Chapter 11

Which of these is appropriate for determining the rate law for a chemical reaction? (a) Theoretical calculations based on balanced equations (b) Measuring the rate of the reaction as a function of the concentrations of the reacting species (c) Measuring the rate of the reaction as a function of temperature

Name at least three factors that affect the rate of a chemical reaction.

Using the rate law, rate \(=k[\mathrm{~A}]^{2}[\mathrm{~B}],\) define the order of the reaction with respect to \(\mathrm{A}\) and \(\mathrm{B}\) and the overall reaction order.

Define the terms "unimolecular elementary reaction" and "bimolecular elementary reaction," and give an example of each.

Define the terms "activation energy" and "frequency factor." Write an equation that relates activation energy and frequency factor to reaction rate

Write a one- or two-sentence definition in your own words for each term: active site substrate cofactor polypeptide enzyme polysaccharide protein

Explain the difference between a homogeneous and a heterogeneous catalyst. Give an example of each.

Consider dissolving sugar as a simple process in which kinetics is important. Suppose that you dissolve an equal mass of each kind of sugar listed. Which dissolves the fastest? Which dissolves the slowest? Explain why in terms of rates of heterogeneous reactions. (If you are not sure which is fastest or slowest, try them all.) (a) Rock candy sugar (large sugar crystals) (b) Sugar cubes (c) Granular sugar (d) Powdered sugar

A cube of aluminum \(1.0 \mathrm{~cm}\) on each edge is placed into \(9-\mathrm{M} \mathrm{NaOH}(\mathrm{aq})\), and the rate at which \(\mathrm{H}_{2}\) gas is given off is measured. (a) Calculate by what factor this reaction rate will change if the aluminum cube is cut exactly in half and the two halves are placed in the solution. Assume that the reaction rate is proportional to the surface area, and that all of the surface of the aluminum is in contact with the \(\mathrm{NaOH}(\mathrm{aq})\) (b) If you had to speed up this reaction as much as you could without raising the temperature, what would you do to the aluminum?

Using data given in the table for the reaction \(\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}\) calculate the average rate of reaction during each of these intervals: \(\begin{array}{ll}0.50 \mathrm{~h} . & \text { (b) } 0.50 \text { to } 1.0 \mathrm{~h} .\end{array}\) 0.00 to (a) 1.0 to (c) \(2.0 \mathrm{~h}\) (d) 2.0 to \(3.0 \mathrm{~h}\). \(4.0 \mathrm{~h}\) (f) 4.0 to \(5.0 \mathrm{~h}\). (e) 3.0 to \begin{tabular}{cccc} \hline Time (h) & {\(\left[\mathrm{N}_{2} \mathrm{O}_{5}\right](\mathrm{mol} / \mathrm{L})\)} & Time \((\mathrm{h})\) & {\(\left[\mathrm{N}_{2} \mathrm{O}_{5}\right](\mathrm{mol} / \mathrm{L})\)} \\ \hline 0.00 & 0.849 & 3.00 & 0.352 \\ 0.50 & 0.733 & 4.00 & 0.262 \\ 1.00 & 0.633 & 5.00 & 0.196 \\ 2.00 & 0.472 & & \\ \hline \end{tabular}

For the reaction $$ 2 \mathrm{NO}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) $$ make qualitatively correct plots of the concentrations of \(\mathrm{NO}_{2}(\mathrm{~g}), \mathrm{NO}(\mathrm{g}),\) and \(\mathrm{O}_{2}(\mathrm{~g})\) versus time. Draw all three graphs on the same axes; assume that you start with \(\mathrm{NO}_{2}(\mathrm{~g})\) at a concentration of \(1.0 \mathrm{~mol} / \mathrm{L}\). Explain how you would determine, from these plots, (a) the initial rate of the reaction. (b) the final rate (that is, the rate as time approaches infinity).

For the reaction $$ \mathrm{O}_{3}(\mathrm{~g})+\mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{~g}) $$ make qualitatively correct plots of the concentrations of \(\mathrm{O}_{3}(\mathrm{~g}), \mathrm{O}(\mathrm{g}),\) and \(\mathrm{O}_{2}(\mathrm{~g})\) versus time. Draw all three graphs on the same axes, assume that you start with \(\mathrm{O}_{3}(\mathrm{~g})\) and \(\mathrm{O}(\mathrm{g})\), each at a concentration of \(1.0 \mu \mathrm{mol} / \mathrm{L}\). Explain how you would determine, from these plots, (a) the initial rate of the reaction. (b) the final rate (that is, the rate as time approaches infinity).

