Thermodynamics & Heat
Intermediate

Ideal Gas Law

Relates pressure, volume, moles and temperature.

Formula

PV=nRTPV = nRT

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Variables

PPressure
VVolume
nMoles
RGas constant
TTemperature

How it works

The ideal gas law connects how much gas you have, how much space it occupies, how hard it pushes on its container, and how hot it is. It works because, for a dilute gas, the particles are far enough apart that their individual volumes and intermolecular forces are usually negligible, so the gas behavior is dominated by random motion and collisions with the container walls. The constant R sets the scale so that pressure, volume, amount of substance, and temperature are all in compatible units.

When to use it

Use this law when you need to find one gas property from the other three, especially for gases at moderate pressure and not too close to condensation. It is common in chemistry, physics, engineering, and lab calculations involving sealed containers, reactions that produce gas, or gas sampling.

Worked example, step by step

A container holds 0.80 mol of an ideal gas at 27°C and 2.0 × 10^5 Pa. Find the volume. Step 1: Write the ideal gas law: PV = nRT Step 2: Rearrange for volume: V = nRT / P Step 3: Convert temperature to kelvin: T = 27 + 273 = 300 K Step 4: Substitute values using R = 8.314 J mol^-1 K^-1: V = (0.80 × 8.314 × 300) / (2.0 × 10^5) Step 5: Calculate the numerator: 0.80 × 8.314 × 300 = 1995.36 Step 6: Divide by pressure: V = 1995.36 / (2.0 × 10^5) = 9.98 × 10^-3 m^3 Step 7: Convert to litres if desired: 9.98 × 10^-3 m^3 = 9.98 L Final answer: V ≈ 1.0 × 10^-2 m^3, or about 10 L.

Common mistakes to avoid

  • Using °C instead of kelvin for temperature
  • Mixing units, such as pressure in atm with R in J mol^-1 K^-1 without converting
  • Forgetting to rearrange the formula correctly before substituting values

Did You Know?

The ideal gas law combines three older laws and works remarkably well for real air at everyday conditions.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026