Question

The vapour density of methane and oxygen are in the ratio 1:2 the ratio of rates of diffusion of oxygen and methane is.

Answer 1

We know that, R1/R2=√D2/√D1

SO,Answer is =√2:1.

Answer 2

Answer: The ratio of rates of diffusion of oxygen and methane is $1:\sqrt{2}$

Explanation:

To calculate the molecular mass, we use the equation:

$\text{Molecular mass}=2\times \text{Vapor density}$

We are given:

Ratio of vapor density of methane to vapor density of oxygen = 1 : 2

$\frac{D_{methane}}{D_{oxygen}}=\frac{1}{2}=\frac{M_{methane}}{M_{oxygen}}$

As, vapor density is directly proportional to molar mass of the compound. Thus, their ratio will also be same.

To calculate the rate of diffusion of gas, we use Graham's Law.

This law states that the rate of effusion or diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:

$\text{Rate of diffusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}$

$\frac{Rate_{(oxygen)}}{R_{(methane)}}=\sqrt{\frac{M_{methane}}{M_{oxygen}}}\\\\\frac{Rate_{(oxygen)}}{R_{(methane)}}=\sqrt{\frac{D_{methane}}{D_{oxygen}}}\\\\\frac{Rate_{(oxygen)}}{R_{(methane)}}=\sqrt{\frac{1}{2}}$

Hence, the ratio of rates of diffusion of oxygen and methane is $1:\sqrt{2}$