# Chemistry the Central Science

## Educators UO

Problem 1

An automotive fuel injector dispenses a fine spray of gasoline into the automobile cylinder, as shown in the bottom drawing here. When an injector gets clogged, as
shown in the top drawing, the spray is not as fine or even and the performance of the car declines. How is this observation related to chemical kinetics? [Section 14.1$]$ Sahithi T.

Problem 2

Consider the following graph of the concentration of a substance $X$ over time. Is each of the following statements true or false? $(\mathbf{a})$ $X$ is a product of the reaction. $(\mathbf{b})$ The rate of the reaction remains the same as time progresses.$(\mathbf{c})$
The average rate between points 1 and 2 is greater than the average rate between points 1 and $3 .$ $(\mathbf{d})$ As time progresses, the curve will eventually turn downward toward the $x$ -axis. [Section 14.2$]$

UO
Umut O.
Texas Tech University

Problem 3

You study the rate of a reaction, measuring both the concentration of the reactant and the concentration of the product as a function of time, and obtain the following results:
(a) Which chemical equation is consistent with these data: $$(\mathbf{i}) \mathrm{A} \longrightarrow \mathrm{B},(\mathbf{i} \mathbf{i}) \mathrm{B} \longrightarrow \mathrm{A},(\mathbf{i} \mathbf{i} \mathbf{i}) \mathrm{A} \longrightarrow 2 \mathrm{B} (\mathbf{i v}) \mathrm{B} \longrightarrow 2 \mathrm{A} ?$$ (b) Write equivalent expressions for the rate of the reaction in terms of the appearance or disappearance of the two substances. [ Section 14.2$]$ Sahithi T.

Problem 4

Suppose that for the reaction $\mathrm{K}+\mathrm{L} \longrightarrow \mathrm{M}$ , you monitor the production of M over time, and then plot the following graph from your data:
(a) Is the reaction occurring at a constant rate from $t=0$ to $t=15$ min? (b) Is the reaction completed at $t=15$ min? ( c) Suppose the reaction as plotted here were started with 0.20 mol $\mathrm{K}$ and 0.40 $\mathrm{mol}$ .. After $30 \mathrm{min},$ an additional 0.20 $\mathrm{mol} \mathrm{K}$ are added to the reaction mixture. Which of the following correctly describes how the plot would look from $t=30$ min to $t=60 \min ?(\mathrm{i})[\mathrm{M}]$ would remain at the same constant value it has at $t=30 \mathrm{min}_{1}$ (ii) $[\mathrm{M}]$ would increase with the same slope as $t=0$ to
15 min, until $t=45$ min at which point the plot becomes horizontal again, or (iii) $[\mathrm{M}]$ decreases and reaches 0 at $t=45 \mathrm{min} .[$ Section 14.2$]$

UO
Umut O.
Texas Tech University

Problem 5

The following diagrams represent mixtures of $\mathrm{NO}(g)$ and $\mathrm{O}_{2}(g) .$ These two substances react as follows: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ It has been determined experimentally that the rate is second order in NO and first order in $\mathrm{O}_{2} .$ Based on this fact, which of the following mixtures will have the fastest initial rate? [Section 14.3] Sahithi T.

Problem 6

A friend studies a first-order reaction and obtains the following three graphs for experiments done at two different temperatures. (a) Which two graphs represent experiments done at the same temperature? What accounts for the difference in these two graphs? In what
way are they the same? (b) Which two graphs represent experiments done with the same starting concentration but at different temperatures? Which graph probably represents the lower temperature? How do you know? [Section 14.4$]$

UO
Umut O.
Texas Tech University

Problem 7

\begin{equation} \begin{array}{l}{\text { (a) Given the following diagrams at } t=0 \text { min and }} \\ {t=30 \mathrm{min}, \text { what is the half-life of the reaction if it fol- }} \\ {\text { lows first-order kinetics? }}\end{array} \end{equation} \begin{equation} \begin{array}{l}{\text { (b) After four half-life periods for a first-order reaction, }} \\ {\text { what fraction of reactant remains? [Section } 14.4 ]}\end{array} \end{equation} Sahithi T.

Problem 8

Which of the following linear plots do you expect for a reaction $A \longrightarrow$ products if the kinetics are (a) zero order, (b) first order, or (c) second order? [Section 14.4$]$

UO
Umut O.
Texas Tech University

Problem 9

The following diagram shows a reaction profile. Label the components indicated by the boxes. [Section 14.5$]$ Sahithi T.

Problem 10

The accompanying graph shows plots of ln $k$ versus 1$/ T$ for two different reactions. The plots have been extrapolated to the $y$ -intercepts. Which reaction (red or blue) has
(a) the larger value for $E_{a},$ and (b) the larger value for the frequency factor, $A ?[$ Section 14.5$]$

UO
Umut O.
Texas Tech University

Problem 11

The following graph shows two different reaction pathways for the same overall reaction at the same temperature. Is each of the following statements true or false? (a) The rate is faster for the red path than for the blue path. (b) For both paths, the rate of the reverse reaction is slower than the rate of the forward reaction. (c) The energy change $\Delta E$ is the same for both paths. [ Section 14.6$]$ Sahithi T.

Problem 12

Consider the diagram that follows, which represents two steps in an overall reaction. The red spheres are oxygen, the blue ones nitrogen, and the green ones fluorine. (a) Write the chemical equation for each step in the reaction. (b) Write the equation for the overall reaction.(c) Identify the intermediate in the mechanism. (d) Write the rate law for the overall reaction if the first step is the slow, rate-determining step. [Section 14.6$]$

UO
Umut O.
Texas Tech University

Problem 13

Based on the following reaction profile, how many intermediates are formed in the reaction $A \longrightarrow C ?$ How many transition states are there? Which step, $A \longrightarrow B$ or $B \longrightarrow C,$ is the faster? For the reaction $A \longrightarrow C,$ is $\Delta E$ positive, negative, or zero? [ Section 14.6$]$ Sahithi T.

Problem 14

Draw a possible transition state for the bimolecular reaction depicted here. (The blue spheres are nitrogen atoms, and the red ones are oxygen atoms.) Use dashed lines to
represent the bonds that are in the process of being broken or made in the transition state. [Section 14.6$]$

UO
Umut O.
Texas Tech University

Problem 15

The following diagram represents an imaginary two-step mechanism. Let the red spheres represent element A, the green ones element $B$ , and the blue ones element $\mathrm{C}$ . (a)
Write the equation for the net reaction that is occurring. (b) Identify the intermediate. (c) Identify the catalyst. [Sections 14.6 and 14.7$]$ Sahithi T.

Problem 16

Draw a graph showing the reaction pathway for an overall exothermic reaction with two intermediates that are produced at different rates. On your graph indicate the reactants, products, intermediates, transition states, and activation energies. [Sections 14.6 and 14.7$]$

UO
Umut O.
Texas Tech University

Problem 17

(a) What is meant by the term reaction rate? (b) Name three factors that can affect the rate of a chemical reaction. (c) Is the rate of disappearance of reactants always the same as the rate of appearance of products? Sahithi T.

Problem 18

(a) What are the units usually used to express the rates of reactions occurring in solution? (b) As the temperature increases, does the reaction rate increase or decrease? (c) As a reaction proceeds, does the instantaneous reaction rate increase or decrease?

UO
Umut O.
Texas Tech University

Problem 19

Consider the following hypothetical aqueous reaction: $\mathrm{A}(a q) \rightarrow \mathrm{B}(a q) .$ A flask is charged with 0.065 $\mathrm{mol}$ of $\mathrm{A}$ in a total volume of 100.0 $\mathrm{mL} .$ The following data are collected:(a) Calculate the number of moles of $\mathrm{B}$ at each time in the table, assuming that there are no molecules of $\mathrm{B}$ at
time zero and that A cleanly converts to $\mathrm{B}$ with no intermediates. (b) Calculate the average rate of disappearance of A for each 10 -min interval in units of $M /$ s. (c) Between $t=10 \mathrm{min}$ and $t=30 \mathrm{min},$ what is the average rate of appearance of $\mathrm{B}$ in units of $M / \mathrm{s} ?$ Assume that the volume of the solution is constant. Sahithi T.

