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3.1 Introduction to Heterogeneous Processes 61

v
considered a gien property for a specific catalyst. Then, if the rate coef f icient k is con-
t
stant, the rate coef icients f k , k vs and k are constants too.
m
s
The previously reported relationship (eq. (3.10)) manifests one more important charac-
v teristic of the catalyst leel rate coefficients—for the same reaction, temperature, catalytic
agent, and support but for different surface arrangement, i.e. actie site concentration, v
these coefficients will be different; and this is an advantage of the usage of k , and in gen- t
eral, of turnoy (actie site leel reaction description). v er frequenc v v
In the case of non-porous spherical particles,

S S ex d p 2 (3.11)

d 3
M S V p s p (3.12)
p
6
where S ex denotes the external surface area. Thus,

S 6
S ex (3.13)
s
M S d p p
Then
n S ex n 6 n
(3.14)
M s M s S ex p p d ex S

This result means that the number of actie sites per unit mass of catalyst is v not constant
since it depends on the particle size. the term Again, n S can be considered to be a con-
ex
v
stant property for a gien catalyst, prepared by the same technique, for all catalyst sizes.
Then
1d N 1  M S  S ex M S
r   k vs C S k S C S k m C S
t
n

n
n d t  n  (3.15)

p
k k t k t
t
Then, if the rate coef icient f k is constant, t k is constant too, whereas k m and k vs are not con-
s
stants and are dependent on the particle size of the catalyst (eq. 3.14).
icient The anatomy of rate coef f
In reactions where the rate is expressed as r k f ( C ), the rate coeficient will often f
i
i
depend on the concentrations, because the latter expression does not take into account the
interactions between molecules in a reaction mixture that is thermodynamically nonideal
(Froment and Bishoff, 1990). In such a case, if the concentrations are substituted by acti v-
ities, the rate coef icient is merely independent of the concentration of the reacting species, f
but one should keep in mind that it is still not truly a constant (F 1999). , ogler