The Foundations of Chemistry

4.17 102 M^1  486 M^1

 486 M^1 
 417 M^1  903 M^1

[NOBr]1.11 10 ^3 M (46.2% remains unreacted)

Thus, 53.8% of the original concentration of NOBr reacts within the first 5 minutes. This is
reasonable because, as you can easily verify, the reaction has an initial half-life of 257 seconds,
or 4.29 minutes.

You should now work Exercises 35 and 38.

Zero-Order Reaction

For a reaction aA n products that is zero order, the reaction rate is independent of
concentrations. We can write the rate-law expression as

rate
k

The corresponding integrated rate equation is

[A][A] 0 akt (zero order)

and the half-life is

t1/2 (zero order)

Table 16-2 summarizes the relationships that we have presented in Sections 16-3 and
16-4.

[A] 0



2 ak

[A]



t

1



a

1



903 M^1

1



[NOBr]

1



[NOBr]

16-4 Concentration versus Time: The Integrated Rate Equation 669

TABLE 16-2 Summary of Relationships for Various Orders of the Reaction

aAnProducts

Order

Zero First Second

Rate-law expression ratek ratek[A] ratek[A]^2

Integrated rate equation [A][A] 0 akt ln 

[

[

A

A

]

]

0

akt or 

[A

1

]



[A

1

] 0

akt

log 

[

[

A

A

]

]

^0 

2.

a

3

k

0

t

3



Half-life, t1/2 

[

2

A

a

]

k

^0



ln

ak

2



0.

a

6

k

93

 

ak[

1

A] 0