According to Graham's law, how is the rate of diffusion of a gas related to its molecular weight?

Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight. This means that as the molecular weight of a gas increases, its rate of diffusion decreases. The relationship can be mathematically represented as:

Rate of diffusion ∝ 1/√(molecular weight)

This relationship arises because lighter gases, with lower molecular weights, move faster than heavier gases. Consequently, when comparing two gases, the one with the lower molecular weight will diffuse at a faster rate than the one with the higher molecular weight.

This principle is particularly important in various applications within respiratory care, such as understanding how gases exchange in the lungs or in the use of different gases in therapeutic breathing treatments. Recognizing this inverse relationship helps practitioners predict how different gases will behave under various conditions, ultimately informing decisions about patient care and treatment modalities.