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Chemistry and Chemical Reactivity

John C. Kotz, Paul M. Treichel, Gabriela C. Weaver

Chapter 15

Principles of Reactivity: Chemical Kinetics - all with Video Answers

Educators

Chapter Questions

01:14

Problem 1

Give the relative rates of disappearance of reactants and formation of products for each of the following reactions.
(a) $2 \mathrm{O}_{3}(\mathrm{g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{g})$
(b) $2 \mathrm{HOF}(\mathrm{g}) \longrightarrow 2 \mathrm{HF}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$

Will Li
Will Li
Numerade Educator
00:51

Problem 2

Give the relative rates of disappearance of reactants and formation of products for each of the following reactions.
(a) $2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})$
(b) $\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})$

Will Li
Will Li
Numerade Educator
01:00

Problem 3

In the reaction $2 \mathrm{O}_{3}(\mathrm{g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{g}),$ the rate of formation of $\mathrm{O}_{2}$ is $1.5 \times 10^{-3} \mathrm{mol} / \mathrm{L} \cdot$ s. What is the rate of decomposition of $\mathrm{O}_{3} ?$

Will Li
Will Li
Numerade Educator
01:35

Problem 4

In the synthesis of ammonia, if $-\Delta\left[\mathrm{H}_{2}\right] / \Delta t=4.5 \times 10^{-4}$ $\mathrm{mol} / \mathrm{L} \cdot \mathrm{min},$ what is $\Delta\left[\mathrm{NH}_{3}\right] / \Delta t ?$ $\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})$

Will Li
Will Li
Numerade Educator
01:27

Problem 5

Experimental data are listed here for the reaction $\mathrm{A} \longrightarrow 2 \mathrm{B}.$
$$\begin{array}{ll}\hline \begin{array}{l}\text { Time } \\(\mathrm{s})\end{array} & \begin{array}{l}{[\mathrm{B}]} \\(\mathrm{mol} / \mathrm{L})\end{array} \\\hline 0.00 & 0.000 \\10.0 & 0.326 \\20.0 & 0.572 \\30.0 & 0.750 \\40.0 & 0.890 \\\hline\end{array}$$
(a) Prepare a graph from these data, connect the points with a smooth line, and calculate the rate of change of [B] for each $10-$ s interval from 0.0 to 40.0 s. Does the rate of change decrease from one time interval to the next? Suggest a reason for this result.
(b) How is the rate of change of $[\mathrm{A}]$ related to the rate of change of $[\mathrm{B}]$ in each time interval? Calculate the rate of change of $[\mathrm{A}]$ for the time interval from 10.0 to $20.0 \mathrm{s}$
(c) What is the instantaneous rate when $[\mathrm{B}]=0.750$ $\mathrm{mol} / \mathrm{L} ?$

Aadit Sharma
Aadit Sharma
Numerade Educator
04:16

Problem 6

Phenyl acetate, an ester, reacts with water according to the equation
(Check your book to see figure)
The data in the table were collected for this reaction at $5^{\circ} \mathrm{C}.$
$$\begin{array}{ll}\hline \begin{array}{l}\text { Time } \\(s)\end{array} & \begin{array}{l}\text { [Phenyl acetate] } \\(\mathrm{mol} / \mathrm{L})\end{array} \\\hline 0 & 0.55 \\15.0 & 0.42 \\30.0 & 0.31 \\45.0 & 0.23 \\60.0 & 0.17 \\75.0 & 0.12 \\90.0 & 0.085 \\\hline\end{array}$$
(a) Plot the phenyl acetate concentration versus time, and describe the shape of the curve observed.
(b) Calculate the rate of change of the phenyl acetate concentration during the period $15.0 \mathrm{s}$ to $30.0 \mathrm{s}$ and also during the period $75.0 \mathrm{s}$ to $90.0 \mathrm{s}$. Compare the values, and suggest a reason why one value is smaller than the other.
(c) What is the rate of change of the phenol concentration during the time period $60.0 \mathrm{s}$ to $75.0 \mathrm{s} ?$
(d) What is the instantaneous rate at $15.0 \mathrm{s} ?$

Ronald Prasad
Ronald Prasad
Numerade Educator
00:43

Problem 7

Using the rate equation "Rate $=k[\mathrm{A}]^{2}[\mathrm{B}],$ define the order of the reaction with respect to A and B. What is the total order of the reaction?

Will Li
Will Li
Numerade Educator
01:47

Problem 8

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 A is halved?

Will Li
Will Li
Numerade Educator
01:37

Problem 9

The reaction between ozone and nitrogen dioxide at $231 \mathrm{K}$ is first order in both $\left[\mathrm{NO}_{2}\right]$ and $\left[\mathrm{O}_{3}\right]$
$$2 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{O}_{3}(\mathrm{g}) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g})$$
(a) Write the rate equation for the reaction.
(b) If the concentration of $\mathrm{NO}_{2}$ is tripled, what is the change in the reaction rate?
(c) What is the effect on reaction rate if the concentration of $\mathrm{O}_{3}$ is halved?

Will Li
Will Li
Numerade Educator
01:44

Problem 10

Nitrosyl bromide, NOBr, is formed from NO and Bre:
$$2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})$$
Experiments show that this reaction is second order in NO and first order in $\mathrm{Br}_{2}.$
(a) Write the rate equation for the reaction.
(b) How does the initial reaction rate change if the concentration of $\mathrm{Br}_{2}$ is changed from $0.0022 \mathrm{mol} / \mathrm{L}$ to $0.0066 \mathrm{mol} / \mathrm{L} ?$
(c) What is the change in the initial rate if the concentration of NO is changed from $0.0024 \mathrm{mol} / \mathrm{L}$ to $0.0012 \mathrm{mol} / \mathrm{L} ?$

Will Li
Will Li
Numerade Educator
11:53

Problem 11

The data in the table are for the reaction of $\mathrm{NO}$ and $\mathrm{O}_{2}$ at $660 \mathrm{K}$
$$2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})$$
(Check your book to see table)
(a) Determine the order of the reaction for each reactant.
(b) Write the rate equation for the reaction.
(c) Calculate the rate constant.
(d) Calculate the rate (in $\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}$ ) at the instant when $[\mathrm{NO}]=0.015 \mathrm{mol} / \mathrm{L}$ and $\left[\mathrm{O}_{2}\right]=0.0050 \mathrm{mol} / \mathrm{L}$
(e) At the instant when NO is reacting at the rate $1.0 \times$ $10^{-4} \mathrm{mol} / \mathrm{L} \cdot \mathrm{s},$ what is the rate at which $\mathrm{O}_{2}$ is reacting and $\mathrm{NO}_{2}$ is forming?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
04:33

Problem 12

The reaction
$$2 \mathrm{NO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{N}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$
was studied at $904^{\circ} \mathrm{C},$ and the data in the table were collected.
$$\begin{array}{lll}\hline \begin{array}{l}\text { Reactant Concentration } \\(\mathrm{mol} / \mathrm{L})\end{array} & & \\\hline[\mathrm{N} 0] & {\left[\mathrm{H}_{2}\right]} & \begin{array}{l}\text { Rate of Appearance of } \mathrm{N}_{2} \\(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s})\end{array} \\\hline 0.420 & 0.122 & 0.136 \\0.210 & 0.122 & 0.0339 \\0.210 & 0.244 & 0.0678 \\0.105 & 0.488 & 0.0339 \\\hline\end{array}$$
(a) Determine the order of the reaction for each reactant.
(b) Write the rate equation for the reaction.
(c) Calculate the rate constant for the reaction.
(d) Find the rate of appearance of $\mathrm{N}_{2}$ at the instant when $[\mathrm{NO}]=0.350 \mathrm{mol} / \mathrm{L}$ and $\left[\mathrm{H}_{2}\right]=0.205 \mathrm{mol} / \mathrm{L}.$

Anatole Borisov
Anatole Borisov
Numerade Educator
04:40

Problem 13

Data for the reaction $2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})$ are given in the table.
(Check your book to see figure)
(a) What is the rate law for this reaction?
(b) What is the rate constant for the reaction?
(c) What is the initial rate of the reaction in experiment $4 ?$

Prashant Bana
Prashant Bana
Numerade Educator
04:24

Problem 14

Data for the following reaction are given in the table below.
$$\mathrm{CO}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{NO}(\mathrm{g})$$
(Check your book to see table)
(a) What is the rate law for this reaction?
(b) What is the rate constant for the reaction?
(c) What is the initial rate of the reaction in experiment $4 ?$

