The Ideal Gas Law (PV = nRT) Explained
The ideal gas law is PV = nRT, relating a gas sample's pressure (P), volume (V), amount in moles (n) and absolute temperature (T) through the gas constant R. With pressure in atmospheres and volume in liters, R = 0.08206 L·atm·mol⁻¹·K⁻¹. Knowing any three variables lets you solve for the fourth.
What Each Variable Means
In PV = nRT, P is the pressure the gas exerts, V is the volume it occupies, n is the amount of gas in moles, T is the absolute temperature, and R is the universal gas constant that makes the units balance. The law combines three older gas laws — Boyle's, Charles's and Avogadro's — into one equation.
Because the four state variables are linked, changing one forces the others to adjust. Heat a sealed rigid container and the pressure rises in proportion to absolute temperature; compress a gas at constant temperature and its pressure rises as volume falls.
Choosing the Right Gas Constant
R takes different numerical values depending on your units. For pressure in atmospheres and volume in liters, R = 0.08206 L·atm·mol⁻¹·K⁻¹. For SI units — pressure in pascals and volume in cubic meters — R = 8.314 J·mol⁻¹·K⁻¹.
The key rule is that your units must match the constant you use. Convert pressure to atmospheres (1 atm = 760 mmHg = 101.325 kPa) before using the L·atm value.
Why Temperature Must Be in Kelvin
The ideal gas law is directly proportional to absolute temperature, so temperature must be in kelvin. Celsius has an arbitrary zero point, and using it breaks the proportionality — you could even get a negative or nonsensical result. Convert by adding 273.15 to the Celsius temperature.
A classic result follows from the law: at standard temperature and pressure (0 °C and 1 atm), one mole of an ideal gas occupies 22.4 liters. This molar volume is a reference chemists use constantly to convert between gas volumes and moles.