Express the rate of the reaction $$ 2 \mathrm{~N}_{2} \mathrm{H}_{4}(\ell)+\mathrm{N}_{2} \mathrm{O}_{4}(\ell) \longrightarrow 3 \mathrm{~N}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ in terms of (a) \(\Delta\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]\). (b) \(\Delta\left[\mathrm{N}_{2}\right]\)

Ammonia is produced by the reaction between nitrogen and hydrogen gases. (a) Write a balanced equation using smallest whole-number coefficients for the reaction. (b) Write an expression for the rate of reaction in terms of \(\Delta\left[\mathrm{NH}_{3}\right]\) (c) The concentration of ammonia increases from \(0.257 \mathrm{M}\) to \(0.815 \mathrm{M}\) in \(15.0 \mathrm{~min}\). Calculate the average rate of reaction over this time interval. (d) Based on your result in part (c), calculate the rate of change of concentration of \(\mathrm{H}_{2}\) during the same time interval.

If a reaction has the experimental rate law, Rate \(=k[\mathrm{~A}]^{2}\), explain what happens to the rate when (a) the concentration of A is tripled. (b) the concentration of A is halved.

A reaction has the experimental rate law, Rate = \(k[\mathrm{~A}]^{2}[\mathrm{~B}]\). If the concentration of \(\mathrm{A}\) is doubled and the concentration of \(\mathrm{B}\) is halved, what happens to the reaction rate?

The reaction of \(\mathrm{CO}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{~g})\) is second-order in \(\mathrm{NO}_{2}\) and zeroth-order in \(\mathrm{CO}\) at temperatures less than \(500 \mathrm{~K}\). (a) Write the rate law for the reaction. (b) Determine how the reaction rate changes if the \(\mathrm{NO}_{2}\) concentration is halved. (c) Determine how the reaction rate changes if the concentration of CO is doubled.

Nitrosyl bromide, NOBr, is formed from \(\mathrm{NO}\) and \(\mathrm{Br}_{2}\). $$ 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g}) $$ Experiment shows that the reaction is first-order in \(\mathrm{Br}_{2}\) and second-order in NO. (a) Write the rate law for the reaction. (b) If the concentration of \(\mathrm{Br}_{2}\) is tripled, determine how the reaction rate changes. (c) Determine what happens to the reaction rate when the concentration of \(\mathrm{NO}\) is doubled.

For the reaction of \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\) with water, $$ \mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}^{+}+\mathrm{Cl}^{-} $$ the rate law is Rate \(=k\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]\) with \(k=0.090 \mathrm{~h}^{-1}\). (a) Calculate the initial rate of reaction when the concentration of \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\) is (i) \(0.010 \mathrm{M}\) (ii) \(0.020 \mathrm{M}\) (iii) \(0.040 \mathrm{M}\) (b) Determine how the rate of disappearance of \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\) changes with its initial concentration. (c) How is this related to the rate law? (d) How does the initial concentration of \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\) affect the rate of appearance of \(\mathrm{Cl}^{-}\) in the solution?

The ester methyl acetate, \(\mathrm{CH}_{3} \mathrm{COOCH}_{3}\), reacts with base to break one of the \(\mathrm{C}-\mathrm{O}\) bonds. CC(=O)OCC(O)C(C)O CC(=O)OCCOCCC(=O)O The rate law is rate \(=k\left[\mathrm{CH}_{3} \mathrm{COOCH}_{3}\right]\left[\mathrm{OH}^{-}\right]\) where $$ k=0.14 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1} \text {at } 25^{\circ} \mathrm{C} $$ (a) Calculate the initial rate at which the methyl acetate is converted to products when both reactants, \(\mathrm{CH}_{3} \mathrm{COOCH}_{3}\) and \(\mathrm{OH}^{-}\), have a concentration of \(0.025 \mathrm{M}\). (b) Calculate the rate at which methyl alcohol, \(\mathrm{CH}_{3} \mathrm{OH}\), initially appears in the solution.

