Page 270 - Elements of Chemical Reaction Engineering 3rd Edition

242 Collection and Analysis of Rate Data Chap. 5

For this dissolution of dolomite in HC1, the reaction order was also found to vary
I with temperature.

5.3 Method of Half-Lives
The method of The half-life of a reaction, t1,2, is defined as the time it takes for the concen-
half-1ives requires tration of the reactant to fall to half of its initial value. By determining the
many experiments
half-life of a reaction as a function of the initial concentration, the reaction
order and specific reaction rate can be determined. If two reactants are
involved in the chemical reaction, the experimenter will use the method of
excess in conjunction with the method of half-lives to arrange the rate law in
the form

-rA = kCi (5-1)

For the irreversible reaction
A * products
a mole balance on species A in a constant-volume batch reaction system
results in the following expression:
dCA -
- --- -rA = kC: (E5- 1.1)
dt
Integrating with the initial condition C, = C,, when t = 0, we find that

(5-17)

-
- 1 11
kCz, '(a - 1)
The half-life is defined as the time required for concentration to drop to half of
its initial value; that is,

t= t,,, when C,= iCAo
Substituting for C, in Equation (5-17) gives us

(5-18)

There is nothing special about using the time required for the concentra-
tion to drop to one-half of its initial value. We could just as well use the time
required for the concentration to fall to lln of the initial value, in which case

(5- 19)