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Chemistry

Kenneth W. Whitten, Raymond E. Davis, Larry Peck

Chapter 16

Chemical Kinetics - all with Video Answers

Educators

KY

Chapter Questions

02:13

Problem 1

Briefly summarize the effects of each of the four factors that affect rates of reactions.

KY
Kexin Yang
Numerade Educator
03:00

Problem 2

Describe the basic features of collision theory and transition state theory.

KY
Kexin Yang
Numerade Educator
04:58

Problem 3

What is a rate-law expression? Describe how it is determined for a particular reaction.

KY
Kexin Yang
Numerade Educator
04:41

Problem 4

Distinguish between reactions that are thermodynamically favorable and reactions that are kinetically favorable. What can be said about the relationship between the two?

KY
Kexin Yang
Numerade Educator
01:36

Problem 5

What is meant by the mechanism of a reaction? How does the mechanism relate to the order of the reaction?

KY
Kexin Yang
Numerade Educator
02:56

Problem 6

What, if anything, can be said about the relationship between the coefficients of the balanced overall equation for a reaction and the powers to which concentrations are raised in the rate-law expression? To what are these powers related?

KY
Kexin Yang
Numerade Educator
01:39

Problem 7

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

Narayan Hari
Narayan Hari
Numerade Educator
03:02

Problem 8

Express the rate of reaction in terms of the rate of change of each reactant and each product in the following equations.
(a) $3 \mathrm{ClO}^{-}(\mathrm{aq}) \longrightarrow \mathrm{ClO}_{3}^{-}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})$
(b) $2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{SO}_{3}(\mathrm{~g})$
(c) $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Br}_{2}(\mathrm{~g})$
(d) $\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}+\mathrm{I}_{2} \longrightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{~N}_{2}+2 \mathrm{HI}$
(liquid phase)

KY
Kexin Yang
Numerade Educator
02:02

Problem 9

At a given time, $\mathrm{N}_{2}$ is reacting with $\mathrm{H}_{2}$ at a rate of $0.30 M / \mathrm{min}$ to produce $\mathrm{NH}_{3}$. At that same time, what is the rate at which the other reactant is changing and the rate at which the product is changing?
$$
\mathrm{N}_{2}+3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3}
$$

KY
Kexin Yang
Numerade Educator
02:56

Problem 10

The following equation shows the production of $\mathrm{NO}$ and $\mathrm{H}_{2} \mathrm{O}$ by oxidation of ammonia. At a given time, $\mathrm{NH}_{3}$ is reacting at a rate of $1.20 \mathrm{M} / \mathrm{min}$. At that same time, what is the rate at which the other reactant is changing and the rate at which each product is changing?
$$
4 \mathrm{NH}_{3}+5 \mathrm{O}_{2} \longrightarrow 4 \mathrm{NO}+6 \mathrm{H}_{2} \mathrm{O}
$$

Dominique Jan Tan
Dominique Jan Tan
Numerade Educator
01:32

Problem 11

Why do large crystals of sugar burn more slowly than finely ground sugar?

KY
Kexin Yang
Numerade Educator
02:02

Problem 12

Some fireworks are bright because of the burning of magnesium. Speculate on how fireworks might be constructed using magnesium. How might the sizes of the pieces of magnesium be important? What would you expect to occur if the pieces that were used were too large? too small?

KY
Kexin Yang
Numerade Educator
01:47

Problem 13

A reaction has the experimental rate equation: Rate $=k[\mathrm{~A}]^{2}$. How will the rate change if the concentration of $\mathrm{A}$ is tripled? If the concentration of $\mathrm{A}$ is halved?

Will Li
Will Li
Numerade Educator
02:00

Problem 14

The rate expression for the following reaction at a certain temperature is rate $=k[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right] .$ Two experiments involving this reaction are carried out at the same temperature. In the second experiment the initial concentration of $\mathrm{NO}$ is halved, while the initial concentration of $\mathrm{O}_{2}$ is doubled. The initial rate in the second experiment will be how many times that of the first?
$$
2 \mathrm{NO}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:15

Problem 15

The rate-law expression for the following reaction is found to be rate $=k\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] .$ What is the overall reaction order?
$$
2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \longrightarrow 4 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:07

Problem 16

Use times expressed in seconds to give the units of the rate constant for reactions that are overall (a) first order; (b) second order; (c) third order; $(\mathrm{d})$ of order $1 \frac{1}{2}$.

Narayan Hari
Narayan Hari
Numerade Educator
03:19

Problem 17

Rate data were obtained at $25^{\circ} \mathrm{C}$ for the following reaction. What is the rate-law expression for this reaction? \begin{tabular}{lccc}
& $\mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{C}+2 \mathrm{D}$ & \\
Expt. & Initial [A] $(\mathrm{mol} / \mathrm{L})$ & Initial [B] $(\mathrm{mol} / \mathrm{L})$ & Initial Rate of Formation of C $\left(\boldsymbol{M} \cdot \mathrm{min}^{-1}\right)$ \\
\hline 1 & 0.10 & 0.10 & $3.0 \times 10^{-4}$ \\
2 & 0.30 & 0.30 & $9.0 \times 10^{-4}$ \\
3 & 0.10 & 0.30 & $3.0 \times 10^{-4}$ \\
4 & 0.20 & 0.40 & $6.0 \times 10^{-4}$ \\
\hline
\end{tabular}

Narayan Hari
Narayan Hari
Numerade Educator
02:33

Problem 18

Rate data were obtained for the following reaction at $25^{\circ} \mathrm{C} .$ What is the rate-law expression for the reaction?
$$
2 \mathrm{~A}+\mathrm{B}+2 \mathrm{C} \longrightarrow \mathrm{D}+2 \mathrm{E}
$$

KY
Kexin Yang
Numerade Educator
01:01

Problem 19

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

KY
Kexin Yang
Numerade Educator
07:20

Problem 20

Listed below are the equations for three reactions and the rate-law expressions for them.
Reaction $\quad$ Rate $\underline{L} a v$ \begin{tabular}{ll}
\hline $2 \mathrm{NO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow$ & rate $=k[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right]$ \\
$2 \mathrm{ICl}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{~g}) \stackrel{\mathrm{N}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})}{\longrightarrow}$ & rate $=k[\mathrm{ICl}]\left[\mathrm{H}_{2}\right]$ \\
$2 \mathrm{HCl}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{~g})$ & \\
$\mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \stackrel{2}{\longrightarrow} \mathrm{HBr}(\mathrm{g})$ & rate $=k\left[\mathrm{H}_{2}\right]\left[\mathrm{Br}_{2}\right]$ \\
\hline
\end{tabular}
For which of these reactions will doubling the concentration of $\mathrm{H}_{2}$ double the reaction rate? For which of these reactions will doubling the concentration of $\mathrm{H}_{2}$ quadruple the reaction rate? For which of these reactions will doubling the concentration of $\mathrm{H}_{2}$ have no effect on the rate of the reaction?