Measurements of the initial rate of reaction between two compounds, triphenylmethyl hexachloroantimonate (substance I) and bis-(9-ethyl-3-carbazolyl)methane (substance II), in 1,2 -dichloroethane at \(40^{\circ} \mathrm{C}\) yielded these data: \begin{tabular}{lrl} \hline Initial Concentration \(\times 10^{5}\) \((\mathrm{~mol} / \mathrm{L})\) & & \\ \hline\([[]]\) & [1]] & Initial Rate \(\times 10^{9}\) \(\left(\mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\right)\) \\ \hline 1.65 & 10.6 & 1.50 \\ 14.9 & 10.6 & 17.7 \\ 14.9 & 7.10 & 11.2 \\ 14.9 & 3.52 & 6.30 \\ 14.9 & 1.76 & 3.10 \\ 4.97 & 10.6 & 4.52 \\ 2.48 & 10.6 & 2.70 \\ \hline \end{tabular} (a) Determine the order of the reaction with respect to substance I and substance II. (b) Derive the rate law for this reaction. (c) Calculate the rate constant \(k\) and express it in appropriate units. (d) Calculate the initial rate of reaction when \([\mathbf{I}]=\) \(8.3 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\) and \([\mathrm{II}]=6.78 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\)

For the reaction \(2 \mathrm{NO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) these data were obtained at \(1100 \mathrm{~K}\) : \begin{tabular}{ccc} \hline [NO] (mol/L) & {\(\left[\mathrm{H}_{2}\right](\mathrm{mol} / \mathrm{L})\)} & Initial Rate \(\left(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\right)\) \\ \hline \(5.00 \times 10^{-3}\) & \(2.50 \times 10^{-3}\) & \(3.0 \times 10^{-3}\) \\\ \(15.0 \times 10^{-3}\) & \(2.50 \times 10^{-3}\) & \(9.0 \times 10^{-3}\) \\ \(15.0 \times 10^{-3}\) & \(10.0 \times 10^{-3}\) & \(3.6 \times 10^{-2}\) \\ \hline \end{tabular}

The transfer of an oxygen atom from \(\mathrm{NO}_{2}\) to CO has been studied at \(540 \mathrm{~K}\) : \(\mathrm{CO}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{NO}(\mathrm{g})\) These data were collected: \begin{tabular}{ccc} \hline Initial Rate & \multicolumn{2}{c} { Initial Concentration (mol/L) } \\ \cline { 2 - 3 } (mol \(\mathrm{L}^{-1} \mathrm{~h}^{-1}\) ) & {\(\left[\mathrm{NO}_{2}\right]\)} \\ \hline \(5.1 \times 10^{-4}\) & \(0.35 \times 10^{-4}\) & \(3.4 \times 10^{-8}\) \\ \(5.1 \times 10^{-4}\) & \(0.70 \times 10^{-4}\) & \(1.7 \times 10^{-8}\) \\ \(5.1 \times 10^{-4}\) & \(0.18 \times 10^{-4}\) & \(6.8 \times 10^{-8}\) \\ \(1.0 \times 10^{-3}\) & \(0.35 \times 10^{-4}\) & \(6.8 \times 10^{-8}\) \\ \(1.5 \times 10^{-3}\) & \(0.35 \times 10^{-4}\) & \(10.2 \times 10^{-8}\) \\ \hline \end{tabular} (a) Write the rate law. (b) Determine the reaction order with respect to each reactant (c) Calculate the rate constant and express it in appropriate units.

For each of these rate laws, state the reaction order with respect to the hypothetical substances \(\mathrm{A}\) and \(\mathrm{B}\), and give the overall order. (a) Rate \(=k[\mathrm{~A}][\mathrm{B}]^{3}\) (b) Rate \(=k[\mathrm{~A}][\mathrm{B}]\) (c) Rate \(=k[\mathrm{~A}]\) (d) Rate \(=k[\mathrm{~A}]^{3}[\mathrm{~B}]\)

For each of the rate laws below, determine the order of the reaction with respect to the hypothetical substances \(\mathrm{X}, \mathrm{Y},\) and \(\mathrm{Z}\). What is the overall order? (a) Rate \(=k[\mathrm{X}][\mathrm{Y}][\mathrm{Z}]\) (b) Rate \(=k[\mathrm{X}]^{2}[\mathrm{Y}]^{1 / 2}[\mathrm{Z}]\) (c) Rate \(=k[\mathrm{X}]^{1.5}[\mathrm{Y}]^{-1}\) (d) Rate \(=k[\mathrm{X}] /[\mathrm{Y}]^{2}\)

A reaction \(\mathrm{A}+\mathrm{B} \longrightarrow\) products is found to be secondorder in B. Which rate equation cannot be correct? (a) Rate \(=k[\mathrm{~A}][\mathrm{B}]\) (b) Rate \(=k[\mathrm{~A}][\mathrm{B}]^{2}\) (c) Rate \(=k[\mathrm{~B}]^{2}\)

