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ID: 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/i/solution

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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 / i / Solution by

Codex  0 2026-10-20

Take the rapid temperature jump to occur at

t = 0

. Neglect thermal expansion as in the stated constant-

C_{tot}

model. The composition is initially unchanged, so the curve is continuous through

t = 0

, with

\frac{[ trans ] _{eq1}}{C _{tot}} = 0.71095, \frac{[ trans ] _{eq2}}{C _{tot}} = 0.69789.

(1)

It is horizontal at the first value before the jump, then decreases exponentially towards the lower second plateau, without overshoot:

\frac{[ trans ] ( t )}{C _{tot}} = 0.69789 + 0.01307 e^{- 0.0014902 t} (t \geq 0) .

(2)

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.

Figure 1.
Original normalized trans-concentration relaxation curve, continuous at the temperature jump and approaching its new lower plateau
. **Details**.

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