Chemistry: The Molecular Nature of Matter

Problem 1

Why are chemical reactions usually carried out in solution?

David Collins

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01:06

Problem 2

Give an example from everyday experience of (a) a very fast reaction, (b) a moderately fast reaction, and (c) a slow reaction.

David Collins

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01:10

Problem 3

What is a homogeneous reaction? What is a heterogeneous reaction? Give examples.

David Collins

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Problem 4

How does particle size affect the rate of a heterogeneous reaction? Why?

David Collins

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Problem 5

What is the major factor that affects the rate of a heterogeneous reaction?

David Collins

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01:14

Problem 6

The rate of hardening of epoxy glue depends on the amount of hardener that is mixed into the glue. What factor affecting reaction rates does this illustrate?

David Collins

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Problem 7

A Polaroid $^{\text {TM }}$ instant photograph develops faster if it's kept warm than if it is exposed to cold. Why?

David Collins

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Insects have no way of controlling their body temperatures like mammals do. In cool weather, they become sluggish and move less quickly. How can this be explained using the principles developed in this chapter?

David Collins

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01:29

Problem 9

Persons who have been submerged in very cold water and who are believed to have drowned sometimes can be revived. On the other hand, persons who have been submerged in warmer water for the same length of time have died. Explain this in terms of factors that affect the rates of chemical reactions.

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01:44

Problem 10

How does an instantaneous rate of reaction differ from an average rate of reaction?

Anthony Han

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01:42

Problem 11

What is the difference between the rate of reaction and the reaction rate with respect to one component of the reaction?

David Collins

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01:07

Problem 12

Explain how the initial instantaneous rate of reaction can be determined from experimental concentration versus time data.

David Collins

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01:18

Problem 13

What are the units of reaction rate? What is the sign of a reaction rate?

David Collins

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Problem 14

Describe how to determine the instantaneous rate of
chemical change. What data do you need and how will you use it?

David Collins

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01:25

Problem 15

What are the units of the rate constant for (a) a firstorder reaction, (b) a second-order reaction, and (c) a zero-order reaction?

Anthony Han

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01:28

Problem 16

How does the dependence of reaction rate on concentration differ between a zero-order and a first-order reaction? Between a first-order and second-order reaction?

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Problem 17

Is there any way of using the coefficients in the balanced overall equation for a reaction to predict with certainty what the exponents are in the rate law?

Anthony Han

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Problem 18

If the concentration of a reactant is doubled and the reaction rate is unchanged, what must be the order of the reaction with respect to that reactant?

Anthony Han

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Problem 19

If the concentration of a reactant is doubled and the reaction rate doubles, what must be the order of the reaction with respect to that reactant?

Anthony Han

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Problem 20

If the concentration of a reactant is doubled, by what factor will the rate increase if the reaction is second order with respect to that reactant?

Anthony Han

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Problem 21

In an experiment, the concentration of a reactant was tripled. The rate increased by a factor of $27 .$ What is the order of the reaction with respect to that reactant?

Anthony Han

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Problem 22

Biological reactions usually involve the interaction of an enzyme with a substrate, the substance that actually undergoes the chemical change. In many cases, the rate of reaction depends on the concentration of the enzyme but is independent of the substrate concentration. What is the order of the reaction with respect to the substrate in such instances?

Anthony Han

Numerade Educator

02:13

Problem 23

Rearrange the integrated rate equations for (a) a first-order reaction, (b) a second-order reaction, and (c) a zero-order reaction to calculate $[A]_{t}$. Use the symbol $[A]_{0}$ to represent the initial concentration if needed.

Anthony Han

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01:37

Problem 24

How is the half-life of a first-order reaction affected by the initial concentration of the reactant?

Anthony Han

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Problem 25

How is the half-life of a second-order reaction affected by the initial reactant concentration?

Anthony Han

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Problem 26

How is the half-life of a zero-order reaction affected by the initial reactant concentration?

Anthony Han

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01:49

Problem 27

Derive the equations for $t_{1 / 2}$ for first- and second-order reactions from Equations 13.7 and 13.11 respectively.

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Problem 28

The integrated rate law for a zero-order reaction is $$[A]_{t}=-k t+[A]_{0}$$ Derive an equation for the half-life of a zero-order reaction.

David Collins

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01:06

Problem 29

Which of the following graphs represents the data collected for a first-order reaction? A second-order reaction? zero-order reaction?

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Problem 30

What is the basic postulate of collision theory?

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Problem 31

What two factors influence the effectiveness of molecular collisions in producing chemical change?

Anthony Han

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01:59

Problem 32

In terms of the kinetic theory, why does an increase in temperature increase the reaction rate?

Anthony Han

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Problem 33

Some might say that the collision theory "treats reactions as collisions between hard spheres." Critique this statement and compare to the transition state theory as needed.

David Collins

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Problem 34

What does the transition state theory attempt to describe about chemical reactions?

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01:28

Problem 35

Draw a potential energy diagram for an exothermic reaction and indicate on the diagram the location of the transition state.

Anthony Han

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Problem 36

Some might say that the "transition state theory tries to describe what happens from the moment molecules start to collide until they finally separate." Critique this statement, comparing to the collision theory as needed.

David Collins

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Problem 37

What is the activation energy? How is the activation energy related to the rate of a reaction?

David Collins

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Problem 38

The decomposition of carbon dioxide, $$\mathrm{CO}_{2} \longrightarrow \mathrm{CO}+\mathrm{O}$$ has an activation energy of approximately $460 \mathrm{~kJ} / \mathrm{mol}$. Explain why this large value is consistent with a mechanism that involves the breaking of a $\mathrm{C}=\mathrm{O}$ bond.

David Collins

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01:31

Problem 39

Draw the potential energy diagram for an endothermic reaction. Indicate on the diagram the activation energy for both the forward and reverse reactions. Also indicate the heat of reaction.

Anthony Han

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01:23

Problem 40

What is the definition of an elementary process? How are elementary processes related to the mechanism of a reaction?

David Collins

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Problem 41

What is a rate-determining step?

David Collins

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01:17

Problem 42

What is an intermediate in the context of reaction mechanisms?

Anthony Han

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Problem 43

Free radicals are discussed in Chemistry Outside the Classroom 13.1. What is a free radical? Why are free radical mechanisms important in many reactions?

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01:44

Problem 44

Suppose we compared two reactions, one requiring the simultaneous collision of three molecules and the other requiring a collision between two molecules. From the standpoint of statistics, and all other factors being equal, which reaction should be faster? Explain your answer.

