Chemistry

Paul Flowers, Klaus Theopold, Richard Langley

Chapter 12 Kinetics - all with Video Answers

Educators

Chapter Questions

03:11

Problem 1

What is the difference between average rate, initial rate, and instantaneous rate?

Alexandra Woodruff

Numerade Educator

02:11

Ozone decomposes to oxygen according to the equation $2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g) .$ Write the equation that relates the rate expressions for this reaction in terms of the disappearance of $\mathrm{O}_{3}$ and the formation of oxygen.

Rikhil Makwana

Numerade Educator

04:21

Problem 3

In the nuclear industry, chlorine trifluoride is used to prepare uranium hexafluoride, a volatile compound of uranium used in the separation of uranium isotopes. Chlorine trifluoride is prepared by the reaction $\mathrm{Cl}_{2}(g)+3 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{ClF}_{3}(g) .$ Write the equation that relates the rate expressions for this reaction in terms of the disappearance of $\mathrm{Cl}_{2}$ and $\mathrm{F}_{2}$ and the formation of $\mathrm{ClF}_{3}$

Alexandra Woodruff

Numerade Educator

08:04

Problem 4

A study of the rate of dimerization of $\mathrm{C}_{4} \mathrm{H}_{6}$ gave the data shown in the table: $$2 \mathrm{C}_{4} \mathrm{H}_{6} \longrightarrow \mathrm{C}_{8} \mathrm{H}_{12}$$ $$\begin{array}{|c|c|c|c|c|c|}\hline \text { Hue (9) } & 0 & 1600 & 3200 & 4800 & 6200 \\\hline \text { (elid } 00 & 1.00 \times 10^{-2} & 5.04 \times 10^{-3} & 3.37 \times 10^{-3} & 2.53 \times 10^{-3} & 2.08 \times 10^{-3} \\\hline\end{array}$$
(a) Determine the average rate of dimerization between 0 s and 1600 s, and between 1600 s and 3200 s.
(b) Estimate the instantaneous rate of dimerization at 3200 s from a graph of time versus $\left[\mathrm{C}_{4} \mathrm{H}_{6}\right]$. What are the units of this rate?
(c) Determine the average rate of formation of $\mathrm{C}_{8} \mathrm{H}_{12}$ at $1600 \mathrm{s}$ and the instantaneous rate of formation at $3200 \mathrm{s}$ from the rates found in parts (a) and (b).

Mihir Paranjape

Numerade Educator

07:01

Problem 5

A study of the rate of the reaction represented as $2 A \longrightarrow B$ gave the following data:
$$\begin{array}{|c|c|c|c|c|c|c|c|}\hline \text { Time (e) } & 0.0 & 5.0 & 10.0 & 15.0 & 20.0 & 25.0 & 35.0 \\\hline \text { A1 }(0) & 1.00 & 0.775 & 0.625 & 0.465 & 0.360 & 0.285 & 0.230 \\
\hline\end{array}$$
(a) Determine the average rate of disappearance of $A$ between $0.0 \mathrm{s}$ and $10.0 \mathrm{s}$, and between $10.0 \mathrm{s}$ and $20.0 \mathrm{s}$.
(b) Estimate the instantaneous rate of disappearance of $A$ at 15.0 s from a graph of time versus $[A]$. What are the units of this rate?
(c) Use the rates found in parts (a) and (b) to determine the average rate of formation of $B$ between 0.00 s and 10.0 s, and the instantaneous rate of formation of $B$ at 15.0 s.

Mihir Paranjape

Numerade Educator

01:44

Problem 6

Consider the following reaction in aqueous solution: $5 \mathrm{Br}^{-}(a q)+\mathrm{BrO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{Br}_{2}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l)$ If the rate of disappearance of $\operatorname{Br}^{-}(a q)$ at a particular moment during the reaction is $3.5 \times 10^{-4} \mathrm{mol} \mathrm{L}^{-1} s^{-1},$ what is the rate of appearance of $\mathrm{Br}_{2}(a q)$ at that moment?

Mihir Paranjape

Numerade Educator

05:17

Problem 7

Describe the effect of each of the following on the rate of the reaction of magnesium metal with a solution of hydrochloric acid: the molarity of the hydrochloric acid, the temperature of the solution, and the size of the pieces of magnesium.

Alexandra Woodruff

Numerade Educator

01:57

Problem 8

Explain why an egg cooks more slowly in boiling water in Denver than in New York City. (Hint: Consider the effect of temperature on reaction rate and the effect of pressure on boiling point.)

