Graham's Law of Gas Diffusion

⚫Intoduction:

Graham's law of gas diffusion is a fundamental principle of gas behavior that describes the rate at which gases diffuse through each other. It states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. The law is named after Thomas Graham, a Scottish chemist who first proposed it in 1848.

The law is based on the kinetic theory of gases, which assumes that gases are composed of a large number of small particles that are in constant, random motion. According to the kinetic theory, the rate of diffusion of a gas depends on the speed of its particles, which in turn depends on their mass and temperature.

⚫Mathematical Expression:

Graham's law of gas diffusion can be expressed mathematically as follows:

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Here, rate₁ is the rate of diffusion of gas 1, rate₂ is the rate of diffusion of gas 2, M₁ is the molar mass of gas 1, and M₂ is the molar mass of gas 2.

The law states that the ratio of the rates of diffusion of two gases is equal to the square root of the ratio of their molar masses. This means that a gas with a smaller molar mass will diffuse more rapidly than a gas with a larger molar mass, at the same temperature and pressure.

Graham's law of gas diffusion can be derived from the kinetic theory of gases and the equation for the average speed of gas particles, which is given by:

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Here v_avg is the average speed of the gas particles, R is the gas constant, T is the temperature of the gas in kelvins, and M is the molar mass of the gas.

The equation for the average speed of gas particles shows that the speed of gas particles is inversely proportional to the square root of their molar mass. This means that lighter gases will have faster-moving particles than heavier gases, at the same temperature and pressure.

⚫Practical Expression:

The law has many practical applications in the study of gases. For example, it is used in the production of ammonia, where nitrogen and hydrogen gases are mixed and allowed to diffuse through each other to react and form ammonia. The law is also used in the study of atmospheric pollution, where the diffusion rates of different gases can affect their concentration in the air.

⚫Conclusion:

In conclusion, Graham's law of gas diffusion is a fundamental principle of gas behavior that describes the rate at which gases diffuse through each other. It states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. The law is based on the kinetic theory of gases and has many practical applications in the study of gases.