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01:29

Problem 45

In what way is the rate law for a reaction related to the rate-determining step?

David Collins

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02:29

Problem 46

How does an elementary process relate to (a) the rate law for that process, (b) the rate law for a reaction, and (c) the coefficients of the chemical reaction?

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01:10

Problem 47

How does a catalyst increase the rate of a chemical reaction?

David Collins

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01:28

Problem 48

What is a homogeneous catalyst? How does it function, in general terms?

David Collins

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01:05

Problem 49

What is the purpose of the catalytic converter that most automobiles use today? Is the catalyst heterogeneous or homogeneous?

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01:11

Problem 50

Tell how you would recognize a catalyst in a description of a chemical process or experimental procedure.

David Collins

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01:09

Problem 51

What is the difference in meaning between the terms adsorption and absorption? Which one applies to heterogeneous catalysts?

David Collins

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01:25

Problem 52

Why should leaded gasoline not be used in cars equipped with catalytic converters?

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Problem 53

The following data were collected at a certain temperature for the decomposition of sulfuryl chloride, $\mathrm{SO}_{2} \mathrm{Cl}_{2}$, a chemical used in a variety of organic syntheses. $$\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2}$$ $$\begin{array}{lc}\text { Time (min) } &{\left[\mathrm{SO}_{2}\mathrm{Cl}_{2}\right]\left(\mathrm{mol} \mathrm{L}^{-1}\right)} \\\hline 0 & 0.1000 \\1.00 \times 10^{2} & 0.0876 \\2.00 \times 10^{2} & 0.0768 \\3.00 \times 10^{2} & 0.0673 \\4.00 \times 10^{2} & 0.0590 \\5.00 \times 10^{2} & 0.0517 \\6.00 \times 10^{2} & 0.0453 \\7.00 \times 10^{2} & 0.0397 \\8.00 \times 10^{2} & 0.0348 \\9.00 \times 10^{2} & 0.0305 \\1.000 \times 10^{3} & 0.0267 \\1.100 \times 10^{3} & 0.0234 \\\hline\end{array}$$ Make a graph of concentration versus time and determine the instantaneous rate of formation of $\mathrm{SO}_{2}$ using the tangent to the curve at $t=200$ minutes and $t=600$ minutes.

David Collins

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01:36

Problem 54

The following data were collected for the decomposition of acetaldehyde. $\mathrm{CH}_{3} \mathrm{CHO},$ (used in the manufacture of a variety of chemicals including perfumes, dyes, and plastics), into methane and carbon monoxide. The data were collected at $535^{\circ} \mathrm{C}$. $$\mathrm{CH}_{3} \mathrm{CHO} \longrightarrow \mathrm{CH}_{4}+\mathrm{CO}$$ $$\begin{array}{cc}{\left[\mathrm{CH}_{3} \mathrm{CHO}\right]\left(\mathrm{mol}\mathrm{L}^{-1}\right)} & \text {Time (s) } \\ 0.200 & 0 \\0.153 & 0.20 \times 10^{2} \\0.124 & 0.40 \times 10^{2} \\0.104 & 0.60 \times 10^{2} \\0.090 & 0.80 \times 10^{2} \\0.079 & 1.00 \times 10^{2} \\0.070 & 1.20 \times 10^{2} \\0.063 & 1.40 \times 10^{2} \\0.058 & 1.60 \times 10^{2} \\0.053 & 1.80 \times 10^{2} \\0049 & 2.00 \times 10^{2} \\\hline\end{array}$$ Make a graph of concentration versus time and determine, using the tangent to the curve, the instantaneous rate of reaction of $\mathrm{CH}_{3} \mathrm{CHO}$ after 60 seconds and after 120 seconds.

David Collins

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01:58

Problem 55

For the reaction, $2 A+B \longrightarrow 3 C$, it was found that the rate of disappearance of $B$ was $0.30 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. What were the rates of disappearance of $A$ and the rate of appearance of $C$ ?

Anthony Han

Numerade Educator

01:09

Problem 56

In the reaction, $3 \mathrm{H}_{2}+\mathrm{N}_{2} \longrightarrow 2 \mathrm{NH}_{3}$, how does the rate of disappearance of hydrogen compare to the rate of disappearance of nitrogen? How does the rate of appearance of $\mathrm{NH}_{3}$ compare to the rate of disappearance of nitrogen?

David Collins

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02:25

Problem 57

In the combustion of hexane (a low-boiling component of gasoline),$$2 \mathrm{C}_{6} \mathrm{H}_{14}(g)+19 \mathrm{O}_{2}(g) \longrightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)$$ it was found that the rate of decrease of $\mathrm{C}_{6} \mathrm{H}_{14}$ was $1.20 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
(a) What was the rate of reaction with respect to $\mathrm{O}_{2} ?$
(b) What was the rate of formation of $\mathrm{CO}_{2}$ ?
(c) What was the rate of formation of $\mathrm{H}_{2} \mathrm{O}$ ?

Anthony Han

Numerade Educator

Problem 58

At a certain moment in the reaction, $$2 \mathrm{~N}_{2} \mathrm{O}_{5} \longrightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}$$
$\mathrm{N}_{2} \mathrm{O}_{5}$, is decomposing at a rate of $2.5 \times 10^{-6} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$.
What are the rates of formation of $\mathrm{NO}_{2}$ and $\mathrm{O}_{2}$ ?

Anthony Han

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01:13

Problem 59

Consider the reaction, $$\mathrm{CH}_{3} \mathrm{Cl}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)+3 \mathrm{HCl}(g)$$
(a) Express the rate of the reaction with respect to each of the reactants and products.
(b) If the instantaneous rate of the reaction with respect to $\mathrm{HCl}$ is $0.029 \mathrm{M} \mathrm{s}^{-1}$, what is the instantaneous rate of the reaction?

David Collins

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Problem 60

The decomposition of phosphine, a very toxic gas, forms phosphorus and hydrogen in the following reaction: $$4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g)$$
(a) Express the rate with respect to each of the reactants and products.
(b) If the instantaneous rate with respect to $\mathrm{PH}_{3}$ is $0.34 M \mathrm{~s}^{-1}$, what is the instantaneous rate of the reaction?