Rikhil Makwana

Numerade Educator

05:26

Problem 9

Go to the PhET Reactions \& Rates (http:Ilopenstaxcollege.org/l/16PHETreaction) interactive. Use the single Collision tab to represent how the collision between monatomic oxygen (O) and carbon monoxide (CO) results in the breaking of one bond and the formation of another. Pull back on the red plunger to release the atom and observe the results. Then, click on "Reload Launcher" and change to "Angled shot" to see the difference.
(a) What happens when the angle of the collision is changed?
(b) Explain how this is relevant to rate of reaction.

Crystal Wang

Numerade Educator

01:16

Problem 10

In the PhET Reactions \& Rates (http://openstaxcollege.orgII/16PHETreaction) interactive, use the "Many Collisions" tab to observe how multiple atoms and molecules interact under varying conditions. Select a molecule to pump into the chamber. Set the initial temperature and select the current amounts of each reactant. Select "Show bonds" under Options. How is the rate of the reaction affected by concentration and temperature?

Rikhil Makwana

Numerade Educator

01:26

Problem 11

In the PhET Reactions \& Rates (http:Ilopenstaxcollege.orgII/16PHETreaction) interactive, on the Many Collisions tab, set up a simulation with 15 molecules of A and 10 molecules of BC. Select “Show Bonds" under Options.
(a) Leave the Initial Temperature at the default setting. Observe the reaction. Is the rate of reaction fast or slow?
(b) Click "Pause" and then "Reset All," and then enter 15 molecules of A and 10 molecules of BC once again. Select "Show Bonds" under Options. This time, increase the initial temperature until, on the graph, the total average energy line is completely above the potential energy curve. Describe what happens to the reaction.

Crystal Wang

Numerade Educator

01:53

Problem 12

How do the rate of a reaction and its rate constant differ?

Rikhil Makwana

Numerade Educator

04:28

Problem 13

Doubling the concentration of a reactant increases the rate of a reaction four times. With this knowledge, answer the following questions:
(a) What is the order of the reaction with respect to that reactant?
(b) Tripling the concentration of a different reactant increases the rate of a reaction three times. What is the order of the reaction with respect to that reactant?

Alexandra Woodruff

Numerade Educator

02:44

Problem 14

Tripling the concentration of a reactant increases the rate of a reaction nine-fold. With this knowledge, answer the following questions:
(a) What is the order of the reaction with respect to that reactant?
(b) Increasing the concentration of a reactant by a factor of four increases the rate of a reaction four-fold. What is the order of the reaction with respect to that reactant?

Mihir Paranjape

Numerade Educator

04:52

Problem 15

How much and in what direction will each of the following affect the rate of the reaction:
$\mathrm{CO}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{NO}(g)$ if the rate law for the reaction is rate $=k\left[\mathrm{NO}_{2}\right]^{2} ?$
(a) Decreasing the pressure of $\mathrm{NO}_{2}$ from 0.50 atm to 0.250 atm.
(b) Increasing the concentration of CO from $0.01 M$ to $0.03 M$.

Alexandra Woodruff

Numerade Educator

02:09

Problem 16

How will each of the following affect the rate of the reaction: $\operatorname{CO}(g)+\mathrm{NO}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{NO}(g)$ if the rate law for the reaction is rate $=k\left[\mathrm{NO}_{2}\right][\mathrm{CO}] ?$
(a) Increasing the pressure of $\mathrm{NO}_{2}$ from 0.1 atm to $0.3 \mathrm{atm}$
(b) Increasing the concentration of CO from $0.02 M$ to $0.06 M$.

Rikhil Makwana

Numerade Educator

01:06

Problem 17

Regular flights of supersonic aircraft in the stratosphere are of concern because such aircraft produce nitric oxide, NO, as a byproduct in the exhaust of their engines. Nitric oxide reacts with ozone, and it has been suggested that this could contribute to depletion of the ozone layer. The reaction $\mathrm{NO}+\mathrm{O}_{3} \longrightarrow \mathrm{NO}_{2}+\mathrm{O}_{2}$ is first order with respect to both NO and $\mathrm{O}_{3}$ with a rate constant of $2.20 \times 10^{7} \mathrm{L} / \mathrm{mol} / \mathrm{s}$. What is the instantaneous rate of disappearance of NO when [NO] = 3.3 10 - 6 M and [O 3] = 5.9 $10^{-7} \mathrm{M}$?

