How does molecular mass affect the root-mean-square speed of a gas?

According to the kinetic theory of gases, the root-mean-square speed ($v_{rms}$) of a gas is inversely proportional to the square root of its molecular weight ($M$). This relationship is expressed by the formula:

$$v_{rms}=\sqrt{\frac{3RT}{M}}$$

In this equation, $R$ represents the gas constant and $T$ is the temperature.1

Because of this inverse relationship, light molecules possess higher average speeds than heavy molecules at the same temperature. Consequently, as the molecular mass of a gas increases, its root-mean-square speed decreases. This principle explains why lighter gases, such as helium, exhibit higher molecular speeds and diffuse more rapidly than heavier gases.21