Gas Laws

How the model works

For an ideal gas, pressure P, volume V, amount n (mol) and absolute temperature T (K) are linked by

P V = n R T, R = 8.314 J/(mol·K)

Holding two quantities fixed gives the classic laws:

• Boyle (T, n fixed): P ∝ 1/V, so halving the volume doubles the pressure.
• Charles (P, n fixed): V ∝ T, so the piston rises as the gas warms.
• Gay-Lussac (V, n fixed): P ∝ T.
• Avogadro (P, T fixed): V ∝ n.

The particle picture explains why. Pressure is the momentum delivered per second per unit wall area. Hotter particles move faster (mean kinetic energy ∝ T) and hit harder and more often; a smaller box means more frequent hits. The animation shows a sample of particles (one dot represents many molecules) with speeds drawn from the Maxwell–Boltzmann distribution. The calculated P is exact for the model; the “measured” value from impacts fluctuates around it.

Ideal gas: point particles, no attraction, elastic collisions. Real gases deviate at high pressure and low temperature. The 2-D animation is illustrative; numbers use the 3-D ideal gas law.

Guided experiments

1. Boyle's law. Hold T fixed and halve the volume from 20 L to 10 L. Prediction: P doubles (1 mol at 300 K: 124.7 kPa becomes 249.4 kPa). Impacts become more frequent. Halve the volume
2. Charles's law. Hold P fixed and heat from 300 K to 450 K. Prediction: the piston rises until V is 1.5× larger, and particles visibly speed up. Heat at constant P
3. Pump in more gas. Hold V and T fixed and double n. Prediction: P doubles. Twice as many particles, each hitting as hard as before. Double the amount

Challenge

A sealed 2 L bottle of air at 20 °C and 101 kPa is left in a car at 60 °C. What is the pressure inside? Why must you use kelvin, not °C?

References

• OpenStax, Chemistry 2e, §9.2 “Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law”.
• OpenStax, University Physics Volume 2, §2.2 “Pressure, Temperature, and RMS Speed”.