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Chapter 2: Problem 59

\(\mathrm{NO}_{2}+\mathrm{O}_{3} \rightarrow \mathrm{NO}_{3}+\mathrm{O}_{2}\) \(\quad\) Slow \(\mathrm{NO}_{3}+\mathrm{NO}_{2} \rightarrow \mathrm{N}_{2} \mathrm{O}_{5}\) \(\quad\) Fast A proposed reaction mechanism for the reaction of nitrogen dioxide and ozone is detailed above. Which of the following is the rate law for the reaction? (A) Rate \(=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{O}_{3}\right]\) (B) Rate \(=k\left[\mathrm{NO}_{3}\right]\left[\mathrm{NO}_{2}\right]\) (C) Rate \(=k\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{O}_{3}\right]\) (D) Rate \(=k\left[\mathrm{NO}_{3}\right]\left[\mathrm{O}_{2}\right]\)

Short Answer

Expert verified
The rate law for the reaction is Rate = k[\(NO_{2}\)][\(O_{3}\)]. So, option (A) is correct.

Step by step solution

01

Identify the slow step

Firstly, it's important to recognise the slow step in the reaction mechanism provided. The mechanism consists of two steps, and it is given that the first step is slow while the second step is fast. So, the slow step is \(NO_{2} + O_{3} \rightarrow NO_{3} + O_{2}\).
02

Write down the rate law

The rate law of a reaction is determined by its slowest (rate-determining) step. Therefore, we should write the rate law based on the slow step. Since the reaction \(NO_{2} + O_{3} \rightarrow NO_{3} + O_{2}\) involves one molecule of \(NO_{2}\) and one of \(O_{3}\), the rate law should be: Rate = k[\(NO_{2}\)][\(O_{3}\)]. Here 'k' is the rate constant, [] denote the concentration of the species inside, and the superscripts are the stoichiometric coefficients from the balanced chemical equation for the slow step.

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Most popular questions from this chapter

Consider the Lewis structures for the following molecules: $$\begin{equation} \mathrm{CO}_{2}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{2}^{-}, \text {and } \mathrm{NO}_{3}^{-} \end{equation}$$ Which molecule would have the smallest bond angle between terminal atoms? (A) \(\mathrm{CO}_{2}\) (B) \(\mathrm{CO}_{3}^{2-}\) (C) \(\mathrm{NO}_{2}^{-}\) (D) \(\mathrm{NO}_{3}^{-}\)

Which of the following processes is an irreversible reaction? (A) $\mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$ (B) $\mathrm{HCN}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{CN}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q)$ (C) $\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}(s) \rightarrow \mathrm{Al}^{3+}(a q)+3 \mathrm{NO}_{3}^{-}(a q)$ (D) $2 \mathrm{Ag}^{+}(a q)+\mathrm{Ti}(s) \rightarrow 2 \mathrm{Ag}(s)+\mathrm{Ti}^{2+}(a q)$

Which of the following best explains why the ionization of atoms can occur during photoelectron spectroscopy, even though ionization is not a thermodynamically favored process? (A) It is an exothermic process due to the release of energy as an electron is liberated from the Coulombic attraction holding it to the nucleus. (B) The entropy of the system increases due to the separation of the electron from its atom. (C) Energy contained in the light can be used to overcome the Coulombic attraction between electrons and the nucleus. (D) The products of the ionization are at a lower energy state than the reactants.

Nitrous acid, HNO, \(_{2},\) has a \(\mathrm{pK}_{\mathrm{a}}\) value of \(3.3 .\) If a solution of nitrous acid is found to have a pH of \(4.2,\) what can be said about the concentration of the conjugate acid/base pair found in solution? (A) \(\left[\mathrm{HNO}_{2}\right]>\left[\mathrm{NO}_{2}^{-}\right]\) (B) \(\left[\mathrm{NO}_{2}^{-}\right]>\left[\mathrm{HNO}_{2}\right]\) (C) \(\left[\mathrm{H}_{2} \mathrm{NO}_{2}^{+}\right]>\left[\mathrm{HNO}_{2}\right]\) (D) \(\left[\mathrm{HNO}_{2}\right]>\left[\mathrm{H}_{2} \mathrm{NO}_{2}^{+}\right]\)

Most transition metals share a common oxidation state of \(+2 .\) Which of the following best explains why? (A) Transition metals all have a minimum of two unpaired electrons. (B) Transition metals have unstable configurations and are very reactive. (C) Transition metals tend to gain electrons when reacting with other elements. (D) Transition metals will lose their outermost s-block electrons when forming bonds.
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