The Ideal Gas Law is the equation PV equals nRT, relating the pressure P, volume V, amount of substance n, universal gas constant R, and absolute temperature T of an ideal gas. It provides a compact mathematical description of how these macroscopic properties are related when the gas behaves sufficiently close to the idealised assumptions of negligible molecular volume and negligible intermolecular forces.
The equation can also be written as P equals rho RT divided by M when density rho and molar mass M are used, or as P equals N k T divided by V when the number of individual molecules N and Boltzmann constant k are used. Temperature must be expressed on an absolute scale such as kelvin.
The Ideal Gas Law is called ideal because it represents an approximation rather than the exact behaviour of every real gas. The underlying idealisation assumes that gas molecules occupy negligible volume compared with the container, move continuously and randomly, experience negligible intermolecular attraction or repulsion except during collisions, and undergo essentially elastic collisions. Real gases increasingly depart from these assumptions at high pressures and low temperatures, particularly near condensation conditions. Under ordinary conditions many common gases can nevertheless be approximated effectively by the equation, making it useful for engineering calculations, laboratory work, atmospheric studies and thermodynamic analysis.
The Ideal Gas Law combines several experimentally established relationships. At constant temperature and amount of gas, pressure varies inversely with volume, corresponding to Boyle's law. At constant pressure, volume is proportional to absolute temperature, corresponding to Charles's law. At constant volume, pressure is proportional to absolute temperature, corresponding to the pressure temperature relationship sometimes called Gay Lussac's law. Avogadro's law establishes that volume is proportional to amount of gas at constant pressure and temperature. The Ideal Gas Law unifies these relationships into one equation and therefore provides a general framework for relating changes in multiple state variables.
The equation is a state equation because it relates equilibrium state variables rather than directly describing the detailed molecular trajectory of the gas. If n and T remain fixed, increasing V reduces P, while reducing V increases P. If V and n remain fixed, increasing T increases P. If P and T remain fixed, increasing n requires a proportional increase in V. These relationships are frequently used in gas storage, compression, ventilation, pneumatic systems, chemical processing and laboratory calculations. When the amount of gas changes through leakage, injection or reaction, n must be treated as a variable rather than assumed constant.
The Ideal Gas Law is closely connected with kinetic theory and thermodynamics. Kinetic theory explains gas pressure in terms of molecular motion and collisions with container walls, while temperature is related to average molecular kinetic energy. The law also provides the basis for the ideal gas internal energy model, in which internal energy depends primarily on temperature for an ideal gas. Heat capacity relationships, enthalpy calculations and many thermodynamic processes can therefore be expressed using ideal gas assumptions. The equation is particularly useful when combined with conservation of mass and conservation of energy, although those conservation principles provide information that the Ideal Gas Law alone cannot supply.
Real gases are described more accurately by equations of state that account for molecular interactions and finite molecular size. The van der Waals equation introduces corrections for attractive forces and molecular volume, while more sophisticated equations of state are used extensively in chemical engineering and thermodynamics. A dimensionless compressibility factor Z quantifies deviation from ideal behaviour, with Z equal to one corresponding to ideal behaviour. The reduced pressure and reduced temperature of a gas, together with corresponding states concepts, can help characterise nonideal behaviour. The Ideal Gas Law should therefore not be treated as universally exact, particularly in high pressure, low temperature or near critical conditions.
Correct use of the Ideal Gas Law requires attention to units and definitions. The gas constant R has different numerical values depending on the chosen pressure, volume, amount and energy units, while temperature must be absolute rather than Celsius or Fahrenheit. Pressure may need to be converted between pascals, atmospheres, bar and other units, and volume must be expressed consistently with the chosen value of R. Gauge pressure should not normally be substituted directly for thermodynamic absolute pressure because the equation describes absolute pressure. Errors involving temperature scales, pressure references, molar mass or unit conversions are among the most common practical sources of incorrect results.
The Ideal Gas Law remains important because it provides a simple bridge between measurable macroscopic quantities and molecular behaviour. It is used to estimate gas densities, calculate unknown pressures or volumes, determine amounts of gas, analyse compression and expansion, and provide initial approximations for more sophisticated models. It is especially useful when its assumptions are explicitly recognised rather than ignored.
The equation does not by itself determine heat transfer, reaction rates, fluid velocity, phase changes or the detailed spatial distribution of pressure. Those questions require additional physical laws and constitutive relationships. Its strength is therefore its broad applicability as a simple state relationship within the range where ideal gas behaviour is a reasonable approximation.
