AP Chemistry 5.8: Rate-Determining Steps

Practice AP Chemistry questions on identifying a rate-determining first step and checking whether an elementary-step rate law agrees with the observed overall rate law.

[Maximum number: 1]

The following equation represents the decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ , for which the rate law is rate $=k\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]$ .

2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \rightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)

A sample of pure $\mathrm{N}_{2} \mathrm{O}_{5}(g)$ is placed in an evacuated container and allowed to decompose at a constant temperature of 300 K. The concentration of $\mathrm{N}_{2} \mathrm{O}_{5}(g)$ in the container is measured over a period of time, and the measurements are recorded in the following table.

Table for Question 5.8.A—Identify the rate law for a reaction from a mechanism in which the first step is rate limiting question 1 — AP Chemistry

The following mechanism is proposed for the decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}(g)$ .

\begin{aligned} & \text { Step 1: } \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{NO}_{3}(g) \\ & \text { Step 2: } \mathrm{NO}_{2}(g)+\mathrm{NO}_{3}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{NO}(g)+\mathrm{O}_{2}(g) \\ & \text { Step 3: } \mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{NO}(g) \rightarrow 3 \mathrm{NO}_{2}(g) \end{aligned}

Identify which step of the proposed mechanism (1, 2, or 3) is the rate-determining step. Justify your answer in terms of the rate law given.

For the correct answer and a valid justification: 1 point
Step 1 is the rate-determining step. The rate law of elementary step 1 is rate $=k\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]$ , which is consistent with the first order kinetics of the overall rate law.

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5.8.A—Identify the rate law for a reaction from a mechanism in which the first step is rate limiting question 1