What is Graham's Law of Diffusion?
Diffusion refers to the process in which particles of a substance move from an area of higher concentration to an area of lower concentration. The diffusion of gases describes how molecules of one gas distribute themselves throughout another gas.
Graham's law of diffusion (formulated by Scottish chemist Thomas Graham in 1848) states that:
The rate of diffusion or effusion of a gas is inversely proportional to the square root of its molecular (molar) mass.
The mathematical formula for Graham's law is:
r₁ / r₂ = √(M₂ / M₁)
where r₁ and r₂ are the rates of effusion or diffusion of Gas 1 and Gas 2, and M₁ and M₂ are their respective molar masses.
This means lighter gases (lower molar mass) effuse faster than heavier gases. For example, hydrogen (H₂, M = 2.016 g/mol) effuses approximately four times faster than oxygen (O₂, M = 32 g/mol), since √(32/2.016) ≈ 3.98.
Derivation of Graham's Law
The derivation is rooted in the kinetic theory of gases. At the same temperature, two different gas molecules have equal average kinetic energies:
½ m₁ v₁² = ½ m₂ v₂²
Multiplying both sides by 2 and rearranging:
v₁² / v₂² = m₂ / m₁
Taking the square root and replacing individual molecular masses with molar masses M:
v₁ / v₂ = √(M₂ / M₁)
Since the rate of effusion is proportional to the average molecular speed, this gives us Graham's law directly.
Diffusion vs. Effusion
Diffusion occurs when a partition between gases is removed and molecules spread freely, distributing throughout the available space. You experience diffusion every day — when you smell perfume from across a room, the fragrant molecules are diffusing through the air.
Effusion is the process by which gas molecules escape through a tiny opening or porous barrier. A classic example is a helium balloon that slowly deflates over time — helium atoms effuse through the microscopic pores of the rubber material. Since helium is very light (M = 4.003 g/mol), it effuses significantly faster than heavier air molecules.
Industrial Applications
- Uranium enrichment — The most famous industrial application. Uranium hexafluoride (UF₆) is used in gaseous diffusion plants to separate uranium-235 from the heavier uranium-238. Because the molar mass difference between ²³⁵UF₆ and ²³⁸UF₆ is small (~0.85%), thousands of separation stages are required.
- Gas leak detection — Lighter gases (hydrogen, helium) diffuse much faster and can be detected more quickly, which is important for safety monitoring in laboratories and industrial plants.
- Membrane separation — Industrial membranes exploit differences in effusion rates to separate gas mixtures, including oxygen enrichment for medical or industrial use.
- Analytical chemistry — Mass spectrometry and other analytical techniques rely on predictable diffusion behavior of gases.
- Vacuum technology — Understanding effusion rates is critical for designing vacuum pumps and gas handling equipment.
Unit Systems
Molar mass is typically measured in:
- g/mol (grams per mole) — standard metric unit, used in most scientific work
- lb/mol (pounds per mole) — American/Imperial unit (1 lb/mol ≈ 453.592 g/mol)
The rate ratio calculated by Graham's law is dimensionless — it does not depend on the unit system chosen, as long as both molar masses use the same units. Our calculator supports both metric (g/mol) and American Imperial (lb/mol) inputs.
Frequently Asked Questions
What does Graham's law calculate?
Graham's law calculates the relative rates of effusion or diffusion of two gases based on their molar masses. The lighter the gas, the faster it effuses.
Can Graham's law be used for any two gases?
Yes, Graham's law applies to any two ideal gases at the same temperature and pressure. The approximation becomes less accurate for real gases at high pressures or low temperatures, where intermolecular forces become significant.
How do I find the molar mass of an unknown gas?
If you know the effusion rates of two gases and the molar mass of one gas, you can rearrange Graham's law to find the unknown molar mass: M₂ = M₁ × (r₁/r₂)². Use the "Find Molar Mass" mode in this calculator.
Why does a helium balloon deflate?
Rubber is a porous material with microscopic openings. Helium atoms (M = 4.003 g/mol) are very small and light, so they effuse through these openings at a high rate. Air molecules (average M ≈ 29 g/mol) effuse much more slowly. This is why helium balloons lose their lift within hours to days.
What is the difference between Graham's law and Fick's law?
Graham's law compares the effusion rates of two different gases. Fick's law (Fick's first law of diffusion) describes how fast a single substance diffuses through a medium based on its concentration gradient, cross-sectional area, and distance. Both are related to the broader science of gas transport.