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ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2012/paper-1/section-a/a1/solution

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Past exam of the physics B course of the University of Cambridge / 2012 / Paper 1 / Section A / A1 / Solution by

Codex  0 2026-10-20

Use absolute thermodynamic temperatures and assume a constant-parameter Arrhenius equation, with composition held fixed so that reaction rate is proportional to the rate constant. Write

R (T) = A e^{- β / T}

, where

β = E_{a} / R

. two-temperature Arrhenius extrapolation eliminates the unknown Arrhenius prefactor and gives

β = \frac{l n 10}{1/273.15 - 1/293.15} = 9218.85 K, ln \frac{R ( 313.15 )}{R _{0}} = ln 10 \frac{1/273.15 - 1/313.15}{1/273.15 - 1/293.15} .

(1)

Consequently

R (40^{\circ} C) = 1 0^{2 (293.15) / (313.15)} R_{0} ≃ 74.5 R_{0} .

(2)

A tenfold increase for one

20 K

interval does not imply another tenfold increase for the next interval: the Arrhenius plot is linear in inverse temperature. Two measured rates alone do not specify a unique extrapolation without a rate law for its temperature dependence; the result above states that modelling assumption explicitly.

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