Preeti Kumari
Preeti Kumari
Numerade Educator
02:06

Problem 21

For a reaction involving the decomposition of $Y$, the following data are obtained:
$\begin{array}{lllll}\text { Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{min}) & 0.228 & 0.245 & 0.202 & 0.158 \\ {[\mathrm{Y}]} & 0.200 & 0.170 & 0.140 & 0.110\end{array}$
(a) Determine the order of the reaction.
(b) Write the rate expression for the decomposition of Y.
(c) Calculate $k$ for the above experiment.

Ronald Prasad
Ronald Prasad
Numerade Educator
13:02

Problem 22

Rate data were collected for the following reaction at a particular temperature.
$2 \mathrm{ClO}_{2}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow \mathrm{ClO}_{3}^{-}(\mathrm{aq})+\mathrm{ClO}_{2}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$
(a) What is the rate-law expression for this reaction?
(b) Describe the order of the reaction with respect to each reactant and to the overall order. (c) What is the value, with units, for the specific rate constant?

Preeti Kumari
Preeti Kumari
Numerade Educator
11:04

Problem 23

The reaction
$$
\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}+\mathrm{I}_{2} \longrightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{~N}_{2}+2 \mathrm{HI}
$$
gives the following initial rates.
(a) Write the rate-law expression. (b) What is the value, with units, for the specific rate constant?

Preeti Kumari
Preeti Kumari
Numerade Educator
09:17

Problem 24

Given these data for the reaction $\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}$, write the rate-law expression.

Preeti Kumari
Preeti Kumari
Numerade Educator
08:24

Problem 25

(a) Given these data for the reaction $\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}$ write the rate-law expression.
(b) What is the value, with units, for the specific rate constant?

Preeti Kumari
Preeti Kumari
Numerade Educator
09:03

Problem 26

(a) Given these data for the reaction $\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}$ write the rate-law expression. (b) What is the value, with units, for the specific rate constant?

Preeti Kumari
Preeti Kumari
Numerade Educator
06:40

Problem 27

Consider a chemical reaction between compounds $\mathrm{A}$ and $\mathrm{B}$ that is first order in $\mathrm{A}$ and first order in $\mathrm{B}$. From the information shown here, fill in the blanks.

Preeti Kumari
Preeti Kumari
Numerade Educator
05:54

Problem 28

Consider a chemical reaction of compounds $A$ and $B$ that was found to be first order in $\mathrm{A}$ and second order in $\mathrm{B}$. From the following information, fill in the blanks.

Preeti Kumari
Preeti Kumari
Numerade Educator
04:20

Problem 29

The rate of decomposition of $\mathrm{NO}_{2}$ by the following reaction at a particular temperature is $5.4 \times 10^{-5} \mathrm{~mol}$ $$ \begin{array}{r}\mathrm{NO}_{2} / \mathrm{L} \cdot \mathrm{s} \text { when }\left[\mathrm{NO}_{2}\right]=0.0110 \mathrm{~mol} / \mathrm{L} \\ 2 \mathrm{NO}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2 (\mathrm{~g}) \end{array} $$ (a) Assume that the rate law is rate $=k\left[\mathrm{NO}_{2}\right]$. What rate of disappearance of $\mathrm{NO}_{2}$ would be predicted when $\left[\mathrm{NO}_{2}\right]=$ $0.00550 \mathrm{~mol} / \mathrm{L} ?$ (b) Now assume that the rate law is rate $=$ $k\left[\mathrm{NO}_{2}\right]^{2}$. What rate of disappearance of $\mathrm{NO}_{2}$ would be predicted when $\left[\mathrm{NO}_{2}\right]=0.00550 \mathrm{~mol} / \mathrm{L} ?$ (c) The rate
when $\left[\mathrm{NO}_{2}\right]=0.00550 \mathrm{~mol} / \mathrm{L}$ is observed to be $1.4 \times 10^{-5}$
$\mathrm{mol} \mathrm{NO}_{2} / \mathrm{L}$ 's. Which rate law is correct? (d) Calculate the rate constant. (Reminder: Express the rate of reaction in terms of rate of disappearance of $\mathrm{NO}_{2} .$ )

Ronald Prasad
Ronald Prasad
Numerade Educator
02:16

Problem 30

What is meant by the half-life of a reactant?

Preeti Kumari
Preeti Kumari
Numerade Educator
01:21

Problem 31

The rate law for the reaction of sucrose in water
$$
\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \longrightarrow 2 \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}
$$
is rate $=k\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right]$. After 2.57 hours at $25^{\circ} \mathrm{C}, 6.00 \mathrm{~g} / \mathrm{L}$
of $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}$ has decreased to $5.40 \mathrm{~g} / \mathrm{L}$. Evaluate $k$ for this reaction at $25^{\circ} \mathrm{C}$.

Narayan Hari
Narayan Hari
Numerade Educator
01:10

Problem 32

The rate constant for the decomposition of nitrogen dioxide
$$
2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2}
$$
with a laser beam is $1.70 \mathrm{M}^{-1} \cdot \mathrm{min}^{-1}$. Find the time, in seconds, needed to decrease $2.00 \mathrm{~mol} / \mathrm{L}$ of $\mathrm{NO}_{2}$ to $1.25 \mathrm{~mol} / \mathrm{L}$

Narayan Hari
Narayan Hari
Numerade Educator
04:56

Problem 33

The second-order rate constant for the following gasphase reaction is $0.0442 M^{-1} \cdot \mathrm{s}^{-1} .$ We start with 0.135 $\operatorname{mol} \mathrm{C}_{2} \mathrm{~F}_{4}$ in a 2.00 -liter container, with no $\mathrm{C}_{4} \mathrm{~F}_{8}$ initially present.
$$
2 \mathrm{C}_{2} \mathrm{~F}_{4} \longrightarrow \mathrm{C}_{4} \mathrm{~F}_{8}
$$
(a) What will be the concentration of $\mathrm{C}_{2} \mathrm{~F}_{4}$ after 1.00 hour?
(b) What will be the concentration of $\mathrm{C}_{4} \mathrm{~F}_{8}$ after 1.00 hour?
(c) What is the half-life of the reaction for the initial $\mathrm{C}_{2} \mathrm{~F}_{4}$ concentration given in part (a)?
(d) How long will it take for half of the $\mathrm{C}_{2} \mathrm{~F}_{4}$ that remains after 1.00 hour to disappear?