Will Li
Will Li
Numerade Educator
02:20

Problem 15

Carbon monoxide reacts with $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$ :
$$2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{g})$$
Information on this reaction is given in the table below.
$$\begin{array}{lll}\hline[\mathrm{CO}](\mathrm{mol} / \mathrm{L}) & {\left[\mathrm{O}_{2}\right](\mathrm{mol} /\mathrm{L})} & \text { Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{min}) \\\hline 0.02 & 0.02 & 3.68 \times 10^{-5} \\0.04 & 0.02 & 1.47 \times 10^{-4} \\0.02 & 0.04 & 7.36 \times 10^{-5} \\\hline\end{array}$$
(a) What is the rate law for this reaction?
(b) What is the order of the reaction with respect to CO? What is the order with respect $\mathrm{O}_{2} ?$ What is the overall order of the reaction?
(c) What is the value for the rate constant, $k ?$

Will Li
Will Li
Numerade Educator
04:09

Problem 16

Data for the reaction
$$\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow \mathrm{HPO}_{4}^{2-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$$
are provided in the table.
$$\begin{array}{llll}\hline & & & \text { Initial Rate } \\\text { Experiment } & {\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right](\mathrm{M})} &{\left[\mathrm{OH}^{-}\right](\mathrm{M})} & (\mathrm{mol} / \mathrm{L} \cdot \mathrm{min}) \\\hline 1 & 0.0030 & 0.00040 & 0.0020 \\2 & 0.0030 & 0.00080 & 0.0080 \\3 & 0.0090 & 0.00040 & 0.0060 \\4 & ? & 0.00033 & 0.0020 \\\hline\end{array}$$
(a) What is the rate law for this reaction?
(b) What is the value of $k ?$
(c) What is the concentration of $\mathrm{H}_{2} \mathrm{PO}_{4}^{-}$ in experiment 4?

Anatole Borisov
Anatole Borisov
Numerade Educator
01:42

Problem 17

The rate equation for the hydrolysis of sucrose to fructose and glucose
$$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow 2 \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{aq})$$
is " $-\Delta[\text { sucrose }] / \Delta t=k\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right] .$ After $2.57 \mathrm{h}$ at $27^{\circ} \mathrm{C}$ the sucrose concentration decreased from $0.0146 \mathrm{M}$ to $0.0132 \mathrm{M} .$ Find the rate constant, $k.$

Anatole Borisov
Anatole Borisov
Numerade Educator
01:40

Problem 18

The decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ in $\mathrm{CCl}_{4}$ is a first-order reaction. If $2.56 \mathrm{mg}$ of $\mathrm{N}_{2} \mathrm{O}_{5}$ is present initially, and $2.50 \mathrm{mg}$ is present after 4.26 min at $55^{\circ} \mathrm{C},$ what is the value of the rate constant, $k ?$

Anatole Borisov
Anatole Borisov
Numerade Educator
01:16

Problem 19

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is a first-order reaction:
$$\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$$
The rate constant for the reaction is $2.8 \times 10^{-3} \mathrm{min}^{-1}$ at $600 \mathrm{K} .$ If the initial concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $1.24 \times 10^{-3}$ mol/L, how long will it take for the concentration to drop to $0.31 \times 10^{-3} \mathrm{mol} / \mathrm{L} ?$

Anatole Borisov
Anatole Borisov
Numerade Educator
00:51

Problem 20

The conversion of cyclopropane to propene, described in Example $15.5,$ occurs with a first-order rate constant of $5.4 \times 10^{-2} \mathrm{h}^{-1} .$ How long will it take for the concentration of cyclopropane to decrease from an initial concentration $0.080 \mathrm{mol} / \mathrm{L}$ to $0.020 \mathrm{mol} / \mathrm{L} ?$

Anatole Borisov
Anatole Borisov
Numerade Educator
01:41

Problem 21

Ammonium cyanate, NH_NCO, rearranges in water to give urea, (NH$_{2}$) $_{2}$ CO:
$$\mathrm{NH}_{4} \mathrm{NCO}(\mathrm{aq}) \longrightarrow\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}(\mathrm{aq})$$
The rate equation for this process is "Rate $=k$ $\left[\mathrm{NH}_{4} \mathrm{NCO}\right]^{2}, "$ where $k=0.0113 \mathrm{L} / \mathrm{mol} \cdot$ min. If the original concentration of $\mathrm{NH}_{4} \mathrm{NCO}$ in solution is $0.229 \mathrm{mol} / \mathrm{L}$ how long will it take for the concentration to decrease to $0.180 \mathrm{mol} / \mathrm{L} ?$

Will Li
Will Li
Numerade Educator
00:52

Problem 22

The decomposition of nitrogen dioxide at a high temperature
$$\mathrm{NO}_{2}(\mathrm{g}) \longrightarrow \mathrm{NO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})$$
is second order in this reactant. The rate constant for this reaction is $3.40 \mathrm{L} / \mathrm{mol} \cdot$ min. Determine the time needed for the concentration of $\mathrm{NO}_{2}$ to decrease from $2.00 \mathrm{mol} / \mathrm{L}$ to $1.50 \mathrm{mol} / \mathrm{L}.$

Anatole Borisov
Anatole Borisov
Numerade Educator
03:10

Problem 23

Hydrogen peroxide, $\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}),$ decomposes to $\mathrm{H}_{2} \mathrm{O}(\ell)$ and $\mathrm{O}_{2}(\mathrm{g})$ in a reaction that is first order in $\mathrm{H}_{2} \mathrm{O}_{2}$ and has a rate constant $k=1.06 \times 10^{-3} \mathrm{min}^{-1}$
(a) How long will it take for $15 \%$ of a sample of $\mathrm{H}_{2} \mathrm{O}_{2}$ to decompose?
(b) How long will it take for $85 \%$ of the sample to decompose?

Will Li
Will Li
Numerade Educator
01:57

Problem 24

The thermal decomposition of $\mathrm{HCO}_{2} \mathrm{H}$ is a first-order reaction with a rate constant of $2.4 \times 10^{-3} \mathrm{s}^{-1}$ at a given temperature. How long will it take for three fourths of a sample of HCO, H to decompose?

Will Li
Will Li
Numerade Educator
02:54

Problem 25

The rate equation for the decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ (giving $\mathrm{NO}_{2}$ and $\mathrm{O}_{2}$ ) is $^{*}-\Delta\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] / \Delta t=k\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] .$ "The value of $k$ is $5.0 \times 10^{-4} \mathrm{s}^{-1}$ for the reaction at a particular temperature.
(a) Calculate the half-life of $\mathrm{N}_{2} \mathrm{O}_{5}$
(b) How long does it take for the $\mathrm{N}_{2} \mathrm{O}_{5}$ concentration to drop to one tenth of its original value?

Will Li
Will Li
Numerade Educator
03:59

Problem 26

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$
$$\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$$
is first order in $\mathrm{SO}_{2} \mathrm{Cl}_{2}$, and the reaction has a half-life of 245 min at $600 \mathrm{K}$. If you begin with $3.6 \times 10^{-3} \mathrm{mol}$ of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ in a $1.0-\mathrm{L}$ flask, how long will it take for the amount of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to decrease to $2.00 \times 10^{-4}$ mol?

Will Li
Will Li
Numerade Educator
02:57

Problem 27

Gaseous azomethane, $\mathrm{CH}_{3} \mathrm{N}=\mathrm{NCH}_{3},$ decomposes in a first-order reaction when heated:
$$\mathrm{CH}_{3} \mathrm{N}=\mathrm{NCH}_{3}(\mathrm{g}) \longrightarrow \mathrm{N}_{2}(\mathrm{g})+\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})$$
The rate constant for this reaction at $425^{\circ} \mathrm{C}$ is $40.8 \mathrm{min}^{-1}$ If the initial quantity of azomethane in the flask is $2.00 \mathrm{g}$ how much remains after 0.0500 min? What quantity of $\mathrm{N}_{2}$ is formed in this time?

Anatole Borisov
Anatole Borisov
Numerade Educator
02:40

Problem 28

The compound $\mathrm{Xe}\left(\mathrm{CF}_{3}\right)_{2}$ decomposes in a first-order reaction to elemental Xe with a half-life of 30. min. If you place $7.50 \mathrm{mg}$ of $\mathrm{Xe}\left(\mathrm{CF}_{3}\right)_{2}$ in a flask, how long must you wait until only 0.25 mg of $\mathrm{Xe}\left(\mathrm{CF}_{3}\right)_{2}$ remains?