Problem 20

A flask is charged with 0.100 mol of A and allowed to react to form $B$ according to the hypothetical gas-phase reaction $A(g) \longrightarrow \mathrm{B}(g) .$ The following data are collected:(a) Calculate the number of moles of $\mathrm{B}$ at each time in the table, assuming that $\mathrm{A}$ is cleanly converted to $\mathrm{B}$ with no intermediates. (b) Calculate the average rate of disappearance of A for each 40 s interval in units of mol/s. (c) Which of the following would be needed to calculate the rate in units of concentration per time: (i) the pressure of
the gas at each time, (ii) the volume of the reaction flask, (iii) the temperature, or (iv) the molecular weight of A?

UO
Umut O.
Texas Tech University

Problem 21

The isomerization of methyl isonitrile $\left(\mathrm{CH}_{3} \mathrm{NC}\right)$ to acetonitrile $\left(\mathrm{CH}_{3} \mathrm{CN}\right)$ was studied in the gas phase at $215^{\circ} \mathrm{C}$ and the following data were obtained: (a) Calculate the average rate of reaction, in $M / s,$ for the time interval between each measurement. (b) Calculate the average rate of reaction over the entire time of the data from $t=0$ to $t=15,000$ s. (c) Which is greater, the Sahithi T.

Problem 22

The rate of disappearance of $\mathrm{HCl}$ was measured for the following reaction:
$$\mathrm{CH}_{3} \mathrm{OH}(a q)+\mathrm{HCl}(a q) \rightarrow \mathrm{CH}_{3} \mathrm{Cl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$$ The following data were collected:(a) Calculate the average rate of reaction, in $M / s,$ for the time interval between each measurement. (b) Calculate
the average rate of reaction for the entire time for the data from $t=0.0$ min to $t=430.0$ min. (c) Which is greater,the average rate between $t=54.0$ and $t=215.0 \mathrm{min},$ or between $t=107.0$ and $t=430.0 \mathrm{min}$ ? (\boldsymbol{d} ) ~ G r a p h ~ $[\mathrm{HCl}]$ versus time and determine the instantaneous rates in $M /$ min and $M / \mathrm{s}$ at $t=75.0 \mathrm{min}$ and $t=250 \mathrm{min} .$

UO
Umut O.
Texas Tech University

Problem 23

For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product:
$\begin{array}{l}{\text { (a) } \mathrm{H}_{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)} \\ {\text { (b) } 2 \mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)} \\ {\text { (c) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (d) } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{NH}_{3}(g)}\end{array}$ Sahithi T.

Problem 24

For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product and disappearance of each reactant:
$\begin{array}{l}{\text { (a) } 2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)} \\ {\text { (b) } 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)} \\ {\text { (c) } 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (d) } \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)}\end{array}$

UO
Umut O.
Texas Tech University

Problem 25

(a) Consider the combustion of hydrogen, $2 \mathrm{H}_{2}(g)+$ $\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) .$ If hydrogen is burning at the rate of 0.48 $\mathrm{mol} / \mathrm{s}$ , what is the rate of consumption of oxygen? What is the rate of formation of water vapor? (b) The reaction $2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)$ is carried out in a closed vessel. If the partial pressure of $\mathrm{NO}$ is decreasing at the rate of 56 torr/min, what is the rate of change of the total pressure of the vessel? Sahithi T.

Problem 26

(a) Consider the combustion of ethylene, $\mathrm{C}_{2} \mathrm{H}_{4}(g)+$ $3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) .$ If the concentration of $\mathrm{C}_{2} \mathrm{H}_{4}$ is decreasing at the rate of $0.036 \mathrm{M} / \mathrm{s},$
what are the rates of change in the concentrations of $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O} ?(\mathbf{b})$ The rate of decrease in $\mathrm{N}_{2} \mathrm{H}_{4}$ partial pressure in a closed reaction vessel from the reaction $\mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$ is 74 torr per hour. What
are the rates of change of $\mathrm{NH}_{3}$ partial pressure and total pressure in the vessel?

UO
Umut O.
Texas Tech University

Problem 27

A reaction $\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}$ obeys the following rate law:
Rate $=k[\mathrm{B}]^{2}$ . (a) If [A] is doubled, how will the rate change? Will the rate constant change? (b) What are the reaction orders for $\mathrm{A}$ and $\mathrm{B} ?$ What is the overall reaction order? (c) What are the units of the rate constant? Sahithi T.

Problem 28

Consider a hypothetical reaction between $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$ that is first order in $\mathrm{A},$ zero order in $\mathrm{B},$ and second order in C. (a) Write the rate law for the reaction. (b) How does the rate change when [A] is doubled and the other reactant concentrations are held constant? (c) How does the rate change when [B] is tripled and the other reactant concentrations are held constant? (d) How does the rate change when $[C]$ is tripled and the other reactant concentrations are held constant? (e) By what factor does the
rate change when the concentrations of all three reactants are tripled? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

UO
Umut O.
Texas Tech University

Problem 29

The decomposition reaction of $\mathrm{N}_{2} \mathrm{O}_{5}$ in carbon tetrachloride is $2 \mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}$ . The rate law is first order in $\mathrm{N}_{2} \mathrm{O}_{5}$ . At $64^{\circ} \mathrm{C}$ the rate constant is $4.82 \times 10^{-3} \mathrm{s}^{-1}$ (a) Write the rate law for the reaction. (b) What is the rate
of reaction when $\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]=0.0240 M ?(\mathbf{c})$ What happens to the rate when the concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$ is doubled to 0.0480$M ?(\mathbf{d})$ What happens to the rate when the concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$ is halved to 0.0120 $\mathrm{M} ?$ Sahithi T.

Problem 30

Consider the following reaction: $$2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ (a) The rate law for this reaction is first order in $\mathrm{H}_{2}$ and second order in $\mathrm{NO}$ . Write the rate law. (b) If the rate
constant for this reaction at 1000 $\mathrm{K}$ is $6.0 \times 10^{4} M^{-2} \mathrm{s}^{-1}$
what is the reaction rate when $[\mathrm{NO}]=0.035 M$ and $\left[\mathrm{H}_{2}\right]=0.015 M ?$ (c) What is the reaction rate at 1000 $\mathrm{K}$ when the concentration of $\mathrm{NO}$ is increased to 0.10 $\mathrm{M}$while the concentration of $\mathrm{H}_{2}$ is 0.010$M ?$ (d) What is the reaction rate at 1000 $\mathrm{K}$ if $[\mathrm{NO}]$ is decreased to 0.010 $\mathrm{M}$ and $\left[\mathrm{H}_{2}\right]$ is increased to 0.030 $\mathrm{M}$ ?

UO
Umut O.
Texas Tech University

Problem 31

Consider the following reaction: $$\mathrm{CH}_{3} \mathrm{Br}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(a q)+\mathrm{Br}^{-}(a q)$$ The rate law for this reaction is first order in $\mathrm{CH}_{3} \mathrm{Br}$ and first order in $\mathrm{OH}^{-} .$ When $\left[\mathrm{CH}_{3} \mathrm{Br}\right]$ is $5.0 \times 10^{-3} \mathrm{M}$ and
$\left[\mathrm{OH}^{-}\right]$ is $0.050 \mathrm{M},$ the reaction rate at 298 $\mathrm{K}$ is 0.0432 $\mathrm{M} / \mathrm{s}$ . (a) What is the value of the rate constant? (\mathbf{b} )What are the units of the rate constant? (c) What would happen to the rate if the concentration of OH $^{-}$ were tripled? (d) What would happen to the rate if the concentration of both reactants were tripled? Sahithi T.

Problem 32

The reaction between ethyl bromide $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}\right)$
and hydroxide ion in ethyl alcohol at 330 $\mathrm{K}$ , $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}(a l c)+\mathrm{OH}^{-}(a l c) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{Br}^{-}(a l c)$ is first order each in ethyl bromide and hydroxide ion.
When $\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}\right]$ is 0.0477 $\mathrm{M}$ and $\left[\mathrm{OH}^{-}\right]$ is $0.100 \mathrm{M},$ the rate of disappearance of ethyl bromide is $1.7 \times 10^{-7} \mathrm{M} / \mathrm{s}$ (a) What is the value of the rate constant? (b) What are the units of the rate constant? (c) How would the rate of disappearance of ethyl bromide change if the solution were diluted by adding an equal volume of pure ethyl alcohol to the solution?

