Physical Chemistry , 1st ed.

time scale considered, neither plot makes a good case for a particular order

of kinetics.

A good experimenter exploring the kinetics of an unknown reaction needs

to apply care not only in the experimental measurements (here, the [A]t

measurements) but also in the definition of the experimental conditions: the

initial [A], initial [B], elapsed time, and so on. Understand that these condi-

tions are chosen by the experimenter. If we include data from Table 20.1a, we

can extend the time of the experiment and try to make an obvious fit to a

straight line. Figure 20.8 shows plots of all the data. Now it should be more ob-

vious what the rate law of the reaction is.

20.4 Equilibrium for a Simple Reaction

Kinetics describes how reactions proceed, but we should understand from

thermodynamics that virtually all reactions do not proceed to completion.

Instead, in time a reverse reaction begins to occur, and when the rate of the re-

verse reaction equals the rate of the forward reaction, net change ceases and

the system is at a dynamic equilibrium.Although we have stated previously that

thermodynamics and kinetics are separate considerations, the previous state-

ment—that the rate of forward reaction equals the rate of reverse reaction for

a system at equilibrium—suggests that there are some connections between ki-

netics and thermodynamics.

In our discussion of initial rates, we were implicitly confining ourselves to

short periods of time near the beginning of the reaction. That is, we assumed

was small. For equilibrium conditions, however, we need to consider a dif-

ferent time regime, that where approaches its maximum value. What this im-

plies is that a reverse chemical process will become important in our under-

standing of how concentrations are changing. This reverse reaction is an

additional consideration that we have so far ignored.

Consider the following simple chemical process:

kf

A B (20.29)

kr

Here,kfis the rate constant for the forward reaction and kris the rate constant

for the reverse reaction. Furthermore, we will assume that each reaction is first-

JQPJ

694 CHAPTER 20 Kinetics

Table 20.1a Additional kinetic data for

Figure 20.8

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

10 2.138 0.7599 0.4677

15 1.855 0.6179 0.5390

20 1.664 0.5092 0.6011

25 1.448 0.3702 0.6907

30 1.276 0.2437 0.7835

1.0

0.0

0

Time (min)

35

ln[A]

t

30252015105

0.8

0.6

0.4

0.2

0.8

0.3

0

Time (min)

35

1/[A]

t

30252015105

0.7

0.6

0.5

0.4

Figure 20.8 If the time of the measurements is extended (using data from Table 20.1a), it be-

comes clear that a first-order plot fits the data better than a second-order plot: a straight-line fit

is more obvious for the first-order plot over longer periods of time. In experimental kinetics, it

is extremely important to extend an experiment to a long enough time that the appropriate

straight line—and therefore the correct order of the reaction—is determined conclusively.