Will Li
Will Li
Numerade Educator
01:35

Problem 29

The radioactive isotope $^{64} \mathrm{Cu}$ is used in the form of $\mathrm{cop}$ per(II) acetate to study Wilson's disease. The isotope has a half-life of $12.70 \mathrm{h}$. What fraction of radioactive copper (II) acetate remains after $64 \mathrm{h} ?$

Will Li
Will Li
Numerade Educator
01:32

Problem 30

Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.7 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 1.0 day?

Anatole Borisov
Anatole Borisov
Numerade Educator
01:17

Problem 31

Formic acid decomposes at $550^{\circ} \mathrm{C}$ according to the equation
$$\mathrm{HCO}_{2} \mathrm{H}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$
The reaction follows first-order kinetics. In an experiment, it is determined that $75 \%$ of a sample of $\mathrm{HCO}_{2} \mathrm{H}$ has decomposed in 72 seconds. Determine $t_{1 / 2}$ for this reaction.

Will Li
Will Li
Numerade Educator
01:44

Problem 32

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to $\mathrm{SO}_{2}$ and $\mathrm{Cl}_{2}$ at high temperature is a first-order reaction with a half-life of $2.5 \times 10^{3}$ min. What fraction of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ will remain after 750 min?

Anatole Borisov
Anatole Borisov
Numerade Educator
02:59

Problem 33

Common sugar, sucrose, breaks down in dilute acid solution to form glucose and fructose. Both products have the same formula, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}.$
$$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow 2 \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{aq})$$
The rate of this reaction has been studied in acid solution, and the data in the table were obtained.
$$\begin{array}{cc}\hline \begin{array}{c}\text { Time } \\(\text { min })\end{array} & \begin{array}{c}{\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathbf{0}_{11}\right]} \\(\mathrm{mol} / \mathrm{L})\end{array} \\\hline 0 & 0.316 \\39 & 0.274 \\80 & 0.238 \\140 & 0.190 \\210 & 0.146 \\\hline\end{array}$$
(a) Plot ln [sucrose] versus time and $1 /$ [sucrose] versus time. What is the order of the reaction?
(b) Write the rate equation for the reaction, and calculate the rate constant, $k.$
(c) Estimate the concentration of sucrose after 175 min.

Prashant Bana
Prashant Bana
Numerade Educator
02:01

Problem 34

Data for the reaction of phenyl acetate with water are given in Study Question 6. Plot these data as ln phenyl acetate and 1/ phenyl acetate versus time. Based on the appearance of the two graphs, what can you conclude about the order of the reaction with respect to phenyl acetate? Working from the data and the rate law, deter- mine the rate constant for the reaction.

Prashant Bana
Prashant Bana
Numerade Educator
02:56

Problem 35

Data for the decomposition of dinitrogen oxide
$$2 \mathrm{N}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{N}_{2} (\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$
on a gold surface at $900^{\circ} \mathrm{C}$ are given below. Verify that the reaction is first order by preparing a graph of $\ln \left[\mathrm{N}_{2} \mathrm{O}\right]$ versus time. Derive the rate constant from the slope of the line in this graph. Using the rate law and value of $k$, determine the decomposition rate at $900^{\circ} \mathrm{C}$ when $\left[\mathrm{N}_{2} \mathrm{O}\right]=$ $0.035 \mathrm{mol} / \mathrm{L}.$
$$\begin{array}{cc}\hline \begin{array}{c}\text { Time } \\\text { (min) }\end{array} & \begin{array}{c}{\left[\mathrm{N}_{2} 0\right]} \\(\mathrm{mol} / \mathrm{L})\end{array} \\\hline 15.0 & 0.0835 \\30.0 & 0.0680 \\80.0 & 0.0350 \\120.0 & 0.0220 \\\hline\end{array}$$

Prashant Bana
Prashant Bana
Numerade Educator
03:39

Problem 36

Ammonia decomposes when heated according to the equation
$$\mathrm{NH}_{3}(\mathrm{g}) \longrightarrow \mathrm{NH}_{2}(\mathrm{g})+\mathrm{H}(\mathrm{g})$$
The data in the table for this reaction were collected at a high temperature.
$$\begin{array}{ll}\hline \begin{array}{l}\text { Time } \\\text { (h) }\end{array} & \begin{array}{l}{\left[\mathrm{NH}_{3}\right]} \\(\mathrm{mol} / \mathrm{L})\end{array} \\\hline 0 & 8.00 \times 10^{-7} \\25 & 6.75 \times 10^{-7} \\50 & 5.84 \times 10^{-7} \\75 & 5.15 \times 10^{-7} \\\hline\end{array}$$
Plot $\ln \left[\mathrm{NH}_{3}\right]$ versus time and $1 /\left[\mathrm{NH}_{3}\right]$ versus time. What is the order of this reaction with respect to NH $_{3} ?$ Find the rate constant for the reaction from the slope.

Prashant Bana
Prashant Bana
Numerade Educator
01:01

Problem 37

Gaseous $\left[\mathrm{NO}_{2}\right]$ decomposes at $573 \mathrm{K}$
$$2 \mathrm{NO}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$
The concentration of $\mathrm{NO}_{2}$ was measured as a function of time. A graph of $1 /\left[\mathrm{NO}_{2}\right]$ versus time gives a straight line with a slope of $1.1 \mathrm{L} / \mathrm{mol} \cdot$ s. What is the rate law for this reaction? What is the rate constant?

Will Li
Will Li
Numerade Educator
06:17

Problem 38

The decomposition of HOF occurs at $25^{\circ} \mathrm{C}$
$$2 \mathrm{HOF}(\mathrm{g}) \longrightarrow 2 \mathrm{HF}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$
Using the data in the table below, determine the rate law and then calculate the rate constant.
$$\begin{array}{lc}\hline \begin{array}{l}{[\mathrm{HOF}]} \\(\mathrm{mol} / \mathrm{L})\end{array} & \begin{array}{l}\text { Time } \\(\mathrm{min})\end{array} \\\hline 0.850 & 0 \\0.810 & 2.00 \\0.754 & 5.00 \\0.526 & 20.0 \\0.243 & 50.0 \\\hline\end{array}$$

Anatole Borisov
Anatole Borisov
Numerade Educator
00:37

Problem 39

For the reaction $2 \mathrm{C}_{2} \mathrm{F}_{4} \longrightarrow \mathrm{C}_{4} \mathrm{F}_{8},$ a graph of $1 /\left[\mathrm{C}_{2} \mathrm{F}_{4}\right]$ versus time gives a straight line with a slope of $+0.04 \mathrm{L} / \mathrm{mol} \cdot \mathrm{s} .$ What is the rate law for this reaction?

Will Li
Will Li
Numerade Educator
03:02

Problem 40

Butadiene, $\mathrm{C}_{4} \mathrm{H}_{6}(\mathrm{g}),$ dimerizes when heated, forming 1,5-cyclooctadiene, $\mathbf{C}_{8} \mathbf{H}_{12} .$ The data in the table were collected.
(Check your book to see figure)
$$\begin{array}{lc}\hline\left[\mathrm{C}_{4} \mathrm{H}_{6}\right] \\(\mathrm{mol} / \mathrm{L}) & \text { Time }(\mathrm{s}) \\\hline 1.0 \times 10^{-2} & 0 \\8.7 \times 10^{-3} & 200 \\7.7 \times 10^{-3} & 500 \\6.9 \times 10^{-3} & 800 \\5.8 \times 10^{-3} & 1200 \\\hline\end{array}$$
(a) Use a graphical method to verify that this is a secondorder reaction.
(b) Calculate the rate constant for this reaction.

Prashant Bana
Prashant Bana
Numerade Educator
02:57

Problem 41

Calculate the activation energy, $E_{\mathrm{a}},$ for the reaction
$$\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})$$
from the observed rate constants: $k$ at $25^{\circ} \mathrm{C}=3.46 \times$ $10^{-5} s^{-1}$ and $k$ at $55^{\circ} \mathrm{C}=1.5 \times 10^{-3} \mathrm{s}^{-1}.$

Will Li
Will Li
Numerade Educator
01:42

Problem 42

If the rate constant for a reaction triples when the temperature rises from $3.00 \times 10^{2} \mathrm{K}$ to $3.10 \times 10^{2} \mathrm{K},$ what is the activation energy of the reaction?

