Past exam of the chemistry A course of the University of Cambridge / 2023 / Paper 2 / A8 / a / ii / Solution

For an ideal gas, translation makes the molecular partition function proportional to volume. Define the molecular partition function density and number concentration byThenBoth $f_i$ and $c_i$ have units of inverse volume, so their ratio is dimensionless. If concentrations are specified in moles per volume instead, replace $c_i$ in this microscopic expression by $N_A$ times that molar concentration, with consistent volume units.