Page 42 - The engineering of chemical reactions

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

where Ai is N2, A2 is 02, etc. This is a simplification of all the possible reactions involving
N and 0 atoms, since we have not included stable molecules such as N20, N202, N03,
and NzOs.
We can generalize this notation to any set of reactions as

VijAj = 0 i = 1,2,..., R
2
j=l
El
as a set of R reactions among S species, with j(= 1 to S) the index of chemical species
and i(= 1 to R) the index of the reaction. Thus we call Vij the stoichiometric coefficient
of species j in reaction i. We will use this standard notation throughout this book, and we
suggest that you always give the is and js these meanings and never reverse them.

REACTION RATES

We next need to describe the rates of transformations of chemical species among each
other. For this we use the symbol r for a single reaction and ri for the ith reaction in a
multiple reaction system. Reaction rates are basically empirical expressions that describe
the dependence of the rate of transformation on the parameters in the system.

Rate of a single irreversible reaction
It is found by experiment that rates almost always have power-law dependences on the
densities (such as concentration, density on a surface, or partial pressure) of chemical
species. For example, our first example of the homogeneous reaction of cyclopropane to
propylene exhibits a rate of decomposition that can be written as
r = k [cyclopropane]
while the homogeneous NO2 formation from NO and oxygen has a rate

r = k[N0]2[0~]
In these expressions we write the rate as a positive quantity, designated by lower-case r,
with dimensions of amount converted per unit volume per unit time.
We usually use the number of gram moles Nj of species j in a reactor of volume V to
describe the amount of that species. For density we will usually use concentration (moles
per volume),

which is usually expressed in moles per liter (one liter equals one cubic decimeter or dm3
in SI units). This unit is especially useful for densities of species in liquid solution, but we
can also use it for gaseous and solid solutions. For symbols of concentration we use the
following notations for species A
CA = [A] = [cyclopropane]