The Foundations of Chemistry

Figure 16-8 Data conversion and
plots for Example 16-10. (a) The
data are used to calculate the two
columns ln [A] and 1/[A]. (b) Test
for zero-order kinetics: a plot of [A]
versus time. The nonlinearity of this
plot shows that the reaction does not
follow zero-order kinetics. (c) Test
for first-order kinetics: a plot of ln
[A] versus time. The observation
that this plot gives a straight line
indicates that the reaction follows
first-order kinetics. (d) Test for
second-order kinetics: a plot of 1/[A]
versus time. If the reaction had
followed second-order kinetics, this
plot would have resulted in a
straight line and the plot in part (c)
would not.

EXAMPLE 16-10 Graphical Determination of Reaction Order

We carry out the reaction A nB
C at a particular temperature. As the reaction proceeds,

we measure the molarity of the reactant, [A], at various times. The observed data are tabu-

lated in the margin. (a) Plot [A] versus time. (b) Plot ln [A] versus time. (c) Plot 1/[A] versus

time. (d) What is the order of the reaction? (e) Write the rate-law expression for the reac-

tion. (f ) What is the value of kat this temperature?

Plan

For parts (a)–(c), we use the observed data to make the required plots, calculating related

values as necessary. (d) We can determine the order of the reaction by observing which of

these plots gives a straight line. (e) Knowing the order of the reaction, we can write the

rate-law expression. (f ) The value of kcan be determined from the slope of the straight-

line plot.

Solution

(a) The plot of [A] versus time is given in Figure 16-8b.

(b) We first use the given data to calculate the ln [A] column in Figure 16-8a. These data

are then used to plot ln [A] versus time, as shown in Figure 16-8c.

(c) The given data are used to calculate the 1/[A] column in Figure 16-8a. Then we plot

1/[A] versus time, as shown in Figure 16-8d.

(d) It is clear from the answer to part (b) that the plot of ln [A] versus time gives a straight

line. This tells us that the reaction is first order in [A].

(e) In the form of a rate-law expression, the answer to part (d) gives ratek[A].

Time (min)

2.5

[A]

02 4 6 8 10

(b) Example 16-10(a).

2.0

1.5

1.0

0.5

0

Time

(min) [A] ln [A] 1 [A]

2.000

1.107

0.612

0.338

0.187

0.103

0.693

–0.491

–1.085

–1.677

–2.273

1.63

2.95

5.35

9.71

0.00

2.00

4.00

6.00

8.00

(a) Data for Example 16-10.

10.00

0.102

0.5000

0.9033

Time (min)

1

ln [A]

0 2 6 8 10 12

(c) Example 16-10(b).

Q

P

1.5 8.5

0.5

0

• 0.5
  –1
  –1.5
  –2
  –2.5
  –3

0.2

–1.83

Time (min)

12

1/ [A]

024 6 810

(d) Example 16-10(c).

0

10

8

6

4

2

(Enrichment, continued)

Time [A]
(min) (mol/L)

0.00 2.000

2.00 1.107

4.00 0.612

6.00 0.338

8.00 0.187

10.00 0.103