Ronald Prasad
Ronald Prasad
Numerade Educator
04:46

Problem 34

The decomposition reaction of carbon disulfide, $\mathrm{CS}_{2},$ to carbon monosulfide, CS, and sulfur is first order with $k=$ $2.8 \times 10^{-7} \mathrm{~s}^{-1}$ at $1000^{\circ} \mathrm{C}$
$$
\mathrm{CS}_{2} \longrightarrow \mathrm{CS}+\mathrm{S}
$$
(a) What is the half-life of this reaction at $1000^{\circ} \mathrm{C} ?$
(b) How many days would pass before a 2.00 -gram sample of $\mathrm{CS}_{2}$ had decomposed to the extent that 0.75 gram of $\mathrm{CS}_{2}$ remained? (c) Refer to part (b). How many grams of CS would be present after this length of time? (d) How much of a 2.00 -gram sample of $\mathrm{CS}_{2}$ would remain after 45.0 days?

Ronald Prasad
Ronald Prasad
Numerade Educator
01:48

Problem 35

The first-order rate constant for the conversion of (a) What cyclobutane to ethylene at $1000 .{ }^{\circ} \mathrm{C}$ is $87 \mathrm{~s}^{-1}$. is the half-life of this reaction at $1000 .{ }^{\circ} \mathrm{C} ?(\mathrm{~b})$ If you started with $4.00 \mathrm{~g}$ of cyclobutane, how long would it take to consume $2.50 \mathrm{~g}$ of it? (Hint: Write the ratio of concentrations, $[\mathrm{A}]_{0} /[\mathrm{A}],$ in terms of mass, molecular weight, and volume.) (c) How much of an initial $1.00-\mathrm{g}$ sample of cyclobutane would remain after $1.00 \mathrm{~s}$ ?

Narayan Hari
Narayan Hari
Numerade Educator
05:13

Problem 36

For the reaction $$ 2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2} $$ the rate equation is
$$ \text { rate }=1.4 \times 10^{-10} \mathrm{M}^{-1} \cdot \mathrm{s}^{-1}\left[\mathrm{NO}_{2}\right]^{2} \text { at } 25^{\circ} \mathrm{C} $$ (a) If $3.00 \mathrm{~mol}$ of $\mathrm{NO}_{2}$ is initially present in a sealed 2.00-L vessel at $25^{\circ} \mathrm{C}$, what is the half-life of the reaction? (b) Refer to part (a). What concentration and how many grams of $\mathrm{NO}_{2}$ remain after 115 years? (c) Refer to part (b). What concentration of NO would have been produced during the same period of time?

Ronald Prasad
Ronald Prasad
Numerade Educator
01:01

Problem 37

The first-order rate constant for the radioactive decay of radium- 223 is 0.0606 day $^{-1}$. What is the half-life of radium-223?

Narayan Hari
Narayan Hari
Numerade Educator
01:07

Problem 38

The first-order rate constant for the radioactive decay of radium- 223 is 0.0606 day $^{-1}$. What is the half-life of radium-223?

Narayan Hari
Narayan Hari
Numerade Educator
01:16

Problem 39

The rate constant for the first-order reaction
$$
\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}
$$
is $1.20 \times 10^{-2} \mathrm{~s}^{-1}$ at $45^{\circ} \mathrm{C},$ and the initial concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$ is $0.01500 \mathrm{M}$. (a) How long will it take for the concentration to decrease to $0.00100 \mathrm{M}$ ? (b) How much longer will it take for a further decrease to $0.000900 \mathrm{M?}$

Narayan Hari
Narayan Hari
Numerade Educator
07:36

Problem 40

The familiar rule of thumb that the rate of a reaction roughly doubles for every $10^{\circ} \mathrm{C}$ rise in temperature (around room temperature) has been shown to be consistent with the Arrhenius equation, using a typical activation energy of $50 \mathrm{~kJ} / \mathrm{mol} .$ How much would the rate of such a reaction change if the temperature of the reaction were changed from $90^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ or from $0^{\circ} \mathrm{C}$ to $10^{\circ} \mathrm{C} ?$

Preeti Kumari
Preeti Kumari
Numerade Educator
03:12

Problem 41

The thermal decomposition of ammonia at high temperatures was studied in the presence of inert gases. Data at $2000 . \mathrm{K}$ are given for a single experiment.
$$ \begin{array}{cr} \mathrm{NH}_{3} \longrightarrow & \mathrm{NH}_{2}+\mathrm{H} \\ t \text { (hours) } & {\left[\mathrm{NH}_{3}\right](\mathrm{mol} / \mathrm{L})} \\ \hline 0 & 8.000 \times 10^{-7} \\ 25 & 6.75 \times 10^{-7} \\ 50 & 5.84 \times 10^{-7} \\ 75 & 5.15 \times 10^{-7} \\ \hline \end{array} $$
Plot the appropriate concentration expressions against time to find the order of the reaction. Find the rate constant of the reaction from the slope of the line. Use the given data and the appropriate integrated rate equation to check your answer.

Ronald Prasad
Ronald Prasad
Numerade Educator
03:04

Problem 42

The following data were obtained from a study of the decomposition of a sample of HI on the surface of a gold wire.
(a) Plot the data to find the order of the reaction, the rate constant, and the rate equation.
(b) Calculate the HI concentration in $\mathrm{mmol} / \mathrm{L}$ at $600 . \mathrm{s}$.
\begin{array}{cc}
t \text { (seconds) } & {[\mathrm{HI}](\mathrm{mmol} / \mathrm{L})} \\
\hline 0 . & 5.46 \\
250 . & 4.10 \\
500 . & 2.73 \\
750 . & 1.37 \\
\hline
\end{array}

Ronald Prasad
Ronald Prasad
Numerade Educator
04:25

Problem 43

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ in the gas phase,
$$
\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2}
$$
can be studied by measuring the concentration of $\mathrm{Cl}_{2}$ as the reaction proceeds. We begin with $\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]_{0}=0.250 \mathrm{M}$. Holding the temperature constant at $320 .{ }^{\circ} \mathrm{C},$ we monitor the $\mathrm{Cl}_{2}$ concentration, with the following results. $$ \begin{array}{cc} t \text { (hours) } & {\left[\mathrm{Cl}_{2}\right](\mathrm{mol} / \mathrm{L})} \\ \hline 0.00 & 0.000 \\ 2.00 & 0.037 \\ 4.00 & 0.068 \\ 6.00 & 0.095 \\ 8.00 & 0.117 \\ 10.00 & 0.137 \\ 12.00 & 0.153 \\ 14.00 & 0.168 \\ 16.00 & 0.180 \\ 18.00 & 0.190 \\ 20.00 & 0.199 \\ \hline \end{array} $$
(a) Plot $\left[\mathrm{Cl}_{2}\right]$ versus $t$. (b) Plot $\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]$ versus $t$.
(c) Determine the rate law for this reaction.
(d) What is the value, with units, for the specific rate constant at $320 .{ }^{\circ} \mathrm{C} ?$
(e) How long would it take for $95 \%$ of the original $\mathrm{SO}, \mathrm{Cl}$, to react?

