The Foundations of Chemistry

Initial Rate of

Initial Initial Formation of C

Experiment [A] [B] (Ms^1 )

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

2 1.0 10 ^2 M 2.0 10 ^2 M 3.0 10 ^6

3 2.0 10 ^2 M 1.0 10 ^2 M 6.0 10 ^6

Because we are describing the same reaction in each experiment, all the experiments

are governed by the same rate-law expression,

ratek[A]x[B]y

The initial concentration of A is the same in experiments 1 and 2, so any change in

the initial rates for these experiments would be due to different initial concentrations of

B. To evaluate y,we solve the ratio of the rate-law expressions of these two experiments

for y.We can divide the first rate-law expression by the corresponding terms in the second

rate-law expression.



r

r

a

a

t

t

e

e

1

2



k

k

[

[

A

A

]

]

1

2

x

x

[

[

B

B

]

]

1

2

y

y

The value of kalways cancels from such a ratio because it is constant at a particular temper-

ature. The initial concentrations of A are equal, so they too cancel. Thus, the expression

simplifies to



r

r

a

a

t

t

e

e

1

2




[

[

B

B

]

]

1

2



y

The only unknown in this equation is y.We substitute data from experiments 1 and 2 into

the equation, which gives us




y

0.5(0.5)y so y 1

Thus far, we know that the rate-law expression is

ratek[A]x[B]^1

Next we evaluate x.In experiments 1 and 3, the initial concentration of B is the same, so

any change in the initial rates for these experiments would be due to the different initial

concentrations of A. We solve the ratio of the rate-law expressions of these two experi-

ments for x.We divide the third rate-law expression by the corresponding terms in the

first rate-law expression.



r

r

a

a

t

t

e

e

3

1



k

k

[

[

A

A

]

]

3

1

x

x

[

[

B

B

]

]

3

1

1

 1

The value kcancels, and so do the concentrations of B because they are equal. Thus, the

expression simplifies to



r

r

a

a

t

t

e

e

3

1



[

[

A

A

]

]

3

1

x

x


[

[

A

A

]

]

3

1



x

1.0 10 ^2 M



2.0 10 ^2 M

1.5 10 ^6 Ms^1



3.0 10 ^6 Ms^1

It does not matter which way we take
the ratio. We would get the same value
for yif we divide the second rate-law
expression by the first—try it!

660 CHAPTER 16: Chemical Kinetics