• Home
  • Textbooks
  • Chemistry The Central Science
  • Chemical Kinetics

Chemistry The Central Science

Theodore E. Brown, Theodore L. Brown, H. Eugene LeMaytion Compounds

Chapter 14

Chemical Kinetics - all with Video Answers

Educators

Chapter Questions

06:21

Problem 1

For which one of the following vessels for the reaction $\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}$ is the reaction the fastest? Assume all vessels are at the same temperature. [Section 4.1$]$

Sanu Kumar
Sanu Kumar
Numerade Educator
07:23

Problem 2

Consider the following graph of the concentration of a substance over time. (a) Is X a reactant or product of the reaction?
(b) Is the reaction speeding up, slowing down, or not changing its rate as time progresses? (c) Why is the average rate of the reaction different between points 1 and 2 than between points 2 and 3 ? [Section 14.2]

Sanu Kumar
Sanu Kumar
Numerade Educator
03:27

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:

Which chemical equation is consistent with these data: (a) $\mathrm{A} \longrightarrow \mathrm{B},(\mathbf{b}) \mathrm{B} \longrightarrow \mathrm{A},(\mathrm{c}) \mathrm{A} \longrightarrow 2 \mathrm{~B}$
(d) $\mathrm{B} \longrightarrow 2 \mathrm{~A} ?$
Explain your choice. [Section 14.2$]$

Sanu Kumar
Sanu Kumar
Numerade Educator
05:43

Problem 4

You perform the reaction $\mathrm{K}+\mathrm{L} \rightarrow \mathrm{M}$, monitor the production of $M$ over time, and then plot this graph from your data:

(a) Is the reaction occurring at a constant rate from $t=0$ to $t=15 \mathrm{~min}$ ? Explain. (b) Is the reaction completed at $t=15$ min? Explain.

Sanu Kumar
Sanu Kumar
Numerade Educator
03:01

Problem 5

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 . [Section 14.3$]$

Sanu Kumar
Sanu Kumar
Numerade Educator
01:21

Problem 6

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 Talasila
Sahithi Talasila
Numerade Educator
03:30

Problem 7

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 Ozuguzel
Texas Tech University
06:04

Problem 8

(a) Given the following diagrams at $t=0 \mathrm{~min}$ and $t=30 \mathrm{~min}$, what is the half-life of the reaction if it follows first-order kinetics?

(b) After four half-life periods for a first-order reaction, what fraction of reactant remains? [Section 14.4$]$

Sanu Kumar
Sanu Kumar
Numerade Educator
01:19

Problem 9

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

Sahithi Talasila
Sahithi Talasila
Numerade Educator
04:15

Problem 10

You study the effect of temperature on the rate of two reactions and graph the natural logarithm of the rate constant for each reaction as a function of $1 / T$. How do the two graphs compare (a) if the activation energy of the second reaction is higher than the activation energy of the first reaction but the two reactions have the same frequency factor, and $(b)$ if the frequency factor of the second reaction is higher than the frequency factor of the first reaction but the two reactions have the same activation energy? [Section 14.5$]$

Sanu Kumar
Sanu Kumar
Numerade Educator
03:40

Problem 11

The following graph shows two different reaction pathways for the same overall reaction at the same temperature. (a) Which pathway is slower? Why? (b) How can there be two different reaction pathways for the same reaction at the same temperature? Discuss. [Section 14.6$]$

Sanu Kumar
Sanu Kumar
Numerade Educator
02:48

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 Ozuguzel
Texas Tech University
03:57

Problem 13

Based on the following reaction profile, how many intermediates are formed in the reaction $\mathrm{A} \longrightarrow \mathrm{C} ?$ How many transition states are there? Which step is the fastest? Is the reaction $\mathrm{A} \longrightarrow \mathrm{C}$ exothermic or endothermic? [Section 14.6$]$

Sanu Kumar
Sanu Kumar
Numerade Educator
01:33

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 Ozuguzel
Texas Tech University
01:58

Problem 15

The following diagram represents an imaginary two-step mechanism. Let the red spheres represent element $A,$ the green ones element $\mathrm{B}$, and the blue ones element 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 Talasila
Sahithi Talasila
Numerade Educator
01:48

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 Ozuguzel
Texas Tech University
01:42

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? Explain.

Sahithi Talasila
Sahithi Talasila
Numerade Educator
04:39

Problem 18

(a) What are the units usually used to express the rates of reactions occurring in solution? (b) From your everyday experience, give two examples of the effects of temperature on the rates of reactions. (c) What is the difference between average rate and instantaneous rate?

Sanu Kumar
Sanu Kumar
Numerade Educator
08:47

Problem 19

Consider the following hypothetical aqueous reaction:
$\mathrm{A}(a q) \longrightarrow \mathrm{B}(a q)$. 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:
$$
\begin{array}{lccccc}
\hline \text { Time (min) } & 0 & 10 & 20 & 30 & 40 \\
\hline \text { Moles of A } & 0.065 & 0.051 & 0.042 & 0.036 & 0.031 \\
\hline
\end{array}
$$
(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 $B$ with no intermediates.
(b) Calculate the average rate of disappearance of $\mathrm{A}$ for each 10 -min interval in units of $M / \mathrm{s}$. (c) Between $t=10 \mathrm{~min}$ and $t=30 \mathrm{~min},$ what is the average rate of appearance of $\mathrm{B}$ in units of $M / s$ ? Assume that the volume of the solution is constant.

Sanu Kumar
Sanu Kumar
Numerade Educator
05:39

Problem 20

A flask is charged with $0.100 \mathrm{~mol}$ of $\mathrm{A}$ and allowed to react to form $\mathrm{B}$ according to the hypothetical gas-phase reaction $\mathrm{A}(g) \longrightarrow \mathrm{B}(g)$. The following data are collected:
$$
\begin{array}{lccccc}
\hline \text { Time (s) } & 0 & 40 & 80 & 120 & 160 \\
\hline \text { Moles of A } & 0.100 & 0.067 & 0.045 & 0.030 & 0.020 \\
\hline
\end{array}
$$
(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 $\mathrm{mol} / \mathrm{s}$. (c) What additional information would be needed to calculate the rate in units of concentration per time?

