The Ideal Gas Law (PV = nRT)

Uses the ideal gas law PV = nRT to find the amount of gas. Pressure is in kilopascals, volume in litres and temperature in degrees Celsius, with R = 8.314 J/(mol·K).

Explanation

The pressure, volume, temperature and amount of a gas are tied together by a single equation.

PV = nRT

$P$ — pressure in pascals
$V$ — volume in cubic metres
$n$ — amount in moles
$R$ — the gas constant, $8.314$ J/(mol·K)
$T$ — the absolute temperature in kelvin

Notice what is missing: the identity of the gas. Oxygen or hydrogen, it makes no difference. At the same temperature and pressure, equal volumes hold equal numbers of molecules — Avogadro's law.

Example

Find the amount of gas in 22.4 L at 0 °C and one atmosphere (101.325 kPa).

n = \dfrac{PV}{RT} = \dfrac{101325 \times 0.0224}{8.314 \times 273.15} = 0.999\ \text{mol}

Essentially one mole. The familiar textbook fact that a mole of gas fills 22.4 L at standard conditions comes straight out of this equation. The exact figure is 22.414 L, which is why using 22.4 gives 0.999 rather than a clean 1.

Kelvin, always

The most frequent error is plugging in degrees Celsius.

$T$ must be absolute. Enter 0 °C as zero and the equation collapses to $PV = 0$ , which is nonsense. Add 273.15 every time.

T\ (\mathrm{K}) = t\ (°\mathrm{C}) + 273.15

What "ideal" assumes

The law describes a gas whose molecules take up no space and do not attract one another. Real gases obey it very well at everyday temperatures and pressures.

It fails when the pressure is enormous, so that molecular size can no longer be ignored, or when the temperature is very low, where attraction between molecules starts pulling the gas towards a liquid.