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Balance of Degree of Reduction, Atomic Degrees of Reduction, and the COD Balance

In the previously defined "growth reference" system, yi was introduced as the degree of reduction of compound i. This parameter is important in stoichiometric calculations, because due to the principle of electron conservation, an electron balance can be defined. This is the so-called balance of degree of reduction. This is not an additional conservation principle (in addition to C, H, O, N, and charge conservation). The balance of degree of reduction can be obtained from the usual C, H, O, N, and charge balances by eliminating (by suitable substitutions) H + , H2O, HCO—, and the N source. Hence, the balance of degree of reduction is a suitable linear combination of already available conservation equations. The importance of the balance of degree of reduction is that, by definition, in this balance, only biomass formation, consumption of electron donor, and consumption of electron acceptor are related. Based on the previous definition of the reference set of compounds in the growth reference system it is also possible to calculate the degree of reduction of atoms and of electric charge (Table 4).

It should be noted that the atomic degree of reduction for the N atom in biomass depends on the applied N source as a consequence of the defined growth reference system as explained earlier. Using the y values of atoms and electric charge in Table 4, it is straightforward to calculate the y values for any chemical compound for which the elemental composition is known (Example 6a). This is an equivalent alternative to writing the reference redox half reaction to obtain y (Example 5).

EXAMPLE 6a

Direct calculation of y from elemental composition

Using the atomic degrees of reduction (Table 4) it can easily be checked that indeed for the reference chemicals y = 0:

For the degree of reduction of biomass (yX) it is easy to show that this is a function of the N source used. Using the standard elemental biomass composition CH18O0.5N0 2 and using the N degree of reduction for the different N sources (Table 4) one obtains

— NH+ as N-source yX = 1 x 4 + 1.8 x 1 + 0.5( —2) + 0.2(—3) = 4.2

— NO— as N-source yX = 1 x 4 + 1.8 x 1 + 0.5 x ( — 2) + 0.2(5) = 5.8

For the electron content of an organic substrate (e.g., acetate ion, C2H3O—) the amount of electrons is 2 x 4 + 3 x 1 + 2(—2) + 1(+1) = 8. Because for organic compounds y is defined as the number of electrons per C atom, we obtain for acetate with 2 carbon atoms y = 8/2 = 4.

The degree of reduction balance is also called chemical oxygen demand (COD) balance in wastewater engineering (26). The COD balance is equivalent to the balance of degree of reduction. COD is a number assigned to each chemical and represents the consumed O2 on total oxidation in g O2/g compound. There is a direct link with degree of reduction. Each mole of electrons represents 8 g COD. This is easily understood, because the consumption of 1 mol O2 represents the acceptance of 4 mol electrons (y = —4; see Table 3). One mol O2 represents — 32 g COD and therefore 1 mol electrons = 8 g COD.

EXAMPLE 6b

### Calculation of COD values

Consider glucose, in which 1 mol (= 180 gram) represents (according to Table 3) a total of 6 x 4 electrons = 6 x 4 x 8 = 192 g O2. Clearly glucose has a COD value of 192/180 = 1.0667 g COD/ g glucose.

The NO— /N2 acceptor couple has yA = — 5 electrons. The COD value of NO— — N is then —5 x 8/14 = —2.857 g COD per gram nitrate-nitrogen.

Using the atomic degrees of reduction (Table 4) it can easily be checked that indeed for the reference chemicals y = 0:

h2o |
c = |
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