David Collins

Numerade Educator

01:42

Problem 61

Estimate the rate of the reaction,$$\mathrm{H}_{2} \mathrm{SeO}_{3}+6 \mathrm{I}^{-}+4 \mathrm{H}^{+} \longrightarrow \mathrm{Se}+2 \mathrm{I}_{3}^{-}+3 \mathrm{H}_{2} \mathrm{O}$$given that the rate law for the reaction at $0^{\circ} \mathrm{C}$ is$$\text { rate }=\left(5.0 \times 10^{5} \mathrm{~L}^{5} \mathrm{~mol}^{-5} \mathrm{~s}^{-1}\right)\left[\mathrm{H}_{2} \mathrm{SeO}_{3}\right]\left[\mathrm{I}^{-}\right]^{3}\left[\mathrm{H}^{+}\right]^{2}$$. The reactant concentrations are $\left[\mathrm{H}_{2} \mathrm{SeO}_{3}\right]=2.0 \times 10^{-2} M$, $\left[\mathrm{I}^{-}\right]=2.0 \times 10^{-3} M,$ and $\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-3} M$.

Anthony Han

Numerade Educator

01:14

Problem 62

Estimate the rate of the reaction, $$ \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O} $$ given the rate law for the reaction is$$\text { rate }=\left(1.3 \times 10^{11} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}\right)\left[\mathrm{OH}^{-}\right]\left[\mathrm{H}^{+}\right]$$ for neutral water, where $\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} M$ and $\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} M$

Anthony Han

Numerade Educator

01:24

Problem 63

The oxidation of $\mathrm{NO}$ (released in small amounts in the exhaust of automobiles) produces the brownish-red gas $\mathrm{NO}_{2},$ which is a component of urban air pollution. $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ The rate law for the reaction is rate $=k[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right]$ At $25^{\circ} \mathrm{C}, k=7.1 \times 10^{9} \mathrm{~L}^{2} \mathrm{~mol}^{-2} \mathrm{~s}^{-1}$. What would be the rate of the reaction if $[\mathrm{NO}]=0.0010 \mathrm{~mol} \mathrm{~L}^{-1}$ and $\left[\mathrm{O}_{2}\right]=0.034 \mathrm{~mol} \mathrm{I}^{-1}$.

Anthony Han

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Problem 64

The rate law for the decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ is rate $=$ $k\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] .$ If $k=1.0 \times 10^{-5} \mathrm{~s}^{-1},$ what is the reaction rate when the $\mathrm{N}_{2} \mathrm{O}_{5}$ concentration is $0.0010 \mathrm{~mol} \mathrm{~L}^{-1}$ ?

Anthony Han

Numerade Educator

Problem 65

The rate law for a certain enzymatic reaction is zero order with respect to the substrate. The rate constant for the reaction is $6.4 \times 10^{2} M \mathrm{~s}^{-1}$. If the initial concentration of the substrate is $0.275 \mathrm{~mol} \mathrm{~L}^{-1}$, what is the initial rate of the reaction?

Anthony Han

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01:24

Problem 66

Radon- 220 is radioactive, and decays into polonium- 216 by emitting an alpha particle. This is a first-order process with a rate constant of $0.0125 \mathrm{~s}^{-1}$. When the concentration of radon- 220 is $1.0 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1}$, what is the rate of the reaction?

Anthony Han

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01:31

Problem 67

The following data were collected for the reaction $M+N \longrightarrow P+Q:$ What is the rate law for the reaction? What is the value of
the rate constant (with correct units)?

David Collins

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01:49

Problem 68

Cyclopropane, $\mathrm{C}_{3} \mathrm{H}_{6}$, is a gas used as a general anesthetic. It undergoes a slow molecular rearrangement to propylene. At a certain temperature, the following data were obtained relating concentration and rate: $$\begin{array}{cc}\text { Initial Concentration of } & \text { Initial Rate of Formation } \\\text { Cyclopropane }\left(\mathrm{mol} \mathrm{L}^{-1}\right) & \text {of Propylene }\left(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\right) \\0.050 & 2.95 \times 10^{-5} \\0.100 & 5.90 \times 10^{-5} \\0.150 & 8.85 \times 10^{-5}\end{array}$$ What is the rate law for the reaction? What is the value of
the rate constant, with correct units?

Anthony Han

Numerade Educator

02:15

Problem 69

The reaction of iodide ion with hypochlorite ion, $\mathrm{OCl}^{-}$ (the active ingredient in a "chlorine bleach" such as Clorox), follows the equation $\mathrm{OCl}^{-}+\mathrm{I}^{-} \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-} . \mathrm{It}$ is
a rapid reaction that gives the following rate data: What is the rate law for the reaction? Determine the value of the rate constant with its correct units.

David Collins

Numerade Educator

02:24

Problem 70

The formation of small amounts of nitrogen oxide, $\mathrm{NO},$ in automobile engines is the first step in the formation of smog. As noted in Problem 13.63 , nitrogen oxide is readily oxidized to nitrogen dioxide by the reaction $2 \mathrm{NO}(g)+$ $\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$. The following data were collected in a study of the rate of this reaction: What is the rate law for the reaction? Determine the
alue of the rate constant with its correct units.

David Collins

Numerade Educator

01:54

Problem 71

At a certain temperature, the following data were collected for the reaction, $2 \mathrm{ICl}+\mathrm{H}_{2} \longrightarrow \mathrm{I}_{2}+2 \mathrm{HCl}$ Determine the rate law and the rate constant (with correct units) for the reaction.

David Collins

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01:40

Problem 72

The following data were obtained for the reaction of $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}$ with hydroxide ion at $55^{\circ} \mathrm{C}$. $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}+\mathrm{OH} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}+\mathrm{Br}$ What is the rate law for the reaction? What is the value of
the rate constant (with correct units) at this temperature?

David Collins

Numerade Educator

Problem 73

Data for the decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ according to the equation $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g),$ were given in Problem 13.53. Show graphically that these data fit a first-order rate law. Graphically determine the rate constant for the reaction.

David Collins

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Problem 74

For the data in Problem 13.54 , decide graphically whether the reaction is first or second order. Graphically determine the rate constant for the reaction described in that problem.

David Collins

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02:49

Problem 75

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ described in Problem 13.53 has a first-order rate constant, $k=2.2 \times 10^{-5} \mathrm{~s}^{-1}$ at $320^{\circ} \mathrm{C}$. If the initial $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ concentration in a container is $0.0040 \mathrm{M}$, what will its concentration be (a) after 1.00 hour and $(\mathbf{b})$ after 1.00 day?

