Ideal Gas Law — PV = nRT

The ideal gas law PV = nRT explained: pressure, volume, moles and temperature, the gas constant R, and a worked example.

What it means

The ideal gas law ties together the four measurable properties of a gas: squeeze the volume and the pressure rises; heat the gas and the pressure rises; add more molecules and the pressure rises. Temperature must be in kelvin — the law counts molecular kinetic energy, which hits zero at absolute zero, not at 0 °C. R is just the unit-conversion constant that makes the units work. Real gases deviate at high pressure and low temperature, but for air in tires, balloons and lungs, PV = nRT is remarkably accurate.

Variables

Assumptions

• Gas molecules are point particles with no intermolecular forces
• Collisions are perfectly elastic
• Temperature is low enough that molecules don't dissociate, high enough that quantum effects are negligible

Derivation

Boyle's law ($PV$ = const), Charles's law ($V/T$ = const) and Avogadro's law ($V/n$ = const) each fix one variable. Combining all three proportionalities gives $PV = nRT$, where the single constant R absorbs the three individual constants.

Worked example

Given:

• n = 2 mol
• T = 300 K
• V = 0.05 m³
• R = 8.314 J/(mol·K)

1. Write the law and rearrange: $P = nRT/V$

2. Substitute: $P = (2)(8.314)(300) / 0.05$

3. Numerator: $2 \times 8.314 \times 300 = 4988.4$

4. Divide: $P = 4988.4 / 0.05 = 99{,}768\ \mathrm{Pa}$