Physical Chemistry Third Edition

492 11 The Rates of Chemical Reactions

EXAMPLE11.3

The gas-phase reaction

NO 3 −→NO 2 +

1

2

O 2

obeys second-order kinetics. At a temperature of 20◦C and an initial concentration of NO 3

equal to 0.0500 mol L−^1 , the concentration after 60.0 minutes is equal to 0.0358 mol L−^1.

Assuming the reverse reaction to be negligible, find the value of the forward rate constant.

Solution

kf

1

t

(

1

[NO 3 ]t

−

1

[NO 3 ] 0

)



1

3600 s

[

1

0 .0358 mol L−^1

−

1

0 .0500 mol L−^1

]

 2. 2 × 10 −^3 L mol−^1 s−^1

Exercise 11.5

a.Find the concentration of NO 3 in the experiment of the previous example after an elapsed

time of 145 minutes. Assume the reverse reaction to be negligible.

b.Find the concentration after 145 minutes if the initial concentration is 0.100 mol L−^1.

c.Assuming the gases to be ideal, find the value of the rate constant in atm−^1 min−^1. Assume

the reverse reaction to be negligible.

d.Find the pressure of NO 3 after an elapsed time of 175 min with the initial concentration of

0.0500 mol L−^1. Assume the reverse reaction to be negligible.

If the reverse reaction can be neglected, the half-life of a second-order reaction is

given by

1

[A] 0 / 2

−

1

[A] 0



2

[A] 0

−

1

[A] 0



1

[A] 0

kft 1 / 2 (11.2-12)

t 1 / 2 

1

k[A] 0

(second order, no reverse reaction) (11.2-13)

EXAMPLE11.4

Find the half-life of the reaction of the previous example with the given initial concentration.

Solution

t 1 / 2 

1

k[NO 3 ] 0



1

(2. 2 × 10 −^3 L mol−^1 s−^1 )(0.0500 mol L−^1 )(60 s min−^1 )

150 min

Exercise 11.6

a.Find the half-life of the reaction of the previous example if the initial concentration is equal

to 0.0200 mol L−^1.