Chapter 13

If we plot the concentration of reactants and products as a function of time for any sequence of two spontaneous chemical reactions, such as $$A \rightarrow B \rightarrow C$$ will the maximum concentration of final product C always appear after the maximum concentration of B?

Using data in Appendix \(4,\) calculate \(\Delta H^{-}\) for the reaction $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$

Using data in Appendix \(4,\) calculate \(\Delta H^{\circ}\) for the reaction $$\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{NO}_{2}(g)$$

Nitrogen and oxygen can combine to form different nitrogen oxides that play a minor role in the chemistry of smog. Write balanced chemical equations for the reactions of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) that produce (a) \(\mathrm{N}_{2} \mathrm{O}\) and (b) \(\mathrm{N}_{2} \mathrm{O}_{5}\).

Nitrogen oxides such as \(\mathrm{N}_{2} \mathrm{O}\) and \(\mathrm{N}_{2} \mathrm{O}_{5}\) are present in the air in low concentrations, in part because of their reactivity. Write balanced chemical equations for the following reactions: a. The conversion of \(\mathrm{N}_{2} \mathrm{O}\) to \(\mathrm{NO}_{2}\) in the presence of oxygen b. The decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) to \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\)

Explain the difference between the average rate and the instantaneous rate of a chemical reaction.

Can the average rate and instantaneous rate of a chemical reaction ever be the same?

Why do the average rates of most reactions change with time?

Bacterial Degradation of Ammonia Nitrosomonas bacteria convert ammonia into nitrite in the presence of oxygen by the following reaction: \(2 \mathrm{NH}_{3}(a q)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}^{+}(a q)+2 \mathrm{NO}_{2}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell)\) A. How are the rates of formation of \(\mathrm{H}^{+}\) and \(\mathrm{NO}_{2}^{-}\) related to the rate of consumption of \(\mathrm{NH}_{3} ?\) b. How is the rate of formation of \(\mathrm{NO}_{2}^{-}\) related to the rate of consumption of \(\mathrm{O}_{2} ?\) c. How is the rate of consumption of \(\mathrm{NH}_{3}\) related to the rate of consumption of \(\mathrm{O}_{2} ?\)

Catalytic Converters and Combustion Catalytic converters in automobiles combat air pollution by converting \(\mathrm{NO}\) and \(\mathrm{CO}\) into \(\mathrm{N}_{2}\) and \(\mathrm{CO}_{2}\) : $$2 \mathrm{CO}(g)+2 \mathrm{NO}(g) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{CO}_{2}(g)$$ a. How is the rate of formation of \(\mathrm{N}_{2}\) related to the rate of consumption of CO? b. How is the rate of formation of \(\mathrm{CO}_{2}\) related to the rate of consumption of NO? c. How is the rate of consumption of CO related to the rate of consumption of NO?

Nitryl chloride, \(\mathrm{NO}_{2} \mathrm{Cl}\), is a reactive chlorine- containing species sometimes found in marine sediments in industrial areas. In the gas phase it decomposes to \(\mathrm{NO}_{2}\) and \(\mathrm{Cl}_{2}\) : $$2 \mathrm{NO}_{2} \mathrm{Cl}(g) \rightarrow 2 \mathrm{NO}_{2}(g)+\mathrm{Cl}_{2}(g)$$ Under laboratory conditions, the rate of formation of \(\mathrm{NO}_{2}(g)\) is \(5.7 \times 10^{-6} M \cdot \mathrm{s}^{-1}\) a. What is the rate of formation of \(\mathrm{Cl}_{2}(g) ?\) b. What is the rate of consumption of \(\mathrm{NO}_{2} \mathrm{Cl}(g)\) ?

\(\mathrm{N}_{2} \mathrm{O}_{5},\) when dissolved in water, decomposes to produce \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\) $$2 \mathrm{N}_{2} \mathrm{O}_{5}(a q) \rightarrow 4 \mathrm{NO}_{2}(a q)+\mathrm{O}_{2}(a q)$$ The rate of formation of \(\mathrm{O}_{2}\) is \(4.0 \times 10^{-3} M \cdot \mathrm{min}^{-1}\) a. What is the rate of formation of \(\mathrm{NO}_{2}(a q) ?\) b. What is the rate of disappearance of \(\mathrm{N}_{2} \mathrm{O}_{5}(a q) ?\)