Ronald Prasad
Ronald Prasad
Numerade Educator
01:12

Problem 44

At some temperature, the rate constant for the decomposition of HI on a gold surface is $0.080 \mathrm{M} \cdot \mathrm{s}^{-1}$.
$$
2 \mathrm{HI}(\mathrm{g}) \longrightarrow \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g})
$$
(a) What is the order of the reaction?
(b) How long will it take for the concentration of HI to drop from $1.50 \mathrm{M}$ to $0.15 M ?$

Narayan Hari
Narayan Hari
Numerade Educator
05:14

Problem 45

At body temperature, the first-order rate constant is $1.87 \times$ $10^{-3} \mathrm{~min}^{-1}$ for the elimination of the cancer chemotherapy agent cisplatin. What would be the concentration of cisplatin in a patient 36 hours after the concentration had reached $4.75 \times 10^{-3} \mathrm{M} ?$

Preeti Kumari
Preeti Kumari
Numerade Educator
04:03

Problem 46

The first-order rate constant for the decomposition of an insecticide in moist soil is $3.0 \times 10^{-3} \mathrm{~d}^{-1}$. How long will it take for $75 \%$ of the insecticide to decompose?

Preeti Kumari
Preeti Kumari
Numerade Educator
01:48

Problem 47

The following rearrangement reaction is first order:
$$
\mathrm{CH}_{3} \mathrm{NC} \longrightarrow \mathrm{CH}_{3} \mathrm{CN}
$$
In a table of kinetics data, we find the following values listed for this reaction: $A=3.98 \times 10^{13} \mathrm{~s}^{-1}, E_{\mathrm{a}}=160 . \mathrm{kJ} /$
mol. (a) Calculate the value of the specific rate constant at room temperature, $25^{\circ} \mathrm{C}$. (b) Calculate the value of the specific rate constant at $115^{\circ} \mathrm{C}$.

Narayan Hari
Narayan Hari
Numerade Educator
01:33

Problem 48

The following gas-phase decomposition reaction is first order:
$$
\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{HCl}
$$
In a table of kinetics data, we find the following values listed for this reaction: $A=1.58 \times 10^{13} \mathrm{~s}^{-1}$ $E_{\mathrm{a}}=237 \mathrm{~kJ} / \mathrm{mol}$. (a) Calculate the value of the specific rate constant at room temperature, $25^{\circ} \mathrm{C} .$ (b) Calculate the value of the specific rate constant at $275^{\circ} \mathrm{C}$.

Narayan Hari
Narayan Hari
Numerade Educator
10:53

Problem 49

Draw typical reaction energy diagrams for one-step reactions that release energy and that absorb energy. Distinguish between the net energy change, $\Delta E,$ and the activation energy for each kind of reaction. Indicate potential energies of products and reactants for both kinds of reactions.

Preeti Kumari
Preeti Kumari
Numerade Educator
08:38

Problem 50

Use graphs to illustrate how the presence of a catalyst can affect the rate of a reaction.

Preeti Kumari
Preeti Kumari
Numerade Educator
02:27

Problem 51

How do homogeneous catalysts and heterogeneous catalysts differ?

Preeti Kumari
Preeti Kumari
Numerade Educator
08:26

Problem 52

(a) Why should one expect an increase in temperature to increase the initial rate of reaction? (b) Why should one expect a reaction in the gaseous state to be faster than the same reaction in the solid state?

Preeti Kumari
Preeti Kumari
Numerade Educator
06:15

Problem 53

Assume that the activation energy for a certain reaction is $173 \mathrm{~kJ} / \mathrm{mol}$ and the reaction is started with equal initial concentrations of reactants. How many times faster will the reaction occur at $40^{\circ} \mathrm{C}$ than at $10^{\circ} \mathrm{C}$ ?

Preeti Kumari
Preeti Kumari
Numerade Educator
05:32

Problem 54

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

Preeti Kumari
Preeti Kumari
Numerade Educator
01:53

Problem 55

For a gas-phase reaction, $E_{\mathrm{a}}=103 \mathrm{~kJ} / \mathrm{mol}$, and the rate constant is $0.0850 \mathrm{~min}^{-1}$ at $273 \mathrm{~K}$. Find the rate constant at $323 \mathrm{~K}$

Narayan Hari
Narayan Hari
Numerade Educator
01:19

Problem 56

For a gas-phase reaction, $E_{a}=103 \mathrm{~kJ} / \mathrm{mol}$, and the rate constant is $0.0850 \mathrm{~min}^{-1}$ at $273 \mathrm{~K}$. Find the rate constant at $323 \mathrm{~K}$.

Narayan Hari
Narayan Hari
Numerade Educator
11:05

Problem 57

The rate constant for the decomposition of $\mathrm{N}_{2} \mathrm{O}$
$$
2 \mathrm{~N}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{~N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})
$$
is $2.6 \times 10^{-11} \mathrm{~s}^{-1}$ at $300 .{ }^{\circ} \mathrm{C}$ and $2.1 \times 10^{-10} \mathrm{~s}^{-1}$ at $330 .{ }^{\circ} \mathrm{C}$.
Calculate the activation energy for this reaction. Prepare a reaction coordinate diagram like Figure $16-10$ using $-164.1 \mathrm{~kJ} / \mathrm{mol}$ as the $\Delta E_{\mathrm{rxn}}$

Preeti Kumari
Preeti Kumari
Numerade Educator
09:01

Problem 58

For a particular reaction, $\Delta E=51.51 \mathrm{~kJ} / \mathrm{mol}, k=8.0$ $\times 10^{-7} \mathrm{~s}^{-1}$ at $0.0^{\circ} \mathrm{C},$ and $k=8.9 \times 10^{-4} \mathrm{~s}^{-1}$ at $50.0^{\circ} \mathrm{C}$
Prepare a reaction coordinate diagram like Figure $16-10$ for this reaction.

Preeti Kumari
Preeti Kumari
Numerade Educator
03:01

Problem 59

You are given the rate constant as a function of temperature for the exchange reaction
$\mathrm{Mn}(\mathrm{CO})_{5}\left(\mathrm{CH}_{3} \mathrm{CN}\right)^{+}+\mathrm{NC}_{5} \mathrm{H}_{5} \rightarrow$
$\mathrm{Mn}(\mathrm{CO})_{5}\left(\mathrm{NC}_{5} \mathrm{H}_{5}\right)^{+}+\mathrm{CH}_{3} \mathrm{CN}$
\begin{tabular}{cc}
$T(\mathbf{K})$ & $k\left(\min ^{-1}\right)$ \\
\hline 298 & 0.0409 \\
305 & 0.0818 \\
312 & 0.157 \\
\hline
\end{tabular}
(b) Use the
(a) Calculate $E_{\mathrm{a}}$ from a plot of $\log k$ versus $1 / T$. graph to predict the value of $k$ at $308 \mathrm{~K}$. (c) What is the numerical value of the collision frequency factor, A, in the Arrhenius equation?

