Chemistry, Third edition

MORE ABOUT FIRST-ORDER REACTIONS

Figure 14.10 shows a plot of [CH 3 N 2 CH 3 (g)] against t. The gradual fall in

azomethane concentration follows equation (14.1) and is said to be exponential. The

curvature of the plot is controlled by the value of k– the greater is k, the quicker the

reactant concentration falls (Fig. 14.11).

The rate constant for the decomposition of CH 3 N 2 CH 3 (g) may be calculated

directly from the half-life:

k

0.693

0.693/20003.5 10 ^4 s^1

t (^1) ⁄ 2
259
Half-lives of pesticides
The chemical degradation of a pesticide (P) in a field
Pbyproducts
was found to be roughly first order:
rate of reaction k[P]
withk5.73 10 ^7 s^1. After spraying, a pesticide was washed off plants into a pond. The
initial concentration of pesticide in the pond was 0.10 mg dm^3. What concentration of pesticide
would be left in the pond after 42 days? (Hintstart by calculating the half-life of the pesticide.)
Exercise 14N
0.10
0.08
0.06
0.04
0.02
0
[CH
N 3
CH 2
]/mol dm 3

-^3

4 8 12 16

(Time/s× 10 –3

⎧⎨⎩⎧⎨⎩

t (^1) / 2 t (^1) / 2 t (^1) / 2
0
Fig. 14.10The fall in azomethane concentration at
180 °C. Because the reaction is first order, its half-
life does not depend upon the initial concentration
of azomethane.
(b)
Concentration
Time
(a)
Fig. 14.11The exponential decay of a
reactant in a first-order reaction where (a)
kis large (b) kis small. The larger the
value of k, the faster is the decay.
Calculating half-life from k
Calculate the half-life of the first-order reaction
cis-CHCl=CHCltrans-CHCl=CHCl
at a temperature of 825 K given that k9.6 10 ^3 s^1.
Exercise 14M
Examples of the use of half-lives

1. Radioactive decay

The decay of elements by radioactivity, although not a chemical reaction, follows

first-order kinetics. For example, the half-life of^23982 U is 4.5 109 years. This means