UO
Umut O.
Texas Tech University

Problem 33

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: $\mathrm{OCl}^{-}+\mathrm{I}^{-} \longrightarrow \mathrm{Ol}^{-}+\mathrm{Cl}^{-} .$ This rapid reaction gives the following rate data: (a) Write the rate law for this reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when $\left[\mathrm{OCl}^{-}\right]=2.0 \times 10^{-3} M$ and $\left[\mathrm{I}^{-}\right]=5.0 \times 10^{-4} \mathrm{M}$ Sahithi T.
The reaction 2 \mathrm{ClO}_{2}(a q)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{ClO}_{3}^{-}(a q)+$$\mathrm{ClO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) was studied with the following results:(a) Determine the rate law for the reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when \left[\mathrm{ClO}_{2}\right]=0.100 \mathrm{M} and \left[\mathrm{OH}^{-}\right]=0.050 \mathrm{M} UO Umut O. Texas Tech University Problem 35 The following data were measured for the reaction \mathrm{BF}_{3}(g)+\mathrm{NH}_{3}(g) \stackrel{\rightarrow}{\longrightarrow} \mathrm{F}_{3} \mathrm{BNH}_{3}(g)(a) What is the rate law for the reaction? (b) What is the overall order of the reaction? (c) Calculate the rate constant with proper units? (d) What is the rate when \left[B F_{3}\right]=0.100 M and \left[\mathrm{NH}_{3}\right]=0.500 M ? Sahithi T. Numerade Educator Problem 36 The following data were collected for the rate of disappearance of N O in the reaction 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) (a) What is the rate law for the reaction? (b) What are the units of the rate constant? (c) What is the average value of the rate constant calculated from the three data sets? (d) What is the rate of disappearance of NO when [\mathrm{NO}]=0.0750 M and \left[\mathrm{O}_{2}\right]=0.0100 \mathrm{M} ? (e) What is the rate of disappearance of \mathrm{O}_{2} at the concentrations given in part (d)? UO Umut O. Texas Tech University Problem 37 Consider the gas-phase reaction between nitric oxide and bromine at 273^{\circ} \mathrm{C} : 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \longrightarrow 2 \mathrm{NOBr}(g) The following data for the initial rate of appearance of NOBr were obtained: (a) Determine the rate law. (b) Calculate the average value of the rate constant for the appearance of NOBr from the four data sets. (c) How is the rate of appearance of NOBr related to the rate of disappearance of \mathrm{Br}_{2} ?(\mathbf{d}) What is the rate of disappearance of \mathrm{Br}_{2} when [\mathrm{NO}]=0.075 \mathrm{M} and \left[\mathrm{Br}_{2}\right]=0.25 \mathrm{M} ? Sahithi T. Numerade Educator Problem 38 Consider the reaction of peroxydisulfate ion \left(\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\right) with iodide ion \left(\mathrm{I}^{-}\right) in aqueous solution:$$\quad \mathrm{S}_{2} \mathrm{O}_{8}^{2-}(a q)+3 \mathrm{I}^{-}(a q) \longrightarrow 2 \mathrm{SO}_{4}^{2-}(a q)+\mathrm{I}_{3}^{-}(a q)At a particular temperature, the initial rate of disappearance of \mathrm{S}_{2} \mathrm{O}_{8}^{2-} varies with reactant concentrations in the following manner: (a) Determine the rate law for the reaction and state the units of the rate constant. (b) What is the average value of the rate constant for the disappearance of S_{2} \mathrm{O}_{8}^{2-} based on the four sets of data? (c) How is the rate of disappearance of S_{2} \mathrm{O}_{8}^{2-} related to the rate of disappearance of \mathrm{I}^{-} ?(\mathbf{d}) What is the rate of disappearance of \mathrm{I}^{-} when \left[\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\right]=0.025 M and \left[\mathrm{I}^{-}\right]=0.050 \mathrm{M} ? UO Umut O. Texas Tech University Problem 39 (a) For the generic reaction \mathrm{A} \rightarrow \mathrm{B} what quantity, when graphed versus time, will yield a straight line for a first-order reaction? (b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)? Sahithi T. Numerade Educator Problem 40 (a) For a generic second-order reaction \mathrm{A} \longrightarrow \mathrm{B} , what quantity, when graphed versus time, will yield a straight line? (b) What is the slope of the straight line from part line? (b) What is the slope of the straight line from part (a)? (c) Does the half-life of a second-order reaction increase, decrease, or remain the same as the reaction proceeds? UO Umut O. Texas Tech University Problem 41 (a) The gas-phase decomposition of \mathrm{SO}_{2} \mathrm{Cl}_{2}, \mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g), is first order in \mathrm{SO}_{2} \mathrm{Cl}_{2} . At 600 \mathrm{K} the half-life for this process is 2.3 \times 10^{5} \mathrm{s} . What is the rate constant at this temperature? (b) At 320 "C the rate constant is 2.2 \times 10^{-5} \mathrm{s}^{-1} . What is the half-life at this temperature? Sahithi T. Numerade Educator Problem 42 Moleculariodine, \mathrm{I}_{2}(g), dissociates into iodine atoms at 625 \mathrm{K} with a first-order rate constant of 0.271 \mathrm{s}^{-1} . (a) What is the half-life for this reaction? (b) If you start with 0.050M \mathrm{I}_{2} at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form \mathrm{I}_{2} ? UO Umut O. Texas Tech University Problem 43 As described in Exercise 14.41 , the decomposition of sulfuryl chloride \left(\mathrm{SO}_{2} \mathrm{Cl}_{2}\right) is a first-order process. The rate constant for the decomposition at 660 \mathrm{K} is 4.5 \times 10^{-2} \mathrm{s}^{-1} .half-life for this reaction? (b) If you start with 0.050M \mathrm{I}_{2} at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form \mathrm{I}_{2} ? Sahithi T. Numerade Educator Problem 44 The first-order rate constant for the decomposition of \mathrm{N}_{2} \mathrm{O}_{5}, 2 \mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g), \quad at 70^{\circ} \mathrm{C} is 6.82 \times 10^{-3} \mathrm{s}^{-1} . Suppose we start with 0.0250 \mathrm{mol} of \mathrm{N}_{2} \mathrm{O}_{5}(g) in a volume of 2.0 \mathrm{L} . (a) How many moles of \mathrm{N}_{2} \mathrm{O}_{5} will remain after 5.0 \mathrm{min} ? (b) How many minutes will it take for the quantity of \mathrm{N}_{2} \mathrm{O}_{5} to drop to 0.010 \mathrm{mol} ? (c) What is the half-life of \mathrm{N}_{2} \mathrm{O}_{5} at 70^{\circ} \mathrm{C} ? UO Umut O. Texas Tech University Problem 45 The reaction \mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) is first order in \mathrm{SO}_{2} \mathrm{Cl}_{2} . Using the following kinetic data, determine the magnitude and units of the first-order rate constant: Sahithi T. Numerade Educator Problem 46 From the following data for the first-order gas-phase isomerization of \mathrm{CH}_{3} \mathrm{NC} at 215^{\circ} \mathrm{C} , calculate the first-order rate constant and half-life for the reaction: UO Umut O. Texas Tech University Problem 47 Consider the data presented in Exercise 14.19 . (a) By using appropriate graphs, determine whether the reaction is first order or second order. (b) What is the rate constant for the reaction? (c) What is the half-life for the reaction? Sahithi T. Numerade Educator Problem 48 Consider the data presented in Exercise 14.20 . (a) Determine whether the reaction is first order or second order. (b) What is the rate constant? (c) What is the half-life? UO Umut O. Texas Tech University Problem 49 The gas-phase decomposition of \mathrm{NO}_{2}, 2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g), is studied at 383^{\circ} \mathrm{C} , giving the following data:(a) Is the reaction first order or second order with respect to the concentration of \mathrm{NO}_{2} ? (b) What is the rate constant? (c) Predict the reaction rates at the beginning of the reaction for initial concentrations of 0.200 M, 0.100 M, and 0.050M \mathrm{NO}_{2} . Sahithi T. Numerade Educator Problem 50 Sucrose \left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right), commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} . At 23^{\circ} \mathrm{C} and in 0.5 \mathrm{M} \mathrm{HCl} , the following data were obtained for the disappearance of sucrose: (a) Is the reaction first order or second order with respect to \left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right] ?