The gaseous state: ideal and real gases and pV = nRT — common mistakes

Memorise the key unit conversions: 1 kPa = 1000 Pa, 1 m³ = 1000 dm³, and 1 dm³ = 1000 cm³. The most common mistake is forgetting to convert volume from cm³ or dm³ into m³, or pressure from kPa into Pa. Always convert temperature to Kelvin by adding 273 to the Celsius value.

The Kelvin scale is an absolute temperature scale, where 0 K represents absolute zero – the point at which particles have minimum kinetic energy. Gas laws like Charles's Law (V ∝ T) rely on this direct proportionality. Using Celsius would lead to incorrect results, as 0 °C is not an absolute zero point and the scale allows for negative values, which would imply negative volume or pressure.

You can rearrange the ideal gas equation to R = pV/nT. Then, substitute the SI units for each variable: R = (Pa × m³) / (mol × K). A Pascal is a Newton per square metre (N m⁻²), so Pa × m³ = (N m⁻²) × m³ = N m. A Newton-metre is a Joule (J), the unit of energy. Therefore, the units of R are J mol⁻¹ K⁻¹.

Gases with very weak intermolecular forces and small particle size behave most ideally. Therefore, helium (He) and hydrogen (H₂) are the most ideal of the real gases, as they are small and have only weak London dispersion forces.