Chemistry · Lesson 5

Gas laws & kinetic theory

JAMBWAECNECO

What the syllabus asks

JAMB: kinetic theory, gas laws and their applications, molar volume, ideal and real gases

WAEC: kinetic theory of matter, states of matter and changes of state, diffusion, gas laws (Boyle, Charles, pressure law, general gas equation, ideal gas equation, Dalton's law of partial pressures, Graham's law of diffusion, Gay-Lussac's law of combining volumes, Avogadro's law), molar volume

NECO: kinetic theory of matter, states of matter and changes of state, diffusion, gas laws (Boyle, Charles, pressure law, general gas equation, ideal gas equation, Dalton's law of partial pressures, Graham's law of diffusion, Gay-Lussac's law of combining volumes, Avogadro's law), molar volume

What you will learn

State the assumptions of the kinetic theory and use it to explain the states of matter, pressure and diffusion.
Convert between °C and K and explain absolute zero.
State and apply Boyle's, Charles' and the pressure law, and the general gas equation.
Use the ideal gas equation PV = nRT.
Apply Dalton's law of partial pressures, including gases collected over water.
Apply Graham's law to compare rates and find molar masses.
Apply Gay-Lussac's and Avogadro's laws and molar volume to gas calculations.

Key points

Kinetic theory: particles in constant random motion; average KE ∝ absolute temperature; pressure comes from collisions with walls.
Solids vibrate in place, liquids slide past, gases move fast and far apart; latent heat keeps temperature constant during changes of state.
T(K) = θ(°C) + 273; absolute zero is 0 K = −273 °C.
Boyle: P₁V₁ = P₂V₂ (T constant).
Charles: V₁/T₁ = V₂/T₂; pressure law: P₁/T₁ = P₂/T₂.
General: P₁V₁/T₁ = P₂V₂/T₂; s.t.p. = 273 K, 760 mmHg.
Ideal gas: PV = nRT, R = 8.314 J mol⁻¹ K⁻¹ with Pa and m³.
Dalton: P(total) = sum of partial pressures; dry gas pressure = P(atm) − SVP of water.
Graham: R₁/R₂ = √(M₂/M₁); lighter gases diffuse faster.
Gay-Lussac and Avogadro: gas volume ratio = mole ratio; 1 mol = 22.4 dm³ at s.t.p., 24 dm³ at r.t.p.

Start here: The kinetic theory of matter

Open a bottle of perfume in one corner of a classroom and, within a minute, students at the back can smell it. Nobody carried the scent there. The perfume particles moved by themselves. This simple observation is evidence for one of the most important ideas in chemistry: the kinetic theory ("kinetic" means "to do with motion").

Kinetic theory: all matter is made up of tiny particles (atoms, molecules or ions) that are in constant, random motion. The higher the temperature, the faster they move.

Assumptions of the kinetic theory of gases

A gas consists of a very large number of tiny particles moving randomly in straight lines until they collide.
The volume of the particles themselves is negligible compared with the volume of the container.
There are no forces of attraction or repulsion between the particles (except during collisions).
Collisions with each other and with the walls are perfectly elastic: no kinetic energy is lost overall.
The average kinetic energy of the particles is directly proportional to the absolute temperature.

A gas that obeys these assumptions exactly is an ideal gas. Real gases come close at ordinary temperatures and low pressures.

Evidence for moving particles

Diffusion: the smell of fried plantain spreads through the house; a crystal of potassium permanganate colours still water purple slowly.
Brownian motion: under a microscope, pollen grains in water (or smoke particles in air) jiggle in random zigzag paths, because invisible water or air molecules bombard them unevenly from all sides.

Worked example 5.1

Explain, using the kinetic theory, why a gas exerts pressure on its container.

The particles move randomly and constantly collide with the walls.
Each collision exerts a tiny force on the wall as the particle changes direction (momentum change).
Millions of collisions per second over the wall area give a steady force per unit area: pressure.

Pressure is due to particles colliding with the container walls

⚠️ Common mistake: saying "particles of a gas expand when heated". The particles stay the same size; they move faster and spread further apart.

Try it yourself. Why do smoke particles seen under a microscope move in a zigzag way?

Show solution

They are hit unevenly by fast-moving, invisible air molecules from all sides (Brownian motion).

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Practice questions

1. At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure. This is

Boyle's law
Charles' law
Graham's law
Avogadro's law

Show answer

A: Boyle's law
PV = constant.

2. A gas occupies 200 cm³ at 27 °C. At constant pressure, what is its volume at 127 °C?

940.7 cm³
150 cm³
400 cm³
266.7 cm³

Show answer

D: 266.7 cm³
Charles: V₂ = 200 × 400/300 = 266.7 cm³ (use Kelvin!).

3. Which gas diffuses fastest? (H = 1, C = 12, N = 14, O = 16)

CO₂
N₂
H₂
O₂

Show answer

C: H₂
Graham: rate ∝ 1/√M; H₂ is lightest.

4. The law PV = constant (fixed mass, constant temperature) is

Avogadro's law
Boyle's law
Charles's law
Graham's law

Show answer

B: Boyle's law
Pressure and volume are inversely proportional.

5. A gas occupies 50 cm³ at 2 atm. Find its volume at 1 atm at constant temperature.

100 cm³
25 cm³
50 cm³
200 cm³

Show answer

A: 100 cm³
P₁V₁ = P₂V₂.

Key words

Kinetic theory: The model that matter consists of particles in constant random motion.
Absolute zero: 0 K (−273 °C), the temperature at which particle motion is at a minimum.
Kelvin (K): SI unit of temperature; T(K) = θ(°C) + 273.
Pressure: Force per unit area; in gases, caused by particles colliding with the walls.
STP: Standard temperature and pressure: 273 K and 1 atm (101 325 Pa, 760 mmHg).
Molar volume: The volume of one mole of any gas: 22.4 dm³ at STP.
Partial pressure: The pressure a gas in a mixture would exert if it alone filled the container.
Saturated vapour pressure: Pressure of a vapour in equilibrium with its liquid at a given temperature.
Diffusion: Spreading of particles from a region of high concentration to low concentration.
Effusion: Escape of gas through a tiny hole.
Ideal gas: A gas that obeys the gas laws exactly: no intermolecular forces, negligible particle volume.
Real gas: An actual gas; deviates from ideal behaviour at high pressure and low temperature.

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