(\mathbf{b}) What is the rate constant? (c) Using this rate constant, calculate the concentration of sucrose at 39, 80,140, and 210 min if the initial sucrose concentration was 0.316M and the reaction were zero order in sucrose. UO Umut O. Texas Tech University Problem 51 (a) What factors determine whether a collision between two molecules will lead to a chemical reaction? (b) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature? (c) Which factor is most sensitive to changes in temperature-the frequency of collisions, the orientation factor, or the fraction of molecules with energy greater than the activation energy? Sahithi T. Numerade Educator Problem 52 (a) In which of the following reactions would you expect the orientation factor to be least important in leading to reaction: \mathrm{NO}+\mathrm{O} \longrightarrow \mathrm{NO}_{2} or \mathrm{H}+\mathrm{Cl} \longrightarrow \mathrm{HCl} ? (b) Does the orientation factor depend on temperature? UO Umut O. Texas Tech University Problem 53 Calculate the fraction of atoms in a sample of argon gas at 400 \mathrm{K} that has an energy of 10.0 \mathrm{kJ} or greater. Sahithi T. Numerade Educator Problem 54 (a) The activation energy for the isomerization of methyl isonitrile (Figure 14.6) is 160 \mathrm{kJ} / \mathrm{mol} . Calculate the fraction of methyl isonitrile molecules that has an energy equal to or greater than the activation energy at 500 \mathrm{K} . (b) Calculate this fraction for a temperature of 520 \mathrm{K} .What is the ratio of the fraction at 520 \mathrm{Kto} that at 500 \mathrm{K} ? UO Umut O. Texas Tech University Problem 55 The gas-phase reaction \mathrm{Cl}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{HCl}(g)+\mathrm{Br}(g) has an overall energy change of -66 \mathrm{kJ} . The activation energy for the reaction is 7 \mathrm{kJ} (a) Sketch the energy profile for the reaction, and label E_{a} and \Delta E . (b) What is the activation energy for the reverse reaction? Sahithi T. Numerade Educator Problem 56 For the elementary process \mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{NO}_{3}(g) the activation energy \left(E_{a}\right) and overall \Delta E are 154 \mathrm{kJ} / \mathrm{mol} and 136 \mathrm{kJ} / \mathrm{mol} , respectively. (a) Sketch the energy profile for this reaction, and label E_{a} and \Delta E . (b) What is the activation energy for the reverse reaction? UO Umut O. Texas Tech University Problem 57 Indicate whether each statement is true or false. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. (b) A reaction that has a small rate constant must have a small frequency factor. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants. Sahithi T. Numerade Educator Problem 58 Indicate whether each statement is true or false. \begin{array}{l}{\text { (a) If you measure the rate constant for a reaction at different}} \\ {\text { temperatures, you can calculate the overall }} \\ {\text { enthalpy change for the reaction. }} \\ {\text { (b) Exothermic reactions are faster than endothermic }} \\ {\text { reactions. }} \\ {\text { (c) If you double the temperature for a reaction, you cut }} \\ {\text { the activation energy in half. }}\end{array} UO Umut O. Texas Tech University Problem 59 Based on their activation energies and energy changes and assuming that all collision factors are the same, rank the following reactions from slowest to fastest. \begin{aligned} \text { (a) } E_{a} &=45 \mathrm{kJ} / \mathrm{mol} ; \Delta E=-25 \mathrm{kJ} / \mathrm{mol} \\ \text { (b) } E_{a} &=35 \mathrm{kJ} / \mathrm{mol} ; \Delta E=-10 \mathrm{kJ} / \mathrm{mol} \\ \text { (c) } E_{a} &=55 \mathrm{kJ} / \mathrm{mol} ; \Delta E=10 \mathrm{kJ} / \mathrm{mol} \end{aligned} Sahithi T. Numerade Educator Problem 60 Which of the reactions in Exercise 14.59 will be fastest in the reverse direction? Which will be slowest? UO Umut O. Texas Tech University Problem 61 (a) A certain first-order reaction has a rate constant of 2.75 \times 10^{-2} \mathrm{s}^{-1} at 20^{\circ} \mathrm{C} . What is the value of k at 60^{\circ} \mathrm{C} if E_{a}=75.5 \mathrm{kJ} / \mathrm{mol} ?(\mathbf{b}) Another first-order reaction also has a rate constant of 2.75 \times 10^{-2} \mathrm{s}^{-1} at 20^{\circ} \mathrm{C} . What is the value of k at 60^{\circ} \mathrm{C} if E_{a}=125 \mathrm{kJ} / \mathrm{mol} ?(\mathbf{c}) What assumptions do you need to make in order to calculate answers for parts (a) and (b)? Sahithi T. Numerade Educator Problem 62 Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (NO) to \mathrm{N}_{2} and \mathrm{O}_{2} is second order with a rate constant of 0.0796M^{-1} s^{-1} at 737^{\circ} \mathrm{C} and 0.0815M^{-1} \mathrm{s}^{-1} at 947^{\circ} \mathrm{C} . Calculate the activation energy for the reaction. UO Umut O. Texas Tech University Problem 63 The rate of the reaction \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)$$was measured at several temperatures, and the following data were collected:Calculate the value of E_{a} by constructing an appropriate graph. Sahithi T. Numerade Educator Problem 64 The temperature dependence of the rate constant for a reaction is tabulated as follows: Calculate E_{a} and A UO Umut O. Texas Tech University Problem 65 \begin{array}{l}{\text { (a) What is meant by the term elementary reaction? }} \\ {\text { (b) What is the difference between a unimolecular }} \\ {\text { and a bimolecular elementary reaction? (c) What is a }}\end{array} \begin{array}{l}{\text {reaction mechanism?}(\mathbf{d}) \text { What is meant by the term rate- }} \\ {\text { determining step? }}\end{array} Sahithi T. Numerade Educator Problem 66 (a) Can an intermediate appear as a reactant in the first step of a reaction mechanism? (b) On a reaction energy profile diagram, is an intermediate represented as a peak or a valley? (c) If a molecule like C l_{2} falls apart in an elementary reaction, what is the molecularity of the reaction? UO Umut O. Texas Tech University Problem 67 What is the molecularity of each of the following elementary reactions? Write the rate law for each. \begin{array}{l}{\text { (a) } \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)} \\ {\text { (b) } \mathrm{OCl}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HOCl}(a q)+\mathrm{OH}^{-}(a q)} \\ {\text { (c) } \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g)}\end{array} Sahithi T. Numerade Educator Problem 68 What is the molecularity of each of the following elementary reactions? Write the rate law for each. \begin{array}{l}{\text { (a) } 2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)} \\ {\mathrm{CH}_{2}} \\ {\text { (b) } \mathrm{H}_{2} \mathrm{C}-\mathrm{CH}_{2}(g) \longrightarrow \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{3}(g)} \\ {\text { (c) } \mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{O}(g)}\end{array} UO Umut O. Texas Tech University Problem 69 (a) Based on the following reaction profile, how many intermediates are formed in the reaction A \longrightarrow D? (b) How many transition states are there? (c) Which step is the fastest? (d) For the reaction A \longrightarrow \mathrm{D}, is \Delta E positive, negative, or zero? Check back soon! Problem 70 Consider the following energy profile.(a) How many elementary reactions are in the reaction mechanism? (b) How many intermediates are formed in the reaction? (c) Which step is rate limiting? (d) For the overall reaction, is \Delta E positive, negative, or zero? UO Umut O. Texas Tech University Problem 71 The following mechanism has been proposed for the gasphase reaction of \mathrm{H}_{2} with ICl:$$\begin{array}{c}{\mathrm{H}_{2}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{HI}(g)+\mathrm{HCl}(g)} \\ {\mathrm{HI}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{I}_{2}(g)+\mathrm{HCl}(g)}\end{array}$$\begin{array}{l}{\text { (a) Write the balanced equation for the overall reaction. }} \\ {\text { (b) Identify any intermediates in the mechanism. (c) If }}\end{array} the first step is slow and the second one is fast, which rate law do you expect to be observed for the overall reaction? Sahithi T. Numerade Educator Problem 72 The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism:$$ \begin{array}{c}{\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{I}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{IO}^{-}(a q) \text { (slow) }} \\ {\mathrm{IO}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(\mathrm{g})+\mathrm{I}^{-}(a q) \text { (fast) }}\end{array} $$\begin{array}{l}{\text { (a) Write the chemical equation for the overall process. }} \\ {\text { (b) Identify the intermediate, if any, in the mechanism. }} \\ {\text { (c) Assuming that the first step of the mechanism is rate }} \\ {\text { determining, predict the rate law for the overall process. }}\end{array} UO Umut O. Texas Tech University Problem 73 The reaction 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g) was performed and the following data were obtained under conditions of constant \left[\mathrm{Cl}_{2}\right] : (a) Is the following mechanism consistent with the data?