Page 253 - Elements of Chemical Reaction Engineering Ebook

224 Collection and Analysis of Rate Data Chap. 5

5.1 Batch Reactor Data

Batch reactors are used primarily lo determine rate law parameters for homo-
geneous reactions. This determination is usually achieved by measuring con-
centration as a function of time and then using either the differential, integral,
or least squares method of data analysis to determine the reaction order, a, and
Process data in specific reaction rate, k. If some reaction parameter other than concentration is
Of the monitored, such as pressure, the mole balance must be rewritten in terms of
measured
vanable the measured variable (e.g., pressure).
5.1.1 Differential Method of Rate Analysis

When a reaction is irreversible, it is possible in many cases to determine
the reaction order a and the specific rate constant by numerically differentiat-
ing concentration versus time dam This method is applicable when reaction
conditions are such that the rate is essentially a function of the concentration
of only one reactant: for example, if, for the decomposition reaction
Assume that the A +products
rate law is of the
form
-rA = kCz -rA = kC:
then the differential method may be used.
However, by utilizing the method of excess, it is also possible to deter-
mine the relationship between - rA and the concentration of other reactants.
That is, for the irreversible reaction
A + B -+products
with the rate law

where a and p are both unknown, the reaction could first be run in an excess
of B so that C, remains essentially unchanged during the course of the reac-
tion and

where

P
Method of excess k’ = kCl= kCBo (5-4)
After determining a, the reaction is carried out in an excess of A, for
which the rate law is approximated as

(5-5)
Once a and p are determined, k, can be calculated from the measure-
ment of -rA at known concentrations of A and B: