Page 53 - The engineering of chemical reactions

Reactor Mass Balances 37

that in general kinetics are empirically determined. These arguments show that near
equilibrium the kinetics of reactions must be consistent with thermodynamic equilibrium
requirements.
Note also that the description of a reaction as irreversible simply means that the
equilibrium constant is so large that rr >> rb. The notion of an irreversible reaction is an
operational one, assuming that the reverse reaction is sufficiently small compared to the
forward reaction so that it can be neglected. It is frequently a good approximation to assume
a reaction to be irreversible when AG: << 0.
Returning to the energy diagrams of the previous figure, we see that the difference
between Ef and Eb is the energy difference between reactants and products, which is the
heat of the reaction A HR. The heat of reaction is given by the relation
AHR = CjVjHj
where Hj is the heat of formation of species j. We necessarily described the energy scale
rather loosely, but it can be identified with the enthalpy difference A HR in a reaction system
at constant pressure, an expression similar to that derived from classical thermodynamics.
These relations can be used to estimate rate parameters for a back reaction in
a reversible reaction if we know the rate parameters of the forward reaction and the
equilibrium properties AG: and AH,.
We emphasize several cautions about the relationships between kinetics and thermo-
dynamic equilibrium. First, the relations given apply only for a reaction that is close to
equilibrium, and what is “close” is not always easy to specify. A second caution is that
kinetics describes the rate with which a reaction approaches thermodynamic equilibrium,
and this rate cannot be predicted from its deviation from the equilibrium composition.
A fundamental principle of reaction engineering is that we may be able to find a
suitable catalyst that will accelerate a desired reaction while leaving others unchanged or
an inhibitor that will slow reaction rates. We note the following important points about the
relations between thermodynamics and kinetics:

1. Thermodynamic equilibrium requires that we cannot go from one side of the equilibrium
composition to the other in a single process.
2. Kinetics predicts the rates of reactions and which reactions will go rapidly or slowly
towards equilibrium.

One never should try to make a process violate the Second Law of Thermodynamics, but
one should never assume that AG; alone predicts what will happen in a chemical reactor.

REACTOR MASS BALANCES

We need reaction-rate expressions to insert into species mass-balance equations for a
particular reactor. These are the equations from which we can obtain compositions and
other quantities that we need to describe a chemical process. In introductory chemistry
courses students are introduced to first-order irreversible reactions in the batch reac-
tor, and the impression is sometimes left that this is the only mass balance that is im-
portant in chemical reactions. In practical situations the mass balance becomes more
complicated.