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3.1 Introduction to Heterogeneous Processes 59

phase ( r ), defined as follo 1972): enspiel, v ws (Le
m
1d N
r vs (3.2)
V S t d

1 N d
r (3.3)
s
S t d
1d N
r m (3.4)
M s t d

where:
V S the volume of solid phase
S the surface of the solid phase
M S the mass of the solid phase.
For a specific reaction, the reaction rates, as defined in eqs. (3.2)–(3.4), depend on the
v nature of the catalytic actie site, the surface arrangement of the catalyst, the temperature,
and the reactants concentration. ement Surface arr ang here denotes the macroscopic and
measurable catalyst basic properties:

• the specific area of the catalyst S s S M s
• the number of catalytic actie sites per unit area v n
S
n
These two basic properties of the catalyst M can be related as follows:
s
n S n n
S s (3.5)
M s M s S S

n
The number of actie sites per unit mass of catalyst v M can be referred to as “active
s
sites concentration.”
v
The principal difference between these “catalyst le reaction rates and the turno er v
el”
frequency is that the latter does not depend on the surface arrangement of the catalyst, or
in more practical terms, does not depend on the specific physicochemical characteristics
of the catalyst as a composite of the actie catalytic reagent plus the support. v
v The turnoer frequency and the catalyst leel reaction rates can be related through the v
following equalities:
1d N V S S M S
r r vs s r r m (3.6)
t
n d t n n n
w
It is noteorthy that the form of the rate ( r f (state of the system) does not actually
i
depend on our choice of reaction rate definition. Only the rate coefficients and their dimen-
sions change with each rate definition (Le 1972). v enspiel,