## 3 Results and Discussion
### Uses of Produced VFAs
#### 3.2.1 Microbial Fuel Cells  
The maximum energy that can be recovered though an MFC can be calculated from the change in the Gibbs free energy from the oxidation of the VFAs examined (Table 2).  
The analysis is based on the energy that can be released from the oxidation of VFAs produced from 1 kg VS of substrate used in the dark fermentation process Equation (1),  
\[\mathrm{E}\left[\frac{\mathrm{MJ}}{\mathrm{kgVS}_{\mathrm{substrate}}}\right]= \frac{\sum\mathrm{AG}_{\mathrm{i}}^{\circ}\left[\frac{\mathrm{MJ}}{\mathrm{ mode}}\right]*\frac{\mathrm{m}_{\mathrm{i}}\left[\frac{\mathrm{g}}{\mathrm{ reactor}}\right]}{\mathrm{MW}_{\mathrm{i}}\left[\frac{\mathrm{m }_{\mathrm{i}}}{\mathrm{mRC}}\right]}}{\mathrm{kgVS}_{\mathrm{substrate}}/ \mathrm{L}_{\mathrm{reactor}}} \tag{1}\]  
where E is the energy released from the oxidation of VFAs, \(\mathrm{\Delta G}_{\mathrm{i}}^{\circ}\) the change in the Gibbs free energy from VFA i, m\({}_{\mathrm{i}}\), the g of VFA i produced per L of reactor, and MW\({}_{\mathrm{i}}\) its molecular weight.  
The percentage of electrons produced in an MFC that can be harvested for the production of electricity is called coulombic efficiency (CE), with the rest of the electrons being lost due to biomass production, or oxygen diffusion through the proton exchange  
\begin{table}
\begin{tabular}{c c c} \hline
**VFA** & **Reaction** & \(\Delta\)G\({}^{\circ}\) **(MJ/Mole)** \\ \hline Acetic Acid & C\({}_{2}\)H\({}_{4}\)O\({}_{2}\) + 2 O\({}_{2}\)\(\rightarrow\) 2 CO\({}_{2}\) + 2 H\({}_{2}\)O & \(-\)0.873 \\ Propionic Acid & C\({}_{3}\)H\({}_{6}\)O\({}_{2}\) + 3.5 O\({}_{2}\) \(\rightarrow\) 3 CO\({}_{2}\) + 3 H\({}_{2}\)O & \(-\)1.603 \\ Butyric Acid & C\({}_{4}\)H\({}_{8}\)O\({}_{2}\) + 5 O\({}_{2}\) \(\rightarrow\) 4 CO\({}_{2}\) + 4 H\({}_{2}\)O & \(-\)2.243 \\ Valeric Acid & C\({}_{5}\)H\({}_{10}\)O\({}_{2}\) + 6.5 O\({}_{2}\) \(\rightarrow\) 5 CO\({}_{2}\) + 5 H\({}_{2}\)O & \(-\)2.883 \\ Caprotic Acid & C\({}_{6}\)H\({}_{12}\)O\({}_{2}\) + 8 O\({}_{2}\) \(\rightarrow\) 6 CO\({}_{2}\) + 6 H\({}_{2}\)O & \(-\)3.523 \\ \hline \end{tabular}
\end{table}
Table 2: Oxidation reactions of VFAs produced by dark fermentation and their \(\Delta\)G\({}^{\circ}\) calculated from \(\Delta\)G\({}_{\mathrm{i}}\)\({}^{\circ}\) of pure substances.  
membrane [35; 36]. [PERSON] et al. [35] have reported how different mixtures of VFAs lead to different coulombic efficiencies and developed an empirical formula for its calculation from the distribution of chemical energy in the form of COD fractions of acetic (X1), propionic (X2) and butyric acid (X3) Equation (2).  
\[\text{CE}=29.7\text{X}_{1}+20.4\text{X}_{2}-22.6\text{X}_{3}+0.2\text{X}_{1} \text{X}_{2}+95.3\text{X}_{1}\text{X}_{3}-100.0\text{X}_{2}\text{X}_{3}+475.9 \text{X}_{1}\text{X}_{2}\text{X}_{3} \tag{2}\]  
As it can be observed from Equation (2) [35], the VFA that favors higher CE is acetic acid, while the presence of butyric acid has a negative effect. The presence of acetic acid is beneficial to the process probably because longer-chain VFAs have first to be converted to acetic acid before releasing most of their chemical energy through its oxidation [35]. By multiplying the chemical energy released from the oxidation of the different VFAs mixtures that were produced per kg of substrate through dark fermentation with the corresponding CE (Table 3), the recoverable electric energy can be estimated (Table 4).