AP Chemistry Unit 5.9: Mechanism-Based Rate Laws

Practice AP Chemistry Unit 5.9 questions on deriving an overall rate law when a mechanism requires a pre-equilibrium relationship for an intermediate.

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Nitrogen dioxide, $\mathrm{NO}_{2}(g)$ , is produced as a by-product of the combustion of fossil fuels in internal combustion engines. At elevated temperatures $\mathrm{NO}_{2}(g)$ decomposes according to the equation below.

2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)

The concentration of a sample of $\mathrm{NO}_{2}(g)$ is monitored as it decomposes and is recorded on the graph directly below. The two graphs that follow it are derived from the original data.

Figure for Question 5.9 Pre-Equilibrium Approximation question 1 — AP Chemistry

Consider two possible mechanisms for the decomposition reaction.

Is the rate law described by mechanism II shown below consistent with the rate law you wrote in part (b) ? Justify your answer.
Mechanism II

Table for Question 5.9 Pre-Equilibrium Approximation question 1 — AP Chemistry

6 \mathrm{H}^{+}(a q)+2 \mathrm{MnO}_{4}^{-}(a q)+5 \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightarrow 10 \mathrm{CO}_{2}(g)+8 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{Mn}^{2+}(a q)

Yes. Step 2 is slow; therefore, it is the rate-determining step of this
mechanism. The rate law of this elementary reaction is
rate $=k\left[\mathrm{~N}_{2} \mathrm{O}_{4}\right]$ . Because $\mathrm{N}_{2} \mathrm{O}_{4}$ is an intermediate, it cannot appear in
the rate law of the overall reaction. Because $K_{e q}=\frac{\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]}{\left[\mathrm{NO}_{2}\right]^{2}}$ in step 1,
$\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=K_{e q}\left[\mathrm{NO}_{2}\right]^{2}$ . Then, substituting $K_{e q}\left[\mathrm{NO}_{2}\right]^{2}$ for $\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]$ in the
rate law of step 2 gives rate $=\left(k K_{e q}\right)\left[\mathrm{NO}_{2}\right]^{2}$ , which is consistent with
the rate law in part (b).

1 point is earned for the correct answer with justification.

6 \mathrm{H}^{+}(a q)+2 \mathrm{MnO}_{4}^{-}(a q)+5 \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightarrow 10 \mathrm{CO}_{2}(g)+8 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{Mn}^{2+}(a q)

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AP Chemistry Unit 5.9: Mechanism-Based Rate Laws

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5.9 Pre-Equilibrium Approximation question 1