Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 6C / a / Solution

The first reaction is reversible, with reverse rate

k_{- 1} c_{1}

. Applying the law of mass action to each reaction gives

\overset{e}{˙} \overset{s}{˙} \overset{c}{˙}_{1} \overset{c}{˙}_{2} \overset{p}{˙} = - k_{1} es + k_{- 1} c_{1}, = - k_{1} es + k_{- 1} c_{1} - k_{2} c_{1} s, = k_{1} es - k_{- 1} c_{1} - k_{2} c_{1} s + k_{3} c_{2}, = k_{2} c_{1} s - k_{3} c_{2}, = k_{3} c_{2} .

Each term has the sign dictated by whether the corresponding species is consumed or produced.

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