Anthony Han

Numerade Educator

01:22

Problem 76

The decomposition of acetaldehyde, $\mathrm{CH}_{3} \mathrm{CHO},$ was described in Problem $13.54,$ and the order of the reaction and the rate constant for the reaction at $530^{\circ} \mathrm{C}$ were determined in Problem 13.74. If the initial concentration of acetaldehyde is $0.300 \mathrm{M}$, what will the concentration be (a) after 30 minutes, (b) after 180 minutes?

David Collins

Numerade Educator

Problem 77

If it takes 75.0 min for the concentration of a reactant to drop to $25.0 \%$ of its initial value in a first-order reaction, what is the rate constant for the reaction in the units $\min ^{-1} ?$

Anthony Han

Numerade Educator

Problem 78

It takes 15.4 minutes for the concentration of a reactant to drop to $5.0 \%$ of its initial value in a second-order reaction. What is the rate constant for the reaction in the units of $\mathrm{L} \mathrm{mol}^{-1} \min ^{-1}$ ?

David Collins

Numerade Educator

Problem 79

The concentration of a drug in the body is often expressed in units of milligrams per kilogram of body weight. The initial dose of a drug in an animal was $25.0 \mathrm{mg} / \mathrm{kg}$ body weight. After 2.00 hours, this concentration had dropped to $15.0 \mathrm{mg} / \mathrm{kg}$ body weight. If the drug is eliminated metabolically by a first-order process, what is the rate constant for the process in units of $\min ^{-1}$ ?

David Collins

Numerade Educator

Problem 80

Phosphine, $\mathrm{PH}_{3},$ decomposes into phosphorus, $\mathrm{P}_{4},$ and hydrogen at $680^{\circ} \mathrm{C}$, as described in Problem $13.60 .$ If the initial concentration of phosphine is $1.1 \times 10^{-6} \mathrm{~g} \mathrm{~L}^{-1}$, and after $180 \mathrm{~s}$ the concentration has dropped to $0.30 \times$ $10^{-6} \mathrm{~g} \mathrm{~L}^{-1}$, what is the rate constant for this process in $\mathrm{s}^{-1}$?

David Collins

Numerade Educator

01:43

Problem 81

Hydrogen iodide decomposes according to the equation, $$2 \mathrm{HI}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)$$The reaction is second order and has a rate constant equal to $1.6 \times 10^{-3} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $750^{\circ} \mathrm{C}$. If the initial concentration of HI in a container is $3.4 \times 10^{-2} M$, how many minutes will it take for the concentration to be reduced $$\text { to } 8.0 \times 10^{-4} \mathrm{M}$$.

Anthony Han

Numerade Educator

Problem 82

The reaction of $\mathrm{NOBr}(g)$ to form $\mathrm{NO}(g)$ and $\mathrm{Br}_{2}(g)$ is second order: $$2 \mathrm{NOBr}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$ The rate constant is $0.556 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at some temperature. If the initial concentration of NOBr in the container is $0.25 M$, how long will it take for the concentration to decrease to $0.025 \mathrm{M}$ ?

Anthony Han

Numerade Educator

01:23

Problem 83

Using the information determined in Problem 13.79, calculate what the initial dose of the drug must be in order for the drug concentration 3.00 hours afterward to be $5.0 \mathrm{mg} / \mathrm{kg}$ body weight.

David Collins

Numerade Educator

01:48

Problem 84

The second-order rate constant for the decomposition of HI at $750^{\circ} \mathrm{C}$ was given in Problem 13.81. At $2.5 \times 10^{3}$ minutes after a particular experiment had begun, the HI concentration was equal to $4.5 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$. What was the initial molar concentration of HI in the reaction vessel?

Anthony Han

Numerade Educator

02:08

Problem 85

The half-life of a certain first-order reaction is $15 \mathrm{~min}-$ utes. What fraction of the original reactant concentration will remain after 2.0 hours?

Anthony Han

Numerade Educator

01:22

Problem 86

Strontium-90 has a half-life of 28 years. How long will it take for all of the strontium- 90 presently on earth to be reduced to $1 / 32$ of its present amount?

Anthony Han

Numerade Educator

Problem 87

Using the graph from Problem $13.53,$ determine the time required for the $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ concentration to drop from $0.100 \mathrm{~mol} \mathrm{~L}^{-1}$ to $0.050 \mathrm{~mol} \mathrm{~L}^{-1}$. How long does it take for the concentration to drop from $0.050 \mathrm{~mol} \mathrm{~L}^{-1}$ to $0.025 \mathrm{~mol} \mathrm{~L}^{-1}$ ? What is the order of this reaction?

David Collins

Numerade Educator

01:35

Problem 88

Using the graph from Problem 13.54, determine how long it takes for the $\mathrm{CH}_{3} \mathrm{CHO}$ concentration to decrease from $0.200 \mathrm{~mol} \mathrm{~L}^{-1}$ to $0.100 \mathrm{~mol} \mathrm{~L}^{-1}$. How long does it take the concentration to drop from $0.100 \mathrm{~mol} \mathrm{~L}^{-1}$ to $0.050 \mathrm{~mol} \mathrm{~L}^{-1}$ ? What is the order of this reaction?

David Collins

Numerade Educator

Problem 89

Hydrogen peroxide, which decomposes in a first-order reaction, has a half-life of 10 hours in air. How long will it take for hydrogen peroxide to decompose to $10 \%$ of its original concentration?

Anthony Han

Numerade Educator

01:26

Problem 90

$\mathrm{SO}_{2} \mathrm{Cl}_{2}$ decomposes in a first-order process with a half life of $4.88 \times 10^{3} \mathrm{~s}$. If the original concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $0.012 \mathrm{M}$, how many seconds will it take for the $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to reach $0.0020 \mathrm{M}$ ?

Anthony Han

Numerade Educator

01:26

Problem 91

A $500 \mathrm{mg}$ sample of rock was found to have $2.45 \times 10^{-6}$ mol of potassium- $40\left(t_{1 / 2}=1.3 \times 10^{9} \mathrm{yr}\right)$ and $2.45 \times$ $10^{-6}$ mol of argon- 40 . How old was the rock?

David Collins

Numerade Educator

01:13

Problem 92

A tree killed by being buried under volcanic ash was found to have a ratio of carbon-14 atoms to carbon-12 atoms of $4.8 \times 10^{-14}$. How long ago did the eruption occur?

David Collins

Numerade Educator

Problem 93

A wooden door lintel from an excavated site in Mexico would be expected to have what ratio of carbon-14 to carbon-12 atoms if the lintel were $9.0 \times 10^{3}$ years old?

