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Chapter 13: Problem 84

The decomposition of ozone is believed to occur in two steps: $$ \mathrm{O}_{3} \rightleftharpoons \mathrm{O}_{2}+\mathrm{O} $$ (elementary reaction) $$ \mathrm{O}_{3}+\mathrm{O} \longrightarrow 2 \mathrm{O}_{2} $$ (elementary reaction) Identify any reaction intermediate. What is the overall reaction?

Short Answer

Expert verified
The reaction intermediate is \( \mathrm{O} \). The overall reaction is \( 2 \mathrm{O}_3 \rightarrow 3 \mathrm{O}_2 \).

Step by step solution

01

Analyze the First Reaction

The first reaction given is \( \mathrm{O}_3 \rightleftharpoons \mathrm{O}_2 + \mathrm{O} \). This step involves the decomposition of ozone \( \mathrm{O}_3 \) into molecular oxygen \( \mathrm{O}_2 \) and a single oxygen atom \( \mathrm{O} \). The oxygen atom \( \mathrm{O} \) is not a reactant or product in the overall process yet, indicating it could be a potential intermediate.
02

Analyze the Second Reaction

The second reaction is \( \mathrm{O}_3 + \mathrm{O} \longrightarrow 2 \mathrm{O}_2 \). In this step, ozone \( \mathrm{O}_3 \) reacts with the oxygen atom \( \mathrm{O} \) to produce two molecules of molecular oxygen \( 2 \mathrm{O}_2 \). Here, the \( \mathrm{O} \) generated in the first step is consumed, confirming it acts as an intermediate in the reaction process.
03

Identify the Overall Reaction

To determine the overall reaction, we combine both elementary steps while eliminating any intermediates. Combining the two steps gives:1. \( \mathrm{O}_3 \rightarrow \mathrm{O}_2 + \mathrm{O} \)2. \( \mathrm{O}_3 + \mathrm{O} \rightarrow 2 \mathrm{O}_2 \)Adding these reactions together, the \( \mathrm{O} \) on both sides cancels out, resulting in:\( 2 \mathrm{O}_3 \rightarrow 3 \mathrm{O}_2 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ozone Decomposition
Ozone decomposition plays a crucial role in atmospheric chemistry and involves breaking down ozone molecules. The reaction follows a series of steps or mechanisms to transform ozone (\( \mathrm{O}_3 \)) back into oxygen molecules.
The given reactions, each an elementary step, describe how ozone decomposes. Firstly, \( \mathrm{O}_3 \) breaks down into a molecule of oxygen (\( \mathrm{O}_2 \)) and a single oxygen atom (\( \mathrm{O} \)).
Subsequently, this free oxygen atom reacts with another \( \mathrm{O}_3 \) molecule, producing two \( \mathrm{O}_2 \) molecules. Understanding the decomposition helps us grasp how ozone balance is maintained in the atmosphere.
Reaction Intermediates
In chemical reactions, especially those involving multiple steps, intermediates often play a pivotal role. These are species that are formed in one step of the reaction and consumed in a subsequent step.
An intermediate is ever-present as a transition entity that is not part of the overall reactants or products.
In the case of ozone decomposition, the oxygen atom \( \mathrm{O} \) serves as a classic example of an intermediate.
  • Produced in the first step: \( \mathrm{O}_3 \rightarrow \mathrm{O}_2 + \mathrm{O} \)
  • Consumed in the second step: \( \mathrm{O}_3 + \mathrm{O} \rightarrow 2 \mathrm{O}_2 \)
The appearance and disappearance of intermediates like \( \mathrm{O} \) not only confirm their role but also highlight the step-by-step nature of complex reactions.
Elementary Reactions
Elementary reactions are the simplest form of chemical reactions, occurring in a single step with a single transition state. Each given elementary step in the ozone decomposition is such a reaction.
These reactions may involve simple collisions or direct transformations of chemical species. Understanding these elementary steps aids in piecing together the overall reaction mechanism.
The significance of determining such mechanisms includes predicting reaction rates and rationalizing the overall reaction outcome. In ozone's case:
  • Each step is clearly defined with specific reactants and products.
  • The elementary nature means that their stoichiometry directly reflects the molecular events happening.
Through identifying and understanding each elemental transformation, one can seamlessly combine them to depict the bigger picture - the overall reaction resulting from these steps.

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Most popular questions from this chapter

Iron(III) chloride is reduced by tin(II) chloride. $$ 2 \mathrm{FeCl}_{3}(a q)+\mathrm{SnCl}_{2}(a q) \longrightarrow 2 \mathrm{FeCl}_{2}(a q)+\mathrm{SnCl}_{4}(a q) $$ The concentration of \(\mathrm{Fe}^{3+}\) ion at the beginning of an experiment was \(0.03586 M\). After \(4.00 \mathrm{~min}\), it was \(0.02715 \mathrm{M}\). What is the average rate of reaction of \(\mathrm{FeCl}_{3}\) in this time interval?

In the presence of excess thiocyanate ion, \(\mathrm{SCN}^{-},\) the following reaction is first order in chromium(III) ion, \(\mathrm{Cr}^{3+} ;\) the rate constant is \(2.0 \times 10^{-6} / \mathrm{s}\) $$ \mathrm{Cr}^{3+}(a q)+\mathrm{SCN}^{-}(a q) \longrightarrow \operatorname{Cr}(\mathrm{SCN})^{2+}(a q) $$ What is the half-life in hours? How many hours would be required for the initial concentration of \(\mathrm{Cr}^{3+}\) to decrease to each of the following values: \(25.0 \%\) left, \(12.5 \%\) left, \(6.25 \%\) left, \(3.125 \%\) left? mathrm{L} ?$

Sulfuryl chloride, \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\), decomposes when heated. $$ \mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) $$ In an experiment, the initial concentration of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) was \(8.37 \times 10^{-2} \mathrm{~mol} / \mathrm{L}\). If the rate constant is \(2.2 \times 10^{-5} / \mathrm{s}\) what is the concentration of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) after \(7.0 \mathrm{hr}\) ? The reaction is first order. 13.58 Cyclopropane, \(\mathrm{C}_{3} \mathrm{H}_{6},\) is converted to its isomer propylene, \(\mathrm{CH}_{2}=\mathrm{CHCH}_{3},\) when heated. The rate law is first order in cyclopropane, and the rate constant is \(6.0 \times 10^{-4} / \mathrm{s}\) at \(500^{\circ} \mathrm{C}\). If the initial concentration of cyclopropane is \(0.0226 \mathrm{~mol} / \mathrm{L},\) what is the concentration after \(525 \mathrm{~s}\) ?

In the presence of a tungsten catalyst at high temperatures, the decomposition of ammonia to nitrogen and hydrogen is a zero-order process. If the rate constant at a particular temperature is \(3.7 \times 10^{-6} \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s}),\) how long will it take for the ammonia concentration to drop from an initial concentration of \(5.0 \times 10^{-4} M\) to \(5.0 \times 10^{-5} M\) ? What is the half-life of the reaction under these conditions?

Methyl chloride, \(\mathrm{CH}_{3} \mathrm{Cl}\), reacts in basic solution to give methanol. $$ \mathrm{CH}_{3} \mathrm{Cl}+\mathrm{OH}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{OH}+\mathrm{Cl}^{-} $$ This reaction is believed to occur in a single step. If so, what should be the rate law?
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