## 3 Results and Discussion  
### FOS/TAC Titration of Artificial Solutions with Pure NaHCO\({}_{3}\) and NaAc  
The accuracy of the \"FOS/TAC\" determination method developed by [PERSON] (1977) [6] was studied. Solutions at eight equivalent acetic acid concentrations and nine alkalinity concentrations were prepared to simulate different true FOS and TAC concentrations. Some experimental values were missing at extremely low