Shubham Kumar
Shubham Kumar
Numerade Educator
07:38

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:
$$
\begin{array}{rl}
\hline \text { Time (s) } & {\left[\mathrm{CH}_{3} \mathrm{NC}\right](\boldsymbol{M})} \\
\hline 0 & 0.0165 \\
2,000 & 0.0110 \\
5,000 & 0.00591 \\
8,000 & 0.00314 \\
12,000 & 0.00137 \\
15,000 & 0.00074 \\
\hline
\end{array}
$$
(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 $t=15,000 \mathrm{~s}$. (c) Graph [CH $\left._{3} \mathrm{NC}\right]$ versus time and determine the instantaneous rates in $M /$ s at $t=5000 \mathrm{~s}$ and $t=8000 \mathrm{~s}$.

Shubham Kumar
Shubham Kumar
Numerade Educator
07:55

Problem 22

The rate of disappearance of HCl was measured for the following reaction:
$$
\mathrm{CH}_{3} \mathrm{OH}(a q)+\mathrm{HCl}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{Cl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)
$$
The following data were collected:
$$
\begin{array}{rl}
\hline \text { Time (min) } & \text { [HCI] (M) } \\
\hline 0.0 & 1.85 \\
54.0 & 1.58 \\
107.0 & 1.36 \\
215.0 & 1.02 \\
430.0 & 0.580 \\
\hline
\end{array}
$$
(a) Calculate the average rate of reaction, in $M / \mathrm{s}$, for the time interval between each measurement. (b) Calculate the average rate of reaction for the entire time for the data from $t=0.0 \mathrm{~min}$ to $t=430.0 \mathrm{~min} .$
(c) Graph [HCl] versus time and determine the instantaneous rates in $M / \min$ and $M / s$ at $t=75.0 \mathrm{~min}$ and $t=250$ min.

Shubham Kumar
Shubham Kumar
Numerade Educator
01:52

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:
(a) $\mathrm{H}_{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)$
(b) $2 \mathrm{~N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)$
(c) $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$
(d) $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{NH}_{3}(g)$

Sahithi Talasila
Sahithi Talasila
Numerade Educator
04:27

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:
(a) $2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)$
(b) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)$
(c) $2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
(d) $\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)$

UO
Umut Ozuguzel
Texas Tech University
07:56

Problem 25

(a) Consider the combustion of $\mathrm{H}_{2}(g): 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)$
$\longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) .$ 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 $/ \mathrm{min}$, what is the rate of change of the total pressure of the vessel?

Sanu Kumar
Sanu Kumar
Numerade Educator
06:36

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 $\mathrm{H}_{2} \mathrm{O} ?$ (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 Ozuguzel
Texas Tech University
03:59

Problem 27

A reaction $A+B \longrightarrow C$ obeys the following rate law:
Rate $=k[\mathrm{~B}]^{2}$. (a) If $[\mathrm{A}]$ is doubled, how will the rate change? Will the rate constant change? Explain.
(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?

Sanu Kumar
Sanu Kumar
Numerade Educator
05:07

Problem 28

Consider a hypothetical reaction between $A, B,$ and $C$ that is first order in $A,$ zero order in $B,$ and second order in C. (a) Write the rate law for the reaction. (b) How does the rate change when $[\mathrm{A}]$ is doubled and the other reactant concentrations are held constant? (c) How does the rate change when $[\mathrm{B}]$ 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 Ozuguzel
Texas Tech University
01:19

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 $\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]=0.0240 \mathrm{M} ?$ (c) What happens to the rate when the concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$ is doubled to $0.0480 \mathrm{M} ?$ (d) What happens to the rate when the concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$ is halved to $0.0120 \mathrm{M} ?$

Sahithi Talasila
Sahithi Talasila
Numerade Educator
03:33

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 NO. Write the rate law. (b) If the rate constant for this reaction at $1000 \mathrm{~K}$ is $6.0 \times 10^{4} \mathrm{M}^{-2} \mathrm{~s}^{-1}$, what is the reaction rate when $[\mathrm{NO}]=0.035 \mathrm{M}$ and $\left[\mathrm{H}_{2}\right]=0.015 \mathrm{M} ?(\mathrm{c}) \mathrm{What}$ 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 $0.010 \mathrm{M}$ ?

Shubham Kumar
Shubham Kumar
Numerade Educator
01:43

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? (b) What are the units of the rate constant? (c) What would happen to the rate if the concentration of $\mathrm{OH}^{-}$ were tripled? (d) What would happen to the rate if the concentration of both reactants were tripled?

Sahithi Talasila
Sahithi Talasila
Numerade Educator
04:09

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 Ozuguzel
Texas Tech University
04:21

Problem 33

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way:
$\mathrm{OCl}^{-}+\mathrm{I}^{-} \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-}$. This rapid reaction gives the
following rate data:
$$
\begin{array}{lll}
\hline\left[\mathrm{OCl}^{-}\right](M) & {\left[I^{-}\right](M)} & \text { Initial Rate }(M / s) \\
\hline 1.5 \times 10^{-3} & 1.5 \times 10^{-3} & 1.36 \times 10^{-4} \\
3.0 \times 10^{-3} & 1.5 \times 10^{-3} & 2.72 \times 10^{-4} \\
1.5 \times 10^{-3} & 3.0 \times 10^{-3} & 2.72 \times 10^{-4} \\
\hline
\end{array}
$$
(a) Write the rate law for this reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when $\left[\mathrm{OCl}^{-}\right]=2.0 \times 10^{-3} \mathrm{M}$ and $\left[\mathrm{I}^{-}\right]=5.0 \times 10^{-4} \mathrm{M}$

