Explore Boyle's, Charles's, Gay-Lussac's, and the combined ideal gas law interactively.
The gas laws describe some of the most reliably predictable behavior in all of chemistry, which is exactly why they appear so often on AP Chemistry Unit 3, USNCO, and IChO exams — the ideal gas law and its historical special cases let you calculate any gas property from any other with high confidence.
The ideal gas law, PV = nRT, unifies pressure, volume, moles, and temperature into a single equation (R = 0.0821 L·atm/mol·K, or 8.314 J/mol·K in SI units). Historically, this was discovered piecewise: Boyle's law (P1V1 = P2V2, at constant n and T) established that pressure and volume are inversely proportional; Charles's law (V1/T1 = V2/T2, at constant n and P) established that volume and absolute temperature are directly proportional; and Gay-Lussac's law (P1/T1 = P2/T2, at constant n and V) established the same direct relationship between pressure and temperature. All three are special cases of the ideal gas law with one variable held fixed.
Real gases deviate from ideal behavior, especially at high pressure and low temperature, because the ideal gas law assumes gas particles have zero volume and experience no intermolecular attraction — both assumptions break down under those conditions. The van der Waals equation, (P + an²/V²)(V - nb) = nRT, corrects for this: the a term accounts for intermolecular attraction reducing the pressure gas particles actually exert on the container walls, and the b term accounts for the finite volume the gas particles themselves occupy, reducing the space available for particle motion.
Molar volume at STP (0°C, 1 atm, using the older definition, or the current IUPAC 0°C, 1 bar) is 22.4 L/mol for any ideal gas — a useful shortcut, but only valid exactly at STP; problems at non-standard conditions require the full PV = nRT calculation.
This gas laws simulator lets you manipulate pressure, volume, temperature, and moles interactively, compare Boyle's, Charles's, and combined gas law scenarios, and overlay van der Waals real-gas isotherms against ideal behavior — making the deviation between theory and reality directly visible.