The State of Gases: A Guide to the Ideal Gas Law

The Ideal Gas Law is a fundamental equation of state that describes the behavior of a hypothetical 'ideal' gas. It provides a simple and powerful relationship between four key physical properties of a gas: pressure (P), volume (V), the number of moles (n), and temperature (T). The law is a combination of several simpler gas laws (Boyle's, Charles's, and Avogadro's laws) into a single, comprehensive expression. While no gas is truly 'ideal', this law provides an excellent approximation for the behavior of most real gases under a wide range of conditions, making it one of the most important and widely used equations in chemistry and physics.

It is essential for a huge variety of applications, from calculating the volume a gas will occupy under certain conditions in a chemical reaction to understanding how pressure changes in an airplane cabin at altitude. This calculator is a versatile tool designed to make working with the Ideal Gas Law effortless. It allows you to solve for any of the four variables—pressure, volume, moles, or temperature—by simply providing the other three. This is invaluable for students completing homework, for scientists in the lab, and for engineers designing systems that involve gases.

The Ideal Gas Law Equation

The law is famously expressed by the formula:

PV = nRT

Where:

P (Pressure): The force exerted by the gas per unit area on the walls of its container. Must be in units compatible with the R constant, typically atmospheres (atm).
V (Volume): The space occupied by the gas. Must be in units compatible with R, typically Liters (L).
n (Moles): The amount of substance of the gas, measured in moles (mol).
T (Temperature): The absolute temperature of the gas. This must be in Kelvin (K) for the equation to work.
R (Ideal Gas Constant): A fundamental physical constant that acts as the proportionality factor in the equation. Its value depends on the units used for the other variables. A common value, and the one used by this calculator, is 0.08206 L·atm/(mol·K).

Assumptions of an Ideal Gas

The Ideal Gas Law is based on a simplified model of a gas. The key assumptions are:

Gas particles themselves have no volume; they are treated as dimensionless points.
There are no intermolecular attractive or repulsive forces between the gas particles. Collisions between particles and with the container walls are perfectly elastic.

Real gases deviate from this ideal behavior at very high pressures (when the volume of the particles becomes significant compared to the container volume) and at very low temperatures (when intermolecular forces become significant).

Ideal Gas Law Calculator