Shubham Kumar
Shubham Kumar
Numerade Educator
03:45

Problem 34

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 $\left[\mathrm{OH}^{-}\right]=0.050 \mathrm{M}$

Shubham Kumar
Shubham Kumar
Numerade Educator
01:40

Problem 35

The following data were measured for the reaction $\mathrm{BF}_{3}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{F}_{3} \mathrm{BNH}_{3}(g)$

(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 $\left[\mathrm{BF}_{3}\right]=0.100 \mathrm{M}$ and $\left[\mathrm{NH}_{3}\right]=0.500 \mathrm{M} ?$

Sahithi Talasila
Sahithi Talasila
Numerade Educator
11:23

Problem 36

The following data were collected for the rate of disappearance of $\mathrm{NO}$ in the reaction $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$ :
$$
\begin{array}{llll}
\hline \text { Experiment } & {[\mathrm{NO}](M)} & {\left[\mathrm{O}_{2}\right](M)} & \text { Initial Rate }(M / s) \\
\hline 1 & 0.0126 & 0.0125 & 1.41 \times 10^{-2} \\
2 & 0.0252 & 0.0125 & 5.64 \times 10^{-2} \\
3 & 0.0252 & 0.0250 & 1.13 \times 10^{-1}
\end{array}
$$
(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 $\mathrm{NO}$ when $[\mathrm{NO}]=0.0750 \mathrm{M}$ and $\left[\mathrm{O}_{2}\right]=0.0100 \mathrm{M} ?(\mathrm{e})$ What is the rate of disappearance of $\mathrm{O}_{2}$ at the concentrations given in part ( $\mathrm{d}$ )?

Shubham Kumar
Shubham Kumar
Numerade Educator
03:11

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 $\mathrm{Br}_{2}$ ? (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 Talasila
Sahithi Talasila
Numerade Educator
08:17

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:
$$
\mathrm{S}_{2} \mathrm{O}_{8}^{2-}(a q)+3 \mathrm{I}^{-}(a q) \longrightarrow 2 \mathrm{SO}_{4}^{2-}(a q)+\mathrm{I}_{3}^{-}(a q)
$$
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 $\mathrm{S}_{2} \mathrm{O}_{8}{ }^{2-}$ based on the four sets of data? (c) How is the rate of disappearance of $\mathrm{S}_{2} \mathrm{O}_{8}{ }^{2-}$ related to the rate of disappearance of $\mathrm{I}^{-} ?$ (d) What is the rate of disappearance of $\mathrm{I}^{-}$ when $\left[\mathrm{S}_{2} \mathrm{O}_{8}{ }^{2-}\right]=0.025 \mathrm{M}$ and $\left[\mathrm{I}^{-}\right]=0.050 \mathrm{M} ?$

UO
Umut Ozuguzel
Texas Tech University
01:28

Problem 39

(a) Define the following symbols that are encountered in rate equations for the generic reaction $\mathrm{A} \longrightarrow \mathrm{B}:[\mathrm{A}]_{0}, t_{1 / 2}[\mathrm{~A}]_{t}, k$
(b) What quantity, when graphed versus time, will yield a straight line for a first-order reaction? (c) How can you calculate the rate constant for a first-order reaction from the graph you made in part (b)?

Daniel Gosser
Daniel Gosser
Numerade Educator
06:21

Problem 39

(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 (a)? (c) How do the half-lives of first-order and second-order reactions differ?

Shubham Kumar
Shubham Kumar
Numerade Educator
04:33

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 (a)? (c) How do the half-lives of first-order and second-order reactions differ?

Shubham Kumar
Shubham Kumar
Numerade Educator
01:38

Problem 41

For the generic reaction $\mathrm{A} \longrightarrow \mathrm{B}$ that is zero order in $\mathrm{A}$, what would you graph in order to obtain the rate constant?

Shubham Kumar
Shubham Kumar
Numerade Educator
04:26

Problem 42

Sketch a graph for the generic first-order reaction $\mathrm{A} \longrightarrow \mathrm{B}$ that has concentration of $\mathrm{A}$ on the vertical axis and time on the horizontal axis. (a) Is this graph linear? Explain. (b) Indicate on your graph the half-life for the reaction.

Shubham Kumar
Shubham Kumar
Numerade Educator
00:45

Problem 43

(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 $320^{\circ} \mathrm{C}$ the rate constant is $2.2 \times 10^{-5} \mathrm{~s}^{-1}$. What is the half-life at this temperature?

Sahithi Talasila
Sahithi Talasila
Numerade Educator
03:58

Problem 44

Molecular iodine, $\mathrm{I}_{2}(g)$, 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 $0.050 \mathrm{M} \mathrm{I}_{2}$ at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form $\mathrm{I}_{2} ?$

Shubham Kumar
Shubham Kumar
Numerade Educator
05:50

Problem 45

As described in Exercise $14.43,$ 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 $4.5 \times 10^{-2} \mathrm{~s}^{-1}$. (a) If we begin with an initial $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ pressure of 450 torr, what is the pressure of this substance after $60 \mathrm{~s} ?$ (b) At what time will the pressure of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ decline to one-tenth its initial value?

