State how the rate constant, $k$ varies with temperature,$T$.

Determine the activation energy, ${E_{\text{a}}}$, for this reaction.

The rate expression for this reaction is rate $= k{{\text{[}}{{\text{N}}_{\text{2}}}{\text{O]}}^{\text{2}}}$ and the rate constant is ${\text{0.244 d}}{{\text{m}}^{\text{3}}}{\text{mo}}{{\text{l}}^{ - 1}}{{\text{s}}^{ - 1}}$ at 750 °C.

A sample of ${{\text{N}}_{\text{2}}}{\text{O}}$ of concentration ${\text{0.200 mol}}\,{\text{d}}{{\text{m}}^{ - 3}}$ is allowed to decompose. Calculate the rate when 10% of the ${{\text{N}}_{\text{2}}}{\text{O}}$ has reacted.

$k$ increases with increase in $T/k$ decreases with decrease in $T$;

Do not allow answers giving just the Arrhenius equation or involving lnk relationships.

${\text{gradient}} =  - {E_{\text{a}}}/R$;

$- 30000{\text{ }}(K) =  - {E_{\text{a}}}/R$;

Allow value in range –28800–31300 (K).

$0.9 \times 0.200 = 0.180{\text{ (mol}}\,{\text{d}}{{\text{m}}^{ - 3}}{\text{)}}$;

${\text{rate}} = \left( {0.244 \times {{(0.180)}^2} = } \right){\text{ }}7.91 \times {10^{ - 3}}{\text{ mol}}\,{\text{d}}{{\text{m}}^{ - 3}}{{\text{s}}^{ - 1}}$;

Award [2] for correct final answer.

Award [1 max] for either 9.76 $\times$ 10^–3 mol$\,$dm^–3s^–1 or 9.76 $\times$ 10^–5 mol$\,$dm^–3s^–1.

This question on chemical kinetics was very poorly answered by candidates. In (a), many candidates simply gave the Arrhenius equation and failed to describe the explicit relationship between $k$ and $T$.

(b) was answered very poorly and although some candidates had an idea about the gradient expression, most were out by a factor of 100 in their final answer and many totally ignored units.

In (c), the most common error related to the 10% reduction and units also proved challenging.