its particles.
• Since the molar mass of the hydrogen gas is minimum compared to helium and oxygen so the diffusion of hydrogen will be maximum.
• So the hydrogen gas will leak rapidly compared to helium and oxygen. Hence, option 1 is correct.