Shubham Kumar
Shubham Kumar
Numerade Educator
05:37

Problem 46

The first-order rate constant for the decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}, \quad 2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g), \quad$ at $\quad 70^{\circ} \mathrm{C}$ 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 Ozuguzel
Texas Tech University
04:28

Problem 47

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:
$$
\begin{array}{rl}
\hline \text { Time (s) } & \text { Pressure } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { (atm) } \\
\hline 0 & 1.000 \\
2,500 & 0.947 \\
5,000 & 0.895 \\
7,500 & 0.848 \\
10,000 & 0.803 \\
\hline
\end{array}
$$

Shubham Kumar
Shubham Kumar
Numerade Educator
02:04

Problem 48

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 Ozuguzel
Texas Tech University
01:58

Problem 49

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 Talasila
Sahithi Talasila
Numerade Educator
03:22

Problem 50

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 Ozuguzel
Texas Tech University
08:53

Problem 51

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:
$$
\begin{array}{rl}
\hline \text { Time }(\mathbf{s}) & {\left[\mathrm{NO}_{2}\right](M)} \\
\hline 0.0 & 0.100 \\
5.0 & 0.017 \\
10.0 & 0.0090 \\
15.0 & 0.0062 \\
20.0 & 0.0047 \\
\hline
\end{array}
$$
(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) If you used the method of initial rates to obtain the order for $\mathrm{NO}_{2},$ predict what reaction rates you would measure in the beginning of the reaction for initial concentrations of $0.200 \mathrm{M}, 0.100 \mathrm{M},$ and $0.050 \mathrm{M} \mathrm{NO}_{2}$

Shubham Kumar
Shubham Kumar
Numerade Educator
12:01

Problem 52

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:
$$
\begin{array}{rl}
\hline \text { Time }(\mathrm{min}) & {\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right](M)} \\
\hline 0 & 0.316 \\
39 & 0.274 \\
80 & 0.238 \\
140 & 0.190 \\
210 & 0.146 \\
\hline
\end{array}
$$
(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 $0.316 \mathrm{M}$ and the reaction was zero order in sucrose.

Shubham Kumar
Shubham Kumar
Numerade Educator
05:47

Problem 53

(a) What factors determine whether a collision between two molecules will lead to a chemical reaction? (b) According to the collision model, why does temperature affect the value of the rate constant? (c) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature?

Shubham Kumar
Shubham Kumar
Numerade Educator
07:40

Problem 54

(a) What factors determine whether a collision between two molecules will lead to a chemical reaction? (b) According to the collision model, why does temperature affect the value of the rate constant? (c) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature?

Shubham Kumar
Shubham Kumar
Numerade Educator
01:00

Problem 55

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 Talasila
Sahithi Talasila
Numerade Educator
06:32

Problem 56

(a) The activation energy for the isomerization of methyl isonitrile (Figure 14.7 ) is $160 \mathrm{~kJ} / \mathrm{mol}$. Calculate the fraction of methyl isonitrile molecules that has an energy of $160.0 \mathrm{~kJ}$ or greater at $500 \mathrm{~K}$. (b) Calculate this fraction for a temperature of $520 \mathrm{~K}$. What is the ratio of the fraction at $520 \mathrm{~K}$ to that at $500 \mathrm{~K} ?$

Shubham Kumar
Shubham Kumar
Numerade Educator
02:44

Problem 57

The gas-phase reaction $\mathrm{Cl}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{HCl}(g)+\mathrm{Br}(g)$
has an overall enthalpy 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?

Shubham Kumar
Shubham Kumar
Numerade Educator
02:34

Problem 58

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 Ozuguzel
Texas Tech University
03:33

Problem 59

Indicate whether each statement is true or false. If it is false, rewrite it so that it is true.
(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.

Shubham Kumar
Shubham Kumar
Numerade Educator
04:18

Problem 60

Indicate whether each statement is true or false. If it is false, rewrite it so that it is true.
(a) If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction.
(b) Exothermic reactions are faster than endothermic reactions.
(c) If you double the temperature for a reaction, you cut the activation energy in half.

Shubham Kumar
Shubham Kumar
Numerade Educator
01:55

Problem 61

Based on their activation energies and energy changes and assuming that all collision factors are the same, which of the following reactions would be fastest and which would be slowest? Explain your answer.
(a) $E_{a}=45 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-25 \mathrm{~kJ} / \mathrm{mol}$
(b) $E_{a}=35 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-10 \mathrm{~kJ} / \mathrm{mol}$
(c) $E_{a}=55 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=10 \mathrm{~kJ} / \mathrm{mol}$

Shubham Kumar
Shubham Kumar
Numerade Educator
02:36

Problem 62

Which of the reactions in Exercise 14.61 will be fastest in the reverse direction? Which will be slowest? Explain.

Shubham Kumar
Shubham Kumar
Numerade Educator
02:24

Problem 63

(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 $E_{a}=125 \mathrm{~kJ} / \mathrm{mol} ?(\mathrm{c})$ What assumptions do you need to make in order to calculate answers for parts (a) and (b)?

Sahithi Talasila
Sahithi Talasila
Numerade Educator
02:50

Problem 64

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 $0.0796 \mathrm{M}^{-1} \mathrm{~s}^{-1}$ at $737^{\circ} \mathrm{C}$ and $0.0815 \mathrm{M}^{-1} \mathrm{~s}^{-1}$ at $947{ }^{\circ} \mathrm{C}$. Calculate the activation energy for the reaction.

UO
Umut Ozuguzel
Texas Tech University
03:51

Problem 65

The rate of the reaction
$$
\begin{aligned}
\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(a q)+\mathrm{OH}^{-}(a q) & \longrightarrow \\
\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)
\end{aligned}
$$
was measured at several temperatures, and the following data were collected:
$$
\begin{array}{ll}
\hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & \boldsymbol{k}\left(\boldsymbol{M}^{-1} \mathrm{~s}^{-1}\right) \\
\hline 15 & 0.0521 \\
25 & 0.101 \\
35 & 0.184 \\
45 & 0.332 \\
\hline
\end{array}
$$
Calculate the value of $E_{a}$ by constructing an appropriate graph.

