Chapter 13

The order of a reaction is independent of temperature, but the value of the rate constant varies with temperature. Why?

Does reducing the activation energy of a reaction by \(\frac{1}{2}\) increase its rate constant by a factor of \(2 ?\)

According to the Arrhenius equation, does the activation energy of a chemical reaction depend on temperature? Explain your answer.

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 constant for the decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) in a solution of carbon tetrachloride $$2 \mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 2 \mathrm{N}_{2} \mathrm{O}_{4}+\mathrm{O}_{2}$$ was determined over a temperature range of \(20 \mathrm{K},\) with the following results: $$\begin{array}{cc} T(\mathrm{K}) & k \times 10^{4}\left(M^{-1} \mathrm{s}^{-1}\right) \\ 293 & 0.235 \\ \hline 298 & 0.469 \\ \hline 303 & 0.993 \\ \hline 308 & 1.820 \\ \hline 313 & 3.620 \\ \hline \end{array}$$ a. Determine the activation energy for the reaction. b. Calculate the rate constant of the reaction at \(273 \mathrm{K}\)

Activation Energy of Smog-Forming Reactions The initial step in the formation of smog is the reaction between nitrogen and oxygen. At the temperatures indicated, values of the rate constant of the reaction $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g)$$ are as follows: $$\begin{array}{cc}T(\mathrm{K}) & k\left(M^{-1 / 2} \mathrm{s}^{-1}\right) \\\2000 & 318 \\\\\hline 2100 & 782 \\\\\hline 2200 & 1770 \\\\\hline 2300 & 3733 \\\\\hline 2400 & 7396 \\\\\hline\end{array}$$ a. Calculate the activation energy of the reaction. b. Calculate the frequency factor for the reaction. c. Calculate the value of the rate constant at ambient temperature, \(T=300 \mathrm{K}\).

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 \(T=245 \mathrm{K} ?\)

Chlorine atoms react with methane, forming HC1 and \(\mathrm{CH}_{3} .\) The rate constant for the reaction is \(6.0 \times 10^{7} M^{-1} s^{-1}\) at \(298 \mathrm{K} .\) When the experiment was repeated at three other temperatures, the following data were collected: $$\begin{array}{ll}T(\mathrm{K}) & k\left(M^{-1} \mathrm{s}^{-1}\right) \\\303 & 6.5 \times 10^{7} \\\\\hline 308 & 7.0 \times 10^{7} \\\\\hline 313 & 7.5 \times 10^{7} \\\\\hline\end{array}$$ a. Calculate the values of the activation energy and the frequency factor for the reaction. b. What is the value of the rate constant in the lower stratosphere where \(T=218 \mathrm{K} ?\)

The compound 1,1 -difluoroethane decomposes at elevated temperatures to give fluoroethylene and hydrogen fluoride: $$\mathrm{CH}_{3} \mathrm{CHF}_{2}(g) \rightarrow \mathrm{CH}_{2} \mathrm{CHF}(g)+\mathrm{HF}(g)$$ At \(460^{\circ} \mathrm{C}, k=5.8 \times 10^{-6} \mathrm{s}^{-1}\) and \(E_{\mathrm{a}}=265 \mathrm{kJ} / \mathrm{mol} .\) To what temperature would you have to raise the reaction to make it go four times as fast?

The rate law for the reaction of NO with \(\mathrm{Cl}_{2}\) (Rate \(\left.=k[\mathrm{NO}]\left[\mathrm{Cl}_{2}\right]\right)\) is the same as that for the reaction of \(\left.\mathrm{NO}_{2} \text { with } \mathrm{F}_{2} \text { (Rate }=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{F}_{2}\right]\right) .\) Is it possible that these reactions have similar mechanisms?

Under what reaction conditions does a bimolecular reaction obey pseudo-first- order reaction kinetics?

If a reaction is zero order in a reactant, does that mean the reactant is never involved in collisions with other reactants? Explain your answer.

