What is the Equation for Graham’s Law of Effusion?

Graham's Law of Effusion gives the fundamental relationship in chemistry according to which there is no interaction between gas molecules while passing through a small opening or porous membrane. It greatly helps understand and explain the characteristics of gases concerning the properties of gas molecules.

Graham’s Law of Effusion

Graham's Law, first discovered by Scottish chemist Thomas Graham in 1829, states that a gas's effusion rate is inversely proportional to the square root of its molar mass. This can be explained in simple words: the lighter the gas, the faster it effuses than the heavier ones.
Graham's Law of Effusion gives the fundamental relationship in chemistry according to which there is no interaction between gas molecules while passing through a small opening or porous membrane.

Effusion differs from diffusion since gas molecules effuse through a tiny hole without collision. The principle of gas behaviours under various conditions depends on this principle.

The Equation for Graham's Law of Effusion

Mathematically, Graham's Law of Effusion is given by:

The equation for Graham's Law of Effusion is:

r1r2=M2M1​

Where:

  • r1r_1 and r2r_2 are the effusion rates of gases 1 and 2, respectively.
  • M1M_1 and M2M_2 are the molar masses of gases 1 and 2, respectively.

This equation shows that a gas with a lower molar mass will effuse faster than a gas with a higher molar mass.

Real-World Applications of Graham's Law

Separation of Isotopes: Graham's Law is essential for separating isotopes of the same element. The Manhattan Project employed Graham's Law to separate isotopes of uranium through gaseous diffusion.

Breathalyzer Tests: Breath analyzers use Graham's Law to detect ethanol molecules in exhaled breath since ethanol effuses at a more characteristic rate than the other gases.

Industrial Processes: The principle is useful in designing efficient systems for gas purification and leak detection.

Respiratory Therapy: Graham's Law helps in understanding how oxygen and other gases move in and out of the lungs during respiration.

Conclusion

Graham's Law of Effusion is such a simple and profound equation as it expresses the relationship between the rate of effusion and molar mass. It has applied use in all areas, ranging from medicine and industry to nuclear science. Learning this concept makes one appreciate further the fascinating behaviours of gases.

BANTI SINGH

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