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Chemistry

Kenneth W Whitten

Chapter 16

Chemical Kinetics - all with Video Answers

Educators

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
01:50

Problem 4

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

Manik Pulyani
Manik Pulyani
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
03:02

Problem 7

Express the rate of reaction in terms of the rate of change of each reactant and product in the following reactions.
(a) $\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq})+2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{I}^{-}(\mathrm{aq}) \longrightarrow$
$\mathrm{I}_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell)$
(b) $2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})$
(c) $\mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow$
$\mathrm{CH}_{3} \mathrm{COO}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$
(d) $\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \longrightarrow \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{NO}_{3}(\mathrm{~g})$

KY
Kexin Yang
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.
(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 $0.30 \mathrm{M} / \mathrm{min}$ 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
04:12

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?
$$
4 \mathrm{NH}_{3}+5 \mathrm{O}_{2} \longrightarrow 4 \mathrm{NO}+6 \mathrm{H}_{2} \mathrm{O}
$$

Narayan Hari
Narayan Hari
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 pieces that were used were too large? too small?

KY
Kexin Yang
Numerade Educator
03:20

Problem 13

If doubling the initial concentration of a reactant doubles the initial rate of reaction, what is the order of the reaction with respect to the reactant? If this concentration change causes the rate to increase by a factor of 8, what is the order? If the concentration changes and the rate remains the same, what is the order?

SX
Sean Xiao
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
00:38

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?
$$
2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \longrightarrow \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})
$$

Manik Pulyani
Manik Pulyani
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; (d) of order $1 \frac{1}{2}$.

Narayan Hari
Narayan Hari
Numerade Educator
01:06

Problem 17

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

Manik Pulyani
Manik Pulyani
Numerade Educator
01:06

Problem 18

Rate data were obtained for the following reaction at $25^{\circ} \mathrm{C}$. What is the rate-law expression for the reaction?
$$
2 \mathrm{~A}+\mathrm{B}+2 \mathrm{C} \longrightarrow \mathrm{D}+2 \mathrm{E}
$$
$$
\begin{array}{ccccc}
& \begin{array}{c}
\text { Initial } \\
{[\mathrm{A}]} \\
\mathbf{( M})
\end{array} & \begin{array}{c}
\text { Initial } \\
{[\mathrm{B}]}
\end{array} & \begin{array}{c}
\text { Initial } \\
{[\mathrm{C}]} \\
(M)
\end{array} & \begin{array}{c}
\text { Initial Rate of } \\
\text { Formation of D } \\
(M)
\end{array} & \left(M \cdot \min ^{-1}\right) \\
\hline \text { Expt. } & (M) & 0.10 & 0.20 & 5.0 \times 10^{-4} \\
\hline 1 & 0.10 & 0.30 & 0.20 & 1.5 \times 10^{-3} \\
2 & 0.20 & 0.30 & 0.20 & 5.0 \times 10^{-4} \\
3 & 0.30 & 0.10 & 0.60 & 4.5 \times 10^{-3} \\
4 & 0.40 & 0.30 & 0.60 & 4.5 \times 10^{-3} \\
\hline
\end{array}
$$

Manik Pulyani
Manik Pulyani
Numerade Educator
03:20

Problem 19

(a) A certain reaction is zero order in reactant $\mathrm{A}$ and second order in reactant B. If the concentrations of both reactants are doubled, what happens to the reaction rate? (b) What would happen to the reaction rate if the reaction in part (a) were first order in A and first order in B?

SX
Sean Xiao
Numerade Educator
01:26

Problem 20

The rate expression for the following reaction is shown to be rate $=k[\mathrm{~A}]^{2}\left[\mathrm{~B}_{2}\right]$. If, during a reaction, the concentrations of both $\mathrm{A}$ and $\mathrm{B}_{2}$ were suddenly halved, the rate of the reaction would
$$
\mathrm{A}+\mathrm{B}_{2} \longrightarrow \text { products }
$$