Sulfur dioxide emissions in power-plant stack gases may react with carbon monoxide as follows: $$\mathrm{SO}_{2}(g)+3 \mathrm{CO}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+\cos (g)$$ Write an equation relating each of the following pairs of rates: a. The rate of formation of \(\mathrm{CO}_{2}\) to the rate of consumption of CO b. The rate of formation of COS to the rate of consumption of \(\mathrm{SO}_{2}\) c. The rate of consumption of \(\mathrm{CO}\) to the rate of consumption of \(\mathrm{SO}_{2}\)

Nitric oxide (NO) can be removed from gas-fired power-plant emissions by reaction with methane as follows: \(\mathrm{CH}_{4}(g)+4 \mathrm{NO}(g) \rightarrow 2 \mathrm{N}_{2}(g)+\mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) Write an equation relating each of the following pairs of rates: a. The rate of formation of \(\mathrm{N}_{2}\) to the rate of formation of \(\mathrm{CO}_{2}\) b. The rate of formation of \(\mathrm{CO}_{2}\) to the rate of consumption of NO c. The rate of consumption of \(\mathrm{CH}_{4}\) to the rate of formation of \(\mathrm{H}_{2} \mathrm{O}\)

The chemistry of smog formation includes \(\mathrm{NO}_{3}\) as an intermediate in several reactions. a. If \(\Delta\left[\mathrm{NO}_{3}\right] / \Delta t=-2.2 \times 10^{5} \mathrm{m} M / \mathrm{min}\) in the following reaction, what is the rate of formation of \(\mathrm{NO}_{2} ?\) $$\mathrm{NO}_{3}(g)+\mathrm{NO}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$ b. What is the rate of change of \(\left[\mathrm{NO}_{2}\right]\) in the following$$ \begin{array}{l} \text { reaction if } \Delta\left[\mathrm{NO}_{3}\right] / \Delta t=-2.3 \mathrm{mM} / \mathrm{min} \text { ? } \\ \qquad 2 \mathrm{NO}_{3}(g) \rightarrow 2 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \end{array}$$

Nitrite ion reacts with ozone in aqueous solution, producing nitrate ion and oxygen: $$\mathrm{NO}_{2}^{-}(a q)+\mathrm{O}_{3}(g) \rightarrow \mathrm{NO}_{3}^{-}(a q)+\mathrm{O}_{2}(g)$$ The following data were collected for this reaction at \(298 \mathrm{K} .\) Calculate the average reaction rate between 0 and \(100 \mu \mathrm{s}(\text { microseconds })\) and between 200 and \(300 \mu \mathrm{s}\) $$\begin{array}{cc}\text { Time }(\mu \mathrm{s}) & {\left[\mathrm{O}_{3}\right](\mathrm{M})} \\\0 & 1.13 \times 10^{-2} \\\\\hline 100 & 9.93 \times 10^{-3} \\\\\hline 200 & 8.70 \times 10^{-3} \\\\\hline 300 & 8.15 \times 10^{-3} \\\\\hline\end{array}$$

At room temperature in the gas phase, dinitrogen pentoxide \(\left(\mathrm{N}_{2} \mathrm{O}_{5}\right)\) decomposes to dinitrogen tetroxide and oxygen: $$2 \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightarrow 2 \mathrm{N}_{2} \mathrm{O}_{4}(g)+\mathrm{O}_{2}(g)$$ Calculate the average rate of this reaction between consecutive measurements listed in the following table. $$\begin{array}{cc}\text { Time (s) } & {\left[\mathrm{N}_{2} \mathrm{O}_{5}\right](\mathrm{M})} \\\0 & 0.200 \\\\\hline 300 & 0.180 \\\\\hline 600 & 0.161 \\\\\hline 900 & 0.144 \\\\\hline 1200 & 0.130 \\\\\hline\end{array}$$

Tropospheric Ozone Tropospheric (lower atmosphere) ozone is rapidly consumed in many reactions, including $$\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$$ Use the following data to calculate the instantaneous rate of the reaction at \(t=0.000 \mathrm{s}\) and \(t=0.052 \mathrm{s}\) $$\begin{array}{cc}\text { Time (s) } & {[\mathrm{NO}](\mathrm{M})} \\\0.000 & 2.0 \times 10^{-8} \\\\\hline 0.011 & 1.8 \times 10^{-8} \\\\\hline 0.027 & 1.6 \times 10^{-8} \\\\\hline 0.052 & 1.4 \times 10^{-8} \\\\\hline 0.102 & 1.2 \times 10^{-8} \\\\\hline\end{array}$$

Why are the units of the rate constants different for reactions of different order?

