Describing the State of a Gas

The Ideal Gas Law: PV = nRT

One Single Equation to Link Everything

The ideal gas law links the 4 quantities seen previously with a single equation:

P * V = n * R * T

where:

P: the pressure, in pascals (Pa),
V: the volume, in cubic meters (m³),
n: the amount of substance, in moles (mol),
R: the ideal gas constant, R = 8.314 J/(mol·K),
T: the temperature, in kelvins (K).

Where This Law Comes From

This relationship actually combines several laws discovered separately throughout history: Boyle's law (at constant temperature and amount, P and V vary inversely), Charles's law (at constant pressure, V is proportional to T), and Avogadro's law (at constant pressure and temperature, V is proportional to n). The ideal gas law combines them all into a single equation.

Using the Law in Both Directions

You can isolate whichever quantity you're looking for:

V = n*R*T / P      (find a volume)
P = n*R*T / V      (find a pressure)
n = P*V / (R*T)    (find an amount of substance)
T = P*V / (n*R)    (find a temperature)

A Useful Consequence: the Ratio Stays Constant

If a gas changes state (for example it is compressed) without its amount changing, the ratio PV/T stays constant between the initial state (1) and the final state (2):

P1*V1 / T1 = P2*V2 / T2

This form is very handy when you don't know n, but only how a gas evolves from one state to another.

Common Mistake