Describe and explain the effect of relative molecular mass on the rate of diffusion of gases

States of Matter – Diffusion

Objective

Describe and explain how the relative molecular mass of a gas influences its rate of diffusion.

Exam Tip: Remember Graham’s Law:

\$\frac{Rate1}{Rate2} = \sqrt{\frac{M2}{M1}}\$

where \(M\) is the molar mass. Use it to compare rates quickly.

What is Diffusion?

Diffusion is the spontaneous spread of particles from an area of high concentration to an area of low concentration. Think of a drop of food colouring in water – it spreads out until the colour is evenly distributed.

Why Does Molecular Mass Matter?

Gases with lighter molecules move faster because they have higher average kinetic energy at a given temperature. The faster they move, the quicker they spread out.

Graham’s Law shows the relationship:

  • Rate ∝ 1/√(M)

  • Smaller \(M\) → larger rate.

Analogy: The Balloon Race

Imagine two balloons racing on a windy day:

  • Balloon A (light, helium) is like a gas with low molecular mass.

  • Balloon B (heavy, hot air) is like a gas with high molecular mass.

Balloon A zips ahead because it’s lighter and can move faster through the air. The same principle applies to gas molecules.

Real‑World Example

Compare hydrogen (H₂, M = 2 g mol⁻¹) and oxygen (O₂, M = 32 g mol⁻¹) at the same temperature:

GasMolar Mass (g mol⁻¹)Relative Rate (H₂ : O₂)
H₂21 : 0.25
O₂320.25 : 1

Hydrogen diffuses about four times faster than oxygen.

Key Points to Remember

  1. Rate of diffusion is inversely proportional to the square root of molar mass.

  2. All gases diffuse faster at higher temperatures (more kinetic energy).

  3. Use Graham’s Law to solve exam problems quickly.

Exam Tip: When given two gases, calculate the ratio of their rates using the square root of the inverse molar masses. Example:

\$\frac{Rate{CH4}}{Rate{CO2}} = \sqrt{\frac{M{CO2}}{M{CH4}}}\$

Plug in \(M{CH4}=16\) and \(M{CO2}=44\) to find the ratio.

Quick Quiz

Which gas will diffuse fastest at room temperature? (Hint: think of the lightest gas you can name.)

Answer: Hydrogen (H₂) – it has the lowest molar mass.