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Chapter 14: Problem 47

The rate law for the reaction $$ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g) $$ is given by rate \(=k[\mathrm{NO}]\left[\mathrm{Cl}_{2}\right]\). (a) What is the order of the reaction? (b) A mechanism involving these steps has been proposed for the reaction $$ \begin{aligned} \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) & \longrightarrow \mathrm{NOCl}_{2}(g) \\ \mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \longrightarrow & 2 \mathrm{NOCl}(g) \end{aligned} $$ If this mechanism is correct, what does it imply about the relative rates of these two steps?

Short Answer

Expert verified
The order of the reaction is 2. According to the proposed mechanism, the first step is slower and therefore rate-determining, while the second step is faster.

Step by step solution

01

Determine the order of the reaction

The order of a reaction is determined by the sum of the powers of the concentration terms in the rate law. Here the rate law is given as: \(rate = k[\mathrm{NO}][\mathrm{Cl}_2]\). The reaction is first order with respect to both \(\mathrm{NO}\) and \(\mathrm{Cl}_2\). Therefore, the overall order of the reaction is \(1 + 1 = 2\).
02

Understand the proposed mechanism

The proposed mechanism consists of two steps. The first step: \(\mathrm{NO}(g) + \mathrm{Cl}_2(g) \rightarrow \mathrm{NOCl}_2(g)\) and the second step: \(\mathrm{NOCl}_2(g) + \mathrm{NO}(g) \rightarrow 2\mathrm{NOCl}(g)\). The rate law does not contain a term for \([\mathrm{NOCl}_2]\), indicating that the concentration of \(\mathrm{NOCl}_2\) does not directly affect the rate of the reaction.
03

Determine relative rates of the reaction steps

Since the rate law matches the rate-determining (slowest) step of the proposed mechanism, the second step must be faster than the first step, and thus the first step is the rate-determining step. The slow step does not include the intermediate \(\mathrm{NOCl}_2\), implying that it must quickly react in the second step as soon as it is formed in the first step.

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Most popular questions from this chapter

Write an equation relating the concentration of a reactant \(\mathrm{A}\) at \(t=0\) to that at \(t=t\) for a first-order reaction. Define all the terms and give their units.

For the reaction \(X_{2}+Y+Z \longrightarrow X Y+X Z\) it is found that doubling the concentration of \(\mathrm{X}_{2}\) doubles the reaction rate, tripling the concentration of \(Y\) triples the rate, and doubling the concentration of \(Z\) has no effect. (a) What is the rate law for this reaction? (b) Why is it that the change in the concentration of \(Z\) has no effect on the rate? (c) Suggest a mechanism for the reaction that is consistent with the rate law.

The rate of the reaction $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(a q) &+\mathrm{H}_{2} \mathrm{O}(l) \\ \longrightarrow & \mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \end{aligned} $$ shows first-order characteristics-that is, rate \(=\) \(k\left[\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}\right]\) - even though this is a second- order reaction (first order in \(\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}\) and first order in \(\mathrm{H}_{2} \mathrm{O}\) ). Explain.

Consider this elementary step: $$ X+2 Y \longrightarrow X Y_{2} $$ (a) Write a rate law for this reaction. (b) If the initial rate of formation of \(\mathrm{XY}_{2}\) is \(3.8 \times 10^{-3} \mathrm{M} / \mathrm{s}\) and the initial concentrations of \(X\) and \(Y\) are \(0.26 M\) and \(0.88 M\), what is the rate constant of the reaction?

Explain what is meant by the rate law of a reaction.
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