Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 5 / a / iii / Solution

Let $C_{\mathrm{tot}}=[\mathrm{cis}]+[\mathrm{trans}]$, which is conserved for this closed one-to-one isomerization at fixed volume. Substitute $[\mathrm{cis}{]}_{298}=C_{\mathrm{tot}}-[\mathrm{trans}{]}_{298}$ into the equilibrium ratio:ThereforeThe equilibrium split is independent of having started with pure cis, provided equilibration is complete and no side reaction changes the total concentration.