ChemistryGeneral ChemistryHigh school

Gas Laws

Ideal gas law and combined gas law.

Gases are described by four variables: pressure $P$ , volume $V$ , temperature $T$ and amount $n$ . The ideal gas law $PV = nRT$ ties them together, with $R = 0.08206$ L·atm/(mol·K). Boyle's, Charles's and Gay-Lussac's laws are special cases where some variables are held constant.

Temperature must always be in kelvins, $K = {}^\circ C + 273.15$ , because the laws describe proportionality to absolute temperature. At $0^\circ$ C and 1 atm, one mole of an ideal gas occupies about 22.4 L.

Key terms

Ideal gas law: Relates pressure, volume, amount and temperature.
$PV = nRT$

Key ideas

Combined gas law: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$ for a fixed amount of gas.
Boyle: $P_1 V_1 = P_2 V_2$ at constant $T$ .
Charles: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ at constant $P$ .
Match the units of $R$ to your pressure and volume units.

Worked example

A gas occupies 4.0 L at 300 K. What volume does it occupy at 450 K at the same pressure?

Charles's law: $\frac{4.0}{300} = \frac{V_2}{450}$ .
$V_2 = 4.0 \times \frac{450}{300}$ .
$V_2 = 6.0$ L.

Answer: $6.0$ L

Common mistakes

Using degrees Celsius in the gas laws.
Mismatching the units of $R$ .
Inverting the ratio in Boyle's law (pressure and volume move in opposite directions).

Practice questions

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1.Convert $27^\circ$ C to kelvins.
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$300.15$ K
2.A gas at 2 atm and 6 L is compressed to 3 L at constant temperature. New pressure?
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$4$ atm
3.Moles of gas in 24.6 L at 1 atm and 300 K, to two decimals.
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$1.00$

Key terms

Key ideas

Worked example

Common mistakes

Practice questions

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