Mihir Paranjape

Numerade Educator

01:04

Problem 18

Radioactive phosphorus is used in the study of biochemical reaction mechanisms because phosphorus atoms are components of many biochemical molecules. The location of the phosphorus (and the location of the molecule it is bound in) can be detected from the electrons (beta particles) it produces: $$\begin{aligned}&\begin{array}{l}32 \mathrm{P} \longrightarrow 32 \mathrm{S}+\mathrm{e}^{-} \\15^{-} 16^{-}\end{array}\\&\text { rate }=4.85 \times 10^{-2} \text {day }^{-1}\left[^{32} \mathrm{P}\right]\end{aligned}$$
What is the instantaneous rate of production of electrons in a sample with a phosphorus concentration of 0.0033 $\mathrm{M}$ ?

Mihir Paranjape

Numerade Educator

00:56

Problem 19

The rate constant for the radioactive decay of $^{14} \mathrm{C}$ is $1.21 \times 10^{-4}$ year $^{-1}$. The products of the decay are nitrogen atoms and electrons (beta particles):
$_{6}^{14} \mathrm{C} \longrightarrow_{7}^{14} \mathrm{N}+\mathrm{e}^{-}$
rate $=k\left[\begin{array}{l}14 \\ 6\end{array}\right]$ What is the instantaneous rate of production of $\mathrm{N}$ atoms in a sample with a carbon-14 content of $6.5 \times 10^{-9} \mathrm{M}$ ?

Mihir Paranjape

Numerade Educator

01:14

Problem 20

The decomposition of acetaldehyde is a second order reaction with a rate constant of $4.71 \times 10^{-8} \mathrm{L} \mathrm{mol}^{-1} \mathrm{s}^{-1}$ What is the instantaneous rate of decomposition of acetaldehyde in a solution with a concentration of $5.55 \times 10^{-4}$
$M ?$

Mihir Paranjape

Numerade Educator

00:52

Problem 21

Alcohol is removed from the bloodstream by a series of metabolic reactions. The first reaction produces acetaldehyde; then other products are formed. The following data have been determined for the rate at which alcohol is removed from the blood of an average male, although individual rates can vary by $25-30 \% .$ Women metabolize alcohol a little more slowly than men: Determine the rate law, the rate constant, and the overall order for this reaction.

Mihir Paranjape

Numerade Educator

00:55

Problem 22

Under certain conditions the decomposition of ammonia on a metal surface gives the following data:
Determine the rate law, the rate constant, and the overall order for this reaction.

Mihir Paranjape

Numerade Educator

02:57

Problem 23

Nitrosyl chloride, NOCl, decomposes to NO and Cl_ $2 \mathrm{NOCl}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$ Determine the rate law, the rate constant, and the overall order for this reaction from the following data:

Mihir Paranjape

Numerade Educator

03:21

Problem 24

From the following data, determine the rate law, the rate constant, and the order with respect to $A$ for the reaction $A \longrightarrow 2 C$.

Mihir Paranjape

Numerade Educator

03:43

Problem 25

Nitrogen monoxide reacts with chlorine according to the equation:
$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)$
The following initial rates of reaction have been observed for certain reactant concentrations:
What is the rate law that describes the rate's dependence on the concentrations of $\mathrm{NO}$ and $\mathrm{Cl}_{2}$ ? What is the rate constant? What are the orders with respect to each reactant?

Mihir Paranjape

Numerade Educator

05:03

Problem 26

Hydrogen reacts with nitrogen monoxide to form dinitrogen monoxide (laughing gas) according to the equation: $\mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
Determine the rate law, the rate constant, and the orders with respect to each reactant from the following data:

Mihir Paranjape

Numerade Educator

03:13

Problem 27

For the reaction $A \longrightarrow B+C,$ the following data were obtained at $30^{\circ} \mathrm{C}$ :
(a) What is the order of the reaction with respect to $[A]$, and what is the rate law?
(b) What is the rate constant?

Mihir Paranjape

Numerade Educator

03:52

Problem 28

For the reaction $Q \longrightarrow W+X,$ the following data were obtained at $30^{\circ} \mathrm{C}$ :
(a) What is the order of the reaction with respect to $[Q]$, and what is the rate law?
(b) What is the rate constant?

Mihir Paranjape

Numerade Educator

03:32

Problem 29

The rate constant for the first-order decomposition at $45^{\circ} \mathrm{C}$ of dinitrogen pentoxide, $\mathrm{N}_{2} \mathrm{O}_{5}$, dissolved in chloroform, $\mathrm{CHCl}_{3},$ is $6.2 \times 10^{-4} \mathrm{min}^{-1}$ $2 \mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}$ What is the rate of the reaction when $\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]=0.40 \mathrm{M}$ ?