$$ \begin{array}{c}{\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \Longrightarrow \mathrm{NOCl}_{2}(g) \quad(\text { fast })} \\ {\mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \longrightarrow 2 \mathrm{NOCl}(g) \quad(\text { slow })}\end{array}$$(b) Does the linear plot guarantee that the overall rate law is second order? Sahithi T. Numerade Educator Problem 74 You have studied the gas-phase oxidation of HBr by \mathrm{O}_{2} :$$4 \mathrm{HBr}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{Br}_{2}(g)$$You find the reaction to be first order with respect to HBr and first order with respect to \mathrm{O}_{2} . You propose the following mechanism:$$ \begin{array}{c}{\operatorname{HBr}(g)+\mathrm{O}_{2}(g) \longrightarrow \operatorname{HOOBr}(g)} \\ {\operatorname{HOOBr}(g)+\operatorname{HBr}(g) \longrightarrow 2 \mathrm{HOBr}(g)} \\ {\operatorname{HOBr}(g)+\operatorname{HBr}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Br}_{2}(g)}\end{array}$$(a) Confirm that the elementary reactions add to give the overall reaction. (b) Based on the experimentally determined rate law, which step is rate determining? (c) What are the intermediates in this mechanism? (d) If you are unable to detect HOBr or HOOBr among the products, does this disprove your mechanism? UO Umut O. Texas Tech University Problem 75 (a) What is a catalyst? (b) What is the difference between a homogeneous and a heterogeneous catalyst? (c) Do catalysts affect the overall enthalpy change for a reaction, the activation energy, or both? Sahithi T. Numerade Educator Problem 76 (a) Most commercial heterogeneous catalysts are extremely finely divided solid materials. Why is particle size important? (b) What role does adsorption play in the action of a heterogeneous catalyst? UO Umut O. Texas Tech University Problem 77 In Figure 14.21, we saw that \operatorname{Br}^{-}(a q) catalyzes the decomposition of \mathrm{H}_{2} \mathrm{O}_{2}(a q) into \mathrm{H}_{2} \mathrm{O}(l) and \mathrm{O}_{2}(g) . Suppose that some \mathrm{KBr}(s) is added to an aqueous solution of hydrogen peroxide. Make a sketch of \left[\mathrm{Br}^{-}(a q)\right] versus time from the addition of the solid to the end of the reaction. Sahithi T. Numerade Educator Problem 78 In solution, chemical species as simple as \mathrm{H}^{+} and \mathrm{OH}^{-} can serve as catalysts for reactions. Imagine you could measure the \left[\mathrm{H}^{+}\right] of a solution containing an acid catalyzed reaction as it occurs. Assume the reactants and products themselves are neither acids nor bases. Sketch the \left[\mathrm{H}^{+}\right] concentration profile you would measure as a function of time for the reaction, assuming t=0 is when you add a drop of acid to the reaction. UO Umut O. Texas Tech University Problem 79 The oxidation of \mathrm{SO}_{2} to \mathrm{SO}_{3} is accelerated by \mathrm{NO}_{2} . The reaction proceeds according to:$$ \begin{array}{l}{\mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g)} \\ {2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)}\end{array}$$(a) Show that, with appropriate coefficients, the two reactions can be summed to give the overall oxidation of S O_{2} by \mathrm{O}_{2} to give S O_{3} .(\mathbf{b}) Do we consider N O_{2} a catalyst or an intermediate in this reaction? (c) Would you classify NO as a catalyst or as an intermediate? { ( d ) } Is this an example of homogeneous catalysis or heterogeneous catalysis? Sahithi T. Numerade Educator Problem 80 The addition of NO accelerates the decomposition of \mathrm{N}_{2} \mathrm{O}, possibly by the following mechanism:$$\begin{array}{c}{\mathrm{NO}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{NO}_{2}(g)} \\ {2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)}\end{array}$$(a) What is the chemical equation for the overall reaction? Show how the two steps can be added to give the overall equation. (b) Is NO serving as a catalyst or an intermediate in this reaction? (c) If experiments show that during the decomposition of N_{2} \mathrm{O}, \mathrm{NO}_{2} does not accumulate in measurable quantities, does this rule out the proposed mechanism? UO Umut O. Texas Tech University Problem 81 Many metallic catalysts, particularly the precious-metal ones, are often deposited as very thin films on a substance of high surface area per unit mass, such as alumina \left(\mathrm{Al}_{2} \mathrm{O}_{3}\right) or silica \left(\mathrm{Si} \mathrm{O}_{2}\right) (a) Why is this an effective way of utilizing the catalyst material compared to having powdered metals? ( b) How does the surface area affect the rate of reaction? Sahithi T. Numerade Educator Problem 82 (a) If you were going to build a system to check the effectiveness of automobile catalytic converters on cars, what substances would you want to look for in the car exhaust? (b) Automobile catalytic converters have to work at high temperatures, as hot exhaust gases stream through them. In what ways could this be an advantage? In what ways a disadvantage? (c) Why is the rate of flow of exhaust gases over a catalytic converter important? UO Umut O. Texas Tech University Problem 83 When D_{2} reacts with ethylene \left(\mathrm{C}_{2} \mathrm{H}_{4}\right) in the presence of a finely divided catalyst, ethane with two deuteriums, \mathrm{CH}_{2} \mathrm{D} \mathrm{CH}_{2} \mathrm{D}, is formed. (Deuterium, \mathrm{D}, is an isotope of hydrogen of mass 2 . ) Very little ethane forms in which two deuteriums are bound to one carbon (for example, \mathrm{CH}_{3}-\mathrm{CHD}_{2} ). Use the sequence of steps involved in the reaction (Figure 14.23 ) to explain why this is so. Sahithi T. Numerade Educator Problem 84 Heterogeneous catalysts that perform hydrogenation reactions, as illustrated in Figure 14.23, are subject to "poisoning," which shuts down their catalytic ability. Compounds of sulfur are often poisons. Suggest a mechanism by which such compounds might act as poisons. UO Umut O. Texas Tech University Problem 85 The enzyme carbonic anhydrase catalyzes the reaction \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HCO}_{3}^{-}(a q)+\mathrm{H}^{+}(a q) . In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 \mathrm{s}^{-1} at 25^{\circ} \mathrm{C} . In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0 \times 10^{6} \mathrm{s}^{-1} at 25^{\circ} \mathrm{C} . Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction. Sahithi T. Numerade Educator Problem 86 The enzyme urease catalyzes the reaction of urea, \left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right), with water to produce carbon dioxide and ammonia. In water, without the enzyme, the reaction proceeds with a first-order rate constant of 4.15 \times 10^{-5} \mathrm{s}^{-1} at 100^{\circ} \mathrm{C} . In the presence of the enzyme in water, the reaction proceeds with a rate constant of 3.4 \times 10^{4} \mathrm{s}^{-1} at 21^{\circ} \mathrm{C} . (a) Write out the balanced equation for the reaction catalyzed by urease. (b) If the rate of the catalyzed reaction were the same at 100^{\circ} \mathrm{C} as it is at 21^{\circ} \mathrm{C}, what would be the difference in the activation energy between the catalyzed and uncatalyzed reactions? (c) In actuality, what would you expect for the rate of the catalyzed reaction at 100^{\circ} \mathrm{Cas} \mathrm{com}- pared to that at 21^{\circ} \mathrm{C} ?(\mathbf{d}) On the basis of parts (\mathrm{c}) and (\mathrm{d}), what can you conclude about the difference in activation energies for the catalyzed and uncatalyzed reactions? UO Umut O. Texas Tech University Problem 87 The activation energy of an uncatalyzed reaction is 95 \mathrm{kJ} / \mathrm{mol} . The addition of a catalyst lowers the activation energy to 55 \mathrm{kJ} / \mathrm{mol} . Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (a) 25^{\circ} \mathrm{C}, (b) 125^{\circ} \mathrm{C} ? Sahithi T. Numerade Educator Problem 88 Suppose that a certain biologically important reaction is quite slow at physiological temperature \left(37^{\circ} \mathrm{C}\right) in the absence of a catalyst. Assuming that the collision factor remains the same, by how much must an enzyme lower the activation energy of the reaction to achieve a 1 \times 10^{5} -fold increase in the reaction rate? UO Umut O. Texas Tech University Problem 89 Consider the reaction \mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D} . Is each of the following statements true or false? (a) The rate law for the reaction must be Rate =k[\mathrm{A}][\mathrm{B}] . (b) If the reaction is an elementary reaction, the rate law is second order. (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order. (d) The activation energy for the reverse reaction must be greater than that for the forward reaction. Sahithi T. Numerade Educator Problem 90 Hydrogen sulfide \left(\mathrm{H}_{2} \mathrm{S}\right) is a common and troublesome pollutant in industrial wastewaters. One way to remove \mathrm{H}_{2} \mathrm{S} is to treat the water with chlorine, in which case the following reaction occurs:$$ \mathrm{H}_{2} \mathrm{S}(a q)+\mathrm{Cl}_{2}(a q) \longrightarrow \mathrm{S}(s)+2 \mathrm{H}^{+}(a q)+2 \mathrm{Cl}^{-}(a q)$$The rate of this reaction is first order in each reactant. The rate constant for the disappearance of \mathrm{H}_{2} \mathrm{S} at 28^{\circ} \mathrm{C} is 3.5 \times 10^{-2} \mathrm{M}^{-1} \mathrm{s}^{-1} . If at a given time the concentration of \mathrm{H}_{2} \mathrm{S} is 2.0 \times 10^{-4} \mathrm{M} and that of \mathrm{Cl}_{2} is 0.025 \mathrm{M}, what is the rate of formation of \mathrm{Cl}^{-} ? UO Umut O. Texas Tech University Problem 91 The reaction 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) is second order in \mathrm{NO} and first order in \mathrm{O}_{2} . When [\mathrm{NO}]=0.040 \mathrm{M} and \left[\mathrm{O}_{2}\right]=0.035 \mathrm{M}, the observed rate of disappearance of \mathrm{NO} is 9.3 \times 10^{-5} \mathrm{M} / \mathrm{s} . (a) What is the rate of disappearance of \mathrm{O}_{2} at this moment? (b) What is the value of the rate constant? (c) What are the units of the rate constant? (d) What would happen to the rate if the concentration of NO were increased by a factor of 1.8? Sahithi T. Numerade Educator Problem 92 You perform a series of experiments for the reaction \mathrm{A} \longrightarrow \mathrm{B}+\mathrm{C} and find that the rate law has the form rate =k[\mathrm{A}]^{x} . Determine the value of x in each of the following cases: (a) There is no rate change when [\mathrm{A}]_{0} is tripled. (b) The rate increases by a factor of 9 when [\mathrm{A}]_{0} is tripled. (c) When [\mathrm{A}]_{0} is doubled, the rate increases by a factor of 8 . UO Umut O. Texas Tech University Problem 93 Consider the following reaction between mercury(lI) chloride and oxalate ion:$$ 2 \mathrm{HgCl}_{2}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \longrightarrow 2 \mathrm{Cl}^{-}(a q)+2 \mathrm{CO}_{2}(g)+\mathrm{Hg}_{2} \mathrm{Cl}_{2}(s)$$The initial rate of this reaction was determined for several concentrations of \mathrm{HgCl}_{2} and \mathrm{C}_{2} \mathrm{O}_{4}^{2-} , and the following rate data were obtained for the rate of disappearance of \mathrm{C}_{2} \mathrm{O}_{4}^{2-} : (a) What is the rate law for this reaction? (b) What is the value of the rate constant with proper units? (c) What is the reaction rate when the initial concentration of HgCl_ is 0.100M and that of \mathrm{C}_{2} \mathrm{O}_{4}^{2-} is 0.25 \mathrm{M} if the temperature is the same as that used to obtain the data shown? Sahithi T. Numerade Educator Problem 94 The following kinetic data are collected for the initial rates of a reaction 2 \mathrm{X}+\mathrm{Z} \longrightarrow products: (a) What is the rate law for this reaction? (b) What is the value of the rate constant with proper units? (c) What is the reaction rate when the initial concentration of X is 0.75M and that of Z is 1.25M ? UO Umut O. Texas Tech University Problem 95 The reaction 2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2} has the rate constant k=0.63 M^{-1} \mathrm{s}^{-1} . (a) Based on the units for k, is the reaction first or second order in \mathrm{NO}_{2} ? ? (b) If the initial concentration of \mathrm{NO}_{2} is 0.100 \mathrm{M}, how would you determine how long it would take for the concentration to decrease to 0.025 \mathrm{M} ? Sahithi T. Numerade Educator Problem 96 Consider two reactions. Reaction (1) has a constant half-life, whereas reaction (2) has a half life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations? UO Umut O. Texas Tech University Problem 97 A first-order reaction \mathrm{A} \longrightarrow \mathrm{B} has the rate constant k=3.2 \times 10^{-3} \mathrm{s}^{-1} . If the initial concentration of \mathrm{A} is 2.5 \times 10^{-2} \mathrm{M}, what is the rate of the reaction at t=660 \mathrm{s} ? Sahithi T. Numerade Educator Problem 98 (a) The reaction \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\frac{1}{2} \mathrm{O}_{2}(g) is first order. At 300 \mathrm{K} the rate constant equals 7.0 \times 10^{-4} \mathrm{s}^{-1} . Calculate the half-life at this temperature. (b) If the activation energy for this reaction is 75 \mathrm{kJ} / \mathrm{mol}, at what temperature would the reaction rate be doubled? UO Umut O. Texas Tech University Problem 99 Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k=1.6 \times 10^{-3} \mathrm{yr}^{-1} . By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k=0.011 day ^{-1} (a) What are the half-lives of these two isotopes? (b) Which one decays at a faster rate? (c) How much of a 1.00 -mg sample of each isotope remains after three half-lives? (d) How much of a 1.00 -mg sample of each isotope remains after 4 days? Sahithi T. Numerade Educator Problem 100 Urea \left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right) is the end product in protein metabolism in animals. The decomposition of urea in 0.1 \mathrm{M} \mathrm{HCl} occurs according to the reaction$$\mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}^{+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NH}_{4}^{+}(a q)+\mathrm{HCO}_{3}^{-}(a q)$$The reaction is first order in urea and first order overall. When \left[\mathrm{NH}_{2} \mathrm{CONH}_{2}\right]=0.200 M, the rate at 61.05^{\circ} \mathrm{C} is 8.56 \times 10^{-5} \mathrm{M} / \mathrm{s} , (a) What is the rate constant, k ? units of s^{-1} . (c) Calculate the half-life of the reaction. (d) How long does it take for the absorbance to fall to 0.100? UO Umut O. Texas Tech University Problem 101 The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 \mathrm{nm} .The reaction occurs in a 1.00-\mathrm{cm} sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 \times 10^{3} M^{-1} \mathrm{cm}^{-1} at 520 \mathrm{nm} . (a) Calculate the initial concentration of the colored reactant if the absorbance is falls to 0.250 at 30.0 min. Calculate the rate constant in units of s^{-1} (c) Calculate the half-life of the reaction. (d) How long does it take for the absorbance to fall to 0.100? Check back soon! Problem 102 A colored dye compound decomposes to give a colorless product. The original dye absorbs at 608 nm and has an extinction coefficient of 4.7 \times 10^{4} M^{-1} \mathrm{cm}^{-1} at that wave- length. You perform the decomposition reaction in a 1-\mathrm{cm} cuvette in a spectrometer and obtain the following data: From these data, determine the rate law for the reaction "dye \longrightarrow product" and determine the rate constant. UO Umut O. Texas Tech University Problem 103 Cyclopentadiene \left(\mathrm{C}_{5} \mathrm{H}_{6}\right) reacts with itself to form dicyclopentadiene \left(\mathrm{C}_{10} \mathrm{H}_{12}\right) . \mathrm{A} 0.0400 M solution of \mathrm{C}_{5} \mathrm{H}_{6} was monitored as a function of time as the reaction 2 \mathrm{C}_{5} \mathrm{H}_{6} \longrightarrow \mathrm{C}_{10} \mathrm{H}_{12} proceeded. The following data were collected: Plot \left[\mathrm{C}_{5} \mathrm{H}_{6}\right] versus time, \ln \left[\mathrm{C}_{5} \mathrm{H}_{6}\right] versus time, and 1/\left[\mathrm{C}_{5} \mathrm{H}_{6}\right] versus time. (a) What is the order of the reaction? (b) What