Solution (source code)

= Solution

Take the rapid <temperature jump> to occur at $t=0$. Neglect thermal expansion as in the stated constant-$C_{\rm tot}$ model. The composition is initially unchanged, so the curve is continuous through $t=0$, with
$$
\frac{[\mathrm{trans}]_{\rm eq1}}{C_{\rm tot}}=0.71095,\qquad
\frac{[\mathrm{trans}]_{\rm eq2}}{C_{\rm tot}}=0.69789.
$$
It is horizontal at the first value before the jump, then \b[decreases exponentially towards the lower second plateau], without overshoot:
$$
\frac{[\mathrm{trans}](t)}{C_{\rm tot}}=0.69789+0.01307\,e^{-0.0014902t}\quad(t\ge0).
$$
The initial post-jump slope is negative, and the curve is concave upward. A discontinuous vertical step in the composition would incorrectly make a finite reaction happen instantaneously.

\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-relaxation.png]
{title=Original normalized trans-concentration relaxation curve, continuous at the temperature jump and approaching its new lower plateau}