What is Graham's law of diffusion?

Graham's law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

Graham's law of diffusion, named after the Scottish chemist Thomas Graham who first formulated it in the 19th century, is a fundamental principle in the study of physical chemistry. It provides a quantitative relationship between the molar mass of a gas and the rate at which it diffuses. According to this law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases will diffuse faster than heavier ones.

To understand this concept better, let's consider two gases, A and B. If gas A is lighter than gas B, it will diffuse faster. This is because the particles of a lighter gas move more quickly, and therefore spread out more rapidly, than those of a heavier gas. The mathematical representation of Graham's law is: Rate of diffusion of A/Rate of diffusion of B = √(Molar mass of B/Molar mass of A).

This law is particularly useful in predicting the behaviour of gases. For example, it can help us understand why we can smell a waft of perfume almost instantly across a room, or why helium balloons deflate faster than air-filled ones. The perfume molecules are lighter and smaller than the air molecules, so they diffuse quickly. Similarly, helium is lighter than air, so it escapes from the balloon faster.

However, it's important to note that Graham's law applies ideally to gases under low pressure and high temperature conditions, where they behave most ideally. Real gases may not follow Graham's law exactly due to intermolecular forces and molecular size. But despite these limitations, Graham's law provides a useful approximation in many practical situations.