The hypothetical reaction \(\mathrm{A} \rightarrow \mathrm{B}\) has an activation energy of \(50.0 \mathrm{kJ} / \mathrm{mol} .\) Draw a reaction profile for each of the following mechanisms: a. A single elementary step b. A two-step reaction in which the activation energy of the second step is \(15 \mathrm{kJ} / \mathrm{mol}\) c. A two-step reaction in which the activation energy of the second step is the rate-determining barrier

Write the rate laws for the following elementary steps and identify them as uni-, bi-, or termolecular steps: a. \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g)\) c. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}_{3}(g)+\mathrm{NO}(g)\)

Write the rate laws for the following elementary steps and identify them as uni-, bi-, or termolecular steps: a. \(\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)\) b. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(^{\bullet} \mathrm{c} .^{14} \mathrm{C} \rightarrow_{7}^{14} \mathrm{N}+_{-1}^{0} \beta\)

A common classroom demonstration of a reaction involves mixing \(30 \%\) hydrogen peroxide with a solution of potassium iodide. The following mechanism has been proposed for the reaction: $$\begin{array}{ll}\text { Step 1 } & \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{I}^{-}(a q) \rightarrow \mathrm{H}_{2} \mathrm{O}(a q)+\mathrm{IO}^{-}(a q) \quad \text { slow } \\\\\text { Step 2 } & \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{IO}^{-}(a q) \rightarrow \mathrm{H}_{2} \mathrm{O}(a q)+\mathrm{O}_{2}(g)+\mathrm{I}^{-}(a q) \quad \text { fast }\end{array}$$ a. Write the equation for the overall reaction. b. Write the rate law predicted by the mechanism for the overall reaction. c. Which species is a catalyst? d. Identify any intermediates in the reaction.

A proposed mechanism for the reaction of \(\mathrm{NO}_{2}(g)\) and \(\mathrm{CO}(g)\) is $$\begin{array}{ll}\text { Step 1 } & 2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{NO}_{3}(g) \quad \text { slow } \\ \text { Step 2 } & \mathrm{NO}_{3}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{CO}_{2}(g)\end{array}$$ a. Write the equation for the overall reaction. b. Write the rate law predicted by the mechanism for the overall reaction. c. Identify the reactants and products of the reaction. d. Identify any intermediates in the reaction.

In the following mechanism for NO formation, oxygen atoms are produced by breaking \(\mathrm{O}=\mathrm{O}\) bonds at high temperature in a fast reversible reaction. If \(\Delta[\mathrm{NO}] / \Delta t=k\left[\mathrm{N}_{2}\right]\left[\mathrm{O}_{2}\right]^{1 / 2},\) which step in the mechanism is the rate-determining step? $$\begin{aligned} (1)\quad\quad\quad\quad\quad\mathrm{O}_{2}(g) & \rightleftharpoons 2 \mathrm{O}(g) \\ (2)\quad\quad\mathrm{O}(g)+\mathrm{N}_{2}(g) & \rightarrow \mathrm{NO}(g)+\mathrm{N}(g) \\ (3)\quad\quad\mathrm{N}(g)+\mathrm{O}(g) & \rightarrow \mathrm{NO}(g) \\ overall \quad \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & \rightarrow 2 \mathrm{NO}(g) \end{aligned}$$

A proposed mechanism for the gas phase decomposition of hydrogen peroxide at an elevated temperature consists of three elementary steps: $$\begin{aligned} \mathrm{H}_{2} \mathrm{O}_{2}(g) & \rightarrow 2 \mathrm{OH}(g) \\ \mathrm{H}_{2} \mathrm{O}_{2}(g)+\mathrm{OH}(g) & \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{HO}_{2}(g) \\ \mathrm{HO}_{2}(g)+\mathrm{OH}(g) & \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{O}_{2}(g) \end{aligned}$$ If the rate law for the reaction is first order in \(\mathrm{H}_{2} \mathrm{O}_{2},\) which step in the mechanism is the rate-determining step?