Anatole Borisov
Anatole Borisov
Numerade Educator
01:06

Problem 21

Rate data were collected for the following reaction at a particular temperature.
$$
\mathrm{A}+\mathrm{B} \longrightarrow \text { products }
$$
$$
\begin{array}{cccc}
& \begin{array}{c}
\text { Initial } \\
{[\mathrm{A}]} \\
\text { Expt. }
\end{array} & \begin{array}{c}
\text { Initial } \\
{[\mathrm{B}]} \\
(\mathrm{mol} / \mathrm{L})
\end{array} & \begin{array}{c}
\text { Initial Rate of } \\
\text { Formation of C } \\
\left(M \cdot \mathrm{s}^{-1}\right)
\end{array} \\
\hline 1 & 0.10 & 0.10 & 0.0090 \\
2 & 0.20 & 0.20 & 0.072 \\
3 & 0.20 & 0.10 & 0.036 \\
4 & 0.20 & 0.30 & 0.11 \\
\hline
\end{array}
$$

Manik Pulyani
Manik Pulyani
Numerade Educator
01:41

Problem 22

Rate data were collected for the following reaction at a particular temperature.
$2 \mathrm{ClO}_{2}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow \mathrm{ClO}_{3}^{-}(\mathrm{aq})+\mathrm{ClO}_{2}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$
$$
\begin{array}{cccc}
& \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{ClO}_{2}\right]} \\
\text { Expt. }
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{OH}^{-}\right]} \\
(\mathrm{mol} / \mathrm{L})
\end{array} & \begin{array}{c}
\text { Initial Rate of } \\
\text { Formation of C } \\
\left(\boldsymbol{M} \cdot \mathrm{s}^{-1}\right)
\end{array} \\
\hline 1 & 0.012 & 0.012 & 2.07 \times 10^{-4} \\
2 & 0.012 & 0.024 & 4.14 \times 10^{-4} \\
3 & 0.024 & 0.012 & 8.28 \times 10^{-4} \\
4 & 0.024 & 0.024 & 1.66 \times 10^{-3} \\
\hline
\end{array}
$$
(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?

Manik Pulyani
Manik Pulyani
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.
$$
\begin{array}{cccc}
& & & \text { Initial Rate of } \\
\text { Expt. } & \begin{array}{c}
{\left[\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathbf{N H})_{2}\right]_{0}} \\
(\mathrm{~mol} / \mathrm{L})
\end{array} & \begin{array}{c}
{\left[\mathrm{I}_{2}\right]_{0}} \\
(\mathrm{~mol} / \mathrm{L})
\end{array} & \begin{array}{c}
\text { Formation of } \\
\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathbf{N}_{2}
\end{array} \\
\hline 1 & 0.015 & 0.015 & 3.15 M \cdot \mathrm{s}^{-1} \\
2 & 0.015 & 0.045 & 9.45 M \cdot \mathrm{s}^{-1} \\
3 & 0.030 & 0.045 & 18.9 M \cdot \mathrm{s}^{-1} \\
\hline
\end{array}
$$
(a) Write the rate-law expression. (b) What is the value, with units, for the specific rate constant?

Preeti Kumari
Preeti Kumari
Numerade Educator
01:37

Problem 24

A Given these data for the reaction $\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}$, write the rate-law expression.
$$
\begin{array}{cccc}
& & & \text { Initial Rate of } \\
\text { Expt. } & \begin{array}{c}
\text { Initial [A] } \\
(M)
\end{array} & \begin{array}{c}
\text { Initial [B] } \\
(M)
\end{array} & \begin{array}{c}
\text { Formation of C } \\
\left(M \cdot \mathrm{s}^{-1}\right)
\end{array} \\
\hline 1 & 0.10 & 0.20 & 5.0 \times 10^{-6} \\
2 & 0.10 & 0.30 & 7.5 \times 10^{-6} \\
3 & 0.20 & 0.40 & 4.0 \times 10^{-5} \\
\hline
\end{array}
$$

