Understanding Graham's Law of Effusion
Graham's Law of Effusion states that the rate at which a gas effuses (escapes through a tiny hole into a vacuum) is inversely proportional to the square root of its molar mass. This means lighter gases effuse faster than heavier gases under the same conditions of temperature and pressure.
Key Principles and the Role of Molar Mass
The law is a direct consequence of the kinetic molecular theory, which posits that gas particles are in constant, random motion. For two different gases (Gas 1 and Gas 2) at the same temperature, their average kinetic energy is equal. The inverse relationship with the square root of molar mass arises because lighter molecules have higher average speeds at a given temperature, thus encountering and passing through the opening more frequently.
A Practical Example
Consider two gases, hydrogen (H₂, molar mass ≈ 2 g/mol) and oxygen (O₂, molar mass ≈ 32 g/mol). According to Graham's Law, the rate of effusion of hydrogen will be approximately four times faster than that of oxygen (√32 / √2 = √16 = 4). This difference is evident in how quickly balloons filled with helium deflate compared to those filled with air.
Importance and Applications
Graham's Law is important for understanding the behavior of gases and has practical applications, particularly in separating isotopes. For instance, it was historically used in the Manhattan Project to separate uranium isotopes, as the slightly lighter uranium-235 diffused faster than uranium-238, allowing for enrichment.