An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 95

reaction steps. As such, the reaction rate form for elementary reactions strictly follow Eqn
(3.35) , with the order of reaction O Rj ¼n j for reactants and O Rj ¼

0 for products. Since a frac-
tion of a molecule cannot react with other species in an elementary reaction, the order of reac-
tion for elementary reactions is always integer and positive. Therefore, how you write the
reaction can even influence whether the reaction could be elementary or not.

3.3.4. Rate of a Reversible Reaction
One can rewrite a reversible reaction into two simultaneous reactions. For example,

ð v A Þ A þð v B Þ B # v C C / r (3.37)

is considered to be two reactions occurring simultaneously.

ð v A Þ A þð v B Þ B / v C C / r f (3.38)

v C C / ð v A Þ A þð v B Þ B / r b (3.39)

The rate expression is simply a combination of the two reactions. Because the stoichiometric
coefficients are the same in the two reactions (only differing by sign), the same rate is appli-
cable to every species involved, leading to a directly additive rate expression. That is,

r ¼ r f r b (3.40)

3.3.5. 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 reaction i in the set of N R reactions being described by a rate
r i , rate coefficient k i , order of the forward reaction O Rij with respect to species j, etc.
Again, the procedure we follow is first to write the reaction steps with a consistent stoichi-
ometry and then to express the rate of each reaction to be consistent with that stoichiometry.
Thus, if we write 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 reverse the reaction,
the forward and reverse rates would be switched.
For a multiple reaction system with reversible reactions, we can describe each of the N R
reactions through a reaction rate r i ,

r i ¼ r if r ib (3.41)

where i ¼ 1, 2, 3, . , N R .

3.4. APPROXIMATE REACTIONS

Consider the hydrolysis or saponification of an ester (ethyl acetate) into an alcohol
(ethanol) and an acid (acetic acid),

CH COOC H

5 þ

H O # CH COOH þ C H OH (3.42)

3 2 2 3 2 5