David Collins

Numerade Educator

01:46

Problem 94

If a rock sample was found to contain $1.16 \times 10^{-7} \mathrm{~mol}$ of argon-40, how much potassium- $40\left(t_{1 / 2}=1.3 \times 10^{9} \mathrm{yr}\right)$ would also have to be present for the rock to be $1.3 \times 10^{9}$ years old? See assumption in Problem 13.91 .

David Collins

Numerade Educator

02:12

Problem 95

The following data were collected for a reaction: $$ \begin{array}{cc}\text { Rate Constant }\left(\mathrm{L} \mathrm{mol}^{-1} \mathrm{~s}^{-1}\right) & \text {Temperature }\left({ }^{\circ} \mathrm{C}\right) \\2.88 \times 10^{-4} & 3.20 \times 10^{2} \\4.87 \times 10^{-4} & 3.40 \times 10^{2} \\7.96 \times 10^{-4} & 3.60 \times 10^{2} \\1.26 \times 10^{-3} & 3.80 \times 10^{2} \\1.94 \times 10^{-3} & 4.00 \times 10^{2}\end{array}$$ Determine the activation energy for the reaction in $\mathrm{kJ} / \mathrm{mol}$ both graphically and by calculation using Equation 13.16 . For the calculation of $E_{s}$, use the first and last sets of data in the table.

David Collins

Numerade Educator

09:03

Problem 96

Rate constants were measured at various temperatures for the reaction, $\mathrm{HI}(g)+\mathrm{CH}_{3} \mathrm{I}(g) \longrightarrow \mathrm{CH}_{4}(g)+\mathrm{I}_{2}(g)$. The following data were obtained: $$ \begin{array}{cc}\text { Rate Constant }\left(\mathrm{L} \mathrm{mol}^{-1} \mathrm{~s}^{-1}\right) & \text {Temperature }\left({ }^{\circ} \mathrm{C}\right) \\1.91 \times 10^{-2} & 2.05 \times 10^{2} \\2.74 \times 10^{-2} & 2.10 \times 10^{2} \\3.90 \times 10^{-2} & 2.15 \times 10^{2} \\5.51 \times 10^{-2} & 2.20 \times 10^{2} \\7.73 \times 10^{-2} & 2.25 \times 10^{2} \\1.08 \times 10^{-1} & 2.30 \times 10^{2} \\\end{array}$$ Determine the activation energy in $\mathrm{kJ} / \mathrm{mol}$ both graphically and by calculation using Equation 13.16. For the calculation of $E_{\mathrm{n}}$, use the first and last sets of data in the table.

Susan Hallstrom

Numerade Educator

03:44

Problem 97

NOCl decomposes as: $2 \mathrm{NOCl} \longrightarrow 2 \mathrm{NO}+\mathrm{Cl}_{2},$ and has $k=9.3 \times 10^{-5} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $100^{\circ} \mathrm{C}$ and $k=1.0 \times$ $10^{-3} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $130^{\circ} \mathrm{C}$. What is $E_{2}$ for this reaction in $\mathrm{kJ} \mathrm{mol}^{-1}$ ? Use the data at $373 \mathrm{~K}$ to calculate the frequency factor, $A$. What is the rate constant at $473 \mathrm{~K}$ ?

David Collins

Numerade Educator

03:47

Problem 98

The conversion of cyclopropane, an anesthetic, to propylene (see Problem 13.68) has a rate constant $k=1.3 \times$ $10^{-6} \mathrm{~s}^{-1}$ at $673 \mathrm{~K}$ and $k=1.1 \times 10^{-5} \mathrm{~s}^{-1}$ at $703 \mathrm{~K}$. What is the activation energy in $\mathrm{kJ} / \mathrm{mol}$ ? Use the data given at $703 \mathrm{~K}$ to calculate the frequency factor, $A$, for this reaction. What is the rate constant for the reaction at $350^{\circ} \mathrm{C}$ ?

David Collins

Numerade Educator

02:03

Problem 99

The decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ has an activation energy of $103 \mathrm{~kJ} / \mathrm{mol}$ and a frequency factor of $4.3 \times 10^{13} \mathrm{~s}^{-1}$ What is the rate constant for this decomposition at
(a) $25^{\circ} \mathrm{C}$ and
(b) $373 \mathrm{~K}$ ?

Anthony Han

Numerade Educator

01:57

Problem 100

At $35^{\circ} \mathrm{C}$, the rate constant for the reaction $$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$$is $k=6.2 \times 10^{-5} \mathrm{~s}^{-1}$. The activation energy for the reaction is $108 \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is the rate constant for the reaction at $45^{\circ} \mathrm{C}$ ?

Anthony Han

Numerade Educator

Problem 101

The oxidation of $\mathrm{NO}$ to $\mathrm{NO}_{2}$, one of the reactions in the production of $\mathrm{smog}$, appears to involve carbon monoxide. A possible mechanism is
$$
\begin{aligned}
\mathrm{CO}+\cdot \mathrm{OH} & \longrightarrow \mathrm{CO}_{2}+\mathrm{H}^{\cdot} \\
\mathrm{H} \cdot+\mathrm{O}_{2} & \longrightarrow \mathrm{HOO} \\
\mathrm{HOO} \cdot+\mathrm{NO} \longrightarrow & \mathrm{OH}+\mathrm{NO}_{2}
\end{aligned}
$$

David Collins

Numerade Educator

Problem 102

A reaction has the following mechanism: $$\begin{aligned}2 \mathrm{NO} \longrightarrow & \mathrm{N}_{2} \mathrm{O}_{2} \\\mathrm{~N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} & \longrightarrow \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O} \\
\mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow & \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\end{aligned}$$
What is the net overall change that occurs in this reaction? Identify any intermediates in the reaction.

Anthony Han

Numerade Educator

Problem 103

If the reaction $$\mathrm{NO}_{2}+\mathrm{CO} \longrightarrow \mathrm{NO}+\mathrm{CO}_{2}$$ occured by a one-step collision process, what would be the expected rate law for the reaction? The actual rate law is rate $=k\left[\mathrm{NO}_{2}\right]^{2}$. Could the reaction actually occur by a one-step collision between $\mathrm{NO}_{2}$ and CO? Explain.

David Collins

Numerade Educator

Problem 104

If the reaction $$2 \mathrm{NO}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2} \mathrm{~F}(g)$$ occurred by a one-step process, what would be the expected rate law for the reaction? The actual rate law is rate $=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{F}_{2}\right]$, why is this a better rate law?