Ronald Prasad
Ronald Prasad
Numerade Educator
03:21

Problem 60

A The rearrangement of cyclopropane to propene described in Exercise 38 has been studied at various temperatures. The following values for the specific rate constant have been determined experimentally. \begin{tabular}{cc} $T(\mathbf{K})$ & $k\left(\mathrm{~s}^{-1}\right)$ \\ \hline $600 .$ & $3.30 \times 10^{-9}$ \\ $650 .$ & $2.19 \times 10^{-7}$ \\
$700 .$ & $7.96 \times 10^{-6}$ \\ $750 .$ & $1.80 \times 10^{-4}$ \\ $800 .$ & $2.74 \times 10^{-3}$ \\ $850 .$ & $3.04 \times 10^{-2}$ \\$900 .$ & $2.58 \times 10^{-1}$ \\ \hline \end{tabular} (a) From the appropriate plot of these data, determine the value of the activation energy for this reaction. (b) Use the graph to estimate the value of $k$ at $500 \mathrm{~K}$. (c) Use the graph to estimate the temperature at which the value of $k$ would be equal to $5.00 \times 10^{-5} \mathrm{~s}^{-1}$

Ronald Prasad
Ronald Prasad
Numerade Educator
07:32

Problem 61

Biological reactions nearly always occur in the presence of enzymes as catalysts. The enzyme catalase, which acts on peroxides, reduces the $E_{\mathrm{a}}$ for the reaction from $72 \mathrm{~kJ} / \mathrm{mol}$ (uncatalyzed) to $28 \mathrm{~kJ} / \mathrm{mol}$ (catalyzed). By what factor does the reaction rate increase at normal body temperature, $37.0^{\circ} \mathrm{C},$ for the same reactant (peroxide) concentration? Assume that the collision factor, $A$, remains constant.

Preeti Kumari
Preeti Kumari
Numerade Educator
07:38

Problem 62

The enzyme carbonic anhydrase catalyzes the hydration of carbon dioxide. This reaction is involved in the transfer of $\mathrm{CO}_{2}$ from tissues to the lungs via the bloodstream. One enzyme molecule hydrates $10^{6}$ molecules of $\mathrm{CO}_{2}$ per second. How many grams of $\mathrm{CO}_{2}$ are hydrated in one minute in $1 \mathrm{~L}$ by $1.0 \times 10^{-6} M$ enzyme?

Preeti Kumari
Preeti Kumari
Numerade Educator
10:04

Problem 63

The following gas-phase reaction follows first-order kinetics.
$$
\mathrm{ClO}_{2} \mathrm{~F} \longrightarrow \mathrm{ClOF}+\mathrm{O}
$$
The activation energy of this reaction is $186 \mathrm{~kJ} / \mathrm{mol}$. The value of $k$ at $322^{\circ} \mathrm{C}$ is $6.76 \times 10^{-4} \mathrm{~s}^{-1} .$ (a) What would be the value of $k$ for this reaction at $25^{\circ} \mathrm{C} ?$ (b) At what temperature would this reaction have a $k$ value of $3.00 \times 10^{-2} \mathrm{~s}^{-1}$ ?

Preeti Kumari
Preeti Kumari
Numerade Educator
08:44

Problem 64

The following gas-phase reaction is first order.
$$
\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow \mathrm{NO}_{2}+\mathrm{NO}_{3}
$$
The activation energy of this reaction is $88 \mathrm{~kJ} / \mathrm{mol}$. The value of $k$ at $0^{\circ} \mathrm{C}$ is $9.16 \times 10^{-3} \mathrm{~s}^{-1}$. (a) What would be the value of $k$ for this reaction at room temperature, $25^{\circ} \mathrm{C} ?$
(b) At what temperature would this reaction have a $k$ value
$$
\text { of } 3.00 \times 10^{-2} \mathrm{~s}^{-1} ?
$$

Preeti Kumari
Preeti Kumari
Numerade Educator
04:24

Problem 65

Define reaction mechanism. Why do we believe that only bimolecular collisions and unimolecular decompositions are important in most reaction mechanisms?

Preeti Kumari
Preeti Kumari
Numerade Educator
05:43

Problem 66

For the reaction the rate law is: Rate $=k\left[\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}\right]$. Identify each mechanism that is compatible with the rate law.
(a) $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{+}+\mathrm{Br}^{-}$
slow $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{+}+\mathrm{OH}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}$
fast
(b) $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}+\mathrm{OH}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}+\mathrm{Br}^{-}$
(c) $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}+\mathrm{OH}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{2}\left(\mathrm{CH}_{2}\right) \mathrm{CBr}^{-}+\mathrm{H}_{2} \mathrm{O}$ slow
$\begin{array}{ll}\left(\mathrm{CH}_{3}\right)_{2}\left(\mathrm{CH}_{2}\right) \mathrm{CBr}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{2}\left(\mathrm{CH}_{2}\right) \mathrm{C}+\mathrm{Br}^{-} & \text {fast } \\ \left(\mathrm{CH}_{3}\right)_{2}\left(\mathrm{CH}_{2}\right) \mathrm{C}+\mathrm{H}_{2} \mathrm{O} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH} & \text { fast }\end{array}$

Preeti Kumari
Preeti Kumari
Numerade Educator
05:05

Problem 67

Write the overall reaction and the rate expressions that correspond to the following reaction mechanisms. Be sure to eliminate intermediates from the answers.
(a) $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D} \quad$ (fast, equilibrium)
$\mathrm{C}+\mathrm{E} \longrightarrow \mathrm{F} \quad$ (slow)
(b) $\mathrm{A} \rightleftharpoons \mathrm{B}+\mathrm{C} \quad$ (fast, equilibrium)
$$
\mathrm{C}+\mathrm{D} \rightleftharpoons \mathrm{E}
$$
(fast, equilibrium)
$$
\mathbf{E} \longrightarrow \mathbf{F}
$$
(slow)

