= Solution
The forward and reverse pathways pass through the same <transition state>. Measured from the cis minimum, the forward barrier is $E_{a,1}$; measured from the trans minimum, the reverse barrier is $E_{a,-1}$. Since $E_{a,-1}=E_{a,1}+2.23\,\mathrm{kJ\,mol^{-1}}$, the trans minimum lies \b[$2.23\,\mathrm{kJ\,mol^{-1}}$ below the cis minimum] in the elementary energy-profile model:
$$
E_{\rm trans}-E_{\rm cis}=E_{a,1}-E_{a,-1}=-2.23\,\mathrm{kJ\,mol^{-1}}.
$$
The absolute barrier heights cannot be deduced from their difference. The following original profile uses an arbitrary transition-state height and labels that distinction explicitly.
\Image[/past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-isomerization-energy.png]
{title=Original elementary energy profile with trans below cis and the reverse barrier larger by 2.23 kJ per mole}
Back to article page
