Page 166 - Modelling in Transport Phenomena A Conceptual Approach

146 CHAPTER 5. RATE OF GENERATION

In engineering practice the Arrhenius relation, Le.,

k(T) = Ae-'iRT (5.3-31)
is generally considered valid5 and the rate constant can be determined by running
the same reaction at different temperatures. The data from these experiments are
found to be linear on a semi-log plot of k versus 1/T.
The function f(s) depends on the concentration of all the species in the chem-
ical reaction. Since the reaction rate is usually largest at the start of the reaction
and eventually decreases to reach a zero-rate at equilibrium, the function f(~) is
taken to be a power function of the concentration of the reactants.
If f(~) were a power function of the products of the reaction, the reaction
rate would increase, rather than decrease with time. These reactions are called
autocatalytic.
For normal decreasing rate reactions
f(cc) = (5.3-32)
i
where ci is the concentration of a reactant. Thus, the constitutive equation for the
reaction rate is
(5.3-33)

The order of a reaction, n, refers to the powers to which the concentrations are
raised, i.e.,
n=C% (5.3-34)

i
It should be pointed out that there is no necessary connection between the order
and the stoichiometry of the reaction.

NOTATION

A area, m2
C concentration, kmol/ m3
E activation energy, kJ/ kmol
FD drag force, N
9 acceleration of gravity, m/ s2
h elevation, m
k reaction rate constant
L length, m
'Deviations from the Arrhenius relationship are discussed by Maheswari and Akella (1988).