Shubham Kumar
Shubham Kumar
Numerade Educator
06:07

Problem 66

The temperature dependence of the rate constant for a reaction is tabulated as follows:
$$
\begin{array}{lc}
\hline \text { Temperature (K) } & k\left(M^{-1} \mathrm{~s}^{-1}\right) \\
\hline 600 & 0.028 \\
650 & 0.22 \\
700 & 1.3 \\
750 & 6.0 \\
800 & 23 \\
\hline
\end{array}
$$
Calculate $E_{a}$ and $A$.

Shubham Kumar
Shubham Kumar
Numerade Educator
04:52

Problem 67

The activation energy of a certain reaction is $65.7 \mathrm{~kJ} / \mathrm{mol}$. How many times faster will the reaction occur at $50^{\circ} \mathrm{C}$ than at $0^{\circ} \mathrm{C} ?$ State the assumptions you need to make in order to perform this calculation.

Shubham Kumar
Shubham Kumar
Numerade Educator
13:06

Problem 68

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 $\left.59^{\circ} \mathrm{F}\right]$ lowers the reaction rate six times; a 36 -degree drop [from $77^{\circ} \mathrm{F}$ to $\left.41^{\circ} \mathrm{F}\right]$ 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 -degree drop and that the rate of breakdown is first order with a half-life at $25^{\circ} \mathrm{C}$ of 2.7 years, calculate the half-life for breakdown at a temperature of $-15^{\circ} \mathrm{C}$.

Shubham Kumar
Shubham Kumar
Numerade Educator
05:44

Problem 69

(a) What is meant by the term elementary reaction? (b) What is the difference between a unimolecular and a bimolecular elementary reaction? (c) What is a reaction mechanism?

Shubham Kumar
Shubham Kumar
Numerade Educator
06:24

Problem 70

(a) What is meant by the term molecularity?
(b) Why are termolecular elementary reactions so rare? (c) What is an intermediate in a mechanism?

Shubham Kumar
Shubham Kumar
Numerade Educator
05:48

Problem 71

What are the differences between an intermediate and a transition state?

Shubham Kumar
Shubham Kumar
Numerade Educator
01:14

Problem 72

What is meant by the term rate-determining step?

Shubham Kumar
Shubham Kumar
Numerade Educator
01:02

Problem 73

What is the molecularity of each of the following elementary reactions? Write the rate law for each.
(a) $\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)$
(b) $\mathrm{OCl}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HOCl}(a q)+\mathrm{OH}^{-}(a q)$
(c) $\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g)$

Sahithi Talasila
Sahithi Talasila
Numerade Educator
01:16

Problem 74

What is the molecularity of each of the following elementary reactions? Write the rate law for each.
(a) $2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)$

Shubham Kumar
Shubham Kumar
Numerade Educator
03:09

Problem 75

(a) Based on the following reaction profile, how many intermediates are formed in the reaction $\mathrm{A} \longrightarrow \mathrm{D} ?$ (b) How many transition states are there? (c) Which step is the fastest?
(d) Is the reaction $\mathrm{A} \longrightarrow \mathrm{D}$ exothermic or endothermic?

Shubham Kumar
Shubham Kumar
Numerade Educator
04:37

Problem 76

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) Is the overall reaction exothermic or endothermic?

Shubham Kumar
Shubham Kumar
Numerade Educator
01:53

Problem 77

The following mechanism has been proposed for the gasphase reaction of $\mathrm{H}_{2}$ with ICl:
$$
\begin{array}{l}
\mathrm{H}_{2}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{HI}(g)+\mathrm{HCl}(g) \\
\mathrm{HI}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{I}_{2}(g)+\mathrm{HCl}(g)
\end{array}
$$
(a) Write the balanced equation for the overall reaction. (b) Identify any intermediates in the mechanism. (c) If 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 Talasila
Sahithi Talasila
Numerade Educator
01:48

Problem 78

The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism:
$$
\begin{aligned}
\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{I}^{-}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{IO}^{-}(a q) \\
\mathrm{IO}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)+\mathrm{I}^{-}(a q)
\end{aligned}
$$
(a) Write the chemical equation for the overall process.
(b) Identify the intermediate, if any, in the mechanism. (c) Assuming that the first step of the mechanism is rate determining, predict the rate law for the overall process.

Shubham Kumar
Shubham Kumar
Numerade Educator
05:56

Problem 79

The reaction $2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)$ was
performed and the following data obtained:
Is the following mechanism consistent with the data? Explain.
$$
\begin{array}{c}
\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g) \\
\mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \longrightarrow 2 \mathrm{NOCl}(g)
\end{array}
$$

Shubham Kumar
Shubham Kumar
Numerade Educator
07:26

Problem 80

You have studied the gas-phase oxidation of $\mathrm{HBr}$ 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:
$$
\begin{aligned}
\mathrm{HBr}(g)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{HOOBr}(g) \\
\mathrm{HOOBr}(g)+\mathrm{HBr}(g) & \longrightarrow 2 \mathrm{HOBr}(g) \\
\mathrm{HOBr}(g)+\mathrm{HBr}(g) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Br}_{2}(g)
\end{aligned}
$$
(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 Ozuguzel
Texas Tech University
01:33

Problem 81

(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 Talasila
Sahithi Talasila
Numerade Educator
03:10

Problem 82

(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 Ozuguzel
Texas Tech University
23:03

Problem 83

Platinum nanoparticles of diameter $\sim 2 \mathrm{nm}$ are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of $3.924 \AA$. (a) Estimate how many platinum atoms would fit into a $2.0-\mathrm{nm}$ sphere; the volume of a sphere is $(4 / 3) \pi r^{3}$. Recall that $1 \AA=1 \times 10^{-10} \mathrm{~m}$ and $1 \mathrm{nm}=1 \times 10^{-9} \mathrm{~m} .$ (b) Estimate how many platinum atoms are on the surface of a $2.0-\mathrm{nm} \mathrm{Pt}$ sphere, using the surface area of a sphere $\left(4 \pi r^{2}\right)$ and assuming that the "footprint" of one $\mathrm{Pt}$ atom can be estimated from its atomic diameter of $2.8 \AA$. (c) Using your results from (a) and (b), calculate the percentage of $\mathrm{Pt}$ atoms that are on the surface of a $2.0-\mathrm{nm}$ 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?

