Burdge/Overby, Chemistry: Atoms First, 2e FM | Page 11

s EC Tion 19.5

Dependence of Reactant Concentration on Time

837

PREFACE xi

figure 19.13 A plot of [A] versus
time for the first-order reaction
A
products. The half-life of the
reaction is 1 min. The concentration
of A is halved every half-life.

[A]t

[A]0

[A]0 /2

[A]0 /4
[A]0 /8
0
0

1

2

3

4

Time (min)

Chapters 23–25—In response to feedback from professors, we have reduced the size of the
Workedbook by removing the chapter on chemistry of the nonmetals (formerly Chapter 23). Thus,
printed Example 19.6
Chapters 23 and 24 are now Organic Chemistry and Modern Materials, respectively. We realize, of
The decomposition of ethane (C H ) to methyl radicals (CH ) is a first-order reaction with a rate
constant of 5.36 ×coverage of nonmetals is important material—and that some professors will still wish
course, that 10 s at 700°C:
C to
to present it and/or provide it H their2CH
students. Therefore, what was formerly Chapter 23 has been
Calculate the half-life of the reaction in minutes.
renumbered Chapter 25, Nonmetallic Elements and Their Compounds, and is available as a free
strategy Use Equation 19.5 to the text’s online and then convert to minutes.
digital download via calculate t in seconds, learning center and/or the Instructor Resources in Connect.
1 minute
Chapter 25 × __________ = minutes
setup secondsis also available for text customization in McGraw-Hill Create.
–4

–1

2

6

3

2

6

3

1/2

60 seconds

solution
0.693
0.693
t1/2 = _____ = ____________ = 1293 s
k
5.36 × 10–4 s–1
1 min
1293 s × _____ = 21.5 min
60 s
The half-life of ethane decomposition at 700°C is 21.5 min.

Think about it

Half-lives and rate constants can be expressed using any units of time and reciprocal time, respectively.
Track units carefully when you convert from one unit of time to another.
Practice Problem A t t e m p t Calculate the half-life of the decomposition of azomethane,
discussed in Worked Example 19.5.
(Continued on next page)

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