## The Growth Reference System

In the preceding sections, the stoichiometric coefficients for the macrochemical reaction equation of biomass formation have been solved by setting up the proper conservation equations (C, H, O, N, charge, enthalpy) and the Gibbs energy balance. Although this is a sufficient and straightforward method, solving these linear equations remains unattractive and does not provide insight. To simplify these calculations and to gain insight, a special reference system has been designed—the growth reference system. This reference system is based on the observation that, in all chemotrophic growth systems, H2O, HCO—, H + , and N source (mostly NH+) occur as chemical compounds (see earlier section on growth system definition). In this special reference system each chemical compound is assigned three new numbers.

In this reference redox half reaction, 1 C-mol methanol is converted and six electrons are produced, hence y = + 6 for methanol. Using the DG°— values from Table 2, the DGref for the methanol-reference redox half reaction follows as (standard conditions)

DG?i = (7)( —39.87) + 1( —586.85) — (2)( —237.18) — (1)(—181.75) = —216.192 kJ

This gives for the DG01 value of methanol by equation 4a DG01 = — ( — 216192) = +36.032 kJ/e-mol

Obviously DHe can be calculated in a similar way by calculation of DHref.

For biomass the following redox half reaction can be set up, assuming that NH+ is the N source:

y the degree of reduction, which represents the electron content per C-mol (for organic compounds) or per mol (for inorganic compounds) DGe the Gibbs energy per electron present in the compound

DHe the enthalpy per electron present in the compound

— 1CH18O08N0.2 — 2.5H2O + HCO3 + 0.2NH4+ + 5H+ + 4.2e —

Obviously, the degree of reduction for biomass is 4.2. The DG°ef value is obtained similarly as earlier for methanol. DG°i can be calculated to be — 142.128 kJ, giving

Clearly y is a stoichiometric quantity and DGe and DHe are energetic parameters.

The reference system is designed such that for H2O, HCO3, H+ (pH = 7), N source for growth, HPO4—, NO3, SO4—, and Fe3 + , the values of y, DGe, and DHe are zero. For DGe, the biochemical standard conditions (1 mol/L, 1 bar, pH = 7,298 K) are assumed, DHe is calculated for CO2 (gas) because of the large heat effect of HCO— (liq) ^ CO2 (gas) transfer.

The calculation of y, DGe, and DHe follows from the reference redox half reaction where 1 C-mol of organic or 1 mol of inorganic compound is converted into the reference chemicals and a number of electrons. The number of electrons is by definition equal to y (Example 5). From the Gibbs energy and enthalpy of this reference reaction, called DGref and DHref (calculated with the usual thermo-dynamic DGf1 and DHf1 values, see Table 2), the values of DGe and DHe follow from equations 4a and 4b.

DGref