Shubham Kumar
Shubham Kumar
Numerade Educator
02:03

Problem 84

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 Ozuguzel
Texas Tech University
04:41

Problem 85

The oxidation of $\mathrm{SO}_{2}$ to $\mathrm{SO}_{3}$ is catalyzed 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 the two reactions can be summed to give the overall oxidation of $\mathrm{SO}_{2}$ by $\mathrm{O}_{2}$ to give $\mathrm{SO}_{3}$. (b) Why do we consider $\mathrm{NO}_{2}$ a catalyst and not an intermediate in this reaction? (c) Is this an example of homogeneous catalysis or heterogeneous catalysis?

Shubham Kumar
Shubham Kumar
Numerade Educator
08:17

Problem 86

NO catalyzes the decomposition of $\mathrm{N}_{2} \mathrm{O},$ possibly by the following mechanism:
$$
\begin{aligned}
\mathrm{NO}(g)+\mathrm{N}_{2} \mathrm{O}(g) & \longrightarrow \mathrm{N}_{2}(g)+\mathrm{NO}_{2}(g) \\
2 \mathrm{NO}_{2}(g) & \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)
\end{aligned}
$$
(a) What is the chemical equation for the overall reaction? Show how the two steps can be added to give the overall equation. (b) Why is NO considered a catalyst and not an intermediate? (c) If experiments show that during the decomposition of $\mathrm{N}_{2} \mathrm{O}, \mathrm{NO}_{2}$ does not accumulate in measurable quantities, does this rule out the proposed mechanism? If you think not, suggest what might be going on.

Shubham Kumar
Shubham Kumar
Numerade Educator
01:45

Problem 87

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 $\left(\mathrm{SiO}_{2}\right)$. (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 Talasila
Sahithi Talasila
Numerade Educator
03:18

Problem 88

(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 Ozuguzel
Texas Tech University
06:08

Problem 89

When $\mathrm{D}_{2}$ 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, $\left.\mathrm{CH}_{3}-\mathrm{CHD}_{2}\right)$. Use the sequence of steps involved in the reaction (Figure 14.24 ) to explain why this is so.

Shubham Kumar
Shubham Kumar
Numerade Educator
00:52

Problem 90

Heterogeneous catalysts that perform hydrogenation reactions, as illustrated in Figure 14.24 , 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 Ozuguzel
Texas Tech University
09:42

Problem 91

(a) Explain the importance of enzymes in biological systems.
(b) What chemical transformations are catalyzed
(i) by the enzyme catalase, $(i i)$ by nitrogenase? (c) Many enzymes follow this generic reaction mechanism, where $\mathrm{E}$ is enzyme, $\mathrm{S}$ is substrate, ES is the enzyme-substrate complex (where the substrate is bound to the enzyme's active site), and $\mathrm{P}$ is the product:
1. $\mathrm{E}+\mathrm{S} \rightleftharpoons \mathrm{ES}$
2. $\mathrm{ES} \longrightarrow \mathrm{E}+\mathrm{P}$
What assumptions are made in this model with regard to the rate of the bound substrate being chemically transformed into bound product in the active site?

Shubham Kumar
Shubham Kumar
Numerade Educator
02:33

Problem 92

There are literally thousands of enzymes at work in complex living systems such as human beings. What properties of enzymes give rise to their ability to distinguish one substrate from another?

Shubham Kumar
Shubham Kumar
Numerade Educator
02:30

Problem 93

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 Talasila
Sahithi Talasila
Numerade Educator
09:03

Problem 94

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) Assuming the collision factor is the same for both situations, estimate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.

Shubham Kumar
Shubham Kumar
Numerade Educator
02:07

Problem 95

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) $25^{\circ} \mathrm{C},(\mathbf{b}) 125^{\circ} \mathrm{C} ?$

Sahithi Talasila
Sahithi Talasila
Numerade Educator
05:44

Problem 96

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,

Shubham Kumar
Shubham Kumar
Numerade Educator
03:28

Problem 97

Explain why rate laws generally cannot be written from balanced equations. Under what circumstance is the rate law related directly to the balanced equation for a reaction?

Shubham Kumar
Shubham Kumar
Numerade Educator
02:38

Problem 98

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 Ozuguzel
Texas Tech University
03:50

Problem 99

The reaction $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$ is second order in NO and first order in $\mathrm{O}_{2}$. When [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 Talasila
Sahithi Talasila
Numerade Educator
04:49

Problem 100

Consider the following reaction between mercury(II) chloride and oxalate ion:
$$
\begin{aligned}
2 \mathrm{HgCl}_{2}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \longrightarrow & \\
2 \mathrm{Cl}^{-}(a q)+2 \mathrm{CO}_{2}(g)+\mathrm{Hg}_{2} \mathrm{Cl}_{2}(s)
\end{aligned}
$$
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 $\mathrm{HgCl}_{2}$ is $0.100 \mathrm{M}$ and that of $\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right)$ is $0.25 \mathrm{M}$ if the temperature is the same as that used to obtain the data shown?

Shubham Kumar
Shubham Kumar
Numerade Educator
05:00

Problem 101

The reaction $2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2}$ has the rate constant $k=0.63 \mathrm{M}^{-1} \mathrm{~s}^{-1}$. Based on the units for $k$, is the reaction first or second order in $\mathrm{NO}_{2}$ ? 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 $0.025 \mathrm{M}$ ?