David Collins

Numerade Educator

01:01

Problem 105

Consider the general reaction $$A B+C \longrightarrow A C+B$$ If this reaction occurs in one step, what would be the expected rate law for the reaction?

Anthony Han

Numerade Educator

Problem 106

Nitrogen dioxide reacts with carbon monoxide to produce nitrogen monoxide and carbon dioxide in the $$\text { reaction, } \mathrm{NO}_{2}(g)+\mathrm{CO}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g) .$$ The first, and rate determining, step in the reaction is proposed to be two $\mathrm{NO}_{2}$ molecules colliding to form $\mathrm{NO}_{3}$ and $\mathrm{NO}$. The $\mathrm{NO}_{3}$ intermediate then reacts with $\mathrm{CO}$ to form $\mathrm{CO}_{2}$. What is the rate law for this proposed mechanism?

Anthony Han

Numerade Educator

01:41

Problem 107

The oxidation of nitrogen monoxide with oxygen to nitrogen dioxide has a possible mechanism of$$2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2}(g)$$ $\mathrm{N}_{2} \mathrm{O}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$
What are the intermediates in the proposed mechanism? What is the balanced equation for the overall reaction? What is the rate law for the reaction?

David Collins

Numerade Educator

02:00

Problem 108

The reaction of chloroform and chlorine forms carbon tetrachloride and hydrogen chloride in the following proposed mechanism: $\begin{array}{rlr}\mathrm{Cl}_{2}(g) & \rightleftharpoons 2 \mathrm{Cl}(g) & & \text { (fast) } \\ \mathrm{Cl}(g)+\mathrm{CHCl}_{3}(g) & \longrightarrow \mathrm{HCl}(g)+\mathrm{CCl}_{3}(g) & & \text { (slow) } \\ \mathrm{CCl}_{3}(g)+\mathrm{Cl}(g) & \longrightarrow \mathrm{CCl}_{4}(g) & & \text { (fast) }\end{array}$ What are the intermediates in the proposed mechanism? What is the balanced equation for the overall reaction? What is the rate law for the reaction? Make a graph of concentration versus time for the formation of $\mathrm{C}_{2} \mathrm{H}_{4}$ and the decomposition of $\mathrm{C}_{4} \mathrm{H}_{8}$ on the same graph. What are the rates of formation of $\mathrm{C}_{2} \mathrm{H}_{4}$ at $t=1.00 \times 10^{3} \mathrm{~s}$ and $t=9.00 \times 10^{3} \mathrm{~s},$ and the rates of decomposition of $\mathrm{C}_{4} \mathrm{H}_{8}$ at $t=1.00 \times 10^{3} \mathrm{~s}$ and $t=9.00$
$\times 10^{3} \mathrm{~s}$ ? What can be said about the relationship between the values of the rates of formation and decomposition?

David Collins

Numerade Educator

04:43

Problem 109

The following data were collected for the reaction of cyclobutane, $\mathrm{C}_{4} \mathrm{H}_{8}(g)$, to form ethylene, $\mathrm{C}_{2} \mathrm{H}_{4}(g)$. Make a graph of concentration versus time for the formation of $\mathrm{C}_{2} \mathrm{H}_{4}$ and the decomposition of $\mathrm{C}_{4} \mathrm{H}_{8}$ on the same graph. What are the rates of formation of $\mathrm{C}_{2} \mathrm{H}_{4}$ at $t=1.00 \times 10^{3} \mathrm{~s}$ and $t=9.00 \times 10^{3} \mathrm{~s}$, and the rates of
decomposition of $\mathrm{C}_{4} \mathrm{H}_{8}$ at $t=1.00 \times 10^{3} \mathrm{~s}$ and $t=9.00$
$\times 10^{3} s$ ? What can be said about the relationship between the values of the rates of formation and decomposition?

Crystal Wang

Numerade Educator

01:42

Problem 110

The age of wine can be determined by measuring the trace amount of radioactive tritium, ${ }^{3} \mathrm{H}$, present in a sample. Tritium is formed from hydrogen in water vapor in the upper atmosphere by cosmic bombardment, so all naturally occurring water contains a small amount of this isotope. Once the water is in a bottle of wine, however, the formation of additional tritium from the water is negligible, so the tritium initially present gradually diminishes by a first-order radioactive decay with a half-life of 12.5 years. If a bottle of wine is found to have a tritium concentration that is $10.0 \%$ of freshly bottled wine, what is the age of the wine?

Anthony Han

Numerade Educator

01:06

Problem 111

On the following graph, label the products, reactant, $\Delta H_{\text {reaction }}$, the energy of activation $\left(E_{\mathrm{a}}\right)$ and the transition state. Is the reaction exothermic or endothermic? On the graph, draw a path for a catalyzed reaction.

David Collins

Numerade Educator

Problem 112

Carbon-14 dating can be used to estimate the age of formerly living materials because the uptake of carbon-14 from carbon dioxide in the atmosphere stops once the organism dies. If tissue samples from a mummy contain about $81.0 \%$ of the carbon-14 expected in living tissue, how old is the mummy? The half-life for decay of carbon-14 is 5730 years.

David Collins

Numerade Educator

Problem 113

What percentage of cesium chloride made from cesium-137 $\left(t_{1 / 2}=30 \mathrm{yr}\right)$ remains after 150 years? What chemical product forms?

David Collins

Numerade Educator

02:15

Problem 114

For the following reactions, predict how the rate of the reaction will change as the concentration of the reactants triple.
(a) $\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2} \quad$ rate $=k\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$
(b) $2 \mathrm{HI} \longrightarrow \mathrm{H}_{2}+\mathrm{I}_{2}$ rate $=k[\mathrm{HI}]^{2}$
(c) $\mathrm{ClOO} \longrightarrow \mathrm{Cl}+\mathrm{O}_{2} \quad$ rate $=k$
(d) $\mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{2}^{-}(a q) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}$ rate $=k\left[\mathrm{NH}_{4}^{+}\right]\left[\mathrm{NO}_{2}^{-}\right]$
(e) $2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
rate $=k\left[\mathrm{H}_{2}\right][\mathrm{NO}]^{2}$

Anthony Han

Numerade Educator

Problem 115

One of the reactions that occurs in polluted air in urban areas is $2 \mathrm{NO}_{2}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{O}_{2}(g) . \mathrm{It}$ is believed that a species with the formula $\mathrm{NO}_{3}$ is involved in the mechanism, and the observed rate law for the overall reaction is rate $=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{O}_{3}\right] .$ Propose a mechanism for this reaction that includes the species $\mathrm{NO}_{3}$ and is consistent with the observed rate law.

