Chapter 13

Nitrous acid slowly decomposes to \(\mathrm{NO}, \mathrm{NO}_{2},\) and water in the following second-order reaction: $$ 2 \mathrm{HNO}_{2}(a q) \rightarrow \mathrm{NO}(g)+\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) $$ a. Use the data in the table to determine the rate constant for this reaction at \(298 \mathrm{K}\) $$\begin{array}{cc} \text { Time (min) } & {\left[\mathrm{HNO}_{2}\right](\mu M)} \\ 0.0 & 0.1560 \\ \hline 1000.0 & 0.1466 \\ \hline 1500.0 & 0.1424 \\ \hline 2000.0 & 0.1383 \\ \hline 2500.0 & 0.1345 \\ \hline 3000.0 & 0.1309 \\ \hline \end{array}$$ b. Determine the half-life for the decomposition of \(\mathrm{HNO}_{2}.\)

The dimerization of \(\mathrm{ClO}\) $$ 2 \mathrm{ClO}(g) \rightarrow \mathrm{Cl}_{2} \mathrm{O}_{2}(g) $$ is second order in ClO. Use the following data to determine the value of \(k\) at \(298 \mathrm{K}\) $$\begin{array}{cc} \text { Time (s) } & \text { [ClO] (molecules/cm^3) } \\ \hline 0.0 & 2.60 \times 10^{11} \\ \hline 1.0 & 1.08 \times 10^{11} \\ \hline 2.0 & 6.83 \times 10^{10} \\ \hline 3.0 & 4.99 \times 10^{10} \\ \hline 4.0 & 3.93 \times 10^{10} \\ \hline \end{array}$$ Determine the half-life for the dimerization of C1O.

Reaction Rates, Temperature, and the Arrhenius Equation In many familiar reactions, high-energy reactants form lower-energy products. In such a reaction, is the activation energy barrier higher in the forward or in the reverse direction?

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

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

The activation energy for a particular reaction is nearly zero. Is its rate constant very sensitive to temperature changes? Explain why.

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 reaction $$ \mathrm{NO}_{2}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{NO}_{3}(g)+\mathrm{O}_{2}(g) $$ was determined over a temperature range of \(40 \mathrm{K},\) with the following results: $$\begin{array}{cc} T(\mathrm{K}) & k\left(M^{-1} \mathrm{s}^{-1}\right) \\ 203 & 4.14 \times 10^{5} \\ \hline 213 & 7.30 \times 10^{5} \\ \hline 223 & 1.22 \times 10^{6} \\ \hline 233 & 1.96 \times 10^{6} \\ \hline 243 & 3.02 \times 10^{6} \\ \hline \end{array}$$ a. Determine the activation energy for the reaction. b. Calculate the rate constant of the reaction at \(300 \mathrm{K}.\)

Activation Energy of a Smog-Forming Reaction The initial step in the formation of smog is the reaction between nitrogen and oxygen. The activation energy of the reaction can be determined from the temperature dependence of the rate constants. 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, \(T=300 \mathrm{K}.\)

Values of the rate constant for the decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) gas at four temperatures are as follows: $$\begin{array}{cc} T(\mathrm{K}) & k\left(\mathrm{s}^{-1}\right) \\ \hline 658 & 2.14 \times 10^{5} \\ \hline 673 & 3.23 \times 10^{5} \\ \hline 688 & 4.81 \times 10^{5} \\ \hline 703 & 7.03 \times 10^{5} \\ \hline \end{array}$$ a. Determine the activation energy of the decomposition reaction. b. Calculate the value of the rate constant at \(300 \mathrm{K}.\)

Reaction Mechanisms The reaction between \(\mathrm{NO}\) and \(\mathrm{Cl}_{2}\) is first order in each reactant. Does this mean that the reaction could occur in just one step? Explain your answer.

The reaction between \(\mathrm{NO}\) and \(\mathrm{H}_{2}\) is second order in \(\mathrm{NO}\). Does this mean that the reaction could occur in just one step?

If the reaction \(A \rightarrow B\) is first order in \(A\) and first order overall, does it occur in just one step?

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.

Substance A decomposes slowly into substance B, which then rapidly decomposes into substances \(\mathrm{C}\) and \(\mathrm{D}\). Sketch a reaction profile for the reaction \(\mathrm{A} \rightarrow \mathrm{C}+\mathrm{D},\) adding labels in the appropriate locations for the four substances involved.

