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Gases

13 min read

The kinetic theory of gases

A gas is made of tiny particles that are in constant, random motion. For an ideal gas the particles have no volume, there are no forces between them and collisions are perfectly elastic. The pressure of a gas is caused by the particles hitting the walls of the container. The average kinetic energy is proportional to the absolute temperature in kelvin.

The gas laws

The gas lawsThree graphs. For a fixed amount of gas at constant temperature, pressure falls as volume rises along a curve, Boyle’s law. At constant pressure, volume is directly proportional to absolute temperature, Charles’ law, a straight line through the origin. At constant volume, pressure is directly proportional to absolute temperature.VPBoyle's lawP × V constant (T fixed)T (K)VCharles' lawV ∝ T (P fixed)T (K)PPressure lawP ∝ T (V fixed)
LawStatementEquation
BoyleAt constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressurePV = constant
CharlesAt constant pressure, the volume is directly proportional to the absolute temperatureV/T = constant
Pressure lawAt constant volume, the pressure is directly proportional to the absolute temperatureP/T = constant
CombinedCombines all threeP₁V₁/T₁ = P₂V₂/T₂
PV = 12 here. Halving the volume doubles the pressure, so the graph is a curve (a hyperbola).

The ideal gas equation

P = pressure (Pa), V = volume (m³), n = moles, R = 8.314 J mol⁻¹ K⁻¹, T = temperature in kelvin (°C + 273). Using kPa for pressure and dm³ for volume gives the same R.
  • gas constant (8.314 J/(mol K))
  • absolute temperature (K)
Worked exampleMoles of gas

What is the volume of 0.50 mol of an ideal gas at 27 °C and 100 kPa? (R = 8.314)

  1. T = 27 + 273 = 300 K. Use V = nRT ÷ P with P in kPa and V in dm³.

Answer: The volume is about 12.5 dm³.

Try itIdeal gas calculator

Choose the amount of gas, its temperature and pressure. Find the volume it occupies.

Dalton's law and Graham's law

Dalton's law of partial pressures
The total pressure of a mixture of gases is the sum of the pressures each gas would exert alone. The partial pressure of a gas = its mole fraction × the total pressure.
Graham's law of diffusion
At the same temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density (or molar mass).
Graham's law: lighter gases diffuse faster. Hydrogen diffuses four times faster than oxygen (√(32 ÷ 2) = 4).

Real gases

Real gases differ from ideal gases at high pressure (the particles’ own volume is no longer negligible) and low temperature (attractive forces become important and the gas can liquefy). A real gas behaves most like an ideal gas at high temperature and low pressure.

Check yourself What happens to the volume of a gas when the pressure doubles at constant temperature?
Check yourself A gas occupies 2.0 dm³ at 300 K. At constant pressure, what is its volume at 600 K?
Check yourself Which gas diffuses fastest?

Key terms

Ideal gas
A gas whose particles have no volume and no attractions and that obeys PV = nRT.
Partial pressure
The pressure a gas would exert if it alone filled the container.
Diffusion
The spreading of gas particles from high to low concentration.
Absolute temperature
Temperature in kelvin: °C + 273.

Summary

  • Pressure comes from particles hitting the walls; temperature in kelvin measures average kinetic energy.
  • Boyle, Charles and the pressure law combine into PV = nRT.
  • Dalton: total pressure is the sum of partial pressures; Graham: rate ∝ 1/√M.
  • Real gases deviate from ideal behaviour at high pressure and low temperature.
Chemical Bonding Relative Molecular Masses in Solution