Manik Pulyani
Manik Pulyani
Numerade Educator
01:36

Problem 25

$\Delta$ (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?
$$
\begin{array}{cccc}
& \begin{array}{c}
\text { Initial [A] } \\
(\boldsymbol{M})
\end{array} & \begin{array}{c}
\text { Initial [B] } \\
(\boldsymbol{M})
\end{array} & \begin{array}{c}
\text { Initial Rate of } \\
\text { Formation of C } \\
\left(\boldsymbol{M} \cdot \mathrm{s}^{-1}\right)
\end{array} \\
\hline 1 & 0.15 & 0.25 & 8.0 \times 10^{-5} \\
2 & 0.30 & 0.25 & 3.2 \times 10^{-4} \\
3 & 0.60 & 0.50 & 5.12 \times 10^{-3}
\end{array}
$$

Manik Pulyani
Manik Pulyani
Numerade Educator
01:36

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?
$$
\begin{array}{cccc}
& \begin{array}{c}
\text { Initial [A] } \\
(M)
\end{array} & \begin{array}{c}
\text { Initial [B] } \\
(M)
\end{array} & \begin{array}{c}
\text { Initial Rate of } \\
\text { Formation of C } \\
(M / \mathrm{s})
\end{array} \\
\hline 1 & 0.10 & 0.10 & 2.0 \times 10^{-4} \\
2 & 0.10 & 0.20 & 8.0 \times 10^{-4} \\
3 & 0.20 & 0.40 & 2.56 \times 10^{-2}
\end{array}
$$

Manik Pulyani
Manik Pulyani
Numerade Educator
01:19

Problem 27

Consider a chemical reaction between compounds 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.
$$
\begin{array}{cccc}
\text { Expt. } & \text { Rate }\left(M \cdot \mathrm{s}^{-1}\right) & {[\mathrm{A}]} & {[\mathrm{B}]} \\
\hline 1 & 0.24 & 0.20 M & 0.050 M \\
2 & 0.20 & -M & 0.030 M \\
3 & 0.80 & 0.40 M & -M
\end{array}
$$

Manik Pulyani
Manik Pulyani
Numerade Educator
01:19

Problem 28

Consider a chemical reaction of compounds $\mathrm{A}$ and $\mathrm{B}$ that was found to be first order in A and second order in B. From the following information, fill in the blanks.
$$
\begin{array}{cccc}
\text { Expt. } & \text { Rate }\left(M \cdot \mathrm{s}^{-1}\right) & {[\mathrm{A}]} & {[\mathrm{B}]} \\
\hline 1 & 0.150 & 1.00 M & 0.200 M \\
2 & & 2.00 M & 0.200 M \\
3 & & 2.00 M & 0.400 M
\end{array}
$$

Manik Pulyani
Manik Pulyani
Numerade Educator
00:56

Problem 29

A The rate of decomposition of $\mathrm{NO}_{2}$ by the following reaction at a particular temperature is $5.4 \times 10^{-5} \mathrm{~mol} \mathrm{NO}_{2} / \mathrm{L} \cdot \mathrm{s}$
when $\left[\mathrm{NO}_{2}\right]=0.0100 \mathrm{~mol} / \mathrm{L}$.
$$
2 \mathrm{NO}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g})
$$
(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 $\left[\mathrm{NO}_{2}\right]=$ $0.00500 \mathrm{~mol} / \mathrm{L} ?$ (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 $\left[\mathrm{NO}_{2}\right]=0.00500 \mathrm{~mol} / \mathrm{L} ?(\mathrm{c})$ The rate when
$\left[\mathrm{NO}_{2}\right]=0.00500 \mathrm{~mol} / \mathrm{L}$ is observed to be $1.4 \times 10^{-5} \mathrm{~mol}$
$\mathrm{NO}_{2} / \mathrm{L} \cdot \mathrm{s}$. Which rate law is correct? (d) Calculate the rate constant. (Reminder: Express the rate of reaction in terms of rate of disappearance of $\mathrm{NO}_{2}$.)

Manik Pulyani
Manik Pulyani
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 $0.135 \mathrm{~mol}$ $\mathrm{C}_{2} \mathrm{~F}_{4}$ 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
01:15

Problem 34

The decomposition reaction of carbon disulfide, $\mathrm{CS}_{2}$, to carbon monosulfide, $\mathrm{CS}$, 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?

