Rate of diffusion of a gas

The rate of diffusion of a gas is a measure of how quickly it spreads out and mixes with other gases. It is influenced by several factors, including the density and molecular weight of the gas.

Directly proportional to the square root of its molecular weight

The correct answer is option 'D', which states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight.

Explanation

The rate of diffusion is determined by the average speed of the gas molecules. Gas molecules with higher molecular weights have more mass and therefore move more slowly than gas molecules with lower molecular weights. This means that gases with higher molecular weights will diffuse more slowly.

Inversely proportional to the square root of its molecular weight

The relationship between the rate of diffusion and the molecular weight of a gas can be mathematically expressed as:

Rate of diffusion ∝ 1/√(Molecular weight)

This equation shows that as the molecular weight of a gas increases, the rate of diffusion decreases. The inverse relationship is due to the fact that the larger the molecular weight, the slower the gas molecules move and the less distance they can travel in a given amount of time.

Explanation with an example

For example, consider two gases: gas A with a molecular weight of 16 g/mol and gas B with a molecular weight of 32 g/mol. Since the molecular weight of gas B is twice that of gas A, its rate of diffusion will be slower.

This relationship can be explained by considering the kinetic theory of gases. According to this theory, gas molecules are in constant motion, and their speed is related to their temperature. The average speed of gas molecules is inversely proportional to the square root of their molecular weight.

Conclusion

In conclusion, the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight. This means that gases with higher molecular weights will diffuse more slowly than gases with lower molecular weights. Understanding this relationship is important in various fields, such as atmospheric science, where the diffusion of gases plays a crucial role in processes like air pollution and climate change.