Physical Chemistry Third Edition

11.3 Forward Reactions with More Than One Reactant 503

The first term on the right-hand side of this equation has the same value in all of these

experiments. A plot of ln(rinitial) as a function of ln([A] 0 ) should give a straight line

with slope equal toα.

Additional sets of experiments are carried out in which [B] 0 is varied while keeping

[A] 0 and [F] 0 fixed. An equation analogous to Eq. (11.3-14) allows the order with

respect to B to be determined. A third set of experiments is carried out in which [F] 0

is varied while keeping [A] 0 and [B] 0 fixed. If there are only a few experiments, an

algebraic method can be used, as in the following example. After all of the orders are

determined, everything in the right-hand side of Eq. (11.3-13) is known except forkf,

sokfcan be computed from any one of the experiments. Since there is always some

experimental error, a reasonable policy is to calculate the rate constant separately for

each experiment and then average the values.

EXAMPLE11.10

The following data were taken at 298 K for the gas-phase reaction

2NO+Cl 2 −→2 NOCl

[NO]/mol L−^1 [Cl 2 ]/mol L−^1 initial rate/mol L−^1 s−^1

0.0200 0.0200 7. 1 × 10 −^5

0.0400 0.0200 2. 8 × 10 −^4

0.0200 0.0400 1. 4 × 10 −^4

Find the order with respect to each reactant and find the rate constant.

Solution

In this case we proceed algebraically since there are only three experiments. Let the initial

rate in the first experiment ber 1 and that of the second experiment ber 2. We write

r 2

r 1



2. 8 × 10 −^4 mol L−^1 s−^1

7. 1 × 10 −^5 mol L−^1 s−^1

 4. 0



k[NO]α 2 [Cl 2 ]β 2

k[NO]α 1 [Cl 2 ]β 1



[NO]α 2

[NO]α 1



(

0 .0400 mol L−^1

0 .0200 mol L−^1

)α

 2. 00 α

α

ln(4.0)

ln(2.00)

 2. 0

The reaction is second order with respect to NO. The order with respect to Cl 2 is obtained

from the first and the third experiments:

r 3

r 1



1. 4 × 10 −^4 mol L−^1 s−^1

7. 1 × 10 −^5 mol L−^1 s−^1

 2. 0



k[NO]α 3 [Cl 2 ]β 3

k[NO]α 1 [Cl 2 ]β 1



[Cl 2 ]β 3

[Cl 2 ]β 1



(

0 .0400 mol L−^1

0 .0200 mol L−^1

)β

 2. 00 β

β

ln(2.0)

ln(2.00)

 1. 0

The reaction is first order with respect to Cl 2. We compute the rate constant from the data of

the first experiment.