Graham’s Law of Diffusion

Introduction

Thomas Graham, a Scottish physical chemist, proposed Graham’s law of effusion (also known as Graham’s law of diffusion) in 1848. Graham discovered that a Gas’s effusion rate is inversely proportional to the square root of its particles molar mass.

What is Diffusion?

The movement of particles from a higher concentration to a lower concentration is called Diffusion.

For example, when a sugar cube is dropped in a glass of water, the sugar particles mix up in the water as they move from the sugar cube’s higher concentration to the lower concentration of water.

What is Effusion?

Effusion is the process of a gas escaping through a very small hole in the container’s wall. The hole has a smaller diameter than the gas molecules’ mean free path. The difference in pressure between the container and the surrounding environment causes the gas to escape. The effusion rate is used to calculate the density, pressure, and temperature of gases when learning chemistry or physics.

Graham’s Law of Diffusion and Effusion

Graham’s Law of diffusion was a seminal work in chemistry. This Law, also known as Graham’s Law of Diffusion, was discovered in 1848 by Thomas Graham. His research into the effusion rate revealed that heavier molecules travel slower than lighter molecules. When the temperature and pressure remain constant, Graham’s Law of effusion or diffusion states that atoms with a high molar mass effuse more slowly than atoms with a low molar mass. He also stated the rate of diffusion or how molecules would escape.

It also claims that the effusion rate is inversely proportional to the square root of the molar mass. Graham’s diffusion law formula is derived from this statement. It can be used to compare the rates of two gases at a constant temperature and pressure. Assume that r1 and r2 are the Effusion rates of two gases, and M1 and M2 are the molar masses. As a result, the formula can be written like this:

                       r1/r2 = √M1/M2

Calculation of the Rate of Diffusion

Let r1 and r2 be the diffusion rates of two gases with molar masses M1 and M2 and densities d1 and d2 at constant temperature and pressure.

Graham’s law states that

                        r1/r2 = d2/d1

However, the vapour density, or density (d) vapour density, is proportional to the gas density (D). Again, molecular mass equals two vapour densities or M = 2D.

As a result,

                  r1/r2 = M2/M1

The diffusion rate in terms of the molecular weight of gases is calculated using this formula.

Calculation of the Rate of Effusion

The term ‘effusion’ refers to the movement of gaseous particles from a small opening into the vacuum of space or an open container. This space could be a vacuum, a gas, or even an atmosphere. Material molecules escape from a sealed container through the aperture in this process.

 The effusion rate is the process by which material particles from a closed space escape over time. Let’s look at the formula for calculating the rate of effusion. 

The rate of effusion of a gas is inversely proportional to the square of its molar mass. Hence, the formula for rate of effusion is,

                           r2/r1 = √(M2/M1)

Importance of Graham’s Law

The importance of Graham’s Law is as follows: 

• It facilitates the separation of gases with varying densities.
• It aids in the separation of different elements’ isotopes.
• Using diffusion/effusion rates can help determine the molecular weight of an unknown gas.

Applications of Graham’s law of diffusion

Graham’s Law can be applied to the following situations:

• Graham’s Law is mostly used to partially separate components in a gas mixture.

• If the mixture were to be forced out of a tube with porous walls, the lighter components would diffuse out faster than the heavier ones over time.

• When you repeat the process with each diffusion fraction, the concentration of one component rises dramatically compared to the other. This is referred to as atmolysis. This method has concentrated argon by combining it with nitrogen.

• Atmolysis has been used to partially separate the isotopes of neon, chlorine, bromine, oxygen, and other elements.

• Graham’s Law is used to detect methane or marsh gas from coal mines.

Conclusion

The random motion of gaseous particles is unavoidable. Because kinetic energy is present in gaseous particles, diffusion is natural. Because gas molecules have more kinetic energy at higher temperatures, diffusion happens faster. The flow of gas particles through a small hole is called an effusion. As per Graham’s Law, the effusion rate of a gas is inversely proportional to the square root of its particle mass. Graham’s Law is a very practical concept applied in various industries. It is also a very important topic and needs to be thoroughly studied to ace your upcoming exams.