Ozone decomposes thermally to oxygen in the following reaction: $$2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)$$ The following mechanism has been proposed: $$\begin{aligned}\mathrm{O}_{3}(g) & \rightarrow \mathrm{O}(g)+\mathrm{O}_{2}(g) \\ \mathrm{O}(g)+\mathrm{O}_{3}(g) & \rightarrow 2 \mathrm{O}_{2}(g) \end{aligned}$$ The reaction is second order in ozone. What properties of the two elementary steps (specifically, relative rate and reversibility) are consistent with this mechanism?

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. \(\quad \mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}(g)\) \(\mathrm{O}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { fast }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { fast }}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \frac{\mathrm{slow}}{\mathrm{}_{\mathrm{fast}}} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g)+\mathrm{O}_{2}(g)\) c. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g) \stackrel{\text { fast }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

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. \(\quad \mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{N}(g)+\mathrm{O}_{2}(g)\) \(\begin{aligned} \mathrm{N}(g)+& \mathrm{NO}_{2}(g) \frac{\mathrm{fast}}{\mathrm{N}_{2} \mathrm{O}_{2}(g)} \mathrm{N}_{2} \mathrm{O}_{2}(g) \\ & \stackrel{\text { fast }}{\longrightarrow} \mathrm{NO}(g) \end{aligned}\)

Does a catalyst affect both the rate and the rate constant of a reaction?

Is the rate law for a catalyzed reaction the same as that for the uncatalyzed reaction?

Does a substance that increases the rate of a reaction also increase the rate of the reverse reaction?

Can the concentration of a homogeneous catalyst appear in the rate law for the reaction it catalyzes?

The rate of a chemical reaction is too slow to measure at room temperature. We could either raise the temperature or add a catalyst. Which would be a better solution for making an accurate determination of the rate constant?

Is NO a catalyst for the decomposition of \(\mathrm{N}_{2} \mathrm{O}\) in the following two-step reaction mechanism, or is \(\mathrm{N}_{2} \mathrm{O}\) a catalyst for the conversion of \(\mathrm{NO}\) to \(\mathrm{NO}_{2} ?\) (1) \(\quad \mathrm{NO}(g)+\mathrm{N}_{2} \mathrm{O}(g) \rightarrow \mathrm{N}_{2}(g)+\mathrm{NO}_{2}(g)\) (2) \(\quad 2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

Explain why NO is a catalyst in the following two-step process that results in the depletion of ozone in the stratosphere: (1) \(\quad \mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}(g)\) (2) \(\quad \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) Overall: \(\quad \mathrm{O}(g)+\mathrm{O}_{3}(g) \rightarrow 2 \mathrm{O}_{2}(g)\)

On the basis of the frequency factors and activation energy values of the following two reactions, determine which one will have the larger rate constant at room temperature \((298 \mathrm{K})\). \(\mathrm{O}_{3}(g)+\mathrm{O}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{O}_{2}(g)\) \(A=8.0 \times 10^{-12} \mathrm{cm}^{3} /(\text { molecules } \cdot \mathrm{s}) \quad E_{\mathrm{a}}=17.1 \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{O}_{3}(g)+\mathrm{Cl}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)\) \(A=2.9 \times 10^{-11} \mathrm{cm}^{3} /(\text { molecules } \cdot \mathrm{s}) \quad E_{\mathrm{a}}=2.16 \mathrm{kJ} / \mathrm{mol}\)

On the basis of the frequency factors and activation energy values of the following two reactions, determine which one will have the larger rate constant at room temperature \((298 \mathrm{K})\). \(\mathrm{O}_{3}(g)+\mathrm{Cl}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)\) \(A=2.9 \times 10^{-11} \mathrm{cm}^{3} /(\text { molecules } \cdot \mathrm{s}) \quad E_{2}=2.16 \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) \(A=2.0 \times 10^{-12} \mathrm{cm}^{3} /(\text { molecules } \cdot \mathrm{s}) \quad E_{\mathrm{a}}=11.6 \mathrm{kJ} / \mathrm{mol}\)

A student inserts a glowing wood splint into a test tube filled with \(\mathrm{O}_{2}\). The splint quickly catches on fire (Figure P13.121). Why does the splint burn so much faster in pure \(\mathrm{O}_{2}\) than in air? (IMAGE NOT COPY)

Methane gas leaking from the largest underground methane storage facility in the western United States caused thousands of people in southern California to be evacuated from their homes in October \(2015 .\) Methane is an explosion hazard, but a spark must be introduced into the mixture to cause it to react. Why is the spark needed?

