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

States of Matter – Diffusion

Learning objective (Syllabus 1.2)

Describe and explain the effect of relative molecular mass on the rate of diffusion of gases, using kinetic particle theory and Graham’s law.

1. Core – What is diffusion?

• Definition (core requirement): Diffusion is the spontaneous movement of particles from an area of higher concentration to an area of lower concentration.
• Kinetic particle theory (core):
  • Particles are in constant random motion.
  • Collisions between particles (and with the walls of the container) cause them to spread out and mix.
  • In gases the particles are far apart and move rapidly, so diffusion occurs very quickly.

1.1 Diffusion in other states (brief context)

Diffusion also occurs in liquids (much slower) and in solids (practically negligible). The IGCSE only requires you to recognise this trend.

2. Supplement – Effect of relative molecular mass

2.1 Graham’s law of diffusion

At a constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its relative molecular mass (M):

For two gases (1 and 2) the law can be written as:

Condition: The temperature and pressure (or concentration gradient) must be the same for the two gases being compared.

2.2 Why does molecular mass affect the rate?

• From kinetic theory the average speed of a molecule is \[ v = \sqrt{\frac{3RT}{M}} \] (R = gas constant, T = absolute temperature).
  • Heavier molecules (larger M) have a smaller average speed.
  • Lighter molecules move faster, covering a given distance in a shorter time.
• Because diffusion rate is proportional to the average speed, a larger M gives a slower diffusion rate.

Note (extension): The speed formula is useful for deeper study but is not required for the core IGCSE answer.

2.3 Conditions for using Graham’s law (reminder)

• Same temperature for both gases.
• Same pressure (or the same concentration gradient).
• Report the answer with the required number of significant figures (normally 2 sf for IGCSE calculations).

3. Comparative diffusion rates of common gases

Values are calculated from Graham’s law using hydrogen as the reference gas.

3.1 Graphical representation (AO2 – interpreting data)

4. Worked example (AO2 – numerical skill)

Question: At 25 °C, which gas will diffuse faster, chlorine (Cl₂, M = 71) or ammonia (NH₃, M = 17)? Calculate the ratio of their diffusion rates.

Solution:

Ammonia diffuses about twice as fast as chlorine under the same conditions (2 sf).

5. Other factors that influence diffusion (core)

1. Temperature: Higher temperature → higher kinetic energy → faster diffusion for all gases.
2. Pressure / concentration gradient: A larger concentration difference gives a greater driving force, increasing the rate.
3. Relative molecular mass: Lighter gases diffuse faster (Graham’s law).
4. Medium: Diffusion is fastest in gases, slower in liquids, and very slow in solids.

6. Quick revision checklist

• Diffusion = movement from high to low concentration.
• Kinetic particle theory: particles move randomly, collisions cause mixing, gases diffuse rapidly.
• Graham’s law (core): \(r \propto 1/\sqrt{M}\) – temperature and pressure must be the same.
• Lighter gases (smaller M) → higher average speed → higher diffusion rate.
• When doing calculations:
  • Ensure T and P are identical for the gases compared.
  • Give the answer with the required number of significant figures (usually 2 sf).

Suggested classroom diagram

Side‑by‑side illustration of two gases diffusing through a narrow tube: the lighter gas spreads rapidly, the heavier gas lags behind. This visual reinforces the relationship rate ∝ 1/√M.