Page 97 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 3.1 Basic Clefinitions

3.1 .I The Reaction Rate Constant

In the chemical reactions considered in the following paragraphs, we take
as the basis of calculation a species A, which is one of the reactants that is dis-
appearing as a result of the reaction. The limiting reactant is usually chosen as
our basis for calculation. The rate of disappearanc~e of A, - r,, depends on
temperature and composition. For many reactions it can be written as the prod-
uct of a reaction rate constant k and a function of the concentrations (activi-
ties) of the various species involved in the reaction:
The rate law gives
the relationship
between -r~ [kA(T>I[fn(CA,C,,...l
=
reaction rate and
cancentration
The algebraic equation that relates - r, to the species concentrations is called
the kinetic expre:ssion or rate law. The specific rate of reaction, k,, like the
reaction rate - r,, is always refe~d to a particular species in the reacb~ons
and normally should be subscripted with respect to that species. However, for
reactions in which the stoichiometric coefficient is 1 for all species involve~d in
the reaction, for example,

we shall delete the subscript on the specific reaction rate:
=
=
= k ~ = k a ~ ~ ~k~a~l k~20
~l
The reaction rate constant k is not truly a constant, but is merely indepen-
dent of the concentrations of the species involved in the reaction. The quantity
k is also referred to as the specific reaction rate (constant). It is almost
always strongly dependent on temperature. In gas-phase reactions, it depends
on the catalyst and may be a function of total pressure. In liquid systems it can
also be a function of total pressure, and in addition can depend on other
parameters, such as ionic strength and choice of solvent. These other variables
normally exhibit much less effect on the specific reaction rate than does tern-
perature, so for the purposes of the material presented here it will be assurned
that k, depends only on temperature. This assumption is valid in most labora-
tory and industrial reactions and seems to work quite well.
It was the great Swedish chemist Arrhenius who first suggested that the
temperature dependence of the specific reaction rate, k,, could be correlated
by an equation oE the type
m
-
-
Arrhenius equation k, (T) = AePEIRT

where A = preexponential factor or frequency factor
E = activation energy, Jlmol or cal/mol
,R = gas clonstant = 8.3 14 Jlmol . K = 1.987 cal/mol. K
:7" = absolute temperature, K