Shubham Kumar
Shubham Kumar
Numerade Educator
04:48

Problem 102

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 Ozuguzel
Texas Tech University
03:07

Problem 103

When chemists are performing kinetics experiments, the general rule of thumb is to allow the reaction to proceed for 4 half-lives. (a) Explain how you would be able to tell that the reaction has proceeded for 4 half-lives. (b) Let us suppose a reaction $\mathrm{A} \rightarrow \mathrm{B}$ takes 6 days to proceed for 4 half-lives and is first order in A. However, when your lab partner performs this reaction for the first time, he does not realize how long it takes, and he stops taking kinetic data, monitoring the loss of A, after only 2 hours. Your lab partner concludes the reaction is zero order in A based on the data. Sketch a graph of [A] versus time to convince your lab partner the two of you need to be in the lab for a few days to obtain the proper rate law for the reaction.

Shubham Kumar
Shubham Kumar
Numerade Educator
01:43

Problem 104

(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. Near room temperature, the rate constant equals $7.0 \times 10^{-4} \mathrm{~s}^{-1} .$ Calculate the half-life at this temperature.
(b) At $415^{\circ} \mathrm{C},\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}$ decomposes in the gas phase, $\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}(g) \longrightarrow \mathrm{CH}_{4}(g)+\mathrm{CO}(g) .$ If the reaction is first
order with a half-life of 56.3 min at this temperature, calculate the rate constant in $\mathrm{s}^{-1}$.

Shubham Kumar
Shubham Kumar
Numerade Educator
16:44

Problem 105

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 halflives 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 3 half-lives? (d) How much of a 1.00 -mg sample of each isotope remains after 4 days?

Shubham Kumar
Shubham Kumar
Numerade Educator
05:21

Problem 106

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
$$
\begin{aligned}
\mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}^{+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow & \mathrm{NH}_{4}^{+}(a q)+\mathrm{HCO}_{3}^{-}(a q)
\end{aligned}
$$
The reaction is first order in urea and first order overall. When $\left[\mathrm{NH}_{2} \mathrm{CONH}_{2}\right]=0.200 \mathrm{M},$ the rate at $61.05^{\circ} \mathrm{C}$ is $8.56 \times 10^{-5} \mathrm{M} / \mathrm{s}$. (a) What is the rate constant, $k ?$ (b) What is the concentration of urea in this solution after $4.00 \times 10^{3} \mathrm{~s}$ if the starting concentration is $0.500 \mathrm{M}$ ? (c) What is the half-life for this reaction at $61.05^{\circ} \mathrm{C}$ ?

Shubham Kumar
Shubham Kumar
Numerade Educator
11:34

Problem 107

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 $5.60 \times 10^{3} \mathrm{M}^{-1} \mathrm{~cm}^{-1}$ at $520 \mathrm{nm}$. (a) Calculate the initial
concentration of the colored reactant if the absorbance is 0.605 at the beginning of the reaction. (b) The absorbance falls to 0.250 at 30.0 min. Calculate the rate constant in units of $\mathrm{s}^{-1}$. (c) Calculate the half-life of the reaction. (d) How long does it take for the absorbance to fall to $0.100 ?$

Shubham Kumar
Shubham Kumar
Numerade Educator
06:58

Problem 108

A colored dye compound decomposes to give a colorless product. The original dye absorbs at $608 \mathrm{nm}$ and has an extinction coefficient of $4.7 \times 10^{4} \mathrm{M}^{-1} \mathrm{~cm}^{-1}$ at that wavelength. You perform the decomposition reaction in a $1-\mathrm{cm}$ cuvette in a spectrometer and obtain the following data:
$$
\begin{array}{rl}
\hline \text { Time (min) } & \text { Absorbance at } 608 \mathrm{nm} \\
\hline 0 & 1.254 \\
30 & 0.941 \\
60 & 0.752 \\
90 & 0.672 \\
120 & 0.545
\end{array}
$$
From these data, determine the rate law for the reaction "dye $\longrightarrow$ product" and determine the rate constant.

Shubham Kumar
Shubham Kumar
Numerade Educator
05:01

Problem 109

Cyclopentadiene $\left(\mathrm{C}_{5} \mathrm{H}_{6}\right)$ reacts with itself to form dicyclopentadiene $\left(\mathrm{C}_{10} \mathrm{H}_{12}\right) .$ A $0.0400 \mathrm{M}$ 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. What is the order of the reaction? What is the value of the rate constant?

Shubham Kumar
Shubham Kumar
Numerade Educator
05:36

Problem 110

(a) Two reactions have identical values for $E_{a} .$ Does this ensure that they will have the same rate constant if run at the same temperature? Explain. (b) Two similar reactions have the same rate constant at $25^{\circ} \mathrm{C}$, but at $35^{\circ} \mathrm{C}$ one of the reactions has a larger rate constant than the other. Account for these observations.

Shubham Kumar
Shubham Kumar
Numerade Educator
03:47

Problem 111

The first-order rate constant for reaction of a particular organic compound with water varies with temperature as follows:
$$
\begin{array}{ll}
\hline \text { Temperature (K) } & \text { Rate Constant }\left(\mathbf{s}^{-1}\right) \\
\hline 300 & 3.2 \times 10^{-11} \\
320 & 1.0 \times 10^{-9} \\
340 & 3.0 \times 10^{-8} \\
355 & 2.4 \times 10^{-7} \\
\hline
\end{array}
$$
From these data, calculate the activation energy in units of $\mathrm{kJ} / \mathrm{mol}$

Shubham Kumar
Shubham Kumar
Numerade Educator
04:11

Problem 112

The following mechanism has been proposed for the reaction of $\mathrm{NO}$ with $\mathrm{H}_{2}$ to form $\mathrm{N}_{2} \mathrm{O}$ and $\mathrm{H}_{2} \mathrm{O}$ :
$$
\begin{aligned}
\mathrm{NO}(g)+\mathrm{NO}(g) & \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g) \\
\mathrm{N}_{2} \mathrm{O}_{2}(g)+\mathrm{H}_{2}(g) & \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{H}_{2} \mathrm{O}(g)
\end{aligned}
$$
(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 Talasila
Sahithi Talasila
Numerade Educator
03:55

Problem 113

Ozone in the upper atmosphere can be destroyed by the following two-step mechanism:
$$
\begin{array}{l}
\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \\
\mathrm{ClO}(g)+\mathrm{O}(g) \longrightarrow \mathrm{Cl}(g)+\mathrm{O}_{2}(g)
\end{array}
$$
(a) What is the overall equation for this process?
(b) What is the catalyst in the reaction? How do you know?
(c) What is the intermediate in the reaction? How do you distinguish it from the catalyst?