On average, someone who falls through the ice covering a frozen lake is less likely to experience anoxia (lack of oxygen) than someone who falls into a warm pool and is underwater for the same length of time. Why?

Why doesn't a quadrupling of the rate correspond to a reaction order of \(4-\) for example, Rate \(\propto[\mathrm{NO}]^{4} ?\)

If the rate of the reverse reaction is much slower than the rate of the forward reaction, does the method used to determine a rate law from initial concentrations and initial rates also work at some other time \(t ?\)

The rate at which drugs are metabolized depends upon age: children metabolize some drugs more rapidly than adults, while the elderly metabolize drugs more slowly. Diazepam is used to treat anxiety disorders and seizures in patients in all age groups. Its half-life in hours is estimated to be equal to the patient's age in years; in a 50 -year-old, for example, diazepam would have a 50 -hour half-life. How long will it take for \(95 \%\) of a dose of diazepam to be metabolized in a 5-year-old child compared to a 50 -year-old adult assuming a first order process?

A teaching assistant is designing a synthesis experiment for use in a 3 -hour laboratory. The literature preparation specifies that \(125 \mathrm{mL}\) of a \(1.0 \mathrm{M}\) solution of reactant \(\mathrm{A}\) should be mixed with \(125 \mathrm{mL}\) of a \(1.0 \mathrm{M}\) solution of \(\mathrm{B}\) at room temperature in a 500 mL flask. The rate of the reaction was such that, after 6 hours of sitting undisturbed on the lab bench, only \(50 \%\) of the stoichiometric yield of the desired product C was produced. Suggest three reasonable changes in the procedure the assistant could try to improve the yield of product over a 3 -hour period.

Why can't an elementary step in a mechanism have a rate law that is zero order in a reactant?

During the decomposition of dinitrogen pentoxide, $$2 \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$$ how is the rate of consumption of \(\mathrm{N}_{2} \mathrm{O}_{5}\) related to the rate of formation of \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2} ?\)

In the reaction between nitrogen dioxide and ozone, $$2 \mathrm{NO}_{2}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{O}_{2}(g)$$ how are the rates of change in the concentrations of the reactants and products related?

Use the initial rate data from the following table to determine the order of the decomposition reaction of \(\mathrm{N}_{2} \mathrm{O}_{5}:\) $$\begin{array}{|c|c|c|}\text { Experiment } & \left[\mathrm{N}_{2} \mathrm{O}_{5}\right]_{0}(\mathrm{M}) & \text { Initial Rate }(\mathrm{M} / \mathrm{s}) \\\1 & 0.050 & 1.8 \times 10^{-5} \\\\\hline 2 & 0.100 & 3.6 \times 10^{-5} \\\\\hline\end{array}$$

The following table contains kinetics data for the reaction $$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{NOCl}(g)$$ $$\begin{array}{|c|c|c|c|}\hline \text { Experiment } & \text { [NO]o }(M) & \left[\mathrm{Cl}_{2}\right]_{0}(M) & \begin{array}{c}\text { Initial } \\\\\text { Rate }(M / \mathrm{s})\end{array} \\\\\hline 1 & 0.20 & 0.10 & 0.63 \\\\\hline 2 & 0.20 & 0.30 & 5.70 \\\\\hline 3 & 0.80 & 0.10 & 2.58 \\\\\hline 4 & 0.40 & 0.20 & ? \\\\\hline\end{array}$$ Predict the initial rate of reaction in experiment 4.