The reaction $$ 2 \mathrm{NO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ is found to be first-order in \(\mathrm{H}_{2}(\mathrm{~g}) .\) Which rate equation cannot be correct? (a) Rate \(=k[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right]\) (b) Rate \(=k\left[\mathrm{H}_{2}\right]\) $$ \text { (c) Rate }=k\left[\mathrm{NOl}^{2}\left[\mathrm{H}_{3}\right]^{2}\right. $$

The decomposition of ammonia to nitrogen and hydrogen on tungsten at \(1100^{\circ} \mathrm{C}\) is zeroth-order with a rate constant of \(2.5 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \min ^{-1}\). (a) Write the rate expression. (b) Calculate the rate when \(\left[\mathrm{NH}_{3}\right]=0.075 \mathrm{M}\).

When phenacyl bromide and pyridine are both dissolved in methanol, they react to form phenacylpyridinium bromide. \(\mathrm{C}_{6} \mathrm{H}_{5}-\stackrel{\mathrm{O}}{\|} \mathrm{C}-\mathrm{CH}_{2} \mathrm{Br}+\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N} \longrightarrow\) \(\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{C}-\mathrm{CH}_{2} \mathrm{NC}_{5} \mathrm{H}_{5}^{+}+\mathrm{Br}^{-}\) When equal concentrations of reactants were mixed in methanol at \(35^{\circ} \mathrm{C}\), these data were obtained: \begin{tabular}{rc|rr} \hline Time \((\min )\) & [Reactant] \((\mathrm{mol} / \mathrm{L})\) & Time \((\mathrm{min})\) & \([\mathrm{Reactant}]\) \((\mathrm{mol} / \mathrm{L})\) \\ \hline 0 & 0.0385 & \(500 .\) & 0.0208 \\ \(100 .\) & 0.0330 & \(600 .\) & 0.0191 \\ \(200 .\) & 0.0288 & \(700 .\) & 0.0176 \\ \(300 .\) & 0.0255 & \(800 .\) & 0.0163 \\ \(400 .\) & 0.0220 & \(1000 .\) & 0.0143 \\ \hline \end{tabular} (a) Determine the rate law for this reaction. (b) Determine the overall order of this reaction. (c) Determine the rate constant for this reaction. (d) Determine the rate constant for this reaction when the concentration of each reactant is \(0.030 \mathrm{~mol} / \mathrm{L}\)

Radioactive gold-198 is used in the diagnosis of liver problems. \({ }^{198}\) Au decays in a first-order process, emitting a \(\beta\) particle (electron). The half-life of this isotope is 2.7 days. You begin with a 5.6 -mg sample of the isotope. Calculate how much gold-198 remains after 1.0 day.

The compound \(\mathrm{Xe}\left(\mathrm{CF}_{3}\right)_{2}\) decomposes in a first-order reaction to elemental Xe with a half-life of \(30 . \mathrm{min}\). If you place \(7.50 \mathrm{mg} \mathrm{Xe}\left(\mathrm{CF}_{3}\right)_{2}\) in a flask, calculate how long you must wait until only \(0.25 \mathrm{mg} \mathrm{Xe}\left(\mathrm{CF}_{3}\right)_{2}\) remains.

The compound \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) decomposes in a first-order reaction $$ \mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) $$ that has a half-life of \(1.47 \times 10^{4} \mathrm{~s}\) at \(600 . \mathrm{K}\). If you begin with \(1.6 \times 10^{-3} \mathrm{~mol}\) of pure \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) in a \(2.0-\mathrm{L}\) flask, calculate at what time the amount of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) will $$ \text { be } 1.2 \times 10^{-4} \mathrm{~mol} \text { . } $$

The first-order rate constant for the decomposition of a certain hormone in water at \(25^{\circ} \mathrm{C}\) is \(3.42 \times 10^{-4}\) day \(^{-1}\). (a) A \(0.0200-\mathrm{M}\) solution of the hormone is stored at \(25^{\circ} \mathrm{C}\) for two months. Calculate its concentration at the end of that period. (b) Calculate how long it takes for the concentration of the solution to drop from \(0.0200 \mathrm{M}\) to \(0.00350 \mathrm{M}\). (c) Determine the half-life of the hormone.