Alexandra Woodruff

Numerade Educator

01:14

Problem 30

The annual production of $\mathrm{HNO}_{3}$ in 2013 was 60 million metric tons Most of that was prepared by the following sequence of reactions, each run in a separate reaction vessel.
(a) $4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
(b) $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$
(c) $3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)$
The first reaction is run by burning ammonia in air over a platinum catalyst. This reaction is fast. The reaction in equation (c) is also fast. The second reaction limits the rate at which nitric acid can be prepared from ammonia. If equation (b) is second order in NO and first order in $\mathrm{O}_{2}$, what is the rate of formation of $\mathrm{NO}_{2}$ when the oxygen concentration is $0.50 \mathrm{M}$ and the nitric oxide concentration is $0.75 \mathrm{M}$ ? The rate constant for the reaction is $5.8 \times$ $10^{-6} \mathrm{L}^{2} \mathrm{mol}^{-2} \mathrm{s}^{-1}$.

Mihir Paranjape

Numerade Educator

06:06

Problem 31

The following data have been determined for the reaction:
$\mathrm{I}^{-}+\mathrm{OCl}^{-} \longrightarrow \mathrm{IO}^{-}+\mathrm{Cl}^{-}$
Determine the rate law and the rate constant for this reaction.

Mihir Paranjape

Numerade Educator

03:04

Problem 32

Describe how graphical methods can be used to determine the order of a reaction and its rate constant from a series of data that includes the concentration of $A$ at varying times.

Rikhil Makwana

Numerade Educator

02:29

Problem 33

Use the data provided to graphically determine the order and rate constant of the following reaction: $\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2}$

Mihir Paranjape

Numerade Educator

04:49

Problem 34

Pure ozone decomposes slowly to oxygen, $2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g) .$ Use the data provided in a graphical method and determine the order and rate constant of the reaction.

David Collins

Numerade Educator

02:26

Problem 35

From the given data, use a graphical method to determine the order and rate constant of the following reaction: $2 X \longrightarrow Y+Z$

Rikhil Makwana

Numerade Educator

01:02

Problem 36

What is the half-life for the first-order decay of phosphorus-32? $$\left(\frac{32}{15} \mathrm{P} \longrightarrow \frac{32}{16} \mathrm{S}+\mathrm{e}^{-}\right)$$ The rate constant for the decay is $4.85 \times 10^{-2}$ day $^{-1}$.

Mihir Paranjape

Numerade Educator

01:04

Problem 37

What is the half-life for the first-order decay of carbon-14? $$\left(\begin{array}{c}14 \\6
\end{array} \mathbf{C} \longrightarrow_{7}^{14} \mathbf{N}+\mathrm{e}^{-}\right)$$ The rate constant for the decay is $1.21 \times 10^{-4}$ year $^{-1}$.

Mihir Paranjape

Numerade Educator

00:52

Problem 38

What is the half-life for the decomposition of NOCl when the concentration of NOCl is 0.15 $M$ ? The rate constant for this second-order reaction is $8.0 \times 10^{-8} \mathrm{L} \mathrm{mol}^{-1} \mathrm{s}^{-1}$.

Mihir Paranjape

Numerade Educator

00:53

Problem 39

What is the half-life for the decomposition of $\mathrm{O}_{3}$ when the concentration of $\mathrm{O}_{3}$ is $2.35 \times 10^{-6} \mathrm{M}$ ? The rate constant for this second-order reaction is $50.4 \mathrm{L} \mathrm{mol}^{-1} \mathrm{h}^{-1}$.

Mihir Paranjape

Numerade Educator

00:55

Problem 40

The reaction of compound $A$ to give compounds $C$ and $D$ was found to be second-order in $A$. The rate constant for the reaction was determined to be $2.42 \mathrm{L} \mathrm{mol}^{-1} \mathrm{s}^{-1} .$ If the initial concentration is $0.500 \mathrm{mol} / \mathrm{L},$ what is the value of $t_{1 / 2} ?$

Mihir Paranjape

Numerade Educator

05:12

Problem 41

The half-life of a reaction of compound $A$ to give compounds $D$ and $E$ is 8.50 min when the initial concentration of $A$ is 0.150 M. How long will it take for the concentration to drop to 0.0300 M if the reaction is (a) first order with respect to $A$ or (b) second order with respect to $A$ ?

Mihir Paranjape

Numerade Educator

01:29

Problem 42

Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of $3 \times 10^{4} \mathrm{g} / \mathrm{mol}$ that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalyzed reactions can be complex, at low concentrations this reaction can be described by a rate law that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: $1.0 \mathrm{L}$ of a solution containing $0.15 \mu \mathrm{g}\left(0.15 \times 10^{-6} \mathrm{g}\right)$ of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant.

Stephen Ho

Numerade Educator

03:06

Problem 43

Both technetium-99 and thallium-201 are used to image heart muscle in patients with suspected heart problems. The half-lives are $6 \mathrm{h}$ and $73 \mathrm{h}$, respectively. What percent of the radioactivity would remain for each of the isotopes after 2 days (48 h)?