Can the half-life of a second-order reaction have the same units as the half- life of a first-order reaction?

How does the half-life in a first-order reaction depend on the concentration of the reactants?

What effect does doubling the initial concentration of a reactant have on the half-life in a reaction that is second order in the reactant?

Two first-order decomposition reactions of the form \(A \rightarrow B+C\) have the same rate constant at a given temperature. Do the reactants in the two reactions have the same half-lives at this temperature?

For each of the following rate laws, determine the order with respect to each reactant and the overall reaction order. a. Rate \(=k[\mathrm{A}][\mathrm{B}]\) b. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}]\) c. Rate \(=k[\mathrm{A}][\mathrm{B}]^{3}\)

Determine the overall order of the following rate laws and the order with respect to each reactant. a. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}]^{1 / 2}\) b. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}][\mathrm{C}]\) c. Rate \(=k[\mathrm{A}][\mathrm{B}]^{3}[\mathrm{C}]^{1 / 2}\)

Write rate laws and determine the units of the rate constant (by using the units \(M\) for concentration and s for time) for the following reactions: a. The reaction of oxygen atoms with \(\mathrm{NO}_{2}\) is first order in both reactants. b. The reaction between \(\mathrm{NO}\) and \(\mathrm{Cl}_{2}\) is second order in NO and first order in \(\mathrm{Cl}_{2}\). c. The reaction between \(\mathrm{Cl}_{2}\) and chloroform \(\left(\mathrm{CHCl}_{3}\right)\) is first order in \(\mathrm{CHCl}_{3}\) and one-half order in \(\mathrm{Cl}_{2}\) "d. The decomposition of ozone \(\left(\mathrm{O}_{3}\right)\) to \(\mathrm{O}_{2}\) is second order in \(\mathrm{O}_{3}\) and an order of -1 in \(\mathrm{O}\) atoms.

Compounds \(A\) and \(B\) react to give a single product, \(C .\) Write the rate law for each of the following cases and determine the units of the rate constant by using the units \(M\) for concentration and s for time: a. The reaction is first order in \(A\) and second order in \(B\). b. The reaction is first order in \(A\) and second order overall. c. The reaction is independent of the concentration of \(\mathrm{A}\) and second order overall. d. The reaction is second order in both \(\mathrm{A}\) and \(\mathrm{B}\).

Predict the order with respect to NO for the reaction \(\mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightarrow \mathrm{NOBr}_{2}(g)\) under each of the following conditions: a. The rate doubles when \([\mathrm{NO}]\) is doubled and \(\left[\mathrm{Br}_{2}\right]\) remains constant. b. The rate increases by 1.56 times when \([\mathrm{NO}]\) is increased 1.25 times and \(\left[\mathrm{Br}_{2}\right]\) remains constant. c. The rate is halved when \([\mathrm{NO}]\) is doubled and \(\left[\mathrm{Br}_{2}\right]\) remains constant.

The reaction between \(\mathrm{N}_{2} \mathrm{O}_{5}\) and water is a source of nitric acid in the atmosphere: $$\mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow 2 \mathrm{HNO}_{3}(g)$$ a. The reaction is first order in each reactant. Write the rate law for the reaction. b. When \(\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]=0.132 \mathrm{m} \mathrm{M}\) and \(\left[\mathrm{H}_{2} \mathrm{O}\right]=230 \mathrm{m} M,\) the rate of the reaction is \(4.55 \times 10^{-4} \mathrm{mM} / \mathrm{min} .\) What is the rate constant for the reaction?

Each of the following reactions is first order in each reactant and second order overall. Which reaction is fastest if the initial concentrations of all the reactants are the same? a. \(\mathrm{ClO}_{2}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{ClO}_{3}(g)+\mathrm{O}_{2}(g)\) \(k=3.0 \times 10^{-19} \mathrm{cm}^{3} /(\text { molecule } \cdot \mathrm{s})\) b. \(\mathrm{ClO}_{2}(g)+\mathrm{NO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{ClO}(g)\) \(k=3.4 \times 10^{-13} \mathrm{cm}^{3} /(\text { molecule } \cdot \mathrm{s})\) c. \(\mathrm{ClO}(g)+\mathrm{NO}(g) \rightarrow \overline{\mathrm{C} 1(g)}+\mathrm{NO}_{2}(g)\) \(k=1.7 \times 10^{-11} \mathrm{cm}^{3} /(\text { molecule } \cdot \mathrm{s})\) d. \(\mathrm{ClO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{ClO}_{2}(g)+\mathrm{O}_{2}(g)\) \(k=1.5 \times 10^{-17} \mathrm{cm}^{3} /(\text { molecule } \cdot \mathrm{s})\)

