Deriving the Equations

In Example 1, it was shown that one suitably measured stoichiometric coefficient, for example, YDX, allows the calculation of all other stoichiometric coefficients, including the dissipated Gibbs energy 1 / YGX. This means that knowledge of 1/Ygx should enable the calculation of all stoichio-metric coefficients, as shown in Example 4. It has also been shown that YGX can be estimated for arbitrary growth systems under different growth rates and temperatures using the correlations (equations 2 and 3). Here we show that particularly simple equations to calculate all yields from Ygx can be obtained by using the y, DGe, and DHe parameters introduced in the previous section.

The general macrochemical reaction equation can be written as shown in Figure 2b. In this macrochemical equation, the electron donor and acceptor are written in C-mol (for organic compounds) or in mol (for inorganic compounds). The ( . . . ) stoichiometric coefficients are not given separate symbols. They follow easily from the charge balance (for H+), N balance (for N source), from O or H balance (for H2O), and the carbon balance (for HCO—). For autotrophic growth, the HCO— stoichiometric coefficient is — 1. Three balances can be written based on the conservation principles of electrons and enthalpy and the Gibbs energy balance.

Balance of degree of reduction

Gibbs energy balance

From equation 8a it follows that YAX is directly related to YDX (equation 9a)

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