Assume that each gas-phase reaction occurs via a single bimolecular step. For which reaction would you expect the steric factor to be more important? Why? \(\mathrm{Cl}+\mathrm{O}_{3} \longrightarrow \mathrm{ClO}+\mathrm{O}_{2}\) or \(\mathrm{NO}+\mathrm{O}_{3} \longrightarrow \mathrm{NO}_{2}+\mathrm{O}_{2}\)

Assume that each gas-phase reaction occurs via a single bimolecular step. For which reaction would you expect the steric factor to be more important? Why? $$ \begin{aligned} \mathrm{H}_{2} \mathrm{C} &=\mathrm{CH}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3} \text { or } \\ \left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CH}_{2}+\mathrm{HBr} \longrightarrow &\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CBr}-\mathrm{CH}_{3} \end{aligned} $$

Suppose a reaction rate constant has been measured at two different temperatures, \(T_{1}\) and \(T_{2}\), and its values are \(k_{\perp}\) and \(k_{2}\), respectively. (a) Write the Arrhenius equation at each temperature. (b) By combining these two equations, derive an expression for the ratio of the two rate constants, \(k_{1} / k_{2}\). Use this expression to answer the next four questions.

Suppose a chemical reaction has an activation energy of \(76 \mathrm{~kJ} / \mathrm{mol}\), as in the example in Figure \(11.12 .\) Calculate by what factor the rate of the reaction at \(50 .{ }^{\circ} \mathrm{C}\) is increased over its rate at \(25^{\circ} \mathrm{C}\).

Calculate the activation energy for a reaction if its rate constant is found to triple when the temperature is raised from \(600 . \mathrm{K}\) to \(610 . \mathrm{K}\).

These data were obtained for the rate constant for reaction of an unknown compound with water: \begin{tabular}{cc} \hline\(T\left({ }^{\circ} \mathrm{C}\right)\) & \(\mathrm{k}\left(\mathrm{s}^{-1}\right)\) \\ \hline 56.2 & \(1.04 \times 10^{-5}\) \\ 78.2 & \(1.45 \times 10^{-4}\) \\ \hline \end{tabular} (a) Calculate the activation energy and frequency factor for this reaction. (b) Estimate the rate constant of the reaction at a temperature of \(100.0^{\circ} \mathrm{C}\).

\(p\) -Methylphenyl acetate reacts with imidazole to produce \(p\) -methylphenol and acetyl imidazole. The rate constants for this second-order reaction at two temperatures are given in the table. \begin{tabular}{cc} \hline\(T\left({ }^{\circ} \mathrm{C}\right)\) & \(k\left(\mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}\right)\) \\ \hline 10.0 & \(2.34 \times 10^{-2}\) \\ 60.0 & \(1.52 \times 10^{-1}\) \\ \hline \end{tabular} (a) Calculate the activation energy and frequency factor for this reaction. (b) Estimate the rate constant for this reaction at a temperature of \(100.0^{\circ} \mathrm{C}\).

For the reaction of iodine atoms with hydrogen molecules in the gas phase, these rate constants were obtained experimentally. \(2 \mathrm{I}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HI}(\mathrm{g})\) 2 \begin{tabular}{lc} \hline\(T(\mathrm{~K})\) & \(10^{-5} \mathrm{k}\left(\mathrm{L}^{2} \mathrm{~mol}^{-2} \mathrm{~s}^{-1}\right)\) \\ \hline 417.9 & 1.12 \\ 480.7 & 2.60 \\ 520.1 & 3.96 \\ 633.2 & 9.38 \\ 666.8 & 11.50 \\ 710.3 & 16.10 \\ 737.9 & 18.54 \\ \hline \end{tabular} (a) Calculate the activation energy and frequency factor for this reaction. (b) Estimate the rate constant of the reaction at \(400.0 \mathrm{~K}\).

