Page 271 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. !5.4 Differential Reactors 243

For the method of half-lives, taking the natural log of both sides of Equation
(5- 1 8),
Plot r,,2 as a function 20-1 - 1
of C,, or use lnt,,, = In- +(1 -a) InC,,
regressional (OL - l)k
software
we see that the slope of the plot of lntl,2 as a function of lnCAO is equal to
1 minus the reaction order:

Slope = 1 -0
c

In cAO
Figure 5-7 Method of half-lives.
Rearranging:

a = 1 -slope
For the plot shown in Figure 5-7 the slope is - 1 :
a = 1 - (- 1) = 2

The corresponding rate law is
-rA = kC, 2

5.4 Differential Reactors

Data acquisition using the method of initial rates and a differential reactor are
similar in that the rate of reaction is determined for a specified number of pre-
determined initial or entering reactant concentrations. A differential reactor is
normally used io determine the rate of reaction as a function of either coincen-
tration or partial pressure. It consists of a tube containing a very small amount
of catalyst usually arranged in the form of a thin wafer or disk. A typical arrange-
ment lis shown schematically in Figure 5-8. The criterion for a reactor being dif-
ferential is that the conversion of the reactants in the bed is extremely smadl, as
is the change in reactant concentration through the bed. As a result, the reactant
concentration through the reactor is essentially constant and approximately
equal to the inlet concentration. That is, the reactor is considered to be gradi-
entless? and the reaction rate is considered spatially uniform within the hed.

B. Anderson, ed., Experimental Methads in Catalytic Research (San Diego, Calif.:
Academic Press, 1968).