The ideal gas law

Example content

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The model

An ideal gas is a model in which particles have negligible volume and no intermolecular interactions, except during elastic collisions. The equation $PV=nRT$ connects its macroscopic properties.

$$PV=nRT$$

Here $P$ is absolute pressure, $V$ is volume, $n$ is amount of substance, and $T$ is absolute temperature. Use kelvin for temperature and consistent units throughout.

Choosing units

In SI units, use $P$ in pascals, $V$ in cubic metres, and $R = 8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}$. Since $1\,\mathrm{Pa\,m^3}=1\,\mathrm{J}$, the units are consistent.

A worked example

One mole of ideal gas occupies $24.0\,\mathrm{L}$ at $298\,\mathrm{K}$. Converting the volume to $0.0240\,\mathrm{m^3}$ gives:

$$P=\frac{nRT}{V} =\frac{(1.00)(8.314)(298)}{0.0240} \approx 1.03\times10^5\,\mathrm{Pa}.$$

Reading an isotherm

At constant temperature and amount, pressure is inversely proportional to volume. Doubling the volume halves the pressure.

Example diagram — replace with your own figure. Schematic, not to scale.

Limits of the model

Real gases deviate from this model, especially at high pressure or near condensation. An ideal-gas calculation should always begin by checking that the approximation is appropriate.