The following is an important reaction in the formation of photochemical smog: $$\mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$$ The reaction is first order in \(\mathrm{NO}\) and \(\mathrm{O}_{3} .\) The rate constant of the reaction is \(80 M^{-1} \mathrm{s}^{-1}\) at \(25^{\circ} \mathrm{C}\) and \(3000 M^{-1} \mathrm{s}^{-1}\) at \(75^{\circ} \mathrm{C}\) a. If this reaction were to occur in a single step, would the rate law be consistent with the observed order of the reaction for \(\mathrm{NO}\) and \(\mathrm{O}_{3} ?\) b. What is the value of the activation energy of the reaction? c. What is the rate of the reaction at \(25^{\circ} \mathrm{C}\) when \([\mathrm{NO}]=3 \times 10^{-6} \mathrm{Mand}\left[\mathrm{O}_{3}\right]=5 \times 10^{-9} \mathrm{MP}\) d. Predict the values of the rate constant at \(10^{\circ} \mathrm{C}\) and \(35^{\circ} \mathrm{C}\).

Ammonia reacts with nitrous acid to form an intermediate, ammonium nitrite (NH_NO \(_{2}\) ), which decomposes to \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}:\) \(\mathrm{NH}_{3}(g)+\mathrm{HNO}_{2}(a q) \rightarrow \mathrm{NH}_{4} \mathrm{NO}_{2}(a q) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell)\) a. The reaction is first order in ammonia and second order in nitrous acid. What is the rate law for the reaction? What are the units on the rate constant if concentrations are expressed in molarity and time in seconds? b. The rate law for the reaction has also been written as $$ \text { Rate }=k\left[\mathrm{NH}_{4}^{+}\right]\left[\mathrm{NO}_{2}-\right]\left[\mathrm{HNO}_{2}\right] $$ Is this expression equivalent to the one you wrote in part \((a) ?\) c. With the data in Appendix \(4,\) calculate the value of \(\Delta H_{\text {ren }}^{\circ}\) for the overall reaction \(\Delta H_{\mathrm{f}, \mathrm{HNO}_{2}(a q)}^{\circ}=\) \(-128.9 \mathrm{kJ} / \mathrm{mol}\) d. Draw a reaction-energy profile for the process with the assumption that \(E_{\mathrm{a}}\) of the first step is lower than \(E_{\mathrm{a}}\) of the second step.

When ionic compounds such as NaCl dissolve in water, the sodium ions are surrounded by six water molecules. The bound water molecules exchange with those in bulk solution as described by the reaction involving \(^{18} \mathrm{O}\) -enriched water: \(\mathrm{Na}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{+}(a q)+\mathrm{H}_{2}^{18} \mathrm{O}(\ell) \rightarrow \mathrm{Na}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\left(\mathrm{H}_{2}^{18} \mathrm{O}\right)^{+}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)\) a. The following reaction mechanism has been proposed: (1)\(\mathrm{Na}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}+(a q) \rightarrow \mathrm{Na}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}+(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)\) (2) \(\quad \mathrm{Na}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}+(a q)+\mathrm{H}_{2}^{18} \mathrm{O}(\ell) \rightarrow \mathrm{Na}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\left(\mathrm{H}_{2}^{18} \mathrm{O}\right)^{+}(a q)\) What is the rate law if the first step is the rate-determining step? b. If you were to sketch a reaction-energy profile, which would you draw with the higher energy, the reactants or the products?

Nitric oxide (NO) is a gaseous free radical that plays many biological roles, including regulating neurotransmission and the human immune system. One of its many reactions involves the peroxynitrite ion (ONOO'): $$\mathrm{NO}(g)+\mathrm{ONOO}^{-(a q) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{NO}_{2}^{-}(a q)}$$ a. Use the following data to determine the rate law and rate constant of the reaction at the experimental temperature at which these data were generated. $$\begin{array}{cccc}\text { Experiment } & \text { [NO]o (M) } & \text { [ONOO }\left.^{-}\right]_{0}(M) & \text { Rate }(M / \mathrm{s}) \\\\\hline 1 & 1.25 \times 10^{-4} & 1.25 \times 10^{-4} & 2.03 \times 10^{-11} \\\\\hline 2 & 1.25 \times 10^{-4} & 0.625 \times 10^{-4} & 1.02 \times 10^{-11} \\\\\hline 3 & 0.625 \times 10^{-4} & 2.50 \times 10^{-4} & 2.03 \times 10^{-11} \\\\\hline 4 & 0.625 \times 10^{-4} & 3.75 \times 10^{-4} & 3.05 \times 10^{-11} \\\\\hline\end{array}$$ b. Draw the Lewis structure of peroxynitrite ion (including all resonance forms) and assign formal charges. Note which form is preferred. c. Use the average bond energies in Appendix Table A4.1 to estimate the value of \(\Delta H_{\mathrm{rxn}}^{\circ}\) using the preferred structure from part (b).

