Page 111 - Introduction to chemical reaction engineering and kinetics

5.2 Measures of Reaction Extent and Selectivity 93

The instantaneous fractional yield of D with respect to A is

rate of formation of D

52.5 Extent of Reaction

Another stoichiometric variable that may be used is the extent of reaction, 6, defined
by equation 2.3-6 for a simple system. For a complex system involving N species and
represented by R chemical equations in the form

zl vijAi = 0; j = 1,2,. . ., R (1.4-10)

where vij is the stoichiometric coefficient of the ith species (AJ in thejth equation, we
may extend the definition to (for a flow system):

Vij5j = (Fi - Fi,)j; i = 1,2, . . . N; j = 1,2, . . . , R (5.2-9)

Since

,$ Vij[j = ]gl(Fi - Fi,)j = Fi - Fio; i = 1,2, . . . N (5.2-10)
j=l

the flow rate of any species at any point may be calculated from measured values of tj,
one for each equation, at that point:

Fi = Fi, + 5 Vij5j; i = 1,2, . . . N (5.2-11)
j = l

or, for molar amounts in a batch system

ni = nio + 2 Vij5j; i = 1,2, . . N (5.2-12)
j=l

If the R equations are in canonical form with one noncomponent in each equation,
it is convenient to calculate sj from experimental information for the noncomponents.
The utility of this is illustrated in the next section.

5.2.6 Stoichiometric Table for Complex System
A stoichiometric table for keeping track of the amounts or flow rates of all species
during reaction may be constructed in various ways, but here we illustrate, by means
of an example, the use of tj, the extent of reaction variable. We divide the species into
components and noncomponents, as determined by a stoichiometric analysis (Section
5.2.1) and assume experimental information is available for the noncomponents (at
least).