Page 185 - Principles of Catalyst Development

CATALYST CHARACTERIZATION 173

and

I
f
.
. .
1 dCA
- - -- -mo es per Unit time per Unit sur aC1e, tota I (7.20)
S dt or active (areal rate)
An adaptation of rate per unit surface now in common use is the turnover
number, Nt, defined as the number of molecules reacted pe:r site per second.
Although appealing in its molecular simplicity, the turnovt~r number should
be used with caution, since it requires a knowledge of the surface area
under reaction conditions and the stoichiometry or struct.ure of the active
site. Surface area is difficult to measure. The most common approach is to
find the surface area of the fresh catalyst in a separate experiment, where
activation conditions may not be exactly reproduced. NI~xt, the structure
of the active site is needed to relate surface area to site de:nsity. This is the
most elusive property in catalysis and is the subject of much research. It is
not an overstatement to say that there are very few reactions where we can
even approximate these structures. Perhaps in the future, innovative methods
will open a way to use these concepts. In the meanwhile, it is better to
represent rates on the basis of a measurable and known property, such as
volume, mass, or surface area.
Measurements of rates at different concentrations and temperatures
lead to empirical rate equations. If, however, a series of 'catalysts is to be
compared, each must be expressed at a specified temperature and concentra-
tion. Initial rates at zero process time are the most reliable. In the case of
deactivation or surface conditioning by the reactant, rates should be
measured at some standard process time. This must be established carefully
and rates interpolated, but never extrapolated, from rates measured over
the complete range.

7.5.1.2. Rate Constants

Using a rate constant to express activity avoids the problem of specify-
ing concentrations, but not temperatures. The exact form of the rate
equations, however, must be known. This involves extensive experiments,
at least initially. If the function of the rate equation is available with sufficient
confidence, then subsequent measurement of rate constants requires only
a few data points. Rate constants may be expressed in a variety of units,
with respect to volume, mass, or surface area. An example for a first-order
reaction is given in Table 7.14.
A warning on the use of rate constants should be stated at this point.
A common practice in catalysts is to fit kinetic data to the power rate
expression