Chemistry · General chemistry I · Concept

The ideal gas law, PV = nRT

The ideal gas law, PV = nRT, relates a gas’s pressure P, volume V, amount n and absolute temperature T through the gas constant R = 0.08206 L·atm/(mol·K). Solve it for the unknown, with the temperature in kelvin and every unit matching R.

One equation, four variables

Pressure, volume, amount and temperature describe a gas sample, and PV = nRT links them: given any three, the fourth follows. It describes real gases well at ordinary temperatures and pressures, where the particles are far apart.

P V = n R T

Units that match R

With R = 0.08206 L·atm/(mol·K), which is 0.08205821 rounded, pressure must be in atmospheres, volume in liters, amount in moles and temperature in kelvin. With R = 8.314 J/(mol·K), use pascals and cubic meters. Convert before you substitute.

R = 0.08206 \frac{L \cdot atm}{mol \cdot K}

Always use kelvin

Gas laws need absolute temperature, measured from absolute zero. Add 273.15 to a Celsius temperature: 25.0 °C is 298.2 K. A Celsius value in PV = nRT gives wrong answers, and below 0 °C even a negative volume.

T (K) = t (\circ C) + 273.15

The combined gas law

For a fixed amount of gas, nR is constant, so PV/T stays the same when conditions change. Boyle’s law, at constant temperature, and Charles’s law, at constant pressure, are special cases.

\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}

Mixtures: Dalton’s law

In a mixture, each gas exerts its own partial pressure, and the partial pressures add up to the total. Each gas’s partial pressure is its mole fraction times the total pressure.

P_{total} = P_{A} + P_{B} + \dots, P_{A} = χ_{A} P_{total}

\begin{array}{c} P_{total} = P_{A} + P_{B} + \dots \\ P_{A} = χ_{A} P_{total} \end{array}

Molar volume at STP

At 0 °C and 1 atm, one mole of an ideal gas occupies 22.414 L. It makes a quick check, but it holds only at those conditions.

V_{m} = 22.414 L/mol at STP

Common mistakes

Using a Celsius temperature instead of kelvin.
Mixing units: R = 0.08206 L·atm/(mol·K) needs atmospheres and liters, not mmHg or mL.
Using 22.4 L/mol at conditions other than 0 °C and 1 atm.
Using gauge pressure, which reads zero at atmospheric pressure, instead of absolute pressure.

Key terms

Ideal gas law: PV = nRT, linking a gas’s pressure, volume, moles and kelvin temperature. It treats gas particles as having no size and no attractions, so it works best at low pressure and high temperature.
Molar gas constant: R, the constant in PV = nRT. Use the value that matches your units: 8.314 J/(mol·K) with energy, or 0.08206 L·atm/(mol·K) with liters and atmospheres.
Absolute temperature: Temperature in kelvins, measured from absolute zero. Add 273.15 to a Celsius temperature before using it in gas-law or thermodynamics equations.
Combined gas law: For a fixed amount of gas, P₁V₁/T₁ = P₂V₂/T₂, with temperatures in kelvin. It follows from PV = nRT with n constant and contains Boyle’s and Charles’s laws as special cases.
Partial pressure: The pressure one gas in a mixture would exert if it filled the container alone: partial pressure of A = (mole fraction of A) × (total pressure). By Dalton’s law, the partial pressures add up to the total pressure.
Mole fraction: mole fraction of A = (moles of A) ÷ (total moles of everything in the mixture). It has no units, and all the mole fractions in a mixture add up to 1.
Standard temperature and pressure: Reference gas conditions of 0 °C (273.15 K) and 1 atm, the convention Tro uses. IUPAC now defines STP with 1 bar, so check which one a source means.
Molar volume: The volume that one mole of a substance takes up: molar volume = volume ÷ moles. For an ideal gas at 0 °C and 1 atm it is 22.414 L/mol.

Work through an example

What volume does 0.250 mol of nitrogen gas occupy at 25.0 °C and 1.50 atm?

Find a gas volume with PV = nRT →

Use the combined gas law →

Find partial pressures with Dalton’s law →

Sources and scope

Authored study material. Tool results depend on the stated inputs and model assumptions.

Make it concrete

Try in the workspace

Open the example inputs, change a value and keep a useful result on your board.

Solve it in Gas laws & mixtures Check the calculation in a Chemistry box Open worked example on a board Chemistry formulas: gases

Your existing work stays on this device. Examples open as editable copies.