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. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(^{} \mathrm{c} .^{14} \mathrm{C} \rightarrow_{7}^{14} \mathrm{N}+_{-}^{0} \beta\)

Write the overall reaction that consists of the following elementary steps: (1) \(\quad \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightarrow \mathrm{NO}_{3}(g)+\mathrm{NO}_{2}(g)\) (2) \(\quad \mathrm{NO}_{3}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}(g)\) (3) \(\quad 2 \mathrm{O}(g) \rightarrow \mathrm{O}_{2}(g)\)

What overall reaction consists of the following elementary steps? (1) \(\quad \mathrm{ClO}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{HClO}(a q)+\mathrm{OH}^{-}(a q)\) (2) \(\quad \mathrm{I}^{-}(a q)+\mathrm{HClO}(a q) \rightarrow \mathrm{HIO}(a q)+\mathrm{Cl}^{-}(a q)\) (3) \(\quad \mathrm{OH}^{-}(a q)+\mathrm{HIO}(a q) \rightarrow \mathrm{H}_{2} \mathrm{O}(\ell)+1 \mathrm{O}^{-}(a q)^{-}\)

A proposed mechanism for the decomposition of hydrogen peroxide consists of three elementary steps: \(\begin{array}{ll}\text { (1) } & \mathrm{H}_{2} \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{OH}(g)\end{array}\) (2) \(\quad \mathrm{H}_{2} \mathrm{O}_{2}(g)+\mathrm{OH}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{HO}_{2}(g)\) (3) \(\quad \mathrm{HO}_{2}(g)+\mathrm{OH}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{O}_{2}(g)\) 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?

NO and \(\mathrm{Cl}_{2}\) is proportional to the product of the concentrations of the two gases: \([\mathrm{NO}]\left[\mathrm{Cl}_{2}\right] .\) The following two-step mechanism was proposed for the reaction: (1) \(\quad \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{NOCl}_{2}(g)\) (2) \(\quad \mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \rightarrow 2 \mathrm{NOCl}(g)\) Overall \(\quad 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{NOCl}(g)\) Which step must be the rate-determining step if this mechanism is correct?

Mechanism of NO, Destruction Which of the following mechanisms are possible for the thermal decomposition of \(\mathrm{NO}_{2},\) given that the rate \(=k\left[\mathrm{NO}_{2}\right]^{2} ?\) a. \(\quad \mathrm{NO}_{2}(g) \stackrel{\text { then }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}(g)\) \(\mathrm{O}(g)+\mathrm{NO}_{2}(g) \stackrel{\mathrm{Gist}}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { fait }}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \stackrel{\text { thow }}{\mathrm{fist}} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g) \stackrel{\longrightarrow}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) c. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { thm }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g) \stackrel{\mathrm{fitit}}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

The rate laws for the thermal and photochemical decomposition of \(\mathrm{NO}_{2}\) are different. Which of the following mechanisms are possible for the photochemical decomposition of \(\mathrm{NO}_{2}\) given that the rate \(=k\left[\mathrm{NO}_{2}\right] ?\) a. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { thaw }}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(\begin{aligned} \mathrm{N}_{2} \mathrm{O}_{4}(g) & \stackrel{\text { faits }}{\mathrm{cm}+} \mathrm{N}_{2} \mathrm{O}_{3}(g)+\mathrm{O}(g) \\\ \mathrm{N}_{2} \mathrm{O}_{3}(g)+\mathrm{O}(g) & \mathrm{N}_{2} \mathrm{O}_{2}(g)+\mathrm{O}_{2}(g) \\ \mathrm{N}_{2} \mathrm{O}_{2}(g) &\stackrel{(\mathrm{atut}}{\longrightarrow}) \mathrm{NO}(g) \end{aligned}\) b. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { that }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g) \stackrel{\text { fast }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) c. \(\mathrm{NO}_{2}(g) \stackrel{\text { slow. }}{\longrightarrow} \mathrm{N}(g)+\mathrm{O}_{2}(g)\) \(\begin{aligned} \mathrm{N}(g)+& \mathrm{NO}_{2}(g) \stackrel{\text { fist. }}{\mathrm{N}_{2} \mathrm{O}_{2}(g)} & \mathrm{N}_{2} \mathrm{O}_{2}(g) \\ & \stackrel{\pm m}{\longrightarrow} \mathrm{NO}(g) \end{aligned}\)

Does a catalyst affect both the rate and the rate constant of a reaction? Explain your answer.

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?

Does 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 \(\mathrm{NO}_{2} ?\) $$\text { (1) } \quad \mathrm{NO}(g)+\mathrm{N}_{2} \mathrm{O}(g) \rightarrow \mathrm{N}_{2}(g)+\mathrm{NO}_{2}(g)$$ $$\text { (2) } \quad 2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$

NO as a Catalyst for Ozone Destruction Explain why NO is a catalyst in the following two-step process that results in the depletion of ozone in the stratosphere: (1) \(\quad \mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) \(\begin{array}{ll}\text { (2) } & \mathrm{O}(\mathrm{g})+\mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g)\end{array}\) 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 \((298 \mathrm{K})\) \(\mathrm{O}_{3}(g)+\mathrm{O}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{O}_{2}(g)\) \(A=8.0 \times 10^{-18} \mathrm{cm}^{3} /(\text { molecules } \cdot \mathrm{s}) \quad E_{\mathrm{a}}=17.1 \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{O}_{3}(g)+\mathrm{Cl}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)\) \(A=2.9 \times 10^{-11} \mathrm{cm}^{3} /(\text { molecules } \cdot \mathrm{s}) \quad E_{\mathrm{a}}=2.16 \mathrm{kJ} / \mathrm{mol}\)

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 \((298 \mathrm{K})\) \(\mathrm{O}_{3}(g)+\mathrm{Cl}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)\) \(A=2.9 \times 10^{-11} \mathrm{cm}^{3} /(\text { molecules } \cdot \mathrm{s}) \quad E_{2}=2.16 \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) \(A=2.0 \times 10^{-12} \mathrm{cm}^{3} /(\text { molecules } \cdot \mathrm{s}) \quad E_{2}=11.6 \mathrm{kJ} / \mathrm{mol}\)

A backyard chef turns on the propane gas to a barbecue grill. Even though the reaction between propane and oxygen is spontaneous, the gas does not begin to burn until the chef pushes an igniter button to produce a spark. 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?