Shubham Kumar
Shubham Kumar
Numerade Educator
05:02

Problem 114

Using Figure 14.23 as your basis, draw the energy profile for the bromide-catalyzed decomposition of hydrogen peroxide. (a) Label the curve with the activation energies for reactions [14.30] and $[14.31] .(\mathbf{b})$ Notice from Figure 14.22 that when $\mathrm{Br}^{-}(a q)$ is first added, $\mathrm{Br}_{2}$ accumulates to some extent during the reaction and the solution turns brown. What does this tell us about the relative rates of the reactions represented by Equations 14.30 and $14.31 ?$

Shubham Kumar
Shubham Kumar
Numerade Educator
08:35

Problem 115

The following mechanism has been proposed for the gasphase reaction of chloroform $\left(\mathrm{CHCl}_{3}\right)$ and chlorine:

(a) What is the overall reaction? (b) What are the intermediates 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.)

Shubham Kumar
Shubham Kumar
Numerade Educator
10:55

Problem 116

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 dif-
ferent gold compound, $\left(\mathrm{CH}_{3}\right) \mathrm{AuPH}_{3} .$ The following mechanism has been proposed for the decomposition of $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3}:$

(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 rate-determining 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 $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3} ?$

Shubham Kumar
Shubham Kumar
Numerade Educator
01:21

Problem 117

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 Ozuguzel
Texas Tech University
07:11

Problem 118

Enzymes are often described as following the two-step mechanism:
$$
\begin{array}{l}
\mathrm{E}+\mathrm{S} \rightleftharpoons \mathrm{ES} \quad(\text { fast }) \\
\mathrm{ES} \longrightarrow \mathrm{E}+\mathrm{P} \quad(\text { slow })
\end{array}
$$
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 $\mathrm{E}$ with $\mathrm{I}$, an inhibitor.

UO
Umut Ozuguzel
Texas Tech University
09:54

Problem 119

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 $0.600 \mathrm{M} \mathrm{N}_{2} \mathrm{O}_{5}$ solution at $45^{\circ} \mathrm{C}$ over a period of $20.0 \mathrm{hr}$ if the gas is collected in a $10.0-\mathrm{L}$ container. (Assume that the products do not dissolve in chloroform.)

Shubham Kumar
Shubham Kumar
Numerade Educator
12:26

Problem 120

The reaction between ethyl iodide and hydroxide ion in ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ solution, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I}(a l c)+\mathrm{OH}^{-}($ alc $) \longrightarrow$
$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{I}^{-}($ alc $),$ 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) $\mathrm{A}$ solution of $\mathrm{KOH}$ in ethanol is made up by dissolving $0.335 \mathrm{~g}$ $\mathrm{KOH}$ 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 reactant, what is the initial rate at $35^{\circ} \mathrm{C} ?$ (c) Which reagent in the reaction is limiting, assuming the reaction proceeds to completion?
(d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at $50^{\circ} \mathrm{C}$.

Shubham Kumar
Shubham Kumar
Numerade Educator
06:27

Problem 121

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:

Shubham Kumar
Shubham Kumar
Numerade Educator
01:34

Problem 123

The mechanism for the oxidation of $\mathrm{HBr}$ by $\mathrm{O}_{2}$ to form $2 \mathrm{H}_{2} \mathrm{O}$ and $\mathrm{Br}_{2}$ is shown in Exercise $14.80 .$
(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 Talasila
Sahithi Talasila
Numerade Educator
13:21

Problem 124

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 slow in the absence of light. However, $\mathrm{Cl}_{2}(g)$ can absorb light to form $\mathrm{Cl}$ atoms:
Reaction $2: \mathrm{Cl}_{2}(g)+h v \longrightarrow 2 \mathrm{Cl}(g)$
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:
Reaction $3: \mathrm{CH}_{4}(g)+\mathrm{Cl}(g) \longrightarrow \mathrm{CH}_{3}(g)+\mathrm{HCl}(g)$
Reaction $4: \mathrm{CH}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{Cl}(g)+\mathrm{Cl}(g)$
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) $\mathrm{By}$ 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 $\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CH}_{3}(g)+\mathrm{HCl}(g)+\mathrm{Cl}(g) .$
(d) The species $\mathrm{Cl}(g)$ and $\mathrm{CH}_{3}(g)$ 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.

Shubham Kumar
Shubham Kumar
Numerade Educator
05:19

Problem 125

Many primary amines, $\mathrm{RNH}_{2}$, where $\mathrm{R}$ is a carboncontaining fragment such as $\mathrm{CH}_{3}, \mathrm{CH}_{3} \mathrm{CH}_{2},$ 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 $\mathrm{C}$ atom for ${ }^{\text {"R" }}$ ). (b) What kind of reactant with a primary amine can produce a tetrahedral intermediate?

Shubham Kumar
Shubham Kumar
Numerade Educator
20:51

Problem 126

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 $\mathrm{NO}, \mathrm{NO}_{2},$ and $\mathrm{N}_{2} .(\mathbf{b})$ Using a resource such as Table 8.4 , 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.

Shubham Kumar
Shubham Kumar
Numerade Educator