Under the same conditions of temperature and pressure, how many times faster will helium g… — JAMB UTME

Under the same conditions of temperature and pressure, how many times faster will helium gas ( $\text{He}$ ) diffuse compared to methane gas ( $\text{CH}_4$ )? [Relative atomic masses: $\text{H} = 1$ , $\text{C} = 12$ , $\text{He} = 4$ ]

2 times fasterAnswer
B
4 times faster
C
0.5 times as fast
D
8 times faster

Answer

Helium gas diffuses 2 times faster than methane gas.

The rate of diffusion of a gas is inversely proportional to the square root of its molar mass (

r \propto \frac{1}{\sqrt{M}}

). Methane (

\text{CH}_4

) has a molar mass of

16\text{ g/mol}

and helium (

\text{He}

) has a molar mass of

4\text{ g/mol}

. Therefore, the ratio of the diffusion rate of helium to methane is

\sqrt{16/4} = \sqrt{4} = 2

Step-by-Step Solution

Calculate the molar masses of both gases.

\text{Molar mass of He} = 4\text{ g/mol}

;

\text{Molar mass of CH}_4 = 12 + (4 \times 1) = 16\text{ g/mol}

Molar masses are required inputs for Graham's Law.

Apply Graham's Law formula:

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

\frac{r_{\text{He}}}{r_{\text{CH}_4}} = \sqrt{\frac{16}{4}} = \sqrt{4} = 2

The rate of diffusion of a gas is inversely proportional to the square root of its molecular mass.

Key Concept

Graham's Law of Diffusion states that the rate of diffusion (

r

) of a gas is inversely proportional to the square root of its molar mass (

M

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Answer

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Key Concept

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