Gas laws: Boyle's, Charles's and Avogadro's laws
Boyle: PV is constant at fixed temperature. Charles: V/T is constant at fixed pressure. Avogadro: V ∝ n at fixed temperature and pressure.
Pressure, volume and temperature of a gas
The state of a gas is described by its pressure (P), volume (V) and temperature (T). Gas particles move fast in all directions and keep hitting the walls of their container. These hits cause the pressure of the gas. The gas laws tell how P, V and T change together. In every gas law, temperature must be in kelvin.
The three gas laws
| Law | Kept constant | Statement | Formula |
|---|---|---|---|
| Boyle's law | Temperature (and the mass of gas) | Pressure is inversely proportional to volume | P ∝ 1/V, so PV = constant; P₁V₁ = P₂V₂. A graph of P against 1/V is a straight line. |
| Charles's law (law of volume) | Pressure (and the mass of gas) | Volume is directly proportional to temperature in kelvin | V ∝ T, so V/T = constant; V₁/T₁ = V₂/T₂ |
| Avogadro's law | Temperature and pressure | Volume is directly proportional to the number of atoms or molecules | V ∝ n, so V/n = constant |
Gas laws in daily life
- Boyle's law: an air bubble rising from the bottom of a pond grows bigger, because the water pressure on it falls.
- Boyle's law: press the piston of a syringe with its nozzle closed. The air is squeezed into a smaller volume and its pressure rises.
- Charles's law: a balloon left in hot sun swells; a balloon kept in a fridge shrinks.
- Avogadro's law: blowing more air (more molecules) into a balloon makes it bigger.
Using Boyle's law
A gas occupies 4 litres at a pressure of 1 atm. At the same temperature, what will its volume be at 2 atm?
- Given: P₁ = 1 atm, V₁ = 4 L, P₂ = 2 atm, V₂ = ?
- Boyle's law: P₁V₁ = P₂V₂.
- 1 × 4 = 2 × V₂, so V₂ = 4 ÷ 2 = 2 L.
The volume becomes 2 litres: doubling the pressure halves the volume.
Using Charles's law
A balloon holds 3 litres of air at 27 °C. What will its volume be at 127 °C, at the same pressure?
- Change the temperatures to kelvin: T₁ = 27 + 273 = 300 K and T₂ = 127 + 273 = 400 K.
- Charles's law: V₁/T₁ = V₂/T₂, so V₂ = V₁ × T₂/T₁.
- V₂ = 3 L × 400 K ÷ 300 K = 4 L.
The volume becomes 4 litres. Always use kelvin: using °C here would give a wrong answer.
Bubbles from an aquarium pump grow bigger as they rise: Boyle's law. A balloon from a temple festival shrinks in an air-conditioned room and swells in the afternoon sun: Charles's law.
2 marks: “State Boyle's law.” At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: PV = constant.
2 marks: “State Avogadro's law.” At constant temperature and pressure, the volume of a gas is directly proportional to the number of atoms or molecules in it: V ∝ n.
4 marks: “State Charles's law. A gas has a volume of 600 cm³ at 27 °C. Find its volume at 77 °C at constant pressure.” V ∝ T at constant P; T₁ = 300 K, T₂ = 350 K; V₂ = 600 × 350/300 = 700 cm³.
Boyle Below (P up, V down: inverse). Charles Climbs (T up, V up: direct). Avogadro Adds (more molecules, more volume).