Rikhil Makwana

Numerade Educator

05:18

Problem 44

There are two molecules with the formula $\mathrm{C}_{3} \mathrm{H}_{6} .$ Propene, $\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2},$ is the monomer of the polymer polypropylene, which is used for indoor-outdoor carpets. Cyclopropane is used as an anesthetic:
When heated to $499^{\circ} \mathrm{C},$ cyclopropane rearranges (isomerizes) and forms propene with a rate constant of $5.95 \times 10^{-4} \mathrm{s}^{-1} .$ What is the half-life of this reaction? What fraction of the cyclopropane remains after $0.75 \mathrm{h}$ at 499
"C?

Alexandra Woodruff

Numerade Educator

03:35

Problem 45

Fluorine-18 is a radioactive isotope that decays by positron emission to form oxygen-18 with a half-life of 109.7 min. (A positron is a particle with the mass of an electron and a single unit of positive charge; the equation is 18 18 F $\longrightarrow_{18}^{8} \mathrm{O}+_{+1}^{0}$ e) Physicians use $^{18} \mathrm{F}$ to study the brain by injecting a quantity of fluoro-substituted glucose into $^{9} \mathrm{f}^{2} \mathrm{F}$, the blood of a patient. The glucose accumulates in the regions where the brain is active and needs nourishment.
(a) What is the rate constant for the decomposition of fluorine-18?
(b) If a sample of glucose containing radioactive fluorine- 18 is injected into the blood, what percent of the radioactivity will remain after 5.59 h?
(c) How long does it take for 99.99\% of the 18 F to decay?

Mihir Paranjape

Numerade Educator

03:01

Problem 46

Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for $\frac{1}{64}$ of the initial dose to remain in the athlete's body?

Mihir Paranjape

Numerade Educator

02:33

Problem 47

Recently, the skeleton of King Richard III was found under a parking lot in England. If tissue samples from the skeleton contain about $93.79 \%$ of the carbon- 14 expected in living tissue, what year did King Richard III die? The half-life for carbon-14 is 5730 years.

Mihir Paranjape

Numerade Educator

03:27

Problem 48

Nitroglycerin is an extremely sensitive explosive. In a series of carefully controlled experiments, samples of the explosive were heated to $160^{\circ} \mathrm{C}$ and their first-order decomposition studied. Determine the average rate constants for each experiment using the following data:

Crystal Wang

Numerade Educator

04:31

Problem 49

For the past 10 years, the unsaturated hydrocarbon 1,3 -butadiene $$\left(\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2}\right)$$ has ranked 38th among the top 50 industrial chemicals. It is used primarily for the manufacture of synthetic rubber. An isomer exists also as cyclobutene: The isomerization of cyclobutene to butadiene is first-order and the rate constant has been measured as $2.0 \times 10^{-4}$
$\mathrm{s}^{-1}$ at $150^{\circ} \mathrm{C}$ in a 0.53 -L flask. Determine the partial pressure of cyclobutene and its concentration after 30.0 minutes if an isomerization reaction is carried out at $150^{\circ} \mathrm{C}$ with an initial pressure of 55 torr.

Rikhil Makwana

Numerade Educator

04:36

Problem 50

Chemical reactions occur when reactants collide. What are two factors that may prevent a collision from producing a chemical reaction?

Alexandra Woodruff

Numerade Educator

02:04

Problem 51

When every collision between reactants leads to a reaction, what determines the rate at which the reaction occurs?

Rikhil Makwana

Numerade Educator

03:44

Problem 52

What is the activation energy of a reaction, and how is this energy related to the activated complex of the reaction?

Alexandra Woodruff

Numerade Educator

01:17

Problem 53

Account for the relationship between the rate of a reaction and its activation energy.

Rikhil Makwana

Numerade Educator

02:00

Problem 54

Describe how graphical methods can be used to determine the activation energy of a reaction from a series of data that includes the rate of reaction at varying temperatures.

Stephen Ho

Numerade Educator

01:45

Problem 55

How does an increase in temperature affect rate of reaction? Explain this effect in terms of the collision theory of the reaction rate.

Rikhil Makwana

Numerade Educator

01:48

Problem 56

The rate of a certain reaction doubles for every $10^{\circ} \mathrm{C}$ rise in temperature.
(a) How much faster does the reaction proceed at $45^{\circ} \mathrm{C}$ than at $25^{\circ} \mathrm{C}$ ?
(b) How much faster does the reaction proceed at $95^{\circ} \mathrm{C}$ than at $25^{\circ} \mathrm{C}$ ?

