Page 43 - The engineering of chemical reactions

Reaction Rates 27

or for species j

Cj = [Aj]
In gases the most used quantity for the density of species j is the partial pressure Pi.
This can be related to concentration and mole fraction yj through the relations

and
Pj = YjP = CjRT
where P is the total pressure and N is the total number of moles in the system. In this equation
we assume ideal gases (PV = NRT) to relate partial pressure to concentration, while for
nonideal gases (not considered here) we would need an equation of state to describe the
density of each chemical species.
For liquid solutions we could use

Xj = &

where Xj is the mole fraction of species j in liquid solution. However, we will use only the
concentration, Cj = Nj / V, throughout this text.
For an irreversible reaction we can frequently describe the rate to a good approxima-
tion as

r = k fi Cj”j
j=l
where mj is the order of the reaction with respect to the jth species and the product extends
over all species in the reaction with mj = 0 for species that do not affect the rate of reaction.
If the rate is proportional to the concentration of a species raised to a power (mj), we say
that this form of the rate expression is described by “power-law kinetics.” This empirical
function is frequently used to describe reaction rates, but it frequently is not accurate,
especially with surface or enzyme-catalyzed reactions, which we will consider later.
Several alternate definitions of the reaction rate are used in different texts. In our
notation we will always write a chemical reaction as an equation and then define the rate
of that reaction as the positive rate of change for that particular stoichiometry. Consider the
reaction
2A + B + 3C, r = k[A12
In an alternate definition of reaction rates, one writes a rate as the rate offormation
of each species. In that notation one would define rA , rB, and rc, with the definitions
rA = -2k[A]’ = -2r

rB = +k[A12 = r
I-C = +3k[A12 = +3r