Manik Pulyani
Manik Pulyani
Numerade Educator
01:48

Problem 35

The first-order rate constant for the conversion of cyclobutane to ethylene at $1000 .{ }^{\circ} \mathrm{C}$ is $87 \mathrm{~s}^{-1}$. (a) What is the half-life of this reaction at $1000 .{ }^{\circ} \mathrm{C}$ ? (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
01:25

Problem 36

For the reaction
$$
2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2}
$$
the rate equation is
$$
\text { rate }=1.4 \times 10^{-10} M^{-1} \cdot \mathrm{s}^{-1}\left[\mathrm{NO}_{2}\right]^{2} \text { at } 25^{\circ} \mathrm{C}
$$
(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?

Manik Pulyani
Manik Pulyani
Numerade Educator
00:43

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$223 ?$

Ronald Prasad
Ronald Prasad
Numerade Educator
00:44

Problem 38

Cyclopropane rearranges to form propene in a reaction that follows first-order kinetics. At $800 . \mathrm{K}$, the specific rate constant for this reaction is $2.74 \times 10^{-3} \mathrm{~s}^{-1}$. Suppose we start with a cyclopropane concentration of $0.290 M .$ How long will it take for $99.0 \%$ of the cyclopropane to disappear according to this reaction?

Manik Pulyani
Manik Pulyani
Numerade Educator
01:16

Problem 39

The rate constant for the first-order reaction
$$
\mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}
$$
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 $0.00100 M ?$ (b) How much longer will it take for a further decrease to $0.000900 \mathrm{M}$ ?

Narayan Hari
Narayan Hari
Numerade Educator
00:57

Problem 40

It is found that $47.0$ minutes is required for the concentration of substance A to decrease from $0.75 M$ to $0.25 M$. What is the rate constant for this first-order decomposition?
$$
\mathrm{A} \longrightarrow \mathrm{B}+\mathrm{C}
$$

Ronald Prasad
Ronald Prasad
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.
$$
\mathrm{NH}_{3} \longrightarrow \mathrm{NH}_{2}+\mathrm{H}
$$
$$
\begin{array}{cc}
t \text { (hours) } & {\left[\mathbf{N H}_{3}\right](\mathbf{m o l} / \mathbf{L})} \\
\hline 0 & 8.000 \times 10^{-7} \\
25 & 6.75 \times 10^{-7} \\
50 & 5.84 \times 10^{-7} \\
75 & 5.15 \times 10^{-7} \\
\hline
\end{array}
$$
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 $600 . \mathrm{s}$.
$$
\begin{array}{cc}
t \text { (seconds) } & {[\mathrm{HII}(\mathrm{mmol} / \mathrm{L})} \\
\hline 0 . & 5.46 \\
250 . & 4.10 \\
500 . & 2.73 \\
750 . & 1.37
\end{array}
$$

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 $\mathrm{Cl}$, 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 $\mathrm{Cl}$, 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 $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to react?

Ronald Prasad
Ronald Prasad
Numerade Educator
00:53

Problem 44

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

Manik Pulyani
Manik Pulyani
Numerade Educator
01:44

Problem 45

At body temperature, the first-order rate constant is $1.87 \times$ $10^{-3} \min ^{-1}$ 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 $4.75 \times 10^{-3} M ?$

Narayan Hari
Narayan Hari
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 does 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: $A=3.98 \times 10^{13} \mathrm{~s}^{-1}, E_{\mathrm{a}}=160 . \mathrm{kJ} / \mathrm{mol}$.
(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 $115^{\circ} \mathrm{C}$.

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, $\Delta E$, for each kind of reaction and the activation energy. 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 reactions are 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
01:19

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
01:05

Problem 56

The rate constant of a reaction is tripled when the temperature is increased from $298 \mathrm{~K}$ to $308 \mathrm{~K}$. Find $E_{\mathrm{a}}$.

Manik Pulyani
Manik Pulyani
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
01:23

Problem 58

For a particular reaction, $\Delta E^{0}=51.51 \mathrm{~kJ} / \mathrm{mol}, k=8.0 \times$
$10^{-7} \mathrm{~s}^{-1}$ 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.