Ronald Prasad
Ronald Prasad
Numerade Educator
16:00

Problem 68

Write the overall reaction and the rate expressions that correspond to the following mechanisms. Be sure to eliminate intermediates from the answers. $\begin{array}{lll}\text { (a) } 2 \mathrm{~A}+\mathrm{B} & \rightleftharpoons \mathrm{D} & \text { (fast, equilibrium) }\end{array}$ $$ \mathrm{D}+\mathrm{B} \longrightarrow \mathrm{E}+\mathrm{F} \quad \text { (slow) } $$
$\mathrm{F} \longrightarrow \mathrm{G}$ (b) $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C} \quad$ (fast, equilibrium) $$
\mathrm{C}+\mathrm{D} \rightleftharpoons \mathrm{F} $$ (fast, equilibrium) $$ \mathrm{F} \longrightarrow \mathrm{G} $$

Preeti Kumari
Preeti Kumari
Numerade Educator
07:31

Problem 69

The ozone, $\mathrm{O}_{3}$, of the stratosphere can be decomposed by reaction with nitrogen oxide (commonly called nitric oxide), NO, from high-flying jet aircraft. $$ \mathrm{O}_{3}(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \stackrel{\mathrm{NO}_{2}}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) $$ The rate expression is rate $=k\left[\mathrm{O}_{3}\right][\mathrm{NO}] .$ Which of the following mechanisms are consistent with the observed rate expression?
(a)
(b)
(c)
(d)
(e)

Preeti Kumari
Preeti Kumari
Numerade Educator
04:15

Problem 70

A proposed mechanism for the decomposition of ozone, $2 \mathrm{O}_{3} \longrightarrow 3 \mathrm{O}_{2},$ is
$\mathrm{O}_{3} \rightleftharpoons \mathrm{O}_{2}+\mathrm{O} \quad$ (fast, equilibrium)
$\mathrm{O}+\mathrm{O}_{3} \longrightarrow 2 \mathrm{O}_{2} \quad$ (slow)
Derive the rate equation for the net reaction.

Preeti Kumari
Preeti Kumari
Numerade Educator
10:10

Problem 71

A mechanism for the gas-phase reaction $$ \mathrm{H}_{2}+\mathrm{I}_{2} \longrightarrow 2 \mathrm{HI} $$was discussed in the chapter. (a) Show that this mechanism predicts the correct rate law, rate $=k\left[\mathrm{H}_{2}\right]\left[\mathrm{I}_{2}\right]$
$$
\begin{array}{ll}
\mathrm{I}_{2} & \rightleftharpoons 2 \mathrm{I} \\
\mathrm{I}+\mathrm{H}_{2} & \rightleftharpoons \mathrm{H}_{2} \mathrm{I} \\
\mathrm{H}_{2} \mathrm{I}+\mathrm{I} & \longrightarrow 2 \mathrm{HI}
\end{array}
$$
(fast, equilibrium) (fast, equilibrium) (slow)
(b) Identify any reaction intermediates in this proposed mechanism.

Preeti Kumari
Preeti Kumari
Numerade Educator
08:48

Problem 72

The combination of Cl atoms is catalyzed by $\mathrm{N}_{2}(\mathrm{~g}) .$ The following mechanism is suggested. $$
\begin{array}{ll} \mathrm{N}_{2}+\mathrm{Cl} & \rightleftharpoons \mathrm{N}_{2} \mathrm{Cl} & \text { (fast, equilibrium) } \\
\mathrm{N}_{2} \mathrm{Cl}+\mathrm{Cl} & \longrightarrow \mathrm{Cl}_{2}+\mathrm{N}_{2} & \text { (slow) } \end{array} $$
(a) Identify any reaction intermediates in this proposed mechanism. (b) Is this mechanism consistent with the experimental rate law, rate $=k\left[\mathrm{~N}_{2}\right][\mathrm{Cl}]^{2} ?$

Preeti Kumari
Preeti Kumari
Numerade Educator
05:59

Problem 73

The reaction between $\mathrm{NO}$ and $\mathrm{Br}_{2}$ was discussed in Section 16-7. The following mechanism has also been proposed. $$ \begin{array}{lll} 2 \mathrm{NO} & \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2} & \text { (fast, equilibrium) }
\end{array} $$ $\mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{Br}_{2} \longrightarrow 2 \mathrm{NOBr}$ Is this mechanism consistent with the observation that the reaction is second order in $\mathrm{NO}$ and first order in $\mathrm{Br}_{2} ?$

Preeti Kumari
Preeti Kumari
Numerade Educator
09:08

Problem 74

The following mechanism for the reaction between $\mathrm{H}_{2}$ and $\mathrm{CO}$ to form formaldehyde, $\mathrm{H}_{2} \mathrm{CO}$, has been proposed. $$ \begin{aligned}
\mathrm{H}_{2} & \rightleftharpoons 2 \mathrm{H} & & \text { (fast, equilibrium) } \\ \mathrm{H}+\mathrm{CO} & \longrightarrow & \mathrm{HCO} & &(\text { slow }) \\ \mathrm{H}+\mathrm{HCO} & \longrightarrow \mathrm{H}_{2} \mathrm{CO} & & \text { (fast) } \end{aligned} $$ (a) Write the balanced equation for the overall reaction. (b) The observed rate dependence is found to be onehalf order in $\mathrm{H}_{2}$ and first order in CO. Is this proposed reaction mechanism consistent with the observed rate dependence?

Preeti Kumari
Preeti Kumari
Numerade Educator
06:32

Problem 75

The reaction between nitrogen dioxide and ozone, $$ 2 \mathrm{NO}_{2}+\mathrm{O}_{3} \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}+\mathrm{O}_{2} $$ has been studied at $231 \mathrm{~K}$. The experimental rate equation is rate $=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{O}_{3}\right] .$ (a) What is the order of the reaction? (b) Is either of the following proposed mechanisms consistent with the given kinetic data? Show how you arrived at your answer. $\begin{array}{lll}\text { (a) } \mathrm{NO}_{2}+\mathrm{NO}_{2} & \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4} & \text { (fast, equilibrium) }\end{array}$
$$ \begin{aligned} \mathrm{N}_{2} \mathrm{O}_{4}+\mathrm{O}_{3} & \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}+\mathrm{O}_{2} \text { (slow) } \\ \text { (b) } \mathrm{NO}_{2}+\mathrm{O}_{3} & \longrightarrow \mathrm{NO}_{3}+\mathrm{O}_{2} \text { (slow) } \end{aligned} $$ $\mathrm{NO}_{3}+\mathrm{NO}_{2} \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}$

Preeti Kumari
Preeti Kumari
Numerade Educator
07:05

Problem 76

(a) What is the transition state in a reaction mechanism?
(b) Are the energy of activation and the transition state related concepts? Explain. (c) How does the activation energy affect the rate of reaction?

Preeti Kumari
Preeti Kumari
Numerade Educator
02:55

Problem 77

Refer to the reaction and data in Exercise 63 . Assume that we begin with $2.80 \mathrm{~mol}$ of $\mathrm{ClO}_{2} \mathrm{~F}$ in a $3.00-\mathrm{L}$ container.(a) How many moles of $\mathrm{ClO}_{2} \mathrm{~F}$ would remain after 2.00 minutes at $25^{\circ} \mathrm{C} ?$ (b) How much time would be required for $99.0 \%$ of the $\mathrm{ClO}_{2} \mathrm{~F}$ to decompose at $25^{\circ} \mathrm{C} ?$

Ronald Prasad
Ronald Prasad
Numerade Educator
02:54

Problem 78

Refer to the reaction and data in Exercise 64 . Assume that we begin with $2.80 \mathrm{~mol}$ of $\mathrm{N}_{2} \mathrm{O}_{5}$ in a $3.00-\mathrm{L}$ container.
(a) How many moles of $\mathrm{N}_{2} \mathrm{O}_{5}$ would remain after 2.00 minutes at $25^{\circ} \mathrm{C}$ ? (b) How much time would be required for $99.0 \%$ of the $\mathrm{N}_{2} \mathrm{O}_{5}$ to decompose at $25^{\circ} \mathrm{C} ?$

Ronald Prasad
Ronald Prasad
Numerade Educator
05:19

Problem 79

Refer to the reaction and data in Exercise 64 . Assume that we begin with $2.80 \mathrm{~mol}$ of $\mathrm{N}_{2} \mathrm{O}_{5}$ in a $3.00-\mathrm{L}$ container. (a) How many moles of $\mathrm{N}_{2} \mathrm{O}_{5}$ would remain after 2.00 minutes at $25^{\circ} \mathrm{C} ?$ (b) How much time would be required for $99.0 \%$ of the $\mathrm{N}_{2} \mathrm{O}_{5}$ to decompose at $25^{\circ} \mathrm{C} ?$

Ronald Prasad
Ronald Prasad
Numerade Educator
11:00

Problem 80

The rate of the hemoglobin (Hb)-carbon monoxide reaction, $$ 4 \mathrm{Hb}+3 \mathrm{CO} \longrightarrow \mathrm{Hb}_{4}(\mathrm{CO})_{3} $$ has been studied at $20^{\circ} \mathrm{C}$. Concentrations are expressed in micromoles per liter $(\mu \mathrm{mol} / \mathrm{L})$ (a) Write the rate equation for the reaction. (b) Calculate the rate constant for the reaction. (c) Calculate the rate at the instant when $[\mathrm{Hb}]=1.50$ and $[\mathrm{CO}]=0.600 \mu \mathrm{mol} / \mathrm{L}$.

Preeti Kumari
Preeti Kumari
Numerade Educator
02:28

Problem 81

How does an enzyme change the speed with which a reaction reaches equilibrium? Can an enzyme change the final equilibrium concentrations? Explain.

Ronald Prasad
Ronald Prasad
Numerade Educator
05:24

Problem 82

Some reactions occur faster than others due to differences in the shapes of the reactants. Use the collision theory to explain these observations.

Ronald Prasad
Ronald Prasad
Numerade Educator
02:54

Problem 83

How is it possible for two reactant molecules to collide with the correct orientation and still not react?

Preeti Kumari
Preeti Kumari
Numerade Educator
02:43

Problem 84

Write the net ionic equation for the following reaction. Construct a potential energy diagram, like that in Figure $16-10,$ for this reaction.
$$ \mathrm{HCl}(\mathrm{aq})+\mathrm{NaOH}(\mathrm{aq}) \longrightarrow \mathrm{NaCl}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) $$

Ronald Prasad
Ronald Prasad
Numerade Educator
02:41

Problem 85

Starting with only two molecules of each reactant in a reaction that is first order in each reactant, show how the collision theory predicts that the rate of reaction will double if the amount of either reactant is doubled.

Ronald Prasad
Ronald Prasad
Numerade Educator
05:35

Problem 86

A sentence in an introductory chemistry textbook reads, "Dioxygen reacts with itself to form trioxygen, ozone, according to the following equation, $3 \mathrm{O}_{2} \longrightarrow 2 \mathrm{O}_{3} "$ As a student of chemistry, what would you write to criticize this sentence?

Ronald Prasad
Ronald Prasad
Numerade Educator
04:00

Problem 87

A stream of gaseous $\mathrm{H}_{2}$ is directed onto finely divided platinum powder in the open air. The metal immediately glows white-hot and continues to do so as long as the stream continues. Explain.

Ronald Prasad
Ronald Prasad
Numerade Educator
04:52

Problem 88

Is the activation energy of a reaction expected to be higher or lower when the same reactants are in the gaseous state rather than the liquid or solid state? Explain.

Ronald Prasad
Ronald Prasad
Numerade Educator
02:11

Problem 89

Construct a diagram like that in Figure 16-10a. (a) Write a generic equation that would have such a potential energy diagram. (b) Is the reaction exothermic or endothermic? (c) Label the energy of activation. It is equal to the difference between what two points on your drawing?

Ronald Prasad
Ronald Prasad
Numerade Educator
02:43

Problem 90

Construct a diagram like that in Figure $16-10 \mathrm{~b}$. (a) Write a generic equation that would have such a potential energy diagram. (b) Is the reaction exothermic or endothermic? (c) Label the energy of activation. It is equal to the difference between what two points on your drawing?

Ronald Prasad
Ronald Prasad
Numerade Educator
01:42

Problem 91

In $1946 \mathrm{~W}$. M. Grant and $\mathrm{V}$. E. Kinsey reported on the rate of hydrolysis of $\mathrm{di}(2$ -chloroethyl $)$ sulfide $\left[\left(\mathrm{ClCH}_{2} \mathrm{CH}_{2}\right)_{2} \mathrm{~S}\right.$, commonly known as mustard gas] in aqueous solution: $$ \begin{array}{r} \left(\mathrm{ClCH}_{2} \mathrm{CH}_{2}\right)_{2} \mathrm{~S}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{SCH}_{2} \mathrm{CH}_{2} \mathrm{OH} \\ +\mathrm{H}^{+}+\mathrm{Cl}^{-} \end{array} $$
What are some of the quantities that could be measured to observe the rate of this reaction?

Ronald Prasad
Ronald Prasad
Numerade Educator
01:45

Problem 92

When vinegar ( $5 \%$ acetic acid) is added to solid baking soda (sodium hydrogen carbonate), they react to produce sodium acetate, water, and carbon dioxide gas: $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq})+\mathrm{NaHCO}_{3}(\mathrm{~s}) \longrightarrow & \mathrm{NaCH}_{3} \mathrm{COO}(\mathrm{aq}) \\ &+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{CO}_{2}(\mathrm{~g}) \end{aligned} $$ List four ways that the rate of this reaction can be increased.

