Physical Chemistry , 1st ed.

should look if 1/[A]twere plotted on the y-axis and time were plotted on the
x-axis. Once again, the appearance of a straight line for a plot of 1/[A]tversus
tis specific for a second-order reaction. Plotting these variables will yield a
straight line if and only if the reaction is second order with respect to the
species A.

Example 20.4

What are the units for the rate constant for a second-order reaction that has

the rate law

d[

d

A

t

]k[A]^2

if the units on the amounts are molarity?

Solution

The rate itself has units of M/s. If the term [A]^2 contributes units of M^2 (mo-

larity squared), then the rate constant must have units of 1/(Ms):

M^2 

M

1

s



M

s



Although this may seem like a strange unit for a rate constant, it is necessary

for the dimensional analysis to give the proper units for the experimentally

determined rate of the reaction.

Example 20.5

Consider the following reaction:

CS 2 (g) 3O 2 (g) →CO 2 (g) 2SO 2 (g)

If the rate law for the reaction can be written as



d[C

dt

S 2 ]

3.07 10 ^4 

M

1

s

[CS 2 ]^2

how long will it take for the concentration of CS 2 to drop to half of the ini-

tial concentration for the following initial concentrations?

a.0.05000 mol/L

b.0.00500 mol/L

c.Comment on the answers.

Solution

This is another half-life problem, but it is not as straightforward as it is for

first-order reactions.

a.We can use equation 20.20 by letting [A] 0 0.05000 mol/L and [A]t

0.02500 mol/L, which is half of the original concentration:



0.02500

1

mol/L



0.05000

1

mol/L

3.07 10 ^4 

M

1

s

t

40.00 

m

L

ol

20.00 

m

L

ol

3.07 10 ^4 

M

1

s

t

20.00 

m

L

ol

3.07 10 ^4 

M

1

s

t

20.3 Characteristics of Specific Initial Rate Laws 689