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+ 39.744

— 25.75

HCO— /C2H5OH. From Table 3 we read for the glucose couple that DGe = +39.744 and for the ethanol couple DGe = +30.353. Now glucose is the donor and HCO— /ethanol is the acceptor.

Because the catabolic reaction liberates the Gibbs energy required for the anabolism, it is important to calculate this amount of energy. Using the DGe approach, we can then write directly equations 6a and 6b to calculate the Gibbs energy of reaction (DGCAT) of the catabolic reaction. DGed and DGEA are the electron Gibbs energy of the acceptor and donor couples:

For autotrophic growth using inorganic electron donors, the DGed values are, in general, much lower than DGEX (consider NH++ /NO—, F2 + /F3+, etc., in Table 4). For auto-trophic growth (CO2 as C source), this means that for these electron donors there is a need for Gibbs energy input in order to realize CO2 reduction to biomass. This is achieved by RET. Knowing this we can write equation 7c to recognize RET.

DGex > DGed

The enthalpy of reaction DHCAT of the catabolic reaction can be calculated similarly:

DGcat and DHCAT represent the Gibbs energy and enthalpy of reaction of the catabolic reaction consuming 1 C-mol organic or 1 mol inorganic compound of electron donor. Dimensions are kJ/(C)-mol donor. yD is the degree of reduction of the donor couple in mol electrons/(C)-mol donor, which is always positive. According to the second law of thermodynamics DGCAT must be negative. Therefore equation 6c, the second law of thermodynamics, holds:

DGed > DGea

This shows that indeed the electron donor couple always has the highest DGe value.

Finally, it is now easy to calculate the heat production and Gibbs energy dissipation in oxidative catabolism of organic compounds. As stated earlier, for organic compounds the average DGed = 32 kJ/e-mol and for O2 as acceptor DGea = —78.719 kJ/e-mol. Hence, per mole of electron transferred between donor and acceptor, the available Gibbs energy is 32 — ( — 78.719) = 110.72 kJ. Per mole of consumed O2 (which accepts four electrons, yA = —4) in the combustion of any organic compound, the Gibbs energy made available by combustion of the organic compound is then 4 X 110.72 = 443 kJ per consumed mol O2. Analogously, one can find for the produced heat per mole of O2 in the combustion of organic compounds a value of 460 kJ per mole O2. It is also obvious that the mentioned inaccuracy in the average DGE or DHE values for organic compounds only results in a minor error of 5 to 8% in the calculated Gibbs energy dissipation and heat production. These are very important rules of thumb for the fermentation industry (1).

EXAMPLE 8b

Calculation of catabolic Gibbs energy production using DGe

Consider the catabolic reactions in Example 8a. For aerobic glucose oxidation we can calculate, using equation 6a and Table 3

This is the Gibbs energy released for the aerobic combustion of 1 C-mol glucose. For 1 mol of glucose (6 C-atoms) the Gibbs energy of the catabolic reaction is 6 x (— 473.852) = —2,843 kJ.

For anaerobic ethanol fermentation of glucose we can calculate for the catabolic reaction ( — DGCAT) = 4 x (39.744 — 30.353) = 37.564 kJ per C-mol glucose. For 1 mol glucose the catabolic Gibbs energy of the catabolic reaction becomes 6 x ( — 37.564) = — 225.34 kJ. This is the same as calculated in Example 3b.

The use of DGe and DHe now also reveals some interesting energetic regularities (4). Table 3 shows that for many organic donor compounds, the DHe and DGe values are rather close, with an average DGe = +32 ± 8 kJ/e-mol and average DHe = — 28 ± 5 kJ/e-mol. These values are also close to the DGE and DHE value of biomass. Hence we can write for organic electron donors the important regularity

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