Anatole Borisov
Anatole Borisov
Numerade Educator
01:18

Problem 43

When heated to a high temperature, cyclobutane, $\mathrm{C}_{4} \mathrm{H}_{8}$ decomposes to ethylene:
$$\mathrm{C}_{4} \mathrm{H}_{8}(\mathrm{g}) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})$$
The activation energy, $E_{\mathrm{a}}$, for this reaction is $260 \mathrm{kJ} / \mathrm{mol}$. At $800 \mathrm{K}$, the rate constant $k=0.0315 \mathrm{s}^{-1} .$ Determine the value of $k$ at $850 \mathrm{K}.$

Anatole Borisov
Anatole Borisov
Numerade Educator
01:50

Problem 44

When heated, cyclopropane is converted to propene (see Example 15.5 ). Rate constants for this reaction at $470^{\circ} \mathrm{C}$ and $510^{\circ} \mathrm{C}$ are $k=1.10 \times 10^{-4} \mathrm{s}^{-1}$ and $k=1.02 \times10^{-3} \mathrm{s}^{-1},$ respectively. Determine the activation energy, $E_{\mathrm{a}}$ from these data.

Anatole Borisov
Anatole Borisov
Numerade Educator
02:06

Problem 45

The reaction of $\mathrm{H}_{2}$ molecules with $\mathrm{F}$ atoms
$$\mathrm{H}_{2}(\mathrm{g})+\mathrm{F}(\mathrm{g}) \longrightarrow \mathrm{HF}(\mathrm{g})+\mathrm{H}(\mathrm{g})$$
has an activation energy of $8 \mathrm{kJ} / \mathrm{mol}$ and an energy change of $-133 \mathrm{kJ} / \mathrm{mol} .$ Draw a diagram similar to Figure 15.13 for this process. Indicate the activation energy and enthalpy of reaction on this diagram.

Anatole Borisov
Anatole Borisov
Numerade Educator
00:48

Problem 46

Answer questions (a) and (b) based on the accompanying reaction coordinate diagram.
(a) Is the reaction exothermic or endothermic?
(b) Does the reaction occur in more than one step? If so, how many?
(Check your book to see figure)

Anatole Borisov
Anatole Borisov
Numerade Educator
00:54

Problem 47

What is the rate law for each of the following elementary reactions?
(a) $\mathrm{NO}(\mathrm{g})+\mathrm{NO}_{3}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})$
(b) $\mathrm{Cl}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{HCl}(\mathrm{g})+\mathrm{H}(\mathrm{g})$
(c) $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}(\mathrm{aq}) \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{+}(\mathrm{aq})+\mathrm{Br}^{-}(\mathrm{aq})$

Will Li
Will Li
Numerade Educator
00:53

Problem 48

What is the rate law for each of the following elementary reactions?
(a) $\mathrm{Cl}(\mathrm{g})+\mathrm{ICl}(\mathrm{g}) \longrightarrow \mathrm{I}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$
(b) $\mathbf{O}(\mathrm{g})+\mathbf{O}_{3}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{g})$
(c) $2 \mathrm{NO}_{2}(\mathrm{g}) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})$

Will Li
Will Li
Numerade Educator
03:53

Problem 49

Ozone, $\mathrm{O}_{3},$ in the earth's upper atmosphere decomposes according to the equation
$$2 \mathrm{O}_{3}(\mathrm{g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{g})$$
The mechanism of the reaction is thought to proceed through an initial fast, reversible step followed by a slow, second step.
Step 1 $\quad$ Fast, reversible $\mathbf{O}_{3}(\mathrm{g}) \rightleftarrows \mathrm{O}_{2}(\mathrm{g})+\mathrm{O}(\mathrm{g})$
Step 2 Slow $\quad \mathrm{O}_{3}(\mathrm{g})+\mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{g})$
(a) Which of the steps is rate-determining?
(b) Write the rate equation for the rate-determining step.

Will Li
Will Li
Numerade Educator
02:49

Problem 50

The reaction of $\mathrm{NO}_{2}(\mathrm{g})$ and $\mathrm{CO}(\mathrm{g})$ is thought to occur in two steps:
Step 1 Slow $\quad \mathrm{NO}_{2}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) \longrightarrow \mathrm{NO}(\mathrm{g})+\mathrm{NO}_{3}(\mathrm{g})$
Step 2 Fast $\quad \mathrm{NO}_{3}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})$
(a) Show that the elementary steps add up to give the overall, stoichiometric equation.
(b) What is the molecularity of each step?
(c) For this mechanism to be consistent with kinetic data, what must be the experimental rate equation?
(d) Identify any intermediates in this reaction.

Will Li
Will Li
Numerade Educator
03:42

Problem 51

(a) Show that the three elementary steps add up to give the overall, stoichiometric equation.
(b) What is the molecularity of each step?
(c) For this mechanism to be consistent with kinetic data, what must be the experimental rate equation?
(d) Identify any intermediates in the elementary steps in this reaction.

Anatole Borisov
Anatole Borisov
Numerade Educator
04:42

Problem 52

The mechanism for the reaction of $\mathrm{CH}_{3} \mathrm{OH}$ and $\mathrm{HBr}$ is believed to involve two steps. The overall reaction is exothermic.
Step 1 $\quad$ Fast, endothermic
$$\mathrm{CH}_{3} \mathrm{OH}+\mathrm{H}^{+} \rightleftarrows \mathrm{CH}_{3} \mathrm{OH}_{2}^{+}$$
Step 2 Slow
$$\mathrm{CH}_{3} \mathrm{OH}_{2}^{+}+\mathrm{Br}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{Br}+\mathrm{H}_{2} \mathrm{O}$$
(a) Write an equation for the overall reaction.
(b) Draw a reaction coordinate diagram for this reaction.
(c) Show that the rate law for this reaction is $-\Delta\left[\mathrm{CH}_{3} \mathrm{OH}\right] / \Delta t=k\left[\mathrm{CH}_{3} \mathrm{OH}\right]\left[\mathrm{H}^{+}\right]\left[\mathrm{Br}^{-}\right]$

Anatole Borisov
Anatole Borisov
Numerade Educator
02:13

Problem 53

A proposed mechanism for the reaction of $\mathrm{NO}_{2}$ and $\mathrm{CO}$ is Step 1 Slow, endothermic
$$2 \mathrm{NO}_{2}(\mathrm{g}) \longrightarrow \mathrm{NO}(\mathrm{g})+\mathrm{NO}_{3}(\mathrm{g})$$
Step 2 $\quad$ Fast, exothermic
$$\mathrm{NO}_{3}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})$$
Overall Reaction Exothermic
$$\mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{NO}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})$$
(a) Identify each of the following as a reactant, product, or intermediate: $\mathrm{NO}_{2}(\mathrm{g}), \mathrm{CO}(\mathrm{g}), \mathrm{NO}_{3}(\mathrm{g}), \mathrm{CO}_{2}(\mathrm{g})$ $\mathrm{NO}(\mathrm{g})$
(b) Draw a reaction coordinate diagram for this reaction. Indicate on this drawing the activation energy for each step and the overall reaction enthalpy.

Will Li
Will Li
Numerade Educator
02:36

Problem 54

A three-step mechanism for the reaction of $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}$ and $\mathrm{H}_{2} \mathrm{O}$ is proposed:
Step 1 Slow
$$\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{+}+\mathrm{Br}^{-}$$
Step 2 Fast
$$\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}_{2}^{+}$$
Step 3 Fast
$$\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}_{2}^{+}+\mathrm{Br}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}+\mathrm{HBr}$$
(a) Write an equation for the overall reaction.
(b) Which step is rate-determining?
(c) What rate law is expected for this reaction?

Anatole Borisov
Anatole Borisov
Numerade Educator
01:26

Problem 55

A reaction has the following experimental rate equation:
Rate $=k[\mathrm{A}]^{2}[\mathrm{B}] .$ If the concentration of $\mathrm{A}$ is doubled and the concentration of $\mathrm{B}$ is halved, what happens to the reaction rate?

Anatole Borisov
Anatole Borisov
Numerade Educator
01:23

Problem 56

After five half-life periods for a first-order reaction, what fraction of reactant remains?

