Page 110 - Introduction to chemical reaction engineering and kinetics

92 Chapter 5: Complex Systems

where k is a noncomponent index, C is the number of components, and N is the number
of species.
For a simple system with only one noncomponent, say D,

YDIA = fA (simple system) (5.2-2a)

As defined above, YDIA is normalized so that

0 5 Y,,, 5 1 (5.2-3)

5.2.4 Overall and Instantaneous Fractional Yield
The fractional yield of a product is a measure of how selective a particular reactant
is in forming a particular product, and hence is sometimes referred to as se1ectivity.l
Two ways of representing selectivity are (1) the overall fractional yield (from inlet to
a particular point such as the outlet); and (2) the instantaneous fractional yield (at a
point). We consider each of these in turn.
For the stoichiometric scheme in Section 5.2.3, the overall fractional yield of D with
,.
respect to A, S,,,, is

moles A reacted to form D
iD/A = mole A reacted (5.2-4a)

_ bAlD nD - lZDo (BR, constant or variable p) (5.2-413)
VD nAo - IzA
_ I"AI~ F~ -F~o (flow reactor, constant or variable p) (5.2-4~)
VD FAo -FA
_ IVAIDCD - coo (BR, or flow reactor, constant p) (5.2-4d)
VD cAo - cA

n
From the definitions of fA, Yo,A, and SD,,, it follows that

,.
YDIA = ~ASDIA (5.2-5)

The sum of the overall fractional yields of the noncomponents is unity:

1
bAlk *k - nko _ nAo - nA = 1 (5.2-6)
llAo - nA

AS in the cases of fA and Yn/A, SD/A is normalized in the definitions so that

‘Other definitions and notation may be used for selectivity by various authors.