The Foundations of Chemistry




x

4.0(2.0)x so x 2

The power to which [A] is raised in the rate-law expression is 2, so the rate-law expres-

sion for this reaction is the same as that obtained earlier.

ratek[A]^2 [B]^1 or ratek[A]^2 [B]

EXAMPLE 16-3 Method of Initial Rates

Given the following data, determine the rate-law expression and the value of the rate constant
for the reaction

2A
B
C88nD
E

Initial Initial Initial Initial Rate of
Experiment [A] [B] [C] Formation of E

1 0.20 M 0.20 M 0.20 M 2.4 10 ^6 Mmin^1

2 0.40 M 0.30 M 0.20 M 9.6 10 ^6 Mmin^1

3 0.20 M 0.30 M 0.20 M 2.4 10 ^6 Mmin^1

4 0.20 M 0.40 M 0.60 M 7.2 10 ^6 Mmin^1

Plan

The rate law is of the form Ratek[A]x[B]y[C]z. We must evaluate x, y, z,and k.We use the
reasoning outlined earlier; in this presentation the first method is used.

Solution

Dependence on[B]: In experiments 1 and 3, the initial concentrations of A and C are unchanged.
Thus, any change in the rate would be due to the change in concentration of B. But we see
that the rate is the same in experiments 1 and 3, even though the concentration of B is different.
Thus, the reaction rate is independent of [B], so y0. We can neglect changes in [B] in the
subsequent reasoning. The rate law must be

ratek[A]x[C]z

Dependence on[C]: Experiments 1 and 4 involve the same initial concentration of A; thus the
observed change in rate must be due entirely to the changed [C]. So we compare experiments
1 and 4 to find z.

[C] has been multipliedby a factor of 3.0[C] ratio

The rate changes by a factor of

3.0rate ratio

The exponent zcan be deduced from

rate ratio([C] ratio)z

3.0(3.0)z so z 1 The reaction is first order in [C].

7.2 10 ^6



2.4 10 ^6

0.60



0.20

2.0 10 ^2 M



1.0 10 ^2 M

6.0 10 ^6 Ms^1



1.5 10 ^6 Ms^1

The coefficient of E in the balanced

equation is 1, so the rate of reaction is

equal to the rate of formation of E.

16-3 Concentrations of Reactants: The Rate-Law Expression 661

[B]^0  1

The alternative algebraic method

outlined above can also be used.