Chapter 13: Problem 79
How does the magnitude of a reaction's activation energy influence the rate of a reaction?
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Chapter 13: Problem 79
How does the magnitude of a reaction's activation energy influence the rate of a reaction?
These are the key concepts you need to understand to accurately answer the question.
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The kinetics of the reaction between chlorine dioxide and ozone are relevant to the study of atmospheric ozone destruction. The value of the rate constant for the reaction between chlorine dioxide and ozone was measured at four temperatures between 193 and \(208 \mathrm{K}\). The results were as follows: $$\begin{array}{cc}T(\mathrm{K}) & k\left(M^{-1} \mathrm{s}^{-1}\right) \\\193 & 34.0 \\\\\hline 198 & 62.8 \\\\\hline 203 & 112.8 \\\\\hline 208 & 196.7 \\\\\hline\end{array}$$ a. Calculate the values of the activation energy and the frequency factor for the reaction. b. What is the value of the rate constant higher in the stratosphere where \(T=245 \mathrm{K} ?\)
How does the half-life in a first-order reaction depend on the concentration of the reactants?
Does a catalyst affect both the rate and the rate constant of a reaction?
The rate constant for the reaction of ozone with oxygen atoms was determined at four temperatures. Calculate the activation energy and frequency factor \(A\) for the reaction $$\mathrm{O}(g)+\mathrm{O}_{3}(g) \rightarrow 2 \mathrm{O}_{2}(g)$$ given the following data: $$\begin{array}{cc}T(\mathrm{K}) & k\left[\mathrm{cm}^{3} /(\text { molecule } \cdot \mathrm{s})\right] \\\250 & 2.64 \times 10^{-4} \\\\\hline 275 & 5.58 \times 10^{-4} \\\\\hline 300 & 1.04 \times 10^{-3} \\\\\hline 325 & 1.77 \times 10^{-3} \\\\\hline\end{array}$$
The rate laws for the thermal and photochemical decomposition of \(\mathrm{NO}_{2}\) are different. Which of the following mechanisms are possible for the thermal decomposition of \(\mathrm{NO}_{2},\) and which are possible for the photochemical decomposition of \(\mathrm{NO}_{2}\) ? For the thermal decomposition, Rate \(=k\left[\mathrm{NO}_{2}\right]^{2},\) and for the photochemical decomposition, Rate \(=k\left[\mathrm{NO}_{2}\right]\). a. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \stackrel{\text { fast }}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{3}(g)+\mathrm{O}(g)\) \(\mathrm{N}_{2} \mathrm{O}_{3}(g)+\mathrm{O}(g) \stackrel{\text { fast }}{\mathrm{N}_{2} \mathrm{O}_{2}(g)} \stackrel{\mathrm{fast}}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{2}(g)+\mathrm{O}_{2}(g)\) \(\quad \quad \mathrm{NO}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g) \stackrel{\mathrm{fast}}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) c. \(\quad \mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{N}(g)+\mathrm{O}_{2}(g)\) \(\begin{aligned} \mathrm{N}(g)+& \mathrm{NO}_{2}(g) \frac{\mathrm{fast}}{\mathrm{N}_{2} \mathrm{O}_{2}(g)} \mathrm{N}_{2} \mathrm{O}_{2}(g) \\ & \stackrel{\text { fast }}{\longrightarrow} \mathrm{NO}(g) \end{aligned}\)
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