In the presence of \(\mathrm{O}_{2}\) NO reacts with sulfur-containing proteins to form S-nitrosothiols, such as \(\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{SNO} .\) This compound decomposes to form a disulfide and \(\mathrm{NO}\) $$2 \mathrm{C}_{6} \mathrm{H}_{13} \mathrm{SNO}(a q) \rightarrow 2 \mathrm{NO}(g)+\mathrm{C}_{12} \mathrm{H}_{26} \mathrm{S}_{2}(a q)$$ The following data were collected for the decomposition reaction at \(69^{\circ} \mathrm{C}\) $$\begin{array}{cc}\text { Time (min) } & {\left[\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{SNO}\right](\mathrm{M})} \\\0 & 1.05 \times 10^{-3} \\\\\hline 10 & 9.84 \times 10^{-4} \\\\\hline 20 & 9.22 \times 10^{-4} \\\\\hline 30 & 8.64 \times 10^{-4} \\\\\hline 60 & 7.11 \times 10^{-4} \\\\\hline\end{array}$$ Calculate the value of the first-order rate constant for the reaction.

Solutions of nitrous acid (HNO \(_{2}\) ) in \(^{18} \mathrm{O}\) -labeled water undergo isotope exchange: $$\mathrm{HNO}_{2}(a q)+\mathrm{H}_{2}^{18} \mathrm{O}(\ell) \rightarrow \mathrm{HN}^{18} \mathrm{O}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)$$ a. Use the following data at \(24^{\circ} \mathrm{C}\) to determine the dependence of the reaction rate on the concentration of \(\mathrm{HNO}_{2}\) \begin{array}{cc}\text { Time (min) } & {\left[\mathrm{HNO}_{2}\right]} \\\\\hline 0 & 5.4 \times 10^{-2} \\\\\hline 20 & 1.5 \times 10^{-3} \\\\\hline 40 & 7.7 \times 10^{-4} \\\\\hline 60 & 5.2 \times 10^{-4} \\\\\hline\end{array} b. Does the reaction rate depend on the concentration of \(\mathrm{H}_{2}^{18} \mathrm{O} ?\)

Adding NH \(_{3}\) to the stack gases at an electric power generating plant can reduce \(\mathrm{NO}_{x}\) emissions. This selective noncatalytic reduction (SNR) process depends on the reaction between \(\mathrm{NH}_{2}\) (an odd- electron compound) and NO: $$\mathrm{NH}_{2}(g)+\mathrm{NO}(g) \rightarrow \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$ The following kinetic data were collected at \(1200 \mathrm{K}\) $$\begin{array}{cllc}\text { Experiment } & \left[\mathrm{NH}_{2}\right]_{0}(\mathrm{M}) & [\mathrm{NO}]_{0}(M) & \text { Rate }(M / \mathrm{s}) \\\1 & 1.00 \times 10^{-5} & 1.00 \times 10^{-5} & 0.12 \\\\\hline 2 & 2.00 \times 10^{-5} & 1.00 \times 10^{-5} & 0.24 \\\\\hline 3 & 2.00 \times 10^{-5} & 1.50 \times 10^{-5} & 0.36 \\\\\hline 4 & 2.50 \times 10^{-5} & 1.50 \times 10^{-5} & 0.45 \\\\\hline\end{array}$$ a. What is the rate law for the reaction? b. What is the value of the rate constant at \(1200 \mathrm{K} ?\)