Biomedical Engineering Reference
In-Depth Information
3.9. ENERGY REGULARITY
In the preceding section, we have reviewed the thermodynamic limitations. For bioreactions,
the chemicals involved often consist of carbon and hydrogen atoms. The lack of detailed
information about most living cells and complex molecules has limited our ability to carry
out thermodynamic estimations. Limiting on the carbon and hydrogen containing chemicals,
biochemical engineers have empirically formulated relations that are of interests to biochem-
icals. The general degree of reduction is one of the parameters used in the correlations.
The generalized degree of reduction is defined as the number of electrons a molecule can
give off to reach the usual state for every atom involved in the molecule. For a carbon and
hydrogen containing molecule, this is given as
g DR ¼ 4n C þ n H 2n O
(3.92)
where
n C is the number of carbon atoms in the molecule,
n H is the number of hydrogen atoms
in the molecule, and
n O is the number of oxygen atoms in the molecule. The degree of reduc-
tion for oxygen (O 2 ) gas is set at zero, although a
2 is set for oxygen atom in a molecule as
shown in Eqn (3.92) . The degree of reduction has a unit of moles of electrons per mole.
Correlating on the organic compounds, the heats and Gibbs free energy of combustion
(producing gaseous CO 2 and liquid H 2 O) have been found to relate to the degree of reduction
via (Sandler S.I., Chemical, Biochemical, and Engineering Thermodynamics, 4 th Ed., John
Wiley & Sons, Inc., 2006).
DG C ¼
112 g DR kJ
=
mole
(3.93)
and
DH C ¼
110
:
9 g DR kJ
=
mole
(3.94)
C are the Gibbs free energy and heat of combustion, respectively. The
combustion products are in their elemental form for all the atoms other than C and H 2 .
Equations (3.93) and (3.94) provide means to estimate the thermodynamic properties of
biochemicals when they are not available.
Figure 3.5 illustrates how the heat of reaction can be computed from the heat of combus-
tion data. As shown in Fig. 3.5 , the total combustion products are shown on the top and are
the identical for those from the reactants to those from the products. Noting that, all the
carbons are converted to carbon dioxide and hydrogen converted to water. All other elements
are converted back to their respective elemental forms. Because the heats of reactions are
state variables, not dependent on the process, we have
C and DH
Where DG
DH R þ DH c ; P DH c ; R ¼ 0
(3.95)
Therefore,
DH R ¼ DH c ; R DH c ; P
(3.96)
We note also that
n j
X
DH C ; R ¼
DH c ;j
(3.97)
j
¼
reactants
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