Ideal Gas Law Simulator (pV = nRT)

The ideal gas equation, pV = nRT, links the pressure, volume, temperature and amount of any gas that behaves ideally. Hold two of the variables constant and it reduces to the classic gas laws: Boyle's law (p ∝ 1/V at constant n and T), Charles's law (V ∝ T at constant n and p), Gay-Lussac's law (p ∝ T at constant n and V) and Avogadro's law (V ∝ n at constant p and T). This simulator shows each relationship three ways at once: as moving particles, as live readings, and as a graph that plots every state you visit.

The particle model explains why. Pressure comes from molecules colliding with the walls of the container. Squeeze the gas into half the volume and each wall is hit twice as often. Heat it and the molecules move faster, so they hit more often and with more momentum. Temperature must always be in kelvin because the average kinetic energy of the molecules is proportional to the absolute temperature: at the same temperature, helium and xenon molecules have the same mean kinetic energy, so the lighter helium atoms move much faster.

In calculations, R = 8.314 J mol⁻¹ K⁻¹ only gives the right answer when every quantity is in SI units: pressure in pascals, volume in cubic metres and temperature in kelvin. The pV = nRT tab shows each conversion explicitly, which is where most exam marks are lost. Finally, the Real Gases tab uses the van der Waals model to show when the ideal gas law breaks down: at high pressure, where the volume of the molecules matters, and at low temperature, where intermolecular forces are significant.