Two reactions in which there is a single reactant have nearly the same magnitude rate constant. One is first order; the other is second order. a. If the initial concentrations of the reactants are both \(1.0 \mathrm{mM},\) which reaction will proceed at the higher rate? b. If the initial concentrations of the reactants are both 2.0 \(M,\) which reaction will proceed at the higher rate?

In the presence of water, NO and \(\mathrm{NO}_{2}\) react to form nitrous acid (HNO,) by the following reaction: $$\mathrm{NO}(g)+\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2 \mathrm{HNO}_{2}(a q)$$ When the concentration of NO or \(\mathrm{NO}_{2}\) is doubled, the initial rate of reaction doubles. If the rate of the reaction does not depend on \(\left[\mathrm{H}_{2} \mathrm{O}\right],\) what is the rate law for this reaction?

During a smog event, trace amounts of many highly reactive substances are present in the atmosphere. One of these is the hydroperoxyl radical, \(\mathrm{HO}_{2},\) which reacts with sulfur trioxide, \(\mathrm{SO}_{3}\). The rate constant for the reaction $$2 \mathrm{HO}_{2}(g)+\mathrm{SO}_{3}(g) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{3}(g)+2 \mathrm{O}_{2}(g)$$ is \(2.6 \times 10^{11} M^{-1} s^{-1}\) at \(298 \mathrm{K} .\) The initial rate of the reaction doubles when the concentration of \(\mathrm{SO}_{3}\) or \(\mathrm{HO}_{2}\) is doubled. What is the rate law for the reaction?

Hydrogen gas reduces NO to \(\mathrm{N}_{2}\) in the following reaction: $$2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g)$$ The initial reaction rates of four mixtures of \(\mathrm{H}_{2}\) and \(\mathrm{NO}\) were measured at \(900^{\circ} \mathrm{C}\) with the following results: $$\begin{array}{cccc}\text { Experiment } & \left[\mathrm{H}_{2}\right]_{0}(\mathrm{M}) & [\mathrm{NO}]_{0}(\mathrm{M}) & \begin{array}{c}\text { Initial } \\\\\text { Rate }(M / \mathrm{s})\end{array} \\\\\hline 1 & 0.212 & 0.136 & 0.0248 \\\\\hline 2 & 0.212 & 0.272 & 0.0991 \\\\\hline 3 & 0.424 & 0.544 & 0.793 \\\\\hline 4 & 0.848 & 0.544 & 1.59 \\\\\hline\end{array}$$ Determine the rate law and the rate constant for the reaction at \(900^{\circ} \mathrm{C}\).

The rate of the reaction $$\mathrm{NO}_{2}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g)$$ was determined in three experiments at \(225^{\circ} \mathrm{C} .\) The results are given in the following table: $$\begin{array}{cccc}\text { Experiment } & \left[\mathrm{NO}_{2}\right]_{0}(\mathrm{M}) & [\mathrm{CO}]_{0}(\mathrm{M}) & \begin{array}{c}\text { Initial Rate } \\\\(M / \mathrm{s})\end{array} \\\\\hline 1 & 0.263 & 0.826 & 1.44 \times 10^{-5} \\\\\hline 2 & 0.263 & 0.413 & 1.44 \times 10^{-5} \\\\\hline 3 & 0.526 & 0.413 & 5.76 \times 10^{-5} \\\\\hline\end{array}$$ a. Determine the rate law for the reaction. b. Calculate the value of the rate constant at \(225^{\circ} \mathrm{C}\) c. Calculate the rate of appearance of \(\mathrm{CO}_{2}\) when \(\left[\mathrm{NO}_{2}\right]=[\mathrm{CO}]=0.500 \mathrm{M}\)

