The ideal gas law is one of the most fundamental equations in chemistry and physics. Written as PV = nRT, it relates four variables that describe the state of a gas: pressure (P), volume (V), the number of moles (n), and temperature (T). The constant R is called the ideal gas constant and takes different values depending on the units you are using. For most chemistry problems, R = 0.08206 L atm / (mol K) is the most convenient choice.
Understanding Each Variable
Pressure is measured in atmospheres (atm), but you will also encounter kilopascals (kPa), mmHg (torr), and bar in different contexts. Volume is typically in liters (L) for gas law calculations. Temperature must always be in Kelvin — this is a common trap for students who forget to convert from Celsius. The number of moles tells you how much gas is present, and you can convert between moles and grams using molar mass.
Worked Example
Suppose you have a 5.0 L container of nitrogen gas at 2.0 atm and 300 K. How many moles of gas are present? Rearranging PV = nRT gives n = PV / (RT). Plugging in: n = (2.0 x 5.0) / (0.08206 x 300) = 10 / 24.618 = 0.406 moles. Our Ideal Gas Law Calculator can solve for any of the four variables when the other three are known.
When the Ideal Gas Law Fails
Real gases deviate from ideal behavior at high pressures and low temperatures. This is because the ideal gas law assumes that gas particles have no volume and do not interact with each other, which is not true for real molecules. At very high pressures, the volume of the gas particles themselves becomes significant relative to the container volume. At low temperatures, intermolecular forces cause gases to condense into liquids. For most situations you will encounter in a general chemistry course, the ideal gas law works perfectly well. If you need more precision, the van der Waals equation corrects for these deviations.
Related Gasgesetze
The ideal gas law is actually a combination of several simpler gas laws. Boyle's Law (P1V1 = P2V2) describes the inverse relationship between pressure and volume at constant temperature. Charles's Law (V1/T1 = V2/T2) shows that volume is directly proportional to temperature at constant pressure. The Combined Gas Law merges these relationships into a single equation for situations where pressure, volume, and temperature all change simultaneously.