Make an Arrhenius plot and calculate the activation energy for the gas-phase reaction \(2 \mathrm{NOCl}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g})\) \begin{tabular}{lc} \hline\(T(\mathrm{~K})\) & Rate Constant \(\left(\mathrm{L} \mathrm{mol}^{-1} \mathrm{~s}^{-1}\right)\) \\ \hline \(400 .\) & \(6.95 \times 10^{-4}\) \\ \(450 .\) & \(1.98 \times 10^{-2}\) \\ \(500 .\) & \(2.92 \times 10^{-1}\) \\ \(550 .\) & 2.60 \\ \(600 .\) & 16.3 \\ \hline \end{tabular}

For the gas-phase reaction $$ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{I}(\mathrm{g}) \longrightarrow \mathrm{CH}_{2} \mathrm{CH}_{2}(\mathrm{~g})+\mathrm{HI}(\mathrm{g}) $$ the activation energy \(E_{\mathrm{a}}\) is \(221 \mathrm{~kJ} / \mathrm{mol}\) and the frequency factor \(A\) is \(1.2 \times 10^{14} \mathrm{~s}^{-1}\). If the concentration of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{I}\) is \(0.012 \mathrm{~mol} / \mathrm{L},\) calculate the rate of the reac- tion at (a) \(400 .{ }^{\circ} \mathrm{C}\) $$ \text { (b) } 800 .{ }^{\circ} \mathrm{C} $$

For the gas-phase reaction cis-CHClCHCl(g)\longrightarrow trans-CHClCHCl(g) the activation energy \(E_{\mathrm{a}}\) is \(234 \mathrm{~kJ} / \mathrm{mol}\) and the frequency factor \(A\) is \(6.3 \times 10^{12} \mathrm{~s}^{-1}\). If the concentration of cis\(\mathrm{CHClCHCl}\) is \(0.0043 \mathrm{~mol} / \mathrm{L},\) calculate the rate of the reaction at (a) \(400 .{ }^{\circ} \mathrm{C}\) $$ \text { (b) } 800 .{ }^{\circ} \mathrm{C} $$

Write the rate law for each of these elementary reactions. (a) \(\mathrm{Cl}(\mathrm{g})+\mathrm{ICl}(\mathrm{g}) \longrightarrow \mathrm{I}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g})\) (b) \(\mathrm{CH}_{3} \mathrm{~N}=\mathrm{NCH}_{3}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(\mathrm{~g})+\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\) (c) \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})\)

Draw an energy versus reaction progress diagram (similar to the one in Question 60 ) for each of the reactions whose activation energy and enthalpy change are given below. Draw arrows to represent the activation energies of the forward and reverse reaction and \(\Delta_{1} H^{\circ} .\) (a) \(\Delta_{r} H^{\circ}=-145 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=75 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(\Delta_{r} H^{\circ}=-70 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=65 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(\Delta_{r} H^{\circ}=70 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=85 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Draw an energy versus reaction progress diagram (similar to the one in Question 60 ) for each of the reactions whose activation energy and enthalpy change are given below. Draw arrows to represent the activation energies of the forward and reverse reaction and \(\Delta_{\mathrm{r}} H^{\circ} .\) (a) \(\Delta_{r} H^{\circ}=105 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=175 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(\Delta_{r} H^{\circ}=-43 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(\Delta_{r} H^{\circ}=15 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=55 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Assuming that each reaction is elementary, predict the rate law. (a) \(\mathrm{NO}(\mathrm{g})+\mathrm{NO}_{3}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})\) (b) \(\mathrm{O}(\mathrm{g})+\mathrm{O}_{3}(\mathrm{~g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{~g})\) (c) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}(\mathrm{aq}) \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{+}(\mathrm{aq})+\mathrm{Br}^{-}(\mathrm{aq})\) (d) \(2 \mathrm{HI}(\mathrm{g}) \longrightarrow \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g})\)

Assuming that each reaction is elementary, predict the rate law. (a) \(\mathrm{Br}(\mathrm{g})+\mathrm{IBr}(\mathrm{g}) \longrightarrow \mathrm{I}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{~g})\) (b) \(\mathrm{Cl}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{HCl}(\mathrm{g})+\mathrm{H}(\mathrm{g})\) (c) \(2 \mathrm{NO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\) (d) Cyclopropane(g) \(\longrightarrow\) propene(g)

Experiments show that the reaction of nitrogen dioxide with fluorine $$ 2 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{FNO}_{2}(\mathrm{~g}) $$ has the rate law $$ \text { Rate }=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{F}_{2}\right] $$ and the reaction is thought to occur in two steps: $$ \begin{array}{l} \text { Step } 1: \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g}) \longrightarrow \mathrm{FNO}_{2}(\mathrm{~g})+\mathrm{F}(\mathrm{g}) \\ \text { Step } 2: \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{F}(\mathrm{g}) \longrightarrow \mathrm{FNO}_{2}(\mathrm{~g}) \end{array} $$ (a) Show that the sum of this sequence of reactions gives the balanced equation for the overall reaction. (b) Which step is rate-determining?