Question
The reaction described by$$2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$is postulated to occur via the mechanism(1) $\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{NO}_{3}(g) \quad$ (slow)(2) $\mathrm{NO}_{3}(g) \rightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g) \quad$ (fast)The rate law for the reaction is$$\text { rate of reaction }=k\left[\mathrm{NO}_{2}\right]^{2}$$Is this mechanism consistent with the observed rate law? Justify your answer.
Step 1
The rate-determining step is the slowest step in a reaction mechanism, which in this case is the first step: $$ \mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{NO}_{3}(g) \quad \text{(slow)} $$ Show more…
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The reaction described by $$ 2 \mathrm{NO}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ has an experimentally determined rate law of $$ \text { rate of reaction }=k[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right] $$ A proposed mechanism for this reaction is (1) $2 \mathrm{NO}(g) \underset{k_{-1}}{\frac{k_{\mathrm{l}}}{k_{2}}} \mathrm{~N}_{2} \mathrm{O}_{2}(g) \quad$ (fast equilibrium) (2) $\mathrm{N}_{2} \mathrm{O}_{2}(g)+\mathrm{H}_{2}(g) \stackrel{k_{2}}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{H}_{2} \mathrm{O}(g) \quad$ (slow) Show that this mechanism is consistent with the observed rate law.
Two mechanisms are proposed for the reaction $$ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g}) $$ \mathrm{Mecbanism } 1 : \mathrm { NO } + \mathrm { O } _ { 2 } $\rightleftharpoons \mathrm{NO}_{3}$ $$ \begin{aligned} &\mathrm{NO}_{3}+\mathrm{NO} \longrightarrow 2 \mathrm{NO}_{2} \\ &\text { Mecbanism } 2: \mathrm{NO}+\mathrm{NO} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2} \end{aligned} $$ slow $$ \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2} $$ slow Show that each mechanism is consistent with the observed rate law: rate $=k[\mathrm{NO}]^{2} \times\left[\mathrm{O}_{2}\right]$
The experimentally determined rate law for the reaction described by the equation $$ 2 \mathrm{NO}_{2}(g)+\mathrm{Br}_{2}(g) \rightarrow 2 \mathrm{NO}_{2} \operatorname{Br}(g) $$ is $$ \text { rate of reaction }=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{Br}_{2}\right] $$ One proposed mechanism for this reaction is (2) $\mathrm{NO}_{2} \mathrm{Br}_{2}(g) \stackrel{k_{2}}{\longrightarrow} \mathrm{NO}_{2} \operatorname{Br}(g)+\operatorname{Br}(g) \quad$ (slow) (3) $\mathrm{Br}(g)+\mathrm{NO}_{2}(g) \stackrel{k_{3}}{\longrightarrow} \mathrm{NO}_{2} \operatorname{Br}(g) \quad$ (fast) Is this mechanism consistent with the experimentally determined rate law?
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