Page 76 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch07 Elementary Physical Chemistry

Chemical Kinetics 61

Reaction rates are usually expressed as the rate of decrease of a given
reactant. Occasionally, the rate is expressed as the rate of increase of a
particular compound. For example, the rate r for the reaction
aA+ bB → cC+ dD (7.3)

can be written as a rate decrease

r = −(1/a)d[A]/dt (7.4a)
r = −(1/b)d[B]/dt (7.4b)

or, as a rate increase

r =+(1/c)d[C]/dt (7.4c)
r =+(1/d)d[D]/dt (7.4d)

Note that there is a difference between the rate of reaction, r,and the rate
of appearance or disappearance of a substance. For example, the rate of
disappearance of A is defined as −d[A]/dt; the rate of appearance of D, is
defined as +d[D]/dt, etc. Thus, for the reaction

N 2 (g) + 3H 2 (g) → 2NH 3(g) (7.5)

the following applies

r = −d[N 2 ]/dt = −1/3d[H 2 ]/dt =1/2d[NH 3 ]/dt (7.6a)
It should also be noted that the rate of formation of NH 3 , on the other hand,
is 2r, whereas the rates of disappearance of N 2 and H 2 are respectively, r and
3r. Thus, the rate of appearance of NH 3 is twice the rate of disappearance
of N 2 and 2/3 times the rate of disappearance of H 2 .

2
d[NH 3 ]/dt =2d[N 2 ]/dt = d[H 2]/dt (7.6b)
3

7.2. Order of Reaction
The reaction rate is often found to be proportional to the concentration of
the reactants raised to some power. For example,
m
n
r = −(1/a)d[A]/dt = k[A] [B] ... (7.7)