Mihir Paranjape

Numerade Educator

02:55

Problem 57

In an experiment, a sample of $\mathrm{NaClO}_{3}$ was $90 \%$ decomposed in 48 min. Approximately how long would this decomposition have taken if the sample had been heated $20^{\circ} \mathrm{C}$ higher? (Hint: Assume the rate doubles for each 10 "C rise in temperature.)

Mihir Paranjape

Numerade Educator

02:00

Problem 58

The rate constant at $325^{\circ} \mathrm{C}$ for the decomposition reaction $\mathrm{C}_{4} \mathrm{H}_{8} \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4}$ is $6.1 \times 10^{-8} \mathrm{s}^{-1},$ and the activation energy is $261 \mathrm{kJ}$ per mole of $\mathrm{C}_{4} \mathrm{H}_{8}$. Determine the frequency factor for the reaction.

Mihir Paranjape

Numerade Educator

03:43

Problem 59

The rate constant for the decomposition of acetaldehyde, $\mathrm{CH}_{3} \mathrm{CHO}$, to methane, $\mathrm{CH}_{4}$, and carbon monoxide, CO, in the gas phase is $1.1 \times 10^{-2} \mathrm{L} \mathrm{mol}^{-1} \mathrm{s}^{-1}$ at $703 \mathrm{K}$ and $4.95 \mathrm{L} \mathrm{mol}^{-1} \mathrm{s}^{-1}$ at $865 \mathrm{K}$. Determine the activation energy for this decomposition.

Mihir Paranjape

Numerade Educator

06:33

Problem 60

An elevated level of the enzyme alkaline phosphate (ALP) in human serum is an indication of possible liver or bone disorder. The level of serum ALP is so low that it is very difficult to measure directly. However, ALP catalyzes a number of reactions, and its relative concentration can be determined by measuring the rate of one of these reactions under controlled conditions. One such reaction is the conversion of p-nitrophenyl phosphate (PNPP) to p-nitrophenoxide ion (PNP) and phosphate ion. Control of temperature during the test is very important; the rate of the reaction increases 1.47 times if the temperature changes from $30^{\circ} \mathrm{C}$ to $37^{\circ} \mathrm{C}$. What is the activation energy for the ALP-catalyzed conversion of PNPP to PNP and phosphate?

Alexandra Woodruff

Numerade Educator

00:49

Problem 61

In terms of collision theory, to which of the following is the rate of a chemical reaction proportional?
(a) the change in free energy per second
(b) the change in temperature per second
(c) the number of collisions per second
(d) the number of product molecules

Rikhil Makwana

Numerade Educator

02:52

Problem 62

Hydrogen iodide, HI, decomposes in the gas phase to produce hydrogen, $\mathrm{H}_{2}$, and iodine, $\mathrm{I}_{2}$. The value of the rate constant, $k,$ for the reaction was measured at several different temperatures and the data are shown here:
What is the value of the activation energy (in $\mathrm{kJ} / \mathrm{mol}$ ) for this reaction?

Stephen Ho

Numerade Educator

01:41

Problem 63

The element Co exists in two oxidation states, $\mathrm{Co}(\mathrm{II})$ and $\mathrm{Co}(\mathrm{III}),$ and the ions form many complexes. The rate at which one of the complexes of $\mathrm{Co}(\text { III) was reduced by } \mathrm{Fe}(\mathrm{II})$ in water was measured. Determine the activation energy of the reaction from the following data:

Rikhil Makwana

Numerade Educator

09:32

Problem 64

The hydrolysis of the sugar sucrose to the sugars glucose and fructose, $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ follows a first-order rate law for the disappearance of sucrose: rate $=k\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right]$ (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.)
(a) In neutral solution, $k=2.1 \times 10^{-11} \mathrm{s}^{-1}$ at $27^{\circ} \mathrm{C}$ and $8.5 \times 10^{-11} \mathrm{s}^{-1}$ at $37^{\circ} \mathrm{C}$. Determine the activation energy, the frequency factor, and the rate constant for this equation at $47^{\circ} \mathrm{C}$ (assuming the kinetics remain consistent with the Arrhenius equation at this temperature).
(b) When a solution of sucrose with an initial concentration of 0.150 M reaches equilibrium, the concentration of sucrose is $1.65 \times 10^{-7} \mathrm{M}$. How long will it take the solution to reach equilibrium at $27^{\circ} \mathrm{C}$ in the absence of $\mathrm{a}$ catalyst? Because the concentration of sucrose at equilibrium is so low, assume that the reaction is irreversible.
(c) Why does assuming that the reaction is irreversible simplify the calculation in part (b)?