Manik Pulyani
Manik Pulyani
Numerade Educator
03:01

Problem 59

14 You are given the rate constant as a function of temperature for the exchange reaction
$\mathrm{Mn}(\mathrm{CO})_{5}\left(\mathrm{CH}_{3} \mathrm{CN}\right)^{+}+\mathrm{NC}_{5} \mathrm{H}_{5} \longrightarrow$
$\mathrm{Mn}(\mathrm{CO})_{5}\left(\mathrm{NC}_{5} \mathrm{H}_{5}\right)++\mathrm{CH}_{3} \mathrm{CN}$
$$
\begin{array}{lc}
T(\mathbf{K}) & k\left(\min ^{-1}\right) \\
\hline 298 & 0.0409 \\
305 & 0.0818 \\
312 & 0.157 \\
\hline
\end{array}
$$

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.
$$
\begin{array}{lc}
T(\mathbf{K}) & k\left(\mathrm{~s}^{-1}\right) \\
\hline 600 . & 3.30 \times 10^{-9} \\
650 . & 2.19 \times 10^{-7} \\
700 . & 7.96 \times 10^{-6} \\
750 . & 1.80 \times 10^{-4} \\
800 . & 2.74 \times 10^{-3} \\
850 . & 3.04 \times 10^{-2} \\
900 . & 2.58 \times 10^{-1} \\
\hline
\end{array}
$$
(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

A 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 $1.0 \times 10^{-6} \mathrm{M}$ 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 $6.76 \times 10^{-4} \mathrm{~s}^{-1} \cdot$ (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 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
View

Problem 66

The rate equation for the reaction
$$
\mathrm{Cl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{~S}(\mathrm{aq}) \longrightarrow \mathrm{S}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq})
$$
is found to be rate $=k\left[\mathrm{Cl}_{2}\right]\left[\mathrm{H}_{2} \mathrm{~S}\right] .$ Which of the following mechanisms are consistent with the rate law?

Stephen Pulliam
Stephen Pulliam
Numerade Educator
05:05

Problem 67

Q 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)
$\mathrm{C}+\mathrm{D} \rightleftharpoons \mathrm{E} \quad$ (fast, equilibrium)
$\mathrm{E} \longrightarrow \mathrm{F} \quad$ (slow)

Ronald Prasad
Ronald Prasad
Numerade Educator
01:23

Problem 68

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

Manik Pulyani
Manik Pulyani
Numerade Educator
01:04

Problem 69

Q 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.
$$
\mathrm{O}_{3}(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})
$$
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?

Crystal Wang
Crystal Wang
Numerade Educator
01:29

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)

Manik Pulyani
Manik Pulyani
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 $=k\left[\mathrm{H}_{2}\right]\left[\mathrm{I}_{2}\right]$.
$$
\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{I}
$$
(fast, equilibrium)
$$
\mathrm{I}+\mathrm{H}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{I}
$$
(fast, equilibrium)
$$
\mathrm{H}_{2} \mathrm{I}+\mathrm{I} \longrightarrow 2 \mathrm{HI}
$$
(slow)
(b) Identify any reaction intermediates in this proposed mechanism.

Preeti Kumari
Preeti Kumari
Numerade Educator
01:32

Problem 72

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

Manik Pulyani
Manik Pulyani
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.
$$
2 \mathrm{NO} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2}
$$
(fast, equilibrium)
$$
\mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{Br}_{2} \longrightarrow 2 \mathrm{NOBr} \quad \text { (slow) }
$$
Is this mechanism consistent with the observation that the reaction is second order in $\mathrm{NO}$ and first order in $\mathrm{Br}$ ?

Preeti Kumari
Preeti Kumari
Numerade Educator
00:45

Problem 74

- The following mechanism for the reaction between $\mathrm{H}_{2}$ and CO to form formaldehyde, $\mathrm{H}_{2} \mathrm{CO}$, has been proposed.
$$
\mathrm{H}_{2} \rightleftharpoons 2 \mathrm{H}
$$
(fast, equilibrium)
$$
\mathrm{H}+\mathrm{CO} \longrightarrow \mathrm{HCO}
$$
(slow)
$$
\mathrm{H}+\mathrm{HCO} \longrightarrow \mathrm{H}_{2} \mathrm{CO}
$$
(fast)
(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?