Anatole Borisov
Anatole Borisov
Numerade Educator
00:54

Problem 57

To determine the concentration dependence of the rate of the reaction
$$\mathrm{H}_{2} \mathrm{PO}_{3}^{-}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow \mathrm{HPO}_{3}^{2-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$$
you might measure $\left[\mathrm{OH}^{-}\right]$ as a function of time using a pH meter. (To do so, you would set up conditions under which $\left[\mathrm{H}_{2} \mathrm{PO}_{3}^{-}\right]$ remains constant, by using a large excess of this reactant.) How would you prove a second-order rate dependence for $\left[\mathrm{OH}^{-}\right] ?$

Anatole Borisov
Anatole Borisov
Numerade Educator
03:40

Problem 58

Gaseous ammonia is made by the reaction
$$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})$$
Use the information on the formation of $\mathrm{NH}_{3}$ given in the table to answer the questions that follow.
$$\begin{array}{lll}\hline\left[\mathrm{N}_{2}\right](\mathrm{M}) & {\left[\mathrm{H}_{2}\right](\mathrm{M})} & \text { Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{min}) \\\hline 0.030 & 0.010 & 4.21 \times 10^{-5} \\0.060 & 0.010 & 1.68 \times 10^{-4} \\0.030 & 0.020 & 3.37 \times 10^{-4} \\\hline\end{array}$$
(a) Determine $n$ and $m$ in the rate equation: Rate $=$ $k\left[\mathrm{N}_{2}\right]^{n}\left[\mathrm{H}_{2}\right]^{m}$
(b) Calculate the value of the rate constant.
(c) What is the order of the reaction with respect to $\left[\mathrm{H}_{2}\right] ?$
(d) What is the overall order of the reaction?

Anatole Borisov
Anatole Borisov
Numerade Educator
01:39

Problem 59

The decomposition of ammonia is first order with respect to $\mathrm{NH}_{3}$. (Compare with Study Question 58.)
$$2 \mathrm{NH}_{3}(\mathrm{g}) \longrightarrow \mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g})$$
(a) What is the rate equation for this reaction?
(b) Calculate the rate constant, $k$, given the following data:
$$\begin{array}{lc}\hline\left[\mathrm{NH}_{3}\right](\mathrm{mol} / \mathrm{L}) & \text { Time }(\mathrm{s}) \\\hline 0.67 & 0 \\0.26 & 19 \\\hline\end{array}$$
(c) Determine the half-life of $\mathrm{NH}_{3}$

Anatole Borisov
Anatole Borisov
Numerade Educator
02:12

Problem 60

Data for the following reaction are given in the table.
$$2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})$$
$$\begin{array}{llll}\hline \text { Experiment } & \begin{array}{l}{[\mathrm{NO}]} \\(\mathrm{M})\end{array} & \begin{array}{l}{\left[\mathrm{Br}_{2}\right]} \\(\mathrm{M})\end{array} & \begin{array}{l}\text { Initial Rate } \\(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s})\end{array} \\\hline 1 & 1.0 \times 10^{-2} & 2.0 \times 10^{-2} & 2.4 \times 10^{-2} \\2 & 4.0 \times 10^{-2} & 2.0 \times 10^{-2} & 0.384 \\3 & 1.0 \times 10^{-2} & 5.0 \times 10^{-2} & 6.0 \times 10^{-2} \\\hline\end{array}$$
(a) What is the order of the reaction with respect to $[\mathrm{NO}] ?$
(b) What is the order with respect to $\left[\mathrm{Br}_{2}\right] ?$
(c) What is the overall order of the reaction?

Anatole Borisov
Anatole Borisov
Numerade Educator
02:04

Problem 61

The decomposition of $\mathrm{CO}_{2}$ is first order with respect to the concentration of $\mathrm{CO}_{2}.$
$$2 \mathrm{CO}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$
Data on this reaction are provided in the table below.
$$\begin{array}{lc}\hline\left[\mathrm{CO}_{2}\right](\mathrm{mol} / \mathrm{L}) & \text { Time }(\mathrm{s}) \\\hline 0.38 & 0 \\0.27 & 12 \\\hline\end{array}$$
(a) Write the rate equation for this reaction.
(b) Use the data to determine the value of $k$
(c) What is the half-life of $\mathrm{CO}_{2}$ under these conditions?

Anatole Borisov
Anatole Borisov
Numerade Educator
04:48

Problem 62

The isomerization of CH aNC occurs slowly when $\mathrm{CH}_{3} \mathrm{NC}$ is heated.
$$\mathrm{CH}_{3} \mathrm{NC}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{CN}(\mathrm{g})$$
To study the rate of this reaction at $488 \mathrm{K},$ data on $\left[\mathrm{CH}_{3} \mathrm{NC}\right]$ were collected at various times. Analysis led to the graph below.
(a) What is the rate law for this reaction?
(b) What is the equation for the straight line in this graph?
(c) Calculate the rate constant for this reaction, giving the correct units.
(d) How long does it take for half of the sample to isomerize?
(e) What is the concentration of $\mathrm{CH}_{3} \mathrm{NC}$ after $10,000 \mathrm{s} ?$

(Check your book to see graph)

Anatole Borisov
Anatole Borisov
Numerade Educator
03:49

Problem 63

When heated, tetrafluoroethylene dimerizes to form octa-fluorocyclobutane.
$$2 \mathrm{C}_{2} \mathrm{F}_{4}(\mathrm{g}) \longrightarrow \mathrm{C}_{4} \mathrm{F}_{8}(\mathrm{g})$$
To determine the rate of this reaction at $488 \mathrm{K},$ the data in the table were collected. Analysis was done graphically, as shown below:
$$\begin{array}{lc}\hline\left[\mathrm{C}_{2} \mathrm{F}_{4}\right](\mathrm{M}) & \text { Time }(\mathrm{s}) \\\hline 0.100 & 0 \\0.080 & 56 \\0.060 & 150 . \\0.040 & 335 \\0.030 & 520 . \\\hline\end{array}$$
(a) What is the rate law for this reaction?
(b) What is the value of the rate constant?
(c) What is the concentration of $\mathrm{C}_{2} \mathrm{F}_{4}$ after $600 \mathrm{s} ?$
(d) How long will it take until the reaction is $90 \%$ complete?

Anatole Borisov
Anatole Borisov
Numerade Educator
03:43

Problem 64

Data in the table were collected at $540 \mathrm{K}$ for the following reaction:
$$\mathrm{CO}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{NO}(\mathrm{g})$$
(a) Derive the rate equation.
(b) Determine the reaction order with respect to each reactant.
(c) Calculate the rate constant, giving the correct units for $k.$
$$\begin{array}{lll}\hline \text { Initial Concentration }(\mathrm{mol} / \mathrm{L}) & {\text { Initial Rate }} \\\hline[\mathrm{C} 0] & {\left[\mathrm{NO}_{2}\right]} & (\mathrm{mol} / \mathrm{L} \cdot \mathrm{h}) \\\hline 5.1 \times 10^{-4} & 0.35 \times 10^{-4} & 3.4 \times 10^{-8} \\5.1 \times 10^{-4} & 0.70 \times 10^{-4} & 6.8 \times 10^{-8} \\5.1 \times 10^{-4} & 0.18 \times 10^{-4} & 1.7 \times 10^{-8} \\1.0 \times 10^{-3} & 0.35 \times 10^{-4} & 6.8 \times 10^{-8} \\1.5 \times 10^{-3} & 0.35 \times 10^{-4} & 10.2 \times 10^{-8} \\\hline\end{array}$$

Anatole Borisov
Anatole Borisov
Numerade Educator
04:01

Problem 65

Ammonium cyanate, NH_NCO, rearranges in water to give urea, $\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}:$
$$\mathrm{NH}_{4} \mathrm{NCO}(\mathrm{aq}) \longrightarrow\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}(\mathrm{aq})$$
$$\begin{array}{ll}\hline \begin{array}{l}\text { Time } \\(\min )\end{array} & \begin{array}{l}{\left[\mathrm{NH}_{4} \mathrm{NCO}\right]} \\(\mathrm{mol} / \mathrm{L})\end{array} \\\hline 0 & 0.458 \\4.50 \times 10^{1} & 0.370 \\1.07 \times 10^{2} & 0.292 \\2.30 \times 10^{2} & 0.212 \\6.00 \times 10^{2} & 0.114 \\\hline\end{array}$$
Using the data in the table:
(a) Decide whether the reaction is first order or second order.
(b) Calculate $k$ for this reaction.
(c) Calculate the half-life of ammonium cyanate under these conditions.
(d) Calculate the concentration of $\mathrm{NH}_{4} \mathrm{NCO}$ after $12.0 \mathrm{h}$.

David Collins
David Collins
Numerade Educator
03:02

Problem 66

Nitrogen oxides, $\mathrm{NO}_{x}$ (a mixture of $\mathrm{NO}$ and $\mathrm{NO}_{2}$ collectively designated as $\mathrm{NO}_{x}$ ), play an essential role in the production of pollutants found in photochemical smog. The $\mathrm{NO}_{x}$ in the atmosphere is slowly broken down to $\mathrm{N}_{2}$ and $\mathrm{O}_{2}$ in a first-order reaction. The average half-life of NO in the smokestack emissions in a large city during daylight is $3.9 \mathrm{h}$
(a) Starting with $1.50 \mathrm{mg}$ in an experiment, what quantity of $\mathrm{NO}_{x}$ remains after $5.25 \mathrm{h} ?$
(b) How many hours of daylight must have elapsed to decrease $1.50 \mathrm{mg}$ of $\mathrm{NO}_{x}$ to $2.50 \times 10^{-6} \mathrm{mg} ?$

Anatole Borisov
Anatole Borisov
Numerade Educator
02:00

Problem 67

At temperatures below $500 \mathrm{K},$ the reaction between carbon monoxide and nitrogen dioxide
$$ \mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{NO}(\mathrm{g}) $$
has the following rate equation: Rate $=k\left[\mathrm{NO}_{2}\right]^{2} .$ Which of the three mechanisms suggested here best agrees with the experimentally observed rate equation?
Mechanism 1 $\quad$ single, elementary step
$$\mathrm{NO}_{2}+\mathrm{CO} \longrightarrow \mathrm{CO}_{2}+\mathrm{NO}$$
Mechanism $2 \quad$ Two steps
$$\begin{aligned}&\text { Slow } \quad \mathrm{NO}_{2}+\mathrm{NO}_{2} \longrightarrow \mathrm{NO}_{3}+\mathrm{NO}\\&\text { Fast } \quad \mathrm{NO}_{3}+\mathrm{CO} \longrightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2}\end{aligned}$$
Mechanism 3 $\quad$ Two steps
$$\begin{aligned}&\text { Slow } \quad \mathrm{NO}_{2} \longrightarrow \mathrm{NO}+\mathrm{O}\\&\text { Fast } \quad \mathrm{CO}+\mathrm{O} \longrightarrow \mathrm{CO}_{2}\end{aligned}$$

Anatole Borisov
Anatole Borisov
Numerade Educator
03:39

Problem 68

Nitryl fluoride can be made by treating nitrogen dioxide with fluorine:
$$2 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{F}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2} \mathrm{F}(\mathrm{g})$$
Use the rate data in the table to do the following:
(a) Write the rate equation for the reaction.
(b) Indicate the order of reaction with respect to each component of the reaction.
(c) Find the numerical value of the rate constant, $k$
(Check your book to see table)

Anatole Borisov
Anatole Borisov
Numerade Educator
01:55

Problem 69

The decomposition of dinitrogen pentaoxide
$$2 \mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \longrightarrow 4 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$
has the following rate equation: $-\Delta\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] / \Delta t=k\left[\mathrm{N}_{2} \mathrm{O}_{5}\right].$ It has been found experimentally that the decomposition is $20 \%$ complete in $6.0 \mathrm{h}$ at $300 \mathrm{K}$. Calculate the rate constant and the half-life at $300 \mathrm{K}$

Anatole Borisov
Anatole Borisov
Numerade Educator
02:06

Problem 70

The data in the table give the temperature dependence of the rate constant for the reaction $\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \longrightarrow$ $2 \mathrm{NO}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) .$ Plot these data in the appropriate way to derive the activation energy for the reaction.
$$\begin{aligned}&\\&\begin{array}{ll}\hline T(\mathrm{K}) & k\left(\mathrm{s}^{-1}\right) \\
\hline 338 & 4.87 \times 10^{-3} \\328 & 1.50 \times 10^{-3} \\318 & 4.98 \times 10^{-4} \\308 & 1.35 \times 10^{-4} \\298 & 3.46 \times 10^{-5} \\273 & 7.87 \times 10^{-7} \\\hline\end{array}\end{aligned}$$

David Collins
David Collins
Numerade Educator
03:53

Problem 71

The decomposition of gaseous dimethyl ether at ordinary pressures is first order. Its half-life is 25.0 min at $500^{\circ} \mathrm{C}$
$$\mathrm{CH}_{3} \mathrm{OCH}_{3}(\mathrm{g}) \longrightarrow \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$
(a) Starting with $8.00 \mathrm{g}$ of dimethyl ether, what mass remains (in grams) after 125 min and after 145 min?
(b) Calculate the time in minutes required to decrease $7.60 \mathrm{ng}$ (nanograms) to 2.25 ng.
(c) What fraction of the original dimethyl ether remains after 150 min?

Anatole Borisov
Anatole Borisov
Numerade Educator
03:11

Problem 72

The decomposition of phosphine, $\mathrm{PH}_{3},$ proceeds according to the equation
$$4 \mathrm{PH}_{3}(\mathrm{g}) \longrightarrow \mathrm{P}_{4}(\mathrm{g})+6 \mathrm{H}_{2}(\mathrm{g})$$
It is found that the reaction has the following rate equation: Rate $=k\left[\mathrm{PH}_{3}\right] .$ The half-life of $\mathrm{PH}_{3}$ is $37.9 \mathrm{s}$ at $120^{\circ} \mathrm{C}$
(a) How much time is required for three fourths of the $\mathrm{PH}_{3}$ to decompose?
(b) What fraction of the original sample of $\mathrm{PH}_{3}$ remains after 1 min?

Anatole Borisov
Anatole Borisov
Numerade Educator
03:41

Problem 73

(b) What is the molecularity for each step in each mechanism?
(c) What are the intermediates formed in mechanisms 2 and $3 ?$
(d) Compare the rate laws that are derived from these three mechanisms. How could you differentiate them experimentally?

Prashant Bana
Prashant Bana
Numerade Educator
02:21

Problem 74

Radioactive iodine-131, which has a half-life of 8.04 days, is used in the form of sodium iodide to treat cancer of the thyroid. If you begin with $25.0 \mathrm{mg}$ of $\mathrm{Na}^{131} \mathrm{I},$ what quantity of the material remains after 31 days?

Anatole Borisov
Anatole Borisov
Numerade Educator
02:51

Problem 75

The ozone in the earth's ozone layer decomposes according to the equation
$$2 \mathrm{O}_{3}(\mathrm{g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{g})$$
The mechanism of the reaction is thought to proceed through an initial fast equilibrium and a slow step:
Step 1 $\quad$ Fast, Reversible $\quad \mathrm{O}_{3}(\mathrm{g}) \rightleftarrows \mathrm{O}_{2}(\mathrm{g})+\mathrm{O}(\mathrm{g})$
Step 2 Slow $\quad \mathrm{O}_{3}(\mathrm{g})+\mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{g})$
Show that the mechanism agrees with this experimental rate law: $-\Delta\left[\mathrm{O}_{3}\right] / \Delta t=k\left[\mathrm{O}_{3}\right]^{2} /\left[\mathrm{O}_{2}\right]$

Anatole Borisov
Anatole Borisov
Numerade Educator
01:35

Problem 76

Hundreds of different reactions can occur in the stratosphere, among them reactions that destroy the earth's ozone layer. The table below lists several (second-order) reactions of Cl atoms with ozone and organic compounds; each is given with its rate constant.
$$\begin{array}{ll}\hline & \text { Rate Constant } \\\text { Reaction } & \left(298 \mathrm{K}, \mathrm{cm}^{3} / \mathrm{molecule} \cdot \mathrm{s}\right) \\\hline \text { (a) } \mathrm{Cl}+0_{3} \longrightarrow \mathrm{Cl} 0+0_{2} & 1.2 \times 10^{-11} \\\text {(b) } \mathrm{Cl}+\mathrm{CH}_{4} \longrightarrow\mathrm{HCl}+\mathrm{CH}_{3} & 1.0 \times 10^{-13} \\\text {(c) } \mathrm{Cl}+\mathrm{C}_{3} \mathrm{H}_{8} \longrightarrow\mathrm{HCl}+\mathrm{C}_{3} \mathrm{H}_{7} & 1.4 \times 10^{-10} \\\text {(d) } \mathrm{Cl}+\mathrm{CH}_{2} \mathrm{FCl} \longrightarrow\mathrm{HCl}+\mathrm{CHFCl} & 3.0 \times 10^{-18} \\\hline\end{array}$$
For equal concentrations of Cl and the other reactant, which is the slowest reaction? Which is the fastest reaction?

Prashant Bana
Prashant Bana
Numerade Educator
02:30

Problem 77

Data for the reaction
$$\begin{aligned}\left[\mathrm{Mn}(\mathrm{CO})_{5}\left(\mathrm{CH}_{3}\mathrm{CN}\right)\right]^{+}+\mathrm{NC}_{5}\mathrm{H}_{5} \longrightarrow & \\&\left[\mathrm{Mn}(\mathrm{CO})_{5}\left(\mathrm{NC}_{5}\mathrm{H}_{5}\right)\right]^{+}+\mathrm{CH}_{3} \mathrm{CN}\end{aligned}$$
are given in the table. Calculate $E_{\mathrm{a}}$ from a plot of $\ln k$ versus $1 / T$
$$\begin{array}{ll}\hline T(\mathrm{K}) & k\left(\min ^{-1}\right) \\\hline 298 & 0.0409 \\308 & 0.0818 \\318 & 0.157 \\\hline\end{array}$$

Prashant Bana
Prashant Bana
Numerade Educator
03:04

Problem 78

The gas-phase reaction
$$2 \mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \longrightarrow 4 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$
has an activation energy of $103 \mathrm{kJ},$ and the rate constant is $0.0900 \min ^{-1}$ at $328.0 \mathrm{K}$. Find the rate constant at $318.0 \mathrm{K}$

Anatole Borisov
Anatole Borisov
Numerade Educator
04:12

Problem 79

In Egg protein albumin is precipitated when an egg is cooked in boiling $\left(100^{\circ} \mathrm{C}\right)$ water. $E_{\mathrm{a}}$ for this first-order reaction is $52.0 \mathrm{kJ} / \mathrm{mol} .$ Estimate the time to prepare a 3-min egg at an altitude at which water boils at $90^{\circ} \mathrm{C}.$

Prashant Bana
Prashant Bana
Numerade Educator
04:14

Problem 80

A Two molecules of the unsaturated hydrocarbon 1,3-butadiene $\left(\mathrm{C}_{4} \mathrm{H}_{6}\right)$ form the "dimer" $\mathrm{C}_{8} \mathrm{H}_{12}$ at higher temperatures.
$$2 \mathrm{C}_{4} \mathrm{H}_{6}(\mathrm{g}) \longrightarrow \mathrm{C}_{8} \mathrm{H}_{12}(\mathrm{g})$$
Use the following data to determine the order of the reaction and the rate constant, $k$. (Note that the total pressure is the pressure of the unreacted $\mathrm{C}_{4} \mathrm{H}_{6}$ at any time and the pressure of the $\mathrm{C}_{8} \mathrm{H}_{12} .$)
$$\begin{array}{cl}\hline \text { Time (min) } & \text { Total Pressure (mm Hg) } \\\hline 0 & 436 \\3.5 & 428 \\11.5 & 413 \\18.3 & 401 \\25.0 & 391 \\32.0 & 382 \\41.2 & 371 \\\hline\end{array}$$

David Collins
David Collins
Numerade Educator
04:21

Problem 81

Hypofluorous acid, HOF, is very unstable, decomposing in a first-order reaction to give HF and $\mathrm{O}_{2}$, with a halflife of only 30 min at room temperature:
$$\mathrm{HOF}(\mathrm{g}) \longrightarrow \mathrm{HF}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})$$
If the partial pressure of HOF in a $1.00-\mathrm{L}$. flask is initially $1.00 \times 10^{2} \mathrm{mm} \mathrm{Hg}$ at $25^{\circ} \mathrm{C},$ what is the total pressure in the flask and the partial pressure of HOF after exactly 30 min? After 45 min?

Prashant Bana
Prashant Bana
Numerade Educator
04:54

Problem 82

We know that the decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is first order in $\mathrm{SO}_{2} \mathrm{Cl}_{2}.$
$$\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$$
with a half-life of 245 min at $600 \mathrm{K}$. If you begin with a partial pressure of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ of $25 \mathrm{mm}$ Hg in a 1.0 -L. flask, what is the partial pressure of each reactant and product after 245 min? What is the partial pressure of each reactant after $12 \mathrm{h} ?$

Anatole Borisov
Anatole Borisov
Numerade Educator
03:36

Problem 83

The substitution of $\mathrm{CO}$ in $\mathrm{Ni}(\mathrm{CO})_{4}$ by another group $\mathrm{L}$ [where L is an electron-pair donor such as $\left.\mathrm{P}\left(\mathrm{CH}_{3}\right)_{3}\right]$ was studied some years ago and led to an understanding of some of the general principles that govern the chemistry of compounds having metal-CO bonds. (See J. P. Day, F. Basolo, and R. G. Pearson: Journal of the American Chemical Society, Vol. $90, \text { p. } 6927,1968 .)$ A detailed study of the kinetics of the reaction led to the following mechanism:
Slow $\quad \mathrm{Ni}(\mathrm{CO})_{4} \longrightarrow \mathrm{Ni}(\mathrm{CO})_{3}+\mathrm{CO}$
Fast $\quad \mathrm{Ni}(\mathrm{CO})_{3}+\mathrm{L} \longrightarrow \mathrm{Ni}(\mathrm{CO})_{3} \mathrm{L}$
(a) What is the molecularity of each of the elementary reactions?
(b) Doubling the concentration of $\mathrm{Ni}(\mathrm{CO})_{4}$ increased the reaction rate by a factor of $2 .$ Doubling the concentration of L. had no effect on the reaction rate. Based on this information, write the rate equation for the reaction. Does this agree with the mechanism described?
(c) The experimental rate constant for the reaction, when $\mathrm{L}=\mathrm{P}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3},$ is $9.3 \times 10^{-3} \mathrm{s}^{-1}$ at $20^{\circ} \mathrm{C} .$ If the initial concentration of $\mathrm{Ni}(\mathrm{CO})_{4}$ is $0.025 \mathrm{M},$ what is the concentration of the product after 5.0 min?

Prashant Bana
Prashant Bana
Numerade Educator
03:10

Problem 84

Screen 15.5 of the General ChemistryNow CD-ROM or website describes how to determine experimentally a rate law using the method of initial rates.
(a) Why is it best to measure the rate of reaction at the beginning of the process for this method to be valid?
(b) The first experiment shows that the initial rate of $\mathrm{NH}_{4} \mathrm{NCO}$ degradation is $2.2 \times 10^{-4} \mathrm{mol} / \mathrm{L} \cdot$ s when $\left[\mathrm{NH}_{4} \mathrm{NCO}\right]=0.14 \mathrm{M} .$ Using the rate law determined on this screen, predict what the rate would be if $\left[\mathrm{NH}_{4} \mathrm{NCO}\right]=0.18 \mathrm{M}$

Prashant Bana
Prashant Bana
Numerade Educator
01:13

Problem 85

Hydrogenation reactions, processes wherein $\mathrm{H}_{2}$ is added to a molecule, are usually catalyzed. An excellent catalyst is a very finely divided metal suspended in the reaction solvent. Tell why finely divided rhodium, for example, is a much more efficient catalyst than a small block of the metal.

Anatole Borisov
Anatole Borisov
Numerade Educator
05:57

Problem 86

It is instructive to use a mathematical model in connection with Study Question 85. Suppose you have 1000 blocks, each of which is $1.0 \mathrm{cm}$ on a side. If all 1000 of these blocks are stacked to give a cube that is $10 . \mathrm{cm}$ on a side, what fraction of the 1000 blocks have at least one surface on the outside surface of the cube? Next divide the 1000 blocks into eight equal piles of blocks and form them into eight cubes, $5.0 \mathrm{cm}$ on a side. What fraction of the blocks now have at least one surface on the outside of the cubes? How does this mathematical model pertain to Study Question 85?

Prashant Bana
Prashant Bana
Numerade Educator
03:14

Problem 87

The following statements relate to the reaction with the following rate law: Rate $=k\left[\mathrm{H}_{2}\right]\left[\mathrm{I}_{2}\right].$
$$\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{HI}(\mathrm{g})$$
Determine which of the following statements are true. If a statement is false, indicate why it is incorrect.
(a) The reaction must occur in a single step.
(b) This is a second-order reaction overall.
(c) Raising the temperature will cause the value of $k$ to decrease.
(d) Raising the temperature lowers the activation energy for this reaction.
(e) If the concentrations of both reactants are doubled, the rate will double.
(f) Adding a catalyst in the reaction will cause the initial rate to increase.