Ronald Prasad
Ronald Prasad
Numerade Educator
02:45

Problem 93

According to the collision theory, the rate of a reaction can be expressed as the product of three factors: \begin{tabular}{l} rate = collision frequency $\times$ energy factor $\times$ probability \\ \hline rate & fact \\ collision frequency total number of collisions per uni \\ volume per unit time \\ energy factor & number of effective collisions per y volume per unit time sufficient energy \\ probability factor & fraction of collisions with prop orientation \\ \hline \end{tabular} \begin{tabular}{l} factor \\ \hline collisions per unit \\
sions per unit \\ ions with \\ with proper \end{tabular} Which of these three factors are most affected by each of the following changes in the reaction conditions or the reacting substances? Increasing the temperature; switching to a similar substance that is a larger, heavier molecule; cutting large solid pieces into much smaller pieces; adding a catalyst; diluting a solution; increasing the pressure of a gas.

Crystal Wang
Crystal Wang
Numerade Educator
17:26

Problem 94

Listed below are the equations and the rate law expressions for the gas-phase decompositions of three compounds:
$\mathrm{N}, \mathrm{O}_{5} \cdot \mathrm{NO}_{2}$, and $\mathrm{NH}_{3}$ For each compound, start with an initial concentration of $0.80 M$ at 8: 00 a.m. and a first half-life of 21 minutes. At what times will the concentration of each starting compound be $0.40 \mathrm{M} ? 0.20 \mathrm{M} ? 0.10 \mathrm{M}$ ?

Preeti Kumari
Preeti Kumari
Numerade Educator
03:25

Problem 95

The following explanation of the operation of a pressure cooker appears in a cookbook: "Boiling water in the presence of air can never produce a temperature higher than $212^{\circ} \mathrm{F}$, no matter how high the heat source. But in a pressure cooker, the air is withdrawn first, so the boiling water can be maintained at higher temperatures." Support or criticize this explanation.

Crystal Wang
Crystal Wang
Numerade Educator
02:59

Problem 96

A cookbook gives the following general guideline for use of a pressure cooker. "For steaming vegetables, cooking time at a gauge pressure of 15 pounds per square inch (psi) is $\frac{1}{3}$ that at atmospheric pressure." Remember that gauge pressure is measured relative to the external atmospheric pressure, which is 15 psi at sea level. From this information, estimate the activation energy for the process of steaming vegetables. (Hint: Clausius and Clapeyron may be able to help you.)

Susan Hallstrom
Susan Hallstrom
Numerade Educator
01:30

Problem 97

For most reactions that involve an enzyme, the rate of product formation versus reactant concentration increases as reactant concentration increases until a maximum value is obtained, after which further increases do not yield increased rates. Using a description like that in Figure $16-19,$ describe how the reaction may be first order with respect to substrate but the amount of enzyme can also be a determining factor.

Manik Pulyani
Manik Pulyani
Numerade Educator
02:43

Problem 98

Using the mechanism and relative energy values shown in Figure $16-12,$ prepare Lewis formulas that illustrate the species that are likely to be present at each of the peaks and troughs in the graphical representation given in Figure 16-12. (Hint: You may need to label some bonds as being weaker, stretched, in the process of being formed, and so on.)

Crystal Wang
Crystal Wang
Numerade Educator
04:17

Problem 99

The activation energy for the reaction $$ 2 \mathrm{HI}(\mathrm{g}) \longrightarrow \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) $$ is $179 \mathrm{~kJ} / \mathrm{mol}$. Based upon Figure $16-12,$ construct a diagram for this multistep reaction. (Hint: Calculate $\Delta H^{0}$ from values in Appendix K. How does $\Delta H^{0}$ compare with $\Delta E$ for this reaction?) Show energy values if known.

Ronald Prasad
Ronald Prasad
Numerade Educator
07:30

Problem 100

The activation energy for the reaction between $\mathrm{O}_{3}$ and $$ \begin{array}{l} \mathrm{NO} \text { is } 9.6 \mathrm{~kJ} / \mathrm{mol} . \\ \mathrm{O}_{3}(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow \mathrm{NO}_{2 (\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \end{array} $$ (a) Use the thermodynamic quantities in Appendix $\mathrm{K}$ to calculate $\Delta H^{0}$ for this reaction. (b) Prepare an activation energy plot similar to that in Figure 16-10 for this reaction. (Hint: How does $\Delta H^{0}$ compare with $\Delta E$ for this reaction?)

Preeti Kumari
Preeti Kumari
Numerade Educator
04:14

Problem 101

Go to en.wikipedia.org/wiki/Arrhenius_equation or another website and locate information on the Arrhenius equation. For a particular reaction, how could one determine the value of $A$ in the Arrhenius equation for that reaction?

Ronald Prasad
Ronald Prasad
Numerade Educator
01:38

Problem 102

Go to www.chemguide.co.uk/physical/basicrates/ arrhenius.html or another website and locate information on the Arrhenius equation. Describe a reaction found at this website that follows a first-order mechanism.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:49

Problem 103

Use the Handbook of Cbemistry and Physics or a website and locate information on kinetics, conversion factors, or rate constants. Which of the units for a second-order reaction found in this handbook or on another website is/are equivalent to the units used in this textbook?

Ronald Prasad
Ronald Prasad
Numerade Educator
03:46

Problem 104

Between 1957 and 1990 , according to NASA, the average amount of ozone in the stratosphere dropped from about 320 to about 130 Dobson Units (a measure of thickness). In a very blunt calculation, the annual percentage drop over this period can be calculated as the quantity $[(320-130) / 320]$ divided by $[1990-1957] .$ The 2007 CDC statistics show that 58,094 Americans were diagnosed with cancerous skin melanomas that year. If the annual percent drop in ozone concentration calculated above held steady, how many additional new cases of skin cancer in the U.S. would have resulted for 2008 as a result of the drop?

Yujie Wang
Yujie Wang
College of San Mateo
01:55

Problem 105

Before the late 1920 s (when Freon was invented), household refrigerators commonly ran on ammonia $\left(\mathrm{NH}_{3}\right)$ or sulfur dioxide $\left(\mathrm{SO}_{2}\right)$ gases. If you aren't already familiar with them, do a quick search on the safety hazards of these compounds. Would you rather have one of these old appliances in your kitchen, or a CFC-based fridge? Does your choice introduce conflict between what's best for the immediate environment and what's best for the global environment?

Manik Pulyani
Manik Pulyani
Numerade Educator
00:47

Problem 106

Another fluorinated hydrocarbon sold by DuPont is a common product you probably have in your home. What is it? (Hint: You won't stick to it.)

Ronald Prasad
Ronald Prasad
Numerade Educator