David Collins

Numerade Educator

03:28

Problem 116

Suppose a reaction occurs with the following mechanism: (1) $2 A \rightleftharpoons A_{2}$ $($ fast $)$(2) $A_{2}+E \longrightarrow B+C$(slow) in which the first step is a very rapid reversible reaction that can be considered to be essentially an equilibrium (forward and reverse reactions occurring at the same rate) and the second is a slow step.
(a) Write the rate law for the forward reaction in step (1).
(b) Write the rate law for the reverse reaction in step (1).
(c) Write the rate law for the rate-determining step.
(d) What is the chemical equation for the net reaction that occurs in this chemical change?
Use the results of parts (a) and (b) to rewrite the rate law of the rate-determining step in terms of the concentrations of the reactants in the overall balanced chemical equation for the reaction.

Anthony Han

Numerade Educator

08:29

Problem 117

The decomposition of urea, $\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO},$ in $0.10 \mathrm{M}$ $\mathrm{HCl}$ follows the equation $$\begin{array}{c}\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}(a q)+2 \mathrm{H}^{+}(a q)+\mathrm{H}_{2} \mathrm{O} \longrightarrow 2 \mathrm{NH}_{4}^{+}(a q)+\mathrm{CO}_{2}(g) \\\text { At } 65^{\circ} \mathrm{C}, k=5.84 \times 10^{-6} \mathrm{~min}^{-1}, \text {and at } 75^{\circ} \mathrm{C}, k=\end{array}$$ $2.25 \times 10^{-5} \mathrm{~min}^{-1}$. If this reaction is run at $85^{\circ} \mathrm{C}$ starting with a urea concentration of $0.0020 \mathrm{M}$, how many minutes will it take for the urea concentration to drop to $0.0012 \mathrm{M}$ ?

Oluwapelumi Kolawole

Numerade Educator

Problem 118

Show that for a reaction that obeys the general rate law, rate $=k[A]^{n}$ a graph of $\log ($ rate $)$ versus $\log [A]$ should yield a straight line with a slope equal to the order of the reaction. For the reaction in Problem $13.57,$ measure the rate of the reaction at $t=150,300,450,$ and $600 \mathrm{~s}$. Then graph $\log ($ rate $)$ versus $\log \left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$ and
determine the order of the reaction with respect to $\mathrm{SO}_{2} \mathrm{Cl}_{2}$.

David Collins

Numerade Educator

01:51

Problem 119

The rates of many reactions approximately double for each $10^{\circ} \mathrm{C}$ rise in temperature. Assuming a starting temperature of $25^{\circ} \mathrm{C}$, what would the activation energy be, in $\mathrm{kJ} \mathrm{mol}^{-1}$, if the rate of a reaction were to be twice as large at $35^{\circ} \mathrm{C} ?$

Anthony Han

Numerade Educator

Problem 120

If the rate constant for a first-order reaction is doubled by heating the reaction, what happens to the rate of the reaction if the concentration is kept the same?

Anthony Han

Numerade Educator

01:02

Problem 121

For the following potential energy diagram, which path represents a catalyzed reaction? How many steps would be proposed in the mechanism for the catalyzed reaction, and which step would be rate-determining?

David Collins

Numerade Educator

06:41

Problem 122

The development of a photographic image on film is a process controlled by the kinetics of the reduction of silver halide by a developer. The time required for development at a particular temperature is inversely proportional to the rate constant for the process. Below are published data on development times for Kodak's TriX film using Kodak $\mathrm{D}-76$ developer. From these data, estimate the activation energy (in units of $\mathrm{kJ} \mathrm{mol}^{-1}$ ) for the development process. Also estimate the development time at $15^{\circ} \mathrm{C}$

Susan Hallstrom

Numerade Educator

06:36

Problem 123

The rate at which crickets chirp depends on the ambient temperature, because crickets are cold-blooded insects whose body temperature follows the temperature of their environment. It has been found that the Celsius temperature can be estimated by counting the number of chirps in 8 seconds and then adding $4 .$ In other words, $t_{c}=($ number of chirps in 8 seconds $)+4$
(a) Calculate the number of chirps in 8 seconds for temperatures of $20,25,30,$ and $35^{\circ} \mathrm{C}$.
(b) The number of chirps per unit of time is directly proportional to the rate constant for a biochemical reaction involved in the cricket's chirp.
(c) On the basis of this assumption, make a graph of $\ln ($ chirps in $8 \mathrm{~s}$ ) versus $(1 / T)$
(d) Calculate the activation energy for the biochemical reaction involved.
(e) How many chirps would a cricket make in 8 seconds at a temperature of $40^{\circ} \mathrm{C}$ ?

David Mccaslin

Numerade Educator

01:35

Problem 124

The cooking of an egg involves the denaturation of a protein called albumen. The time required to achieve a particular degree of denaturation is inversely proportional to the rate constant for the process. This reaction has a high activation energy, $E_{\mathrm{a}}=418 \mathrm{~kJ} \mathrm{~mol}^{-1} .$ Calculate how long it would take to cook a traditional threeminute egg on top of Mt. McKinley in Alaska on a day when the atmospheric pressure there is 355 torr.

David Collins

Numerade Educator

02:01

Problem 125

The following question is based on Chemistry Outside the Classroom 13.1. The reaction of hydrogen and bromine appears to follow the mechanism shown, $$\begin{aligned}\mathrm{Br}_{2} & \longrightarrow 2 \mathrm{Br}^{*} \\\mathrm{Br} \cdot+\mathrm{H}_{2} & \longrightarrow \mathrm{HBr}+\mathrm{H} \\\mathrm{H} \cdot+\mathrm{Br}_{2} & \longrightarrow \mathrm{HBr}+\mathrm{Br} \\2 \mathrm{Br} \cdot &\longrightarrow\mathrm{Br}_{2}\end{aligned}$$
(a) Identify the initiation step in the mechanism.
(b) Identify any propagation steps.
(c) Identify the termination step.
(d) The mechanism also contains the reaction
$$\mathrm{H} \cdot+\mathrm{HBr} \longrightarrow \mathrm{H}_{2}+\mathrm{Br}$$ How does this reaction affect the rate of formation of $\mathrm{HBr}$ ?

