Describe and explain diffusion in terms of kinetic particle theory

Diffusion – Core Definition

Learning Objective

Describe diffusion and explain it in terms of the kinetic particle theory (KPT) as required by the Cambridge IGCSE Chemistry (0620) syllabus.

Key Vocabulary

• Diffusion – the net (macroscopic) movement of particles from a region of higher concentration to a region of lower concentration.
• Concentration gradient – the difference in concentration between two adjoining regions.
• Kinetic particle theory (KPT) – the model that matter consists of particles in continuous, random thermal motion.
• Equilibrium – the state in which the concentration is uniform throughout the system and there is no net movement of particles.
• Effusion – the movement of gas particles through a tiny opening; related but distinct from diffusion.

What is Diffusion?

Diffusion is the spontaneous, net movement of particles down a concentration gradient until the concentration becomes uniform (equilibrium) throughout the system. It is the macroscopic manifestation of the microscopic random motion described by KPT.

Explanation Using Kinetic Particle Theory

KPT states that matter is made up of particles (atoms, molecules or ions) that are in constant random motion. The points most relevant to diffusion are:

1. Particles travel in straight‑line paths until they collide with other particles or with the walls of the container.
2. In gases collisions are essentially elastic, so kinetic energy is conserved. In liquids and solids collisions are inelastic, but the total energy of the system is conserved; thermal energy is redistributed among the particles.
3. The average kinetic energy of the particles is directly proportional to the absolute temperature ( E_kin ∝ T ).
4. Because the motion is random, a region that contains more particles (high concentration) will, by chance, send more particles into a neighbouring low‑concentration region than the reverse. The cumulative effect of many such random “jumps” produces a net flow down the concentration gradient.

Thus diffusion is simply the observable result of the random thermal motion of particles described by KPT.

Reminder of the Three States of Matter (Syllabus 1.1)

State	Particle arrangement	Typical motion	Inter‑particle forces
Solid	Particles fixed in a regular lattice	Vibrations about fixed positions	Strong
Liquid	Particles close together but not ordered	Translational motion (sliding past one another)	Moderate
Gas	Particles far apart	Free, rapid, random motion	Weak (negligible)

Diffusion in Different States of Matter

State	Rate of Diffusion	KPT‑based Reason
Gas	Very fast	Particles are far apart, move freely at high kinetic energy, and collisions are essentially elastic.
Liquid	Moderate	Particles are close together; intermolecular attractions partially hinder motion, but thermal energy still produces random jumps.
Solid	Very slow	Particles are fixed in a lattice; only vibrational motion occurs, so only a tiny fraction can exchange positions.

Factors Affecting the Rate of Diffusion

1. Temperature – Higher temperature → higher average kinetic energy → faster diffusion.
2. Particle size / relative molecular mass
   • Gases: smaller (lighter) molecules diffuse faster (Graham’s law).
   • Liquids & solids: diffusion coefficients decrease as molecular size or mass increases; larger solutes move more slowly.
3. Concentration gradient – A larger difference provides a stronger driving force.
4. Medium of diffusion – Gases > Liquids > Solids because of increasing particle spacing and strength of intermolecular forces.
5. Surface area of contact – Greater area allows more particles to cross the interface simultaneously.

Supplement: Graham’s Law (Quantitative Relationship for Gases)

For gases, the rate of diffusion (or effusion) is inversely proportional to the square‑root of the relative molecular mass.

Graham’s law:

\[ \frac{r_1}{r_2}= \sqrt{\frac{M_{r2}}{M_{r1}}} \]

Worked Example

Calculate how many times faster hydrogen (H₂, M_r=2) diffuses compared with oxygen (O₂, M_r=32).

\[ \frac{r_{\text{H}_2}}{r_{\text{O}_2}}= \sqrt{\frac{M_{r\text{O}_2}}{M_{r\text{H}_2}}}= \sqrt{\frac{32}{2}}= \sqrt{16}=4 \]

Hydrogen diffuses four times faster than oxygen. This explains why a balloon filled with H₂ inflates more quickly than one filled with O₂.

Diffusion vs. Effusion

• Diffusion – movement of particles throughout a bulk phase (gas, liquid or solid) down a concentration gradient.
• Effusion – movement of gas particles through a tiny opening into a vacuum or a region of lower pressure. Graham’s law applies to both, but the syllabus only requires it for diffusion of gases.

Illustrative Graph (Qualitative)

A typical concentration‑vs‑time plot for diffusion in a liquid:

• At t = 0 the concentration is high at the point of introduction and zero elsewhere.
• As time passes the curve flattens: the central concentration falls while the surrounding region rises.
• When the line becomes horizontal the system has reached equilibrium – the concentration is the same everywhere.

(Students can sketch this curve in their notebooks.)

Simple Classroom Demonstrations

1. Liquid‑phase diffusion (coloured water)

1. Fill a shallow tray with 200 mL of room‑temperature water.
2. Place a single drop of coloured aqueous solution at the centre.
3. Without stirring, record the distance the colour front travels every 10 s for 2 min.
4. Plot distance vs. time; the slope gives a qualitative diffusion rate.
5. Repeat the experiment with the water heated to ~40 °C and compare the slopes – the warmer water shows a steeper slope (faster diffusion).

2. Gas‑phase diffusion (perfume or ammonia)

1. Put a few drops of perfume on a small piece of cotton wool and place it in one corner of a sealed transparent jar (≈1 L).
2. Close the jar and note the time taken for the scent to be detectable at the opposite corner (use a second cotton wool as a “detector”).
3. Discuss why the scent spreads rapidly – the high kinetic energy and large free paths of gas particles.

3. Solid‑state diffusion (extension)

When a metal rod is heated, atoms near the hot end migrate slowly toward the cooler end. This solid‑state diffusion is the reason alloying elements become uniformly distributed only after prolonged heating.

Link to Other Topics

• Rate of reaction – Diffusion of reactants can be the rate‑determining step in heterogeneous reactions.
• Gases – Graham’s law, effusion, and the ideal‑gas model are revisited in the “Gases” sub‑topic.
• Atmospheric chemistry – Diffusion of pollutants and the mixing of gases in the troposphere.

Key Points Summary

• Diffusion is the net movement of particles down a concentration gradient, a macroscopic expression of the microscopic random motion described by KPT.
• It continues until equilibrium (uniform concentration) is reached.
• Rate of diffusion increases with temperature, decreases with particle mass (Graham’s law for gases, and with size in liquids/solids), grows with a larger concentration gradient, is fastest in gases, slower in liquids, and very slow in solids, and is enhanced by greater surface area.
• Simple experiments with coloured water, perfume, and heated metals illustrate diffusion in the three states of matter and allow a qualitative (or semi‑quantitative) assessment of rate.
• Remember the distinction: diffusion = movement through a bulk phase; effusion = movement through a tiny opening.