Atmospheric chemistry involves highly reactive, odd-electron molecules such as the hydroperoxyl radical \(\mathrm{HO}_{2},\) which decomposes into \(\mathrm{H}_{2} \mathrm{O}_{2}\) and \(\mathrm{O}_{2} .\) Determine the rate law for the reaction and the value of the rate constant at \(298 \mathrm{K}\) by using the following data obtained at \(298 \mathrm{K}\). $$\begin{array}{cc} \text { Time }(\mu \mathrm{s}) & {\left[\mathrm{HO}_{2}\right](\mu M)} \\\0.0 & 8.5 \\\\\hline 0.6 & 5.1 \\\\\hline 1.0 & 3.6 \\\\\hline 1.4 & 2.6 \\\\\hline 1.8 & 1.8 \\\\\hline 2.4 & 1.1\end{array}$$

In addition to being studied in the gas phase, the decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) has been evaluated in solution. In carbon tetrachloride (CC1,) at \(45^{\circ} \mathrm{C}\), $$2 \mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}$$ is a first-order reaction and \(k=6.32 \times 10^{-4} \mathrm{s}^{-1} .\) How much \(\mathrm{N}_{2} \mathrm{O}_{5}\) remains in solution after \(1 \mathrm{h}\) if the initial concentration of \(\mathrm{N}_{2} \mathrm{O}_{5}\) was \(0.50 \mathrm{mol} / \mathrm{L} ?\) What percent of the \(\mathrm{N}_{2} \mathrm{O}_{5}\) has reacted at that point?

Because the units of concentration in the term \(\ln \left([\mathrm{X}] /[\mathrm{X}]_{0}\right)\) cancel out in the integrated rate law for first- order reactions (Equation 13.16 ), molar concentration can be replaced by any concentration term. With gases, for example, partial pressures may be used. The decomposition of phosphine gas \(\left(\mathrm{PH}_{3}\right)\) at \(600^{\circ} \mathrm{C}\) is first order in \(\mathrm{PH}_{3}\) with \(k=0.023 \mathrm{s}^{-1}\) $$4 \mathrm{PH}_{3}(g) \rightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g)$$ If the initial partial pressure of \(\mathrm{PH}_{3}\) is 375 torr, what percent of \(\mathrm{PH}_{3}\) reacts in \(1 \mathrm{min}\) ?

Laughing Gas Nitrous oxide ( \(\mathrm{N}_{2} \mathrm{O}\) ) is used as an anesthetic (laughing gas) and in aerosol cans to produce whipped cream. It is a potent greenhouse gas and decomposes slowly to \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) : $$2 \mathrm{N}_{2} \mathrm{O}(g) \rightarrow 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)$$ If the plot of \(\ln \left[\mathrm{N}_{2} \mathrm{O}\right]\) as a function of time is linear, what is the rate law for the reaction? b. How many half-lives will it take for the concentration of \(\mathrm{N}_{2} \mathrm{O}\) to reach \(6.25 \%\) of its original concentration?

The unsaturated hydrocarbon butadiene $\left(\mathrm{C}_{4} \mathrm{H}_{6}\right)\( dimerizes to 4 -vinylcyclohexene \)\left(\mathrm{C}_{8} \mathrm{H}_{12}\right) .$ When data collected in studies of the kinetics of this reaction were plotted against reaction time, plots of \(\left[\mathrm{C}_{4} \mathrm{H}_{6}\right]\) or $\ln \left[\mathrm{C}_{4} \mathrm{H}_{6}\right]\( produced curved lines, but the plot of \)1 /\left[\mathrm{C}_{4} \mathrm{H}_{6}\right]$ was linear. a. What is the rate law for the reaction? b. How many half-lives will it take for the $\left[\mathrm{C}_{4} \mathrm{H}_{6}\right]\( to decrease to \)3.1 \%$ of its original concentration?

Radioactive isotopes such as \(^{32} \mathrm{P}\) are used to follow biological processes. The following radioactivity data (in relative radioactivity values) were collected for a sample containing \(^{32} \mathrm{P}\) : $$\begin{array}{cc} \text { Time (days) } & \text { Relative Radioactivity } \\\\\hline 0 & 10.00 \\\\\hline 1 & 9.53 \\\\\hline 2 & 9.08 \\\\\hline 5 & 7.85 \\\\\hline 10 & 6.16 \\\\\hline 20 & 3.79 \\\\\hline\end{array}$$ a. Write the rate law for the decay of \(^{32} \mathrm{P}\). b. Determine the value of the rate constant. c. Determine the half-life of \(^{32} \mathrm{P}\). d. How many days does it take for \(99 \%\) of a sample of \(^{32} \mathrm{P}\) to decay?