Manik Pulyani
Manik Pulyani
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.
$\begin{array}{ll}\text { (a) } \mathrm{NO}_{2}+\mathrm{NO}_{2} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4} & \text { (fast, equilibrium) }\end{array}$
$\mathrm{N}_{2} \mathrm{O}_{4}+\mathrm{O}_{3} \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}+\mathrm{O}_{2} \quad$ (slow)
(b) $\mathrm{NO}_{2}+\mathrm{O}_{3} \longrightarrow \mathrm{NO}_{3}+\mathrm{O}_{2} \quad$ (slow)
$\mathrm{NO}_{3}+\mathrm{NO}_{2} \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}$
(fast)

Preeti Kumari
Preeti Kumari
Numerade Educator
01:19

Problem 76

(a) What is the transition state in a reactant 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?

Manik Pulyani
Manik Pulyani
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 $3.00$ -L container.
(a) How many moles of $\mathrm{ClO}_{2} \mathrm{~F}$ would remain after $2.00 \mathrm{~min}$ 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
00:48

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 $3.00$ -L container.
(a) How many moles of $\mathrm{N}_{2} \mathrm{O}_{5}$ would remain after $2.00 \mathrm{~min}$ 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 $25^{\circ} \mathrm{C}$ ?

Manik Pulyani
Manik Pulyani
Numerade Educator
05:19

Problem 79

The decomposition of gaseous dimethyl ether
$$
\mathrm{CH}_{3} \mathrm{OCH}_{3} \longrightarrow \mathrm{CH}_{4}+\mathrm{CO}+\mathrm{H}_{2}
$$
follows first-order kinetics. Its half-life is $25.0 \mathrm{~min}$ at $500 .{ }^{\circ} \mathrm{C}$. (a) Starting with $12.00 \mathrm{~g}$ of dimethyl ether at $500 .{ }^{\circ} \mathrm{C}$, how many grams would remain after $150 .$ min?
(b) In part (a), how many grams would remain after $180 .$ min? (c) In part (b), what fraction remains, and what fraction reacts? (d) Calculate the time, in minutes, required to decrease $24.0 \mathrm{mg}$ of dimethyl ether to $2.40 \mathrm{mg}$.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:16

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 $(\mathrm{mmol} / \mathrm{L})$.

Manik Pulyani
Manik Pulyani
Numerade Educator
01:03

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 $(\mathrm{mmol} / \mathrm{L})$.
(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 $[\mathrm{CO}]=0.600 \mathrm{mmol} / \mathrm{L}$.

Manik Pulyani
Manik Pulyani
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
01:24

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.

Manik Pulyani
Manik Pulyani
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
01:14

Problem 84

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

Manik Pulyani
Manik Pulyani
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
01:27

Problem 86

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

Manik Pulyani
Manik Pulyani
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
02:09

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.

Manik Pulyani
Manik Pulyani
Numerade Educator
02:43

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
01:02

Problem 90

Construct a diagram like that in Figure 16-10b. (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?

Manik Pulyani
Manik Pulyani
Numerade Educator
03:25

Problem 91

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 92

A 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 92

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 94

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 95

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 $\mathrm{K}$. How does $\Delta H^{0}$ compare with $\Delta E^{0}$ for this reaction?) Show energy values if known.

Ronald Prasad
Ronald Prasad
Numerade Educator
00:50

Problem 96

1. The activation energy for the reaction between $\mathrm{O}_{3}$ and $\mathrm{NO}$ is $9.6 \mathrm{~kJ} / \mathrm{mol}$.
$$
\mathrm{O}_{3}(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})
$$
(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 $\Delta E^{0}$ for this reaction?)

Manik Pulyani
Manik Pulyani
Numerade Educator
04:14

Problem 97

Go to http://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 98

Go to http://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 99

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

Ronald Prasad
Ronald Prasad
Numerade Educator