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

Take the rapid temperature jump to occur at $t=0$. Neglect thermal expansion as in the stated constant-$C_{\mathrm{tot}}$ model. The composition is initially unchanged, so the curve is continuous through $t=0$, withIt is horizontal at the first value before the jump, then decreases exponentially towards the lower second plateau, without overshoot: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.

Subtract the new equilibrium concentration and divide by the initial displacement:At the halfway concentration this ratio is $1/2$, soThis is the half-time of the displacement from equilibrium. It is not the time for the absolute trans concentration to fall to half its initial value; that value lies far below the attainable new equilibrium plateau. The corresponding chemical relaxation time is $671$ s.