The Foundations of Chemistry

We can use the method of initial ratesto deduce the rate law from experimentally

measured rate data. Usually we know the concentrations of all reactants at the start

of the reaction. We can then measure the initial rateof the reaction, corresponding

to these initial concentrations. The following tabulated data refer to the hypothetical

reaction

A
2B88nC

at a specific temperature. The brackets indicate the concentrations of the reacting species

at the beginningof each experimental run listed in the first column—that is, the initial

concentrations for each experiment.

Initial Initial Initial Rate of

Experiment [A] [B] Formation of C

11.0 10 ^2 M 1.0 10 ^2 M 1.5 10 ^6 Ms^1

21.0 10 ^2 M 2.0 10 ^2 M 3.0 10 ^6 Ms^1

32.0 10 ^2 M 1.0 10 ^2 M 6.0 10 ^6 Ms^1

Because we are describing the same reaction in each experiment, each is governed by

the same rate-law expression. This expression has the form

ratek[A]x[B]y

Let’s compare the initial rates of formation of product (reaction rates) for different exper-

imental runs to see how changes in concentrations of reactants affect the rate of reaction.

This lets us evaluate xand y,and then k.

We see that the initial concentration of A is the same in experiments 1 and 2; for these

trials, any change in reaction rate would be due to different initial concentrations of B.

Comparing these two experiments, we see that [B] has been changed by a factor of

2.0[B] ratio

The rate changes by a factor of

2.0rate ratio

The exponent ycan be deduced from

rate ratio([B] ratio)y

2.0(2.0)y so y 1

The reaction is first order in [B]. Thus far we know that the rate expression is

ratek[A]x[B]^1

To evaluate x,we observe that the concentrations of [A] are different in experiments 1

and 3. For these two trials, the initial concentration of B is the same, so any change in

reaction rate would be due to different initial concentrations of A. Comparing these two

experiments, we see that [A] has been multipliedby a factor of

2.0[A] ratio

2.0 10 ^2



1.0 10 ^2

3.0 10 ^6



1.5 10 ^6

2.0 10 ^2



1.0 10 ^2

In such an experiment we often keep
some initial concentrations the same
and vary others by simple factors, such
as 2 or 3. This makes it easier to
access the effect of each change on
the rate.

658 CHAPTER 16: Chemical Kinetics

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 15.5, Determination of Rate
Equations (1): Method of Initial Rates.