Anthony Han

Numerade Educator

01:07

Problem 126

Show that the following two mechanisms give the same net overall reaction. Mechanism 1 $\mathrm{OCl}^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{HOCl}+\mathrm{OH}^{-}$ $\mathrm{HOCl}+\mathrm{I}^{-} \longrightarrow \mathrm{HOI}+\mathrm{Cl}^{-}$ $\mathrm{HOI}+\mathrm{OH}^{-} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{OI}^{-}$ Mechanism 2 $\begin{aligned} \mathrm{OCl}^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow & \mathrm{HOCl}+\mathrm{OH}^{-} \\ \mathrm{I}^{-}+\mathrm{HOCl} & \longrightarrow \mathrm{ICl}+\mathrm{OH}^{-} \\ \mathrm{ICl}+2 \mathrm{OH}^{-} & \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-}+\mathrm{H}_{2} \mathrm{O} \end{aligned}$

David Collins

Numerade Educator

Problem 127

The experimental rate law for the reaction $$ \mathrm{NO}_{2}+\mathrm{CO} \longrightarrow \mathrm{CO}_{2}+\mathrm{NO}
$$ is rate $=k\left[\mathrm{NO}_{2}\right]^{2}$. If the mechanism is $$\begin{array}{rlr}2 \mathrm{NO}_{2} & \longrightarrow \mathrm{NO}_{3}+\mathrm{NO} & (s l o w) \\ \mathrm{NO}_{3}+\mathrm{CO} \longrightarrow & \mathrm{NO}_{2}+\mathrm{CO}_{2} & \text { (fast) } \end{array}$$ show that the predicted rate law is the same as the experimental rate law.

Anthony Han

Numerade Educator

Problem 128

Radioactive samples are considered to become nonhazardous after 10 half-lives. If the half-life is less than 88 days, the radioactive sample can be stored through a decay-in-storage program in which the material is kept in a lead-lined cabinet for at least 10 half-lives. What percent of the initial material will remain after 10 half-lives?

David Collins

Numerade Educator

01:32

Problem 129

Use a spreadsheet to generate a graph for the data in (a) Problem 13.95 and (b) Problem 13.96. Obtain the equation for the straight line and then determine the slope. Use this slope to calculate the activation energy in $\mathrm{kJ} \mathrm{mol}^{-1}$

David Collins

Numerade Educator

04:29

Problem 130

Use a spreadsheet to generate separate graphs for the data
(a) $13.53,$ given in problems
(b) $13.54,$ and
(c) 13.109 . Fit each curve to an appropriate polynomial equation trying several exponents to determine the best fit. Next, take the first derivative of the best equation to determine the slope at the desired time and using this slope, calculate the answer. If you did these calculations by hand, how do the results compare?

Ankit Gupta

Numerade Educator

Problem 131

Radon-220 is radioactive, and decays into polonium- 216 by emitting an alpha particle. This is a firstorder process with a rate constant of $0.0125 \mathrm{~s}^{-1}$. How many alpha particles per second will be emitted by one picogram of ${ }^{220} \mathrm{Rn}$ inhaled on a particle of dust?

David Collins

Numerade Educator

03:26

Problem 132

The catalyzed decomposition of ethanol at $327^{\circ} \mathrm{C}$ has a rate constant of $4.00 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. The plot of concentration of ethanol versus time gives a straight line. The balanced equation for this reaction is $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ If the initial concentration of ethanol is $0.020 \mathrm{~mol} \mathrm{~L}^{-1}$ how long will it take for the pressure to reach $1.4 \mathrm{~atm}$ at $327^{\circ} \mathrm{C} ?$

David Collins

Numerade Educator

03:59

Problem 133

On December $19,2007,$ the T2 Laboratories, Inc., reactor exploded in a runaway reaction. The reaction of methyl cyclopentadienyl dimer and sodium produces sodium methyl cyclopentadiene and hydrogen: The reactor has to be cooled when its temperature reaches $182^{\circ} \mathrm{C}$. On the day of the explosion, the cooling system malfunctioned and the reactor reached $199{ }^{\circ} \mathrm{C},$ at which point a second, more exothermic reaction began to occur. The typical energy of activation for an organic reaction is about $50 \mathrm{~kJ} / \mathrm{mol}$. The heat of this reaction is $40 \mathrm{~kJ} \mathrm{~mol}^{-1},$ and the heat capacity for an industrial scale reaction (i.e., $10,000 \mathrm{~mol}$ ) can be $7.5 \times 10^{6} \mathrm{~J}^{\circ} \mathrm{C}^{-1}$. If the rate constant for a typical reaction is $1 \times 10^{-5} \mathrm{~s}^{-1}$ at $25^{\circ} \mathrm{C}$, what will be the rate constant, if all the heat is supplied to the reaction all at once, without any external cooling? If the reaction were started at $182^{\circ} \mathrm{C}$, would the reaction reach $199{ }^{\circ} \mathrm{C}$ if all the heat were released at once?

Farouq Hanonn

Numerade Educator

01:17

Problem 134

Primary explosives are extremely sensitive to impact, friction, or static electricity, and only a small amount of energy is required to initiate the explosion. Secondary and tertiary explosives require more energy to start a reaction, and often primary explosives are used to initiate their reaction. Using a potential energy diagram, show how a primary explosive would start the reaction of a secondary explosive.

David Collins

Numerade Educator

01:14

Problem 135

Provide three examples of ordinary occurrences that mimic a reaction mechanism and have a rate-limiting step.

David Collins

Numerade Educator

Problem 136

Can a reaction have a negative activation energy? Explain your response.

David Collins

Numerade Educator

01:10

Problem 137

Assume you have a three-step mechanism. Would the potential energy diagram have three peaks? If so, how would you distinguish the rate-limiting step?

David Collins

Numerade Educator

Problem 138

What range of ages can ${ }^{14} \mathrm{C}$ dating reliably determine?

David Collins

Numerade Educator

Problem 139

Why are initial reaction rates used to determine rate laws?

David Collins

Numerade Educator

Problem 140

If a reaction is reversible (i.e., the products can react to re-form the reactants), what would the rate law look like?

David Collins

Numerade Educator

01:09

Problem 141

The ozone layer protects us from high-energy radiation. The description of how the ozone layer works is a kinetics problem concerning the formation and destruction of ozone to produce a steady state. How can we write this mathematically, assuming that the processes are elementary reactions?

David Collins

Numerade Educator