Page 33 - Elements of Chemical Reaction Engineering Ebook

4 Mole Balances Chap. 1

species, r, (e.g., DDT), and the rate of disappearance of another species, -ri
(e.g., chlorobenzene), in a chemical reaction.
In heterogeneous reaction systems, the rate of reaction is usually
expressed in measures other than volume, such as reaction surface area or cat-
alyst weight. Thus for a gas-solid catalytic reaction, the dimensions of this
rate, -rL, are the number of moles of A reacted per unit time per unit mass of
catalyst (mol/s *g catalyst). Most of the introductory discussions on chemical
reaction engineering in this book focus on homogeneous systems.
The mathematica1 definition of a chemical reaction rate has been a source
of confusion in chemical and chemical engineering literature for many years.
The origin of this confusion stems from laboratory bench-scale experiments
that were carried out to obtain chemical reaction rate data. These early experi-
ments were batch-type, in which the reaction vessel was closed and rigid; con-
sequently, the ensuing reaction took place at constant volume. The reactants
were mixed together at time t = 0 and the concentration of one of the reac-
tants, C,, was measured at various times t. The rate of reaction was deter-
mined from the slope of a plot of CA as a function of time. Letting rA be the
rate of formation of A per unit volume (e.g., g mol/s.dm3), the investigators
then defined and reported the chemical reaction rate as

dCA
r, = -
dt
However, this definition was for a constant-volume batch reactol:
As a result of the limitations and restrictions given, Equation (1-1) is a
rather limited and confusing definition of the chemical reaction rate. For
amplification of this point, consider the following steady-flow system in which
the saponification of ethyl acetate is carried out.

Example 1-1 Is Sodium Hydroxide Reacting?

Sodium hydroxide and ethyl acetate are continuously fed to a rapidly stirred tank in
which they react to form sodium acetate and ethanol:
NaOH f CH,COOC,H5 ---+ CH3COONa + C,H,OH

(Figure El-1.1). The product stream, containing sodium acetate and ethanol,
together with the unreacted sodium hydroxide and ethyl acetate, is continuously
withdrawn from the tank at a rate equal to the total feed rate. The contents of the
tank in which this reaction is taking place may be considered to be perfectly mixed.
Because the system is operated at steady state, if we were to withdraw liquid sam-
ples at some location in the tank at various times and analyze them chemically, we
would find that the concentrations of the individual species in the different samples
were identical. That is, the concentration of the sample taken at 1 P.M. is the same
as that of the sample taken at 3 P.M. Because the species concentrations are constant
and therefore do not change with time,

(El-1.1)