Page 48 - The engineering of chemical reactions

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

TABLE 2-l
Units of Reaction-Rate Coefficients
Order Units of k

1 time-’
0 moles liter-l time-1
2 liter mole-’ time-’
3 liter* molec2 time-l
0.5 mole0.5 liter-o.5 time-l
n (litedmoley- ’ time-l

raised to powers mrj equal to their stoichiometric coefficients, while the backward rates
appear to be proportional to the concentrations of products raised to the powers mbj of their
stoichiometric coefficients, or, more formally,

F?lfj = -Vj, Vj < 0
Wlfj = 0, V j > 0

mbj = Vj, V j > 0
Wlbj = 0, Vj < 0
This set of relations between reaction orders and stoichiometric coefficients defines what
we call an elementary reaction, one whose kinetics are consistent with stoichiometry. We
later will consider another restriction on an elementary reaction that is frequently used by
chemists, namely, that the reaction as written also describes the mechanism by which the
process occurs. We will describe complex reactions as a sequence of elementary steps by
which we will mean that the molecular collisions among reactant molecules cause chemical
transformations to occur in a single step at the molecular level.
We note again that there is an arbitrariness in writing a reaction because all these
Vj coefficients can be multiplied by a constant without changing the nature of the reaction
or violating mass conservation. Thus, for NO decomposition, written previously as two
different reaction equations, we would be tempted to write either r = k[NO]‘/* or
r = k[NO]‘. However, one of these must be incorrect, and in some situations neither
equation correctly describes the experimentally observed rates. Only in some simple
situations are reactions described by elementary kinetics.
On a molecular level, reactions occur by collisions between molecules, and the rate
is usually proportional to the density of each reacting molecule. We will return to the
subject of reaction mechanisms and elementary reactions in Chapter 4. Here we define
elementary reactions more simply and loosely as reactions whose kinetics “agree with’
their stoichiometry. This relationship between stoichiometry and kinetics is sometimes
called the Law of Mass Action, although it is by no means a fundamental law of nature, and
it is frequently invalid.
STOICHIOMETRY

Molecules are lost and formed by reaction, and mass conservation requires that amounts
of species are related. In a closed (batch) system the change in the numbers of moles of all
molecular species Nj are related by reaction stoichiometry.