Page 44 - The engineering of chemical reactions

28 Reaction Rates, the Batch Reactor, and the Real World

These rates are the rates of production of species A, B, and C (rj = Vjr); so these rates are
written as negative quantities for reactants and positive quantities for products. This notation
quickly becomes cumbersome for complex reaction stoichiometry, and the notation is not
directly usable for multiple reaction systems.
We will consider the rate r as a single positive quantity describing the rate of a
particular reaction. Note that the rate can now only be defined after we write the chemical
reaction. In our two ways of writing the NO formation reaction previously, the rate would
be smaller by a factor of two when the stoichiometric coefficients are multiplied by a factor
of two.

Rates of reversible reactions

If the reaction is reversible, we frequently find that we can write the rate as a difference
between the rate of the forward reaction rf and the reverse (or back) reaction rb,

r = rf - rb = kf fi C,;” - kb fj Cjmbj
j=l j=l

where mrj and mbj are the orders of the forward and reverse (or back) reactions with respect
to thejth species, and kf and kb are the rate coefficient of the forward and reverse reactions.

Rates of multiple reactions

We also need to describe the rates of multiple-reaction systems. We do this in the same way
as for single reactions with each of the i reactions in the set of R reactions being described
by a rate ri, rate coefficient ki, order of the forward reaction mfij with respect to species j,
etc.
We repeat that the procedure we follow is first to write the reaction steps with a
consistent stoichiometry and then to express the rate of each reaction to be consistent with
that stoichiometry. Thus, if we wrote a reaction step by multiplying each stoichiometric
coefficient by two, the rate of that reaction would be smaller by a factor of two, and if we
wrote the reaction as its reverse, the forward and reverse rates would be switched.
For a multiple-reaction system with reversible reactions, we can describe each of the
R reactions through a reaction rate ri,

ri = rfi - rbi = kfi fi C,!*” - kbi fi cl?bij
j=l j=l

with symbols having corresponding definitions to those used for single reactions.
This looks like a maze of notation, but for most examples this notation merely
formalizes what are usually simple and intuitively obvious expressions. However, we need
this formal notation for situations where intuition fails us, as is the case for most industrial
reaction processes. Whenever a reaction is irreversible, we use k and mj as rate coefficient
and order, respectively, omitting the subscript f.