Chemistry · JEE Advanced only

Diffusion of Gases (JEE Advanced)

Not in the JEE Main syllabus, but it is in JEE Advanced. Study time: about 2 to 3 hours. Spend about 1 hour understanding the concepts and derivations, then 1.5 to 2 hours practicing numerical problems involving Graham's law, molar mass calculations, and mixed gas diffusion scenarios..

Last updated: 26 October 2026

Direct answer

Diffusion of gases is the spontaneous mixing of gas molecules due to their random motion, moving from regions of higher concentration to lower concentration.

Diffusion of gases is the spontaneous mixing of gas molecules due to their random motion, moving from regions of higher concentration to lower concentration. This process depends on molecular speeds, which in turn depend on temperature and molar mass. Graham's law quantifies how lighter gases diffuse faster than heavier ones.

Official syllabus

What the JEE Advanced syllabus says

“Diffusion of gases”

Source: JEE Advanced 2026 Information Bulletin, Annexure-I. Closest JEE Main topic: kinetic theory of gases: assumptions, the concept of pressure.

JEE Main covers kinetic theory basics like pressure and assumptions, but stops short of diffusion and effusion rates. For Advanced, you need to apply Graham's law to compare rates, calculate molar masses, and solve problems involving gas mixtures escaping through porous barriers.

Key ideas

What you must understand

Diffusion is mixing of gases through space; effusion is escape through a tiny hole into vacuum. Both follow similar rate laws.
Rate of diffusion is inversely proportional to the square root of molar mass at constant T and P.
Lighter molecules move faster on average, so they diffuse and effuse more quickly.
Graham's law can be used to find unknown molar masses by comparing diffusion rates of two gases.
At the same temperature, all gases have the same average kinetic energy, but different average speeds depending on mass.
Diffusion rate also depends on pressure, temperature, and the size of the opening for effusion.

Formulas

Formulas and key facts

r ∝ 1/√M (rate inversely proportional to square root of molar mass)
r₁/r₂ = √(M₂/M₁) (Graham's law for comparing two gases)
r ∝ P/√(MT) (rate depends on pressure, molar mass, and temperature)
u_rms = √(3RT/M) (root mean square speed)
u_avg = √(8RT/πM) (average speed)
KE_avg = (3/2)RT per mole (same for all gases at same T)
Time for diffusion: t₁/t₂ = √(M₁/M₂) (for same volume through same hole)
Distance traveled: d₁/d₂ = √(M₂/M₁) (in same time)

Avoid

Common mistakes

Confusing diffusion (mixing in space) with effusion (escape through a hole). The formulas are similar but the physical setup differs.
Forgetting to take the square root when applying Graham's law. The ratio involves √M, not M directly.
Using mass instead of molar mass in Graham's law. Always use molar mass (g/mol), not the mass of a sample.
Inverting the ratio incorrectly. Remember: lighter gas has higher rate, so if M₁ < M₂, then r₁ > r₂.

Worked example

A JEE Advanced-level example

Question. A gas X diffuses through a porous plug at a rate that is one-fourth the rate of diffusion of hydrogen gas under identical conditions. If the molar mass of hydrogen is 2 g/mol, find the molar mass of gas X.

Show solution

Write Graham's law: r_X / r_H₂ = √(M_H₂ / M_X)
Given: r_X = (1/4) × r_H₂, so r_X / r_H₂ = 1/4
Substitute: 1/4 = √(2 / M_X)
Square both sides: 1/16 = 2 / M_X
Solve for M_X: M_X = 2 × 16 = 32 g/mol

Answer: The molar mass of gas X is 32 g/mol (likely O₂ or S).

Solved twice independently; both solutions agree.

FAQs

Frequently asked questions

Is Diffusion of Gases in the JEE Main syllabus?

No. It is in the JEE Advanced 2026 syllabus only. The closest JEE Main topic is kinetic theory of gases: assumptions, the concept of pressure.

How long does Diffusion of Gases take to prepare for JEE Advanced?

About 2 to 3 hours. Spend about 1 hour understanding the concepts and derivations, then 1.5 to 2 hours practicing numerical problems involving Graham's law, molar mass calculations, and mixed gas diffusion scenarios., if you already know the related JEE Main topic.