An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 103

or simply

#-C-moles of P formed
#-C-moles of A initially

Y P = A ¼ (3.68b)

as carbon is implied.
One can observe from the above definitions, yield is for a desired product and is the frac-
tion of all the particular reactant that is converted to the desired product. In many cases, we
do not know the extent of reaction and thus yield becomes not convenient to use. One param-
eter used quite a bit in biochemical engineering is the yield factor. Yield factor is defined as
the maximum fractional yield, and thus a state parameter, which is independent of the reac-
tion kinetics. That is,

¼ jn P j
jn A j

#-C-moles of P that could be formed
#-C-moles of A

YF P = A ¼ (3.69)

which is then only specific to the stoichiometry of the reactions involved. One often extends
this yield factor definition to include reactants as well; in that case, the amount of species
change in the definition is always defined as the absolute value in the net change (either
increase or decrease). Still, A in Eqn (3.69) needs not be restricted to as reactant.
Sometimes, one can find that the yield factor defined above is not convenient to use. For
example, counting the number of biomass or cells is not an easy task. We often use another
definition,

Mass of P that could be produced
Mass of A

YF P = A ¼ (3.70a)

or

Total number of moles of P that could be produced
Total number of moles of A

YF P = A ¼ (3.70b)

The definition used in Eqn (3.70) can however push the yield factor out of the normal
range (0,1) as the total masses (or moles) of P that could be produced and A are used in
Eqn (3.70) .
While the yield factor is the maximum fractional yield which has no units, one must be
careful on the basis used. That is, either C-mole-P/C-mole-A, kg-P/kg-A, or mole-P/
mole-A. They can have very different values. Therefore, it is recommended that units be
retained.
We will learn later that the mass ratios are more convenient for biological reactions. The
yield factors can be efficiently used in part to relate the specific reaction rates ( m 's) instead
of using the stoichiometric coefficients ( n 's) for systems with a single reaction.

Example 3-4. Yield factors. Continue on Example 3-3, find the yield factors of biomass (X)
and oxygen (O 2 ) over the substrate carbon monoxide (CO).
Solution. Based on the solution from Example 3-3
CO þ 0:0068 O

2 þ 0:0036

N

2 þ 0:476

H 2 O /

0:52 CO

2 þ 0:21

CH COOH þ 0:006 CH CH CH COOH þ 0:036 CH O 0 : 5 NO

3 3 2 2 1:8 0:2