Thermodynamics of Bioreactions
103
Using
S° =
1.36 cal (mole K)'1
for
A G / can be calculated from
and 5° just as in Example 4,1
C 0 2 :
AG® = -9 4 .0 5 -0 .2 9 8 -(5 1 .0 6 -1 .3 6 -4 9 ) = -94.26 kcal mole'1
(3)
C2H 5OH : AG“ = -6 6 .3 6 -0 .2 9 8 * (3 8 .4 -2 -1 .3 6 -3 * 3 1 .2 1 -0 .5 - 49) = -4 1 .7 9 kcal m ole1
(4)
The heat of combustion of ethanol by (1) is now calculated as the sum of the heat of formation of the (C O ^
and the (H
2
O)] that make up the ethanol molecule less the heat of formation of ethanol.
Qc = —à H c
= —66.36+ 2*94.05 + 3• 68.28 = 326.6 kcal m ole1
(5)
or 1367 kJ (mole ethanol)'1
AGC
= -327 - 0.298 • (2 • 51.06 + 3 -16.72 - 38.4 - 3 • 49.0) = 317 kcal m ole'
(6)
or 1325 kJ (mole ethanol)'1__________________________________________
4.2 Heat of Reaction
For design of heat exchangers it is important to calculate the heat of reaction, not so much of the
individual biochemical reactions occurring within the cell but rather for the overall conversion of
substrates to biomass and products. Table 4.3 collects heat of combustion data for many of the
compounds involved in bioprocesses. The reference state is changed slightly compared to that used
in the previous examples: C 0 2 is not in the gas phase, but dissolved in water at pH = 7, and for C 0 2
as well as other compounds which may take part in acid-base reactions the sum of the ions which
are formed at pH = 7 is used as the reference concentration unit. The difference between the
“biological” thermodynamic data such as -A
Hc
in Table 4.3 and those used in chemical
thermodynamics is small. Since the values of Table 4.3 are going to be used to find heats of
reaction when e.g. glucose is converted to ethanol and C 0 2 the difference in reference state means
nothing, or hardly anything. The calculations of Examples 4.2 and 4.4 illustrate how the values in
the table may be obtained.
Also included in the table is a column showing the degree of reduction K* of the compounds.
K
of
Chapter 3 is identical to K* for all compounds which do not contain N, but in relation to
combustion calculations it seems more natural to use N2 rather than NH3 as the “redox neutral” N
containing compound. If the elements S and P appear the degree of reduction of S and P is set to 6
and 5 respectively just as in K. Note in particular that K* for “standard” biomass CH] gO0 5N02 is
4.80 whereas K = 4.20.