Anatole Borisov
Anatole Borisov
Numerade Educator
02:27

Problem 88

Chlorine atoms contribute to the destruction of the earth's ozone layer by the following sequence of reactions:
$$\begin{aligned}\mathrm{Cl}+\mathrm{O}_{3} \longrightarrow & \mathrm{ClO}+\mathrm{O}_{2} \\
\mathrm{ClO}+\mathrm{O} \longrightarrow & \mathrm{Cl}+\mathrm{O}_{2}\end{aligned}$$
where the O atoms in the second step come from the decomposition of ozone by sunlight:
$$\mathrm{O}_{3}(\mathrm{g}) \longrightarrow \mathrm{O}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$
What is the net equation on summing these three equations? Why does this lead to ozone loss in the stratosphere? What is the role played by Cl in this sequence of reactions? What name is given to species such as ClO?

Anatole Borisov
Anatole Borisov
Numerade Educator
04:24

Problem 89

Describe each of the following statements as true or false. If false, rewrite the sentence to make it correct.
(a) The rate-determining elementary step in a reaction is the slowest step in a mechanism.
(b) It is possible to change the rate constant by changing the temperature.
(c) As a reaction proceeds at constant temperature, the rate remains constant.
(d) A reaction that is third order overall must involve more than one step.

Anatole Borisov
Anatole Borisov
Numerade Educator
04:22

Problem 90

Identify which of the following statements are incorrect. If the statement is incorrect, rewrite it to be correct.
(a) Reactions are faster at a higher temperature because activation energies are lower.
(b) Rates increase with increasing concentration of reactants because there are more collisions between reactant molecules.
(c) At higher temperatures a larger fraction of molecules have enough energy to get over the activation energy barrier.
(d) Catalyzed and uncatalyzed reactions have identical mechanisms.

Anatole Borisov
Anatole Borisov
Numerade Educator
02:59

Problem 91

The reaction cyclopropane $\longrightarrow$ propene occurs on a platinum metal surface at $200^{\circ} \mathrm{C}$. (The platinum is a catalyst.) The reaction is first order in cyclopropane. Indicate how the following quantities change (increase, decrease, or no change) as this reaction progresses, assuming constant temperature.
(a) [ cyclopropane]
(b) [propene]
(c) [catalyst]
(d) the rate constant, $k$
(e) the order of the reaction
(f) the half-life of cyclopropane

Prashant Bana
Prashant Bana
Numerade Educator
02:31

Problem 92

Isotopes are often used as "tracers" to follow an atom through a chemical reaction, and the following is an example. Acetic acid reacts with methanol by eliminating a molecule of water and forming methyl acetate (See Chapter 11 ).
$$\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}+\mathrm{CH}_{3} \mathrm{OH} \quad \longrightarrow \quad \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{CH}_{3}+\mathrm{H}_{2} \mathrm{O}$$
Explain how you could use the isotope $^{18} \mathrm{O}$ to show whether the oxygen atom in the water comes from the - OH of the acid or the - OH of the alcohol.

Anatole Borisov
Anatole Borisov
Numerade Educator
01:04

Problem 93

Examine the reaction coordinate diagram given here.
(Check your book to see diagram)
(a) How many steps are in the mechanism for the reaction described by this diagram?
(b) Is the reaction overall exothermic or endothermic?

Anatole Borisov
Anatole Borisov
Numerade Educator
01:11

Problem 94

Draw a reaction coordinate diagram for an exothermic reaction that occurs in a single step. Mark the activation energy, and identify the net energy change for the reaction on this diagram. Draw a second diagram that represents the same reaction in the presence of a catalyst. Identify the activation energy of this reaction and the energy change. Is the activation energy in the two drawings different? Does the energy evolved in the two reactions differ?

David Collins
David Collins
Numerade Educator
02:31

Problem 95

Screen 15.2 of the General ChemistryNow CD-ROM or website (Rates of Chemical Reactions) illustrates the rate at which a blue dye is bleached.
(a) What is the difference between an instantaneous rate and an average rate?
(b) Observe the graph of food dye concentration versus time on this screen. (Click the "tool" icon on this screen.) The plot shows the concentration of dye as the reaction progresses. What does the steepness of the plot at any particular time tell you about the rate of the reaction at that time?
(c) As the reaction progresses, the concentration of dye decreases as it is consumed. What happens to the reaction rate as this occurs? What is the relationship between reaction rate and dye concentration?

Prashant Bana
Prashant Bana
Numerade Educator
01:36

Problem 96

Watch the video on Screen 15.4 of the General ChemistryNow CD-ROM or website (Control of Reaction Rates$-$Concentration Dependence).
(a) How does an increase in HCl concentration affect the rate of the reaction of the acid with magnesium metal?
(b) On the second portion of this screen are data for the rate of decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ (click "More"). The initial reaction rate is given for three separate experiments, each beginning with a different concentration of $\mathrm{N}_{2} \mathrm{O}_{5} .$ How is the initial reaction rate related to $\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] ?$

Prashant Bana
Prashant Bana
Numerade Educator
01:05

Problem 97

The "Microscopic View of Reactions" is described on Screen 15.9 of the General ChemistryNow CD-ROM or website.
(a) According to collision theory, what three conditions must be met for two molecules to react?
(b) Examine the animations that play when numbers 1 and 2 are selected. One of these occurs at a higher temperature than the other. Which one? Explain briefly.
(c) Examine the animations that play when numbers 2 and 3 are selected. Would you expect the reaction of
$\mathrm{O}_{3}$ with $\mathrm{N}_{2}$
$$\mathrm{O}_{3}(\mathrm{g})+\mathrm{N}_{2}(\mathrm{g}) \longrightarrow \mathrm{O}_{2}(\mathrm{g})+\mathrm{ONN}(\mathrm{g})$$
to be more or less sensitive to requiring a proper orientation for reaction than the reaction displayed on this screen? Explain briefly.

Banhishikha Sinha
Banhishikha Sinha
Numerade Educator
03:28

Problem 98

"Reaction Mechanisms and Rate Equations" are described on Screen 15.13 of the General ChemistryNow CD-ROM or website.
(a) What is the relationship between the stoichiometric coefficients of the reactants in an elementary step and the rate law for that step?
(b) What is the rate law for Step 2 of mechanism $2 ?$
(d) Examine the "Isotopic Labeling" sidebar to this screen. If the transfer of an oxygen atom from $\mathrm{NO}_{2}$ to $\mathrm{CO}$ occurred in a single-step, would any $\mathrm{N}^{16} \mathrm{O}^{18} \mathrm{O}$ be found if the reaction is started using a mixture of $\mathrm{N}^{16} \mathrm{O}_{2}$ and $\mathrm{N}^{18} \mathrm{O}_{2} ?$ Why or why not?

Anthony Han
Anthony Han
Numerade Educator
01:30

Problem 99

The mechanism for the iodide ion-catalyzed decomposition of $\mathrm{H}_{2} \mathrm{O}_{2}$ is described on Screen 15.14 (Catalysis and Reaction Rate) of the General ChemistryNow CD-ROM or website.
(a) Examine the mechanism for the iodide ion-catalyzed decomposition of $\mathrm{H}_{2} \mathrm{O}_{2} .$ Explain how the mechanism shows that I' is a catalyst.
(b) How does the reaction coordinate diagram show that the catalyzed reaction is expected to be faster than the uncatalyzed reaction?

Prashant Bana
Prashant Bana
Numerade Educator
04:23

Problem 100

Many biochemical reactions are catalyzed by acids. A typical mechanism consistent with the experimental results (in which HA is the acid and X is the reactant) is
Step 1 Fast, reversible $\quad \mathrm{HA} \rightleftarrows \mathrm{H}^{+}+\mathrm{A}^{-}$
Step 2 Fast, reversible $\quad \mathrm{X}+\mathrm{H}^{+} \rightleftarrows \mathrm{XH}^{+}$
Step 3 Slow $\mathrm{XH}^{+} \longrightarrow$ products
What rate law is derived from this mechanism? What is the order of the reaction with respect to HA? How would doubling the concentration of HA affect the reaction?

Anatole Borisov
Anatole Borisov
Numerade Educator