The Ideal Gas Law and the van der Waals equation. “All models are wrong, but some are useful.”

The gas laws describe how pressure, volume, temperature, and quantity determine the behavior of gases. The ideal gas law, PV = nRT, treats molecules as point particles with no intermolecular forces, producing a remarkably useful approximation. The van der Waals equation goes further, correcting for the finite size of molecules and the attractions between them. Those additions explain why real gases stray from ideal behavior, especially at high pressures and low temperatures. Together, the equations range from an elegant simplified model to a more realistic picture of molecular crowds interacting. They are used primarily in thermodynamics, chemical engineering, and physical chemistry.