3.2 Ideal Gas Law

The Ideal Gas Law equation

PV = nRT relates pressure (P), volume (V), moles (n), and temperature (T) for an ideal gas. R is the gas constant (0.0821 L·atm/mol·K). Temperature must always be in Kelvin. This law assumes gas particles have negligible volume and no intermolecular attractions — a good approximation at low pressure and high temperature.

Rearranging for other quantities

You can solve PV = nRT for any variable: n = PV/RT lets you find moles from measured P, V, T. Since n = mass/molar mass, the law can find molar mass (M = mRT/PV) or density (d = PM/RT) of a gas. These derived forms are common on the exam.

Real gas deviations

Real gases deviate from ideal behavior at high pressure (particles are forced close, volume no longer negligible) and low temperature (slower particles allow intermolecular attractions to matter). Gases with strong intermolecular forces or larger molecular size deviate more from ideal behavior than small, nonpolar gases like He or H₂.

Key terms

Ideal Gas Law

PV = nRT; relates pressure, volume, moles, and temperature (in Kelvin) of a gas.

Gas constant R

0.0821 L·atm/mol·K (common value); relates the variables in PV = nRT.

Molar mass from Ideal Gas Law

M = mRT/PV, derived by substituting n = mass/molar mass into PV = nRT.

When do gases deviate from ideal behavior?

At high pressure (particle volume matters) and low temperature (intermolecular attractions matter).

Ideal gas assumptions

Gas particles have negligible volume and experience no intermolecular attractions.

Try an AP-style question

What volume does 1.00 mol of an ideal gas occupy at 273 K and 1.00 atm?

1. 22.4 L
2. 1.00 L
3. 24.5 L
4. 0.0821 L