Modeling ethanol production through gas fermentation: a biothermodynamics and mass transfer-based hybrid model for microbial growth in a large-scale bubble column bioreactor

Table 1 Catabolic reactions leading to the production of ethanol and acetate and related standard changes in Gibbs free energy and enthalpy

Reaction^a	\(\Delta G_{\varvec{r}}^{0}\)		\(\Delta H_{\varvec{r}}^{0}\)		Eq nr.
Reaction^a	kJ mol ⁻¹_CS	kJ mol ^−1b_P	kJ mol ⁻¹_CS	kJ mol ^−1b_P	Eq nr.
\(- 6{\text{CO}} - 3{\text{H}}_{2} {\text{O}} + {\text{C}}_{2} {\text{H}}_{5} {\text{OH}} + 4{\text{CO}}_{2}\)	− 37.4	− 224.4	− 57.4	− 344.0	(1)
\(- 6{\text{H}}_{2} - 2{\text{CO}}_{2} + {\text{C}}_{2} {\text{H}}_{5} {\text{OH}} + 3{\text{H}}_{2} {\text{O}}\)	− 52.3	− 104.6	− 178.8	− 357.6	(2)
\(- 4{\text{CO}} - 2{\text{H}}_{2} {\text{O}} + {\text{C}}_{2} {\text{H}}_{3} {\text{O}}_{2}^{ - } + {\text{H}}^{ + } + 2{\text{CO}}_{2}\)	− 33.6	− 134.3	− 65.0	− 260.0	(3)
\(- 4{\text{H}}_{2} - 2{\text{CO}}_{2} + {\text{C}}_{2} {\text{H}}_{3} {\text{O}}_{2}^{ - } + {\text{H}}^{ + } + 2{\text{H}}_{2} {\text{O}}\)	− 28.1	− 56.2	− 134.7	− 269.5	(4)

^aThe stoichiometry of catabolic reactions and the energy changes are defined to satisfy balances on all elements involved, charge and degree of reduction. Standard Gibbs free energy and enthalpy of formation of the compounds involved in Eqs. (1–4) were retrieved from the supplementary material in [43]
^bResults are expressed per mole of product, i.e., the product in Eqs. 1 and 2 is ethanol while acetate is the product in Eqs. 3 and 4

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