Page 109 - Introduction to chemical reaction engineering and kinetics

5.2 Measures of Reaction Extent and Selectivity 91
5.2.2 Fractional Conversion of a Reactant

Fractional conversion of a reactant, fA for reactant A, say, is the ratio of the amount of A
reacted at some point (time or position) to the amount introduced into the system, and
is a measure of consumption of the reactant. It is defined in equation 2.2-3 for a batch
system, and in equation 2.3-5 for a flow system. The definition is the same whether the
system is simple or complex.
In complex systems, fA is not a unique parameter for following the course of a re-
action, unlike in simple systems. For both kinetics and reactor considerations (Chap-
ter 18) this means that rate laws and design equations cannot be uniquely expressed
in terms of fA, and are usually written in terms of molar concentrations, or molar flow
rates or extents of reaction. Nevertheless, fA may still be used to characterize the over-
all reaction extent with respect to reactant A.

5.2.3 Yield of a Product

The yield of a product is a measure of the reaction extent at some point (time or po-
sition) in terms of a specified product and reactant. The most direct way of calculating
the yield of a product in a complex system from experimental data is by means of a
stoichiometric model in canonical form, with the product as a noncomponent. This is
because that product appears only once in the set of equations, as illustrated for each
of CO, CO,, and HCHO in Example 5-1.
Consider reactant A and (noncomponent) product D in the following set of stoichio-
metric equations:

.
IV&A + . . = vnD + . . .
+other equations not involving D

The yield of D with respect to A, YDiA, is

moles A reacted to form D
Y D/A = mole A initially (5.2-la)

moles A reacted to form D x moles D formed
=
mole D formed mole A initially
_ bAiD nD - llDo (BR, constant or variable p) (5.2-lb)

, _ vy,s, FD~‘~DO (flow reactor, constant or variable p) (5.2-1~)
FAO
_ iuy,s, cD - cDo (BR or flow reactor, constant p) (5.2-ld)
VD CA0

where IvAID is the absolute value of vA in the equation involving D, and nDo, FD,, cDo
refer to product D initially (each may be zero).
The sum of the yields of all the noncomponents is equal to the fractional conversion
of A:

N bAik nk - llko _ nAo - “ A = fA (5.2-2)
kz+, “IA = kg+1 Ty - nA0