Physical Chemistry , 1st ed.

In performing an experiment, exact whole-number ratios are difficult to

guarantee, so calculations with logarithms are common. Evaluating the value

ofkusing the first set of data:

2.91 10 ^7 

M

s

k(0.00636 M)^1 (0.00384 M)^2

k3.103 

M

1

2 s

b.To evaluate k , we need to recognize that the pseudo first-order rate con-

stant can be approximated by combining the kand the [B]^2 terms. If we are

given [B] 0.500 M, then

k3.103 

M

1

2 s(0.500 M)

2

k0.776 ^1

s



where the units for k work out as expected. The pseudo first-order rate law

would be, under these conditions,

rate 0.776 

1

s

[A]

To finish this section, let us briefly consider some of the experimental con-

siderations of rate law determinations. It is typical in deriving physical chemical

expressions to presume that our chemical system will follow the predictions of

these equations (in these cases, [A]t) perfectly. For an ideal kinetics experiment,

one would expect to get a plot like that in Figure 20.5 for a first-order reaction.

However, in reality the data are rarely so perfect. In a real experiment in

a real laboratory, a researcher might get some scatter in the plotted data.

Table 20.1 gives some values of concentrations versus time, which are plot-

ted in Figure 20.6. In this case, it might be obvious that a straight line is the

best fit to the experimental data and that the reaction follows first-order ki-

netics, even though there is some scatter in the plotted points. However, an

experimenter should be careful: consider plotting the same data as if it re-

lated to a second-order reaction. This is shown in Figure 20.7. For the short

20.3 Characteristics of Specific Initial Rate Laws 693

Time

ln[A]

t

1.05

0.70

0

Time (min)

8

ln[A]

t

642

1.00

0.95

0.90

0.85

0.80

0.75

Figure 20.5 If a perfect kinetics experiment
were performed on a first-order reaction, your
graph might look like this: all data points on a
line. However, reality isn’t usually this perfect: see
Figures 20.6 and 20.7.

Figure 20.6 Data from Table 20.1 are plotted to see if the reaction fol-
lows first-order kinetics. Note the scatter in the experimental data that
suggests that the fit to a straight line, in this case, is possible but not con-
vincing. Compare with Figure 20.7.

Table 20.1 Kinetic data for Figures 20.6

and 20.7

Time (min) [A]t ln [A]t 1/[A]t

0 2.719 1.000 0.3678

1 2.612 0.9601 0.3829

2 2.586 0.9501 0.3867

3 2.509 0.9199 0.3985

4 2.459 0.8997 0.4066

0.44

0.36

0

Time (min)

8

1/[A]

t

642

0.43

0.42

0.41

0.40

0.39

0.38

0.37

Figure 20.7 Data from Table 20.1 are plotted to see if the reaction fol-

lows second-order kinetics. Note the scatter in the experimental data that

suggests that the fit to this straight line also does not convince us that this

is a second-order reaction. Compare with Figure 20.6.