Page 195 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 165

is useful when the reaction order and specific rate at one temperature
are already known from previous experiments, and the specific reaction
rate at some other temperature is sought. If the reaction rate constant
k at two or more different temperatures is known, it is possible to
determine the activation energy and the frequency factor.
Level 2 involves the trial-and-error method. After trying zero, first,
second, and finally third order, if none of these orders fit the data,
another analysis method should be tried. When the reaction order is
unknown, cannot be guessed, and the reaction is irreversible, proceed
to level 4. If the reaction rate depends on only one species (e.g.,
isomerization or decomposition reactions), use the differential method
that requires only one experiment, or the method of half-lives that
requires many experiments, to determine the specific reaction rate and
order. However, where certain constraints imposed by a given reaction
prevent collating experimental data other than in the initial rate period,
neither the differential nor the half-life method may be suitable.
Examples include a solid-liquid reactions, where flaking or crumbling
of the solid occurs, and certain autocatalytic and simultaneous reac-
tions. In such instances, it is usually best to use the initial rate plot
method given in level 5. In this technique, the initial rate is measured
at various initial concentrations of the reacting species. The reaction
order can be determined from a plot of the logarithm of the initial
reaction rate, ln (–r AO ), against the logarithm of the initial con-
centration, ln C AO . The two methods of analysis that require only one
experiment to determine the reaction order and the specific rate
constant are the integral method (level 2) and the differential method.
If the reaction rate depends on more than one species, use the
method of excess coupled either with the half-life method or the
differential method. If the method of excess is not suitable, an initial
rate plot may be constructed by varying the concentration of one
reactant while the concentrations of the others are held constant. This
process is repeated until the orders of reaction of each species and
the specific reaction rate are evaluated. At level 5, the least-squares
analysis can be employed.
Figure 3-16 is helpful in the logical planning of a series of kinetic
experiments to determine reaction orders and specific rate constants.
However, it is important to remember the main goals and design of
the entire experimental analysis. Table 3-5 gives methods used to
determine direct or indirect measurements of a species concentration.
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