Stephen Ho

Numerade Educator

01:51

Problem 65

Use the PhET Reactions \& Rates interactive simulation (http:llopenstaxcolllege.orgIll 16PHETreaction) to simulate a system. On the "Single collision" tab of the simulation applet, enable the "Energy view" by clicking the "t" icon. Select the first $A+B C \longrightarrow A B+C$ reaction (A is yellow, B is purple, and C is navy blue). Using the "straight shot" default option, try launching the $A$ atom with varying amounts of energy. What changes when the Total Energy line at launch is below the transition state of the Potential Energy line? Why? What happens when it is above the transition state? Why?

Crystal Wang

Numerade Educator

00:36

Problem 66

Use the PhET Reactions \& Rates interactive simulation (http:Ilopenstaxcollege.org/II 16PHETreaction) to simulate a system. On the "single collision" tab of the simulation applet, enable the "Energy view" by clicking the "t" icon. Select the first $A+B C \longrightarrow A B+C$ reaction (A is yellow, B is purple, and C is navy blue). Using the "angled shot" option, try launching the $A$ atom with varying angles, but with more Total energy than the transition state. What happens when the $A$ atom hits the $B C$ molecule from different directions? Why?

Crystal Wang

Numerade Educator

00:39

Problem 67

Why are elementary reactions involving three or more reactants very uncommon?

Rikhil Makwana

Numerade Educator

03:50

Problem 68

In general, can we predict the effect of doubling the concentration of $A$ on the rate of the overall reaction $A+B \longrightarrow C ?$ Can we predict the effect if the reaction is known to be an elementary reaction?

Alexandra Woodruff

Numerade Educator

01:56

Problem 69

Define these terms:
(a) unimolecular reaction
(b) bimolecular reaction
(c) elementary reaction
(d) overall reaction

Rikhil Makwana

Numerade Educator

00:55

Problem 70

What is the rate law for the elementary termolecular reaction $A+2 B \longrightarrow$ products? For $3 A \longrightarrow$ products?

Crystal Wang

Numerade Educator

01:34

Problem 71

Given the following reactions and the corresponding rate laws, in which of the reactions might the elementary reaction and the overall reaction be the same?
(a) $\mathrm{Cl}_{2}+\mathrm{CO} \longrightarrow \mathrm{Cl}_{2} \mathrm{CO}$
rate $=k\left[\mathrm{Cl}_{2}\right]^{3 / 2}[\mathrm{CO}]$
(b) $\mathrm{PCl}_{3}+\mathrm{Cl}_{2} \longrightarrow \mathrm{PCl}_{5}$
rate $\left.=k\left[\mathrm{PCl}_{3}\right] \mathrm{Cl}_{2}\right]$
(c) $2 \mathrm{NO}+\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}$ rate $=k[\mathrm{NO}]\left[\mathrm{H}_{2}\right]$
(d) $2 \mathrm{NO}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2}$
rate $=k[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right]$
(e) $\mathrm{NO}+\mathrm{O}_{3} \longrightarrow \mathrm{NO}_{2}+\mathrm{O}_{2}$
rate $=k[\mathrm{NO}]\left[\mathrm{O}_{3}\right]$

Rikhil Makwana

Numerade Educator

02:46

Problem 72

Write the rate law for each of the following elementary reactions:
(a) $\mathrm{O}_{3} \stackrel{\text { sunlight }}{\longrightarrow} \mathrm{O}_{2}+\mathrm{O}$
(b) $\mathrm{O}_{3}+\mathrm{Cl} \longrightarrow \mathrm{O}_{2}+\mathrm{ClO}$
(c) $\mathrm{ClO}+\mathrm{O} \longrightarrow \mathrm{Cl}+\mathrm{O}_{2}$
(d) $\mathrm{O}_{3}+\mathrm{NO} \longrightarrow \mathrm{NO}_{2}+\mathrm{O}_{2}$
(e) $\mathrm{NO}_{2}+\mathrm{O} \longrightarrow \mathrm{NO}+\mathrm{O}_{2}$

Emily Himsel

Numerade Educator

00:49

Problem 73

Nitrogen monoxide, NO, reacts with hydrogen, H_2, according to the following equation:
$2 \mathrm{NO}+2 \mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O}$ What would the rate law be if the mechanism for this reaction were:
$2 \mathrm{NO}+\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}_{2}$ (slow) $\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}$ (fast)

Nicole Smina

Numerade Educator

06:10

Problem 74

Experiments were conducted to study the rate of the reaction represented by this equation. $2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ Initial concentrations and rates of reaction are given here.
Consider the following questions:
(a) Determine the order for each of the reactants, $\mathrm{NO}$ and $\mathrm{H}_{2}$, from the data given and show your reasoning.
(b) Write the overall rate law for the reaction.
(c) Calculate the value of the rate constant, $k$, for the reaction. Include units.
(d) For experiment $2,$ calculate the concentration of NO remaining when exactly one-half of the original amount of $\mathrm{H}_{2}$ had been consumed.
(e) The following sequence of elementary steps is a proposed mechanism for the reaction.
Step 1: $\mathrm{NO}+\mathrm{NO} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2}$
Step 2: $\mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+\mathrm{N}_{2} \mathrm{O}$
Step 3: $\mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \rightleftharpoons \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}$
Based on the data presented, which of these is the rate determining step? Show that the mechanism is consistent with the observed rate law for the reaction and the overall stoichiometry of the reaction.

Nicole Smina

Numerade Educator

02:32

Problem 75

The reaction of CO with Cl_ gives phosgene (COCl_), a nerve gas that was used in World War I. Use the mechanism shown here to complete the following exercises:
$\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{Cl}(g)$ (fast, $\mathrm{k}_{1}$ represents the forward rate constant, $k_{-1}$ the reverse rate constant) $\mathrm{CO}(g)+\mathrm{Cl}(g) \longrightarrow \operatorname{COCl}(g)$ (slow, $k_{2}$ the rate constant)
$\operatorname{COCl}(g)+\operatorname{Cl}(g) \longrightarrow \operatorname{COCl}_{2}(g)$ (fast, $k_{3}$ the rate constant)
(a) Write the overall reaction.
(b) Identify all intermediates.
(c) Write the rate law for each elementary reaction.
(d) Write the overall rate law expression.

Nicole Smina

Numerade Educator

01:23

Problem 76

Account for the increase in reaction rate brought about by a catalyst.

Stephen Ho

Numerade Educator

01:40

Problem 77

Compare the functions of homogeneous and heterogeneous catalysts.

Rikhil Makwana

Numerade Educator

02:58

Problem 78

Consider this scenario and answer the following questions: Chlorine atoms resulting from decomposition of chlorofluoromethanes, such as $\mathrm{CCl}_{2} \mathrm{F}_{2}$, catalyze the decomposition of ozone in the atmosphere. One simplified mechanism for the decomposition is:
$$\begin{aligned}&\mathrm{O}_{3} \stackrel{\text { sunlight }}{\longrightarrow} \mathrm{O}_{2}+\mathrm{O}\\&\mathrm{O}_{3}+\mathrm{Cl} \longrightarrow \mathrm{O}_{2}+\mathrm{ClO}\\&\mathrm{ClO}+\mathrm{O} \longrightarrow \mathrm{Cl}+\mathrm{O}_{2}\end{aligned}$$
(a) Explain why chlorine atoms are catalysts in the gas-phase transformation:
$2 \mathrm{O}_{3} \longrightarrow 3 \mathrm{O}_{2}$
(b) Nitric oxide is also involved in the decomposition of ozone by the mechanism:
$\mathrm{O}_{3} \stackrel{\text { sunlight }}{\longrightarrow} \mathrm{O}_{2}+\mathrm{O}$
$\mathrm{O}_{3}+\mathrm{NO} \longrightarrow \mathrm{NO}_{2}+\mathrm{O}_{2}$
$\mathrm{NO}_{2}+\mathrm{O} \longrightarrow \mathrm{NO}+\mathrm{O}_{2}$
Is NO a catalyst for the decomposition? Explain your answer.

Alexandra Woodruff

Numerade Educator

01:02

Problem 79

For each of the following pairs of reaction diagrams, identify which of the pair is catalyzed:

Rikhil Makwana

Numerade Educator

02:13

Problem 80

For each of the following pairs of reaction diagrams, identify which of the pairs is catalyzed:

Arun Bana

Numerade Educator

View

Problem 81

For each of the following reaction diagrams, estimate the activation energy $\left(E_{\mathrm{a}}\right)$ of the reaction:

Miguel Perez

Numerade Educator

View

Problem 82

For each of the following reaction diagrams, estimate the activation energy $\left(E_{\mathrm{a}}\right)$ of the reaction:

Miguel Perez

Numerade Educator

00:57

Problem 83

Assuming the diagrams in Exercise 12.81 represent different mechanisms for the same reaction, which of the reactions has the faster rate?

Nicole Smina

Numerade Educator

01:26

Problem 84

Consider the similarities and differences in the two reaction diagrams shown in Exercise $12.82 .$ Do these diagrams represent two different overall reactions, or do they represent the same overall reaction taking place by two different mechanisms? Explain your answer.

Nicole Smina

Numerade Educator