The Foundations of Chemistry

672 CHAPTER 16: Chemical Kinetics

For a reaction aA nproducts that is zero order overall, we can write the rate equa-

tion as

k

In this case, the calculus derivation already described leads to the integrated zero-order rate

equation

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

d[A]



adt

E

nrichment

Using Integrated Rate Equations to Determine Reaction Order

The integrated rate equation can help us to analyze concentration-versus-time data to deter-

mine reaction order. A graphical approach is often used. We can rearrange the integrated

first-order rate equation

ln 

[

[

A

A

]

]

^0 akt

as follows. The logarithm of a quotient, ln (x/y), is equal to the difference of the logarithms,

ln xln y,so we can write

ln [A] 0 ln [A]akt or ln [A]akt
ln [A] 0

Recall that the equation for a straight line may be written as

ymx
b

where yis the variable plotted along the ordinate (vertical axis), xis the variable plotted

along the abscissa (horizontal axis), mis the slope of the line, and bis the intercept of the

line with the yaxis (Figure 16-5). If we compare the last two equations, we find that ln [A]

can be interpreted as y,and tas x.

ln [A]akt
ln [A] 0

gggg

y  mx
 b

  

(Enrichment, continued)

y  y 2  y 1

x  x 2  x 1

y

x

point x 1 , y 1

slope  m  point x^2 , y^2

y  b

x

y

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 15.7, Determination of Rate
Equations (2): Graphical Methods.

Figure 16-5 Plot of the equation
ymx
b,where mand bare
constant. The slope of the line
(positive in this case) is equal to m;
the intercept on the yaxis is equal
to b.