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 following data to determine the rate constant for this reaction at \(298 \mathrm{K}:\) $$\begin{array}{cc} \text { Time (min) } & {\left[\mathrm{HNO}_{2}\right](\mu M)} \\\0 & 0.1560 \\\\\hline 1000 & 0.1466 \\\\\hline 1500 & 0.1424 \\\\\hline 2000 & 0.1383 \\\\\hline 2500 & 0.1345 \\\\\hline 3000 & 0.1309 \\\\\hline\end{array}$$ b. Determine the half-life for the decomposition of \(\mathrm{HNO}_{2}\). c. If the experiment that yielded the results in the preceding table had been continued for 3000 minutes more, what would the concentration of HNO \(_{2}\) have been?

The dimerization of ClO, $$2 \mathrm{ClO}(g) \rightarrow \mathrm{Cl}_{2} \mathrm{O}_{2}(g)$$ is second order in ClO. a. Use the following data to determine the value of \(k\) at \(298 \mathrm{K}\) $$\begin{array}{cc} \text { Time (s) } & \text { [ClO] (molecules/cm }^{3} \text { ) } \\ 0 & 2.60 \times 10^{11} \\ \hline 1.00 & 1.08 \times 10^{11} \\ \hline 2.00 & 6.83 \times 10^{10} \\ \hline 3.00 & 4.99 \times 10^{10} \\ \hline 4.00 & 3.93 \times 10^{10} \\ \hline \end{array}$$ b. Determine the half-life for the dimerization of C1O.

Kinetic data for the reaction \(\mathrm{Cl}_{2} \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{ClO}(g)\) are summarized in the following table. $$\begin{array}{cc}\text { Time }(\mu \mathrm{s}) & {\left[\mathrm{Cl}_{2} \mathrm{O}_{2}\right](\mathrm{M})} \\\\\hline 0 & 6.60 \times 10^{-8} \\\\\hline 172 & 5.68 \times 10^{-8} \\\\\hline 345 & 4.89 \times 10^{-8} \\\\\hline 517 & 4.21 \times 10^{-8} \\\\\hline 690 & 3.62 \times 10^{-8} \\\\\hline 862 & 3.12 \times 10^{-8} \\\\\hline\end{array}$$ Determine the value of the rate constant. b. Determine \(t_{1 / 2}\) for the decomposition of \(\mathrm{Cl}_{2} \mathrm{O}_{2}\).

The metabolism of table sugar (sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) ) begins with the hydrolysis of the disaccharide to glucose and fructose (both \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) ): $$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2 \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)$$ The kinetics of the reaction were studied at \(24^{\circ} \mathrm{C}\) in a reaction system with a large excess of water, so the reaction was pseudo first order in sucrose. Determine the rate law and the pseudo-first-order rate constant for the reaction from the following data: $$\begin{array}{cc} \text { Time (s) } & {\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right](\mathrm{M})} \\ 0 & 0.562 \\ \hline 612 & 0.541 \\ \hline 1600 & 0.509 \\ \hline 2420 & 0.484 \\ \hline 3160 & 0.462 \\ \hline 4800 & 0.442 \\ \hline \end{array}$$

Hydroperoxyl radicals react rapidly with ozone to produce oxygen and OH radicals: $$\mathrm{HO}_{2}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{OH}(g)+2 \mathrm{O}_{2}(g)$$ The rate of this reaction was studied in the presence of a large excess of ozone. Determine the pseudo-first-order rate constant and the second-order rate constant for the reaction from the following data: $$\begin{array}{cll} \text { Time (ms) } & {\left[\mathrm{HO}_{2}\right](\mathrm{M})} & {\left[\mathrm{O}_{3}\right](\mathrm{M})} \\ \hline 0 & 3.2 \times 10^{-5} & 1.0 \times 10^{-3} \\ \hline 10 & 2.9 \times 10^{-5} & 1.0 \times 10^{-3} \\ \hline 20 & 2.6 \times 10^{-6} & 1.0 \times 10^{-3} \\ \hline 30 & 2.4 \times 10^{-6} & 1.0 \times 10^{-2} \\ \hline 80 & 1.4 \times 10^{-6} & 1.0 \times 10^{-3} \\ \hline \end{array}$$

How does the magnitude of a reaction's activation energy influence the rate of a reaction?

Do all spontaneous reactions happen instantaneously at room temperature?

Under what circumstances is the activation energy of a reaction proceeding in the forward direction less than the activation energy of it happening in reverse?

Under what circumstances is the activation energy of a reaction proceeding in the forward direction greater than the activation energy of it happening in reverse?