is the value of the rate constant? Sahithi T. Numerade Educator Problem 104 The first-order rate constant for reaction of a particular organic compound with water varies with temperature as follows: From these data, calculate the activation energy in unit of kJ/mol. UO Umut O. Texas Tech University Problem 105 At 28^{\circ} \mathrm{C}, raw milk sours in 4.0 \mathrm{h} but takes 48 \mathrm{h} to sour in a refrigerator at 5^{\circ} \mathrm{C} . Estimate the activation energy in \mathrm{kJ} / \mathrm{mol} for the reaction that leads to the souring of milk. Sahithi T. Numerade Educator Problem 106 The following is a quote from an article in the August 18 , 1998, issue of The New York Times about the breakdown of cellulose and starch: "A drop of 18 degrees Fahrenheit [from 77^{\circ} \mathrm{F} to 59^{\circ} \mathrm{F} ] lowers the reaction rate six times; a 36 -degree drop [from 77^{\circ} \mathrm{F} to 41^{\circ} \mathrm{F} ] produces a fortyfold decrease in the rate." (a) Calculate activation energies for the breakdown process based on the two estimates of the effect of temperature on rate. Are the values consistent? (b) Assuming the value of E_{a} calculated from the 36^{\circ} drop and that the rate of breakdown is first order with a half-life at 25^{\circ} \mathrm{C} of 2.7 yr, calculate the half-life for breakdown at a temperature of -15^{\circ} \mathrm{C} . UO Umut O. Texas Tech University Problem 107 The following mechanism has been proposed for the reaction of NO with \mathrm{H}_{2} to form \mathrm{N}_{2} \mathrm{O} and \mathrm{H}_{2} \mathrm{O} :$$\mathrm{NO}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)
$\mathrm{N}_{2} \mathrm{O}_{2}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$(a) Show that the elementary reactions of the proposed mechanism add to provide a balanced equation for the reaction. (b) Write a rate law for each elementary reaction in the mechanism. (c) Identify any intermediates in the mechanism. (d) The observed rate law is rate =k[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right] . If the proposed mechanism is correct, what can we conclude about the relative speeds of the first and second reactions? Sahithi T. Numerade Educator Problem 108 Ozone in the upper atmosphere can be destroyed by the following two-step mechanism:$$ \begin{array}{c}{\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)} \\ {\mathrm{ClO}(g)+\mathrm{O}(g) \longrightarrow \mathrm{Cl}(g)+\mathrm{O}_{2}(g)}\end{array}$$(a) What is the overall equation for this process? (b) What is the catalyst in the reaction? (c) What is the intermediate in the reaction? UO Umut O. Texas Tech University Problem 109 The gas-phase decomposition of ozone is thought to occur by the following two-step mechanism. \begin{array}{ll}{\text { Step } 1 :} & {\mathrm{O}_{3}(g) \Longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g) \text { (fast) }} \\ {\text { Step } 2 :} & {\mathrm{O}(g)+\mathrm{O}_{3}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(g) \quad(\text { slow })}\end{array} (a) Write the balanced equation for the overall reaction. (b) Derive the rate law that is consistent with this mechanism. (Hint: The product appears in the rate law.) (c) Is O a catalyst or an intermediate? (d) If instead the reaction occurred in a single step, would the rate law change? If so, what would it be? Sahithi T. Numerade Educator Problem 110 The following mechanism has been proposed for the gasphase reaction of chloroform (CHCl_ ) and chlorine:$$\begin{array}{l}{\text { Step } 1 : \mathrm{Cl}_{2}(g) \frac{k_{1}}{k_{-1}} 2 \mathrm{Cl}(g) \text { (fast) }} \\ {\text { Step } 2 : \mathrm{Cl}(g)+\mathrm{CHCl}_{3}(g) \stackrel{k_{2}}{\longrightarrow} \mathrm{HCl}(g)+\mathrm{CCl}_{3}(g) \text { (slow) }}\end{array} { Step } \quad3 : \quad \mathrm{Cl}(g)+\mathrm{CCl}_{3}(g) \stackrel{k_{3}}{\longrightarrow} \mathrm{CCl}_{4} \quad(\text { fast })$$(a) What is the overall reaction? (b) What are the intermedi- ates in the mechanism? (c) What is the molecularity of each of the elementary reactions? (d) What is the rate-determining step? (e) What is the rate law predicted by this mechanism? (Hint: The overall reaction order is not an integer.) UO Umut O. Texas Tech University Problem 111 Consider the hypothetical reaction 2 \mathrm{A}+\mathrm{B} \longrightarrow 2 \mathrm{C}+\mathrm{D} . The following two-step mechanism is proposed for the reaction:$$ \begin{array}{l}{\text { Step } 1 : \mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{X}} \\ {\text { Step } 2 : \mathrm{A}+\mathrm{X} \longrightarrow \mathrm{C}+\mathrm{D}}\end{array}$$X is an unstable intermediate. (a) What is the predicted rate law expression if Step 1 is rate determining? (b) What is the predicted rate law expression if Step 2 is rate determining? (c) Your result for part (b) might be considered surprising for which of the following reasons: (i) The concentration of a product is in the rate law. (ii) There is a negative reaction order in the rate law. (ii) Both reasons (i) and (ii). (iv) Neither reasons (i) nor (ii). Sahithi T. Numerade Educator Problem 112 In a hydrocarbon solution, the gold compound \left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3} decomposes into ethane \left(\mathrm{C}_{2} \mathrm{H}_{6}\right) and a different gold compound, (CH _{3} ) \mathrm{AuPH}_{3} . The following mechanism has been proposed for the decomposition of \left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3} :$$ \quad Step \quad1.\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3} \frac{\mathrm{k}_{1}}{\mathrm{k}_{-1}}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Au}+\mathrm{PH}_{3}  Step\quad \quad2.\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Au} \stackrel{k_{2}}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{6}+\left(\mathrm{CH}_{3}\right) \mathrm{Au} \quad Step\quad 3 :\left(\mathrm{CH}_{3}\right) \mathrm{Au}+\mathrm{PH}_{3} \stackrel{k_{3}}{\longrightarrow}\left(\mathrm{CH}_{3}\right) \mathrm{AuPH}_{3}$$(a) What is the overall reaction? (b) What are the intermediates in the mechanism? (c) What is the molecularity of each of the elementary steps? (d) What is the ratedetermining step? (e) What is the rate law predicted by this mechanism? (f) What would be the effect on the reaction rate of adding \mathrm{PH}_{3} to the solution of \left(\mathrm{CH}_{3}\right)_{3} AuPH _{3} ? UO Umut O. Texas Tech University Problem 113 Platinum nanoparticles of diameter \sim 2 \mathrm{nm} are important catalysts in carbon monoxide oxidation to carbondioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 A. (a) Estimate how many platinum atoms would fit into a 2.0 -nm sphere; the volume of a sphere is (4 / 3) \pi r^{3} . Recall that 1 \hat{\mathrm{A}}=1 \times 10^{-10} \mathrm{m} and 1 \mathrm{nm}=1 \times 10^{-9} \mathrm{m} . (b) Estimate how many platinum atoms are on the surface of a 2.0-\mathrm{nm} Pt sphere, using the surface area of a sphere \left(4 \pi r^{2}\right) and assuming that the "footprint" of one Pt atom can be estimated from its atomic diameter of 2.8 A. (c) Using your results from (a) and (b), calculate the percentage of Pt atoms that are on the surface of a 2.0 -nm nanoparticle. (d) Repeat these calculations for a 5.0 -nm platinum nanoparticle. (e) Which size of nanoparticle would you expect to be more catalytically active and why? Sahithi T. Numerade Educator Problem 114 One of the many remarkable enzymes in the human body is carbonic anhydrase, which catalyzes the interconversion of carbon dioxide and water with bicarbonate ion and protons. If it were not for this enzyme, the body could not rid itself rapidly enough of the \mathrm{CO}_{2} accumulated by cell metabolism. The enzyme catalyzes the dehydration (release to air) of up to 10^{7} \mathrm{CO}_{2} molecules per second. Which components of this description correspond to the terms enzyme, substrate, and turnover number? UO Umut O. Texas Tech University Problem 115 Suppose that, in the absence of a catalyst, a certain biochemical reaction occurs x times per second at normal body temperature \left(37^{\circ} \mathrm{C}\right) . In order to be physiologically useful, the reaction needs to occur 5000 times faster than when it is uncatalyzed. By how many kJ/mol must an enzyme lower the activation energy of the reaction to make it useful? Sahithi T. Numerade Educator Problem 116 Enzymes are often described as following the two-step mechanism:$$ \begin{array}{c}{\mathrm{E}+\mathrm{S} \rightleftharpoons \mathrm{ES} \text { (fast) }} \\ {\mathrm{ES} \longrightarrow \mathrm{E}+\mathrm{P} \quad(\text { slow })}\end{array}$$where \mathrm{E}= enzyme, \mathrm{S}= substrate,\mathrm{ES}= enzyme-substrate complex, and \mathrm{P}= product.