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 \(t\) ? What concentrations would we use in the case where we use the rate when \(t \neq 0 ?\)

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

Testing for a Banned Herbicide Sodium chlorate was used in weed-control preparations, but its sale has been banned in EU countries since \(2009 .\) A simple colorimetric test for the presence of the chlorate ion in a solution of herbicide relies on the following reaction: \(2 \mathrm{MnO}_{4}^{-}(a q)+5 \mathrm{ClO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \rightarrow\) $$ 2 \mathrm{Mn}^{2+}(a q)+5 \mathrm{ClO}_{4}^{-}(a q)+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$ The table contains rate data for this reaction. $$\begin{array}{ccccc} & \left[\mathrm{MnO}_{4}^{-}\right]_{0} & \left[\mathrm{ClO}_{3}^{-}\right]_{0} & \left[\mathrm{H}^{+}\right]_{0} & \text { Initial Rate } \\ \text { Experiment } & (M) & (M) & (M) & (M / \mathrm{s}) \\ \hline 1 & 0.10 & 0.10 & 0.10 & 5.2 \times 10^{-3} \\ \hline 2 & 0.25 & 0.10 & 0.10 & 3.3 \times 10^{-2} \\ \hline 3 & 0.10 & 0.30 & 0.10 & 1.6 \times 10^{-2} \\ \hline 4 & 0.10 & 0.10 & 0.20 & 7.4 \times 10^{-3} \\ \hline \end{array}$$ Determine the rate law and the rate constant for this reaction.

An important reaction in the formation of photochemical smog is the reaction between ozone and NO: $$ \mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) $$ 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 \([\mathrm{NO}]=\) \(3 \times 10^{-6} M\) and \(\left[\mathrm{O}_{3}\right]=5 \times 10^{-9} \mathrm{M} ?\) 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 of 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 \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the overall reaction \(\left(\Delta H_{\mathrm{f}}^{*}, \mathrm{HNO}_{2}=\right.\) \(-43.1 \mathrm{kJ} / \mathrm{mol})\) d. Draw an energy profile for the process with the assumption that \(E_{a}\) of the first step is lower than \(E_{\mathrm{a}}\) of the second step.

Nitrogen Oxide in the Human Body Nitrogen oxide is a 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"): $$ \mathrm{NO}(a q)+\mathrm{ONOO}^{-}(a q) \rightarrow \mathrm{NO}_{2}(a q)+\mathrm{NO}_{2}^{-}(a q) $$ 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. $$\begin{array}{cccc} \hline \text { Experiment } & \text { [NOlo (M) } & \text { [ONOO Jo (M) } & \text { Rate (M/s) } \\ \hline 1 & 1.25 \times 10^{-4} & 1.25 \times 10^{-4} & 2.03 \times 10^{-11} \\\ \hline 2 & 1.25 \times 10^{-4} & 0.625 \times 10^{-4} & 1.02 \times 10^{-11} \\\ \hline 3 & 0.625 \times 10^{-4} & 2.50 \times 10^{-4} & 2.03 \times 10^{-11} \\\ \hline 4 & 0.625 \times 10^{-4} & 3.75 \times 10^{-4} & 3.05 \times 10^{-11} \\\ \hline \end{array}$$ 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 Table A4.1 to estimate the value of \(\Delta H_{\text {rxn }}\) by using the preferred structure from part (b).

Reducing NO Emissions Adding NH \(_{3}\) to the stack gases at an electric- power-generating plant can reduce \(\mathrm{NO}_{x}\) emissions. This selective noncatalytic reduction process depends on the reaction between \(\mathrm{NH}_{2}\) (an odd-electron molecule) 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 \(1200 \mathrm{K}.\) $$\begin{array}{cccc} \text { Experiment } & \left[\mathrm{NH}_{2}\right]_{0}(\mathrm{M}) & [\mathrm{NO}]_{0}(\mathrm{M}) & \text { Rate }(\mathrm{M} / \mathrm{s}) \\ 1 & 1.00 \times 10^{-5} & 1.00 \times 10^{-5} & 0.12 \\ \hline 2 & 2.00 \times 10^{-5} & 1.00 \times 10^{-5} & 0.24 \\ \hline 3 & 2.00 \times 10^{-5} & 1.50 \times 10^{-5} & 0.36 \\ \hline 4 & 2.50 \times 10^{-5} & 1.50 \times 10^{-5} & 0.45 \\ \hline \end{array}$$ a. What is the rate law for the reaction? b. What is the value of the rate constant at \(1200 \mathrm{K} ?\)