(a) If an enzyme follows this mechanism, what rate law is expected for the reaction? (b) Molecules that can bind to the active site of an enzyme but are not converted into product are called enzyme inhibitors. Write an additional elementary step to add into the preceding mechanism to account for the reaction of E with I, an inhibitor. UO Umut O. Texas Tech University Problem 117 Dinitrogen pentoxide \left(\mathrm{N}_{2} \mathrm{O}_{5}\right) decomposes in chloroform as a solvent to yield \mathrm{NO}_{2} and \mathrm{O}_{2} . The decomposition is first order with a rate constant at 45^{\circ} \mathrm{C} of 1.0 \times 10^{-5} \mathrm{s}^{-1} . Calculate the partial pressure of \mathrm{O}_{2} produced from 1.00 \mathrm{L} of 0.600 \mathrm{MN}_{2} \mathrm{O}_{5} solution at 45^{\circ} \mathrm{C} over a period of 20.0 \mathrm{h} if the gas is collected in a 10.0-\mathrm{L} container. (Assume that the products do not dissolve in chloroform.) Sahithi T. Numerade Educator Problem 118 The reaction between ethyl iodide and hydroxide ion in ethanol \left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right) solution, \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I}(a l c)+\mathrm{OH}^{-}(a l c) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{I}^{-}(a l c), has an activation energy of 86.8 \mathrm{kJ} / \mathrm{mol} and a frequency factor of 2.10 \times 10^{11} \mathrm{M}^{-1} \mathrm{s}^{-1} (a) Predict the rate constant for the reaction at 35^{\circ} \mathrm{C} . (b) A g \mathrm{KOH} in ethanol to form 250.0 \mathrm{mL} of solution. Similarly, 1.453 \mathrm{g} of \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I} is dissolved in ethanol to form 250.0 \mathrm{mL} of solution. Equal volumes of the two solutions are mixed. Assuming the reaction is first order in each reac-solution of \mathrm{KOH} in ethanol is made up by dissolving 0.335 g KOH in ethanol to form 250.0 \mathrm{mL} of solution. Similarly, 1.453 \mathrm{g} of \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I} is dissolved in ethanol to form 250.0 \mathrm{mL} of solution. Equal volumes of the two solutions are mixed. Assuming the reaction is first order in each reactant, what is the initial rate at 35^{\circ} \mathrm{C} ?(\mathbf{c}) Which reagent in the reaction is limiting, assuming the reaction proceeds to completion? Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50^{\circ} \mathrm{C} . UO Umut O. Texas Tech University Problem 119 You obtain kinetic data for a reaction at a set of different temperatures. You plot ln k versus 1/ T and obtain the following graph: Suggest a molecular-level interpretation of these unusual data. Sahithi T. Numerade Educator Problem 120 The gas-phase reaction of NO with \mathrm{F}_{2} to form \mathrm{NOF} and \mathrm{F} has an activation energy of E_{a}=6.3 \mathrm{kJ} / \mathrm{mol} . and a frequency factor of A=6.0 \times 10^{8} M^{-1} \mathrm{s}^{-1} . The reaction is believed to be bimolecular:$$ \mathrm{NO}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{NOF}(g)+\mathrm{F}(g)$$(a) Calculate the rate constant at 100^{\circ} \mathrm{C} . (b) Draw the Lewis structures for the NO and the NOF molecules, given that the chemical formula for NOF is misleading because the nitrogen atom is actually the central atom in the molecule, (c) Predict the shape for the NOF molecule.Draw a possible transition state for the formation of NOF, using dashed lines to indicate the weak bonds that are beginning to form. (e) Suggest a reason for the low activation energy for the reaction. UO Umut O. Texas Tech University Problem 121 The mechanism for the oxidation of HBr by \mathrm{O}_{2} to form 2 \mathrm{H}_{2} \mathrm{O} and \mathrm{Br}_{2} is shown in Exercise 14.74 . (a) Calculate the overall standard enthalpy change for the reaction process. (b) HBr does not react with \mathrm{O}_{2} at a measurable rate at room temperature under ordinary conditions. What can you infer from this about the magnitude of the activation energy for the rate-determining step? (c) Draw a plausible Lewis structure for the intermediate HOOBr. To what familiar compound of hydrogen and oxygen does it appear similar? Sahithi T. Numerade Educator Problem 122 The rates of many atmospheric reactions are accelerated by the absorption of light by one of the reactants. For example, consider the reaction between methane and chlorine to produce methyl chloride and hydrogen chloride:$$Reaction 1 : \mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{Cl}(g)+\mathrm{HCl}(g)$$This reaction is very slowin the absence of light. However, \mathrm{Cl}_{2}(g) can absorb light to form Clatoms:$$ 2 : \mathrm{Cl}_{2}(g)+h v \longrightarrow 2 \mathrm{Cl}(g)$$Once the Cl atoms are generated, they can catalyze the reaction of$\mathrm{CH}_{4}$and$\mathrm{Cl}_{2},$according to the following proposed mechanism:$\begin{array}{l}{\text { Reaction } 3 : \mathrm{CH}_{4}(g)+\mathrm{Cl}(g) \longrightarrow \mathrm{CH}_{3}(g)+\mathrm{HCl}(g)} \\ {\text { Reaction } 4 : \mathrm{CH}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{Cl}(g)+\mathrm{Cl}(g)}\end{array}$The enthalpy changes and activation energies for these two reactions are tabulated as follows: (a) By using the bond enthalpy for$\mathrm{Cl}_{2}$(Table$8.4 ),$determine the longest wavelength of light that is energetic enough to cause reaction 2 to occur. In which portion of the electromagnetic spectrum is this light found? (b) By using the data tabulated here, sketch a quantitative energy profile for the catalyzed reaction represented by reactions 3 and 4 . (c) By using bond enthalpies, estimate where the reactants,$\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g)$should be placed on your diagram in part (b). Use this result to estimate the value of$E_{a}$for the reaction$\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CH}_{3}(g)+\mathrm{HCl}(g)+\mathrm{Cl}(g) .(\mathbf{d})$The species$\mathrm{Cl}(g)$and$\mathrm{CH}_{3}(\mathrm{g})$in reactions 3 and 4 are radicals,that is, atoms or molecules with unpaired electrons. Draw a Lewis structure of$\mathrm{CH}_{3},$and verify that it is a radical. (e) The sequence of reactions 3 and 4 comprises a radical chain mechanism. Why do you think this is called a "chain reaction"? Propose a reaction that will terminate the chain reaction. UO Umut O. Texas Tech University Problem 123 Many primary amines, RNH$_{2},$where$R$is a carbon-containing fragment such as$C H_{3}, C H_{3} C H_{2},$and so on, undergo reactions where the transition state is tetrahedral. (a) Draw a hybrid orbital picture to visualize the bonding at the nitrogen in a primary amine (just use a$C$atom for$^{4} \mathrm{R}^{\prime \prime}$. (b) What kind of reactant with a primary amine can produce a tetrahedral intermediate? Sahithi T. Numerade Educator Problem 124 The$\mathrm{NO}_{x}$waste stream from automobile exhaust includes species such as$\mathrm{NO}$and$\mathrm{NO}_{2}$. Catalysts that convert these species to$\mathrm{N}_{2}$are desirable to reduce air pollution. (a) Draw the Lewis dot and VSEPR structures of NO, NO$_{2}$and$\mathrm{N}_{2} .(\mathbf{b})$Using a resource such as Table$8.3,$look up the energies of the bonds in these molecules. In what region of the electromagnetic spectrum are these energies? (c) Design a spectroscopic experiment to monitor the conversion of$\mathrm{NO}_{x}$into$\mathrm{N}_{2},$describing what wavelengths of light need to be monitored as a function of time. UO Umut O. Texas Tech University Problem 125 As shown in Figure$14.23,$the first step in the heterogeneous hydrogenation of ethylene is adsorption of the ethylene molecule on a metal surface. One proposed explanation for the "sticking" of ethylene to a metal surface is the interaction of the electrons in the$\mathrm{C}-\mathrm{C} \pi\$ bond with vacant orbitals on the metal surface. (a) If this notion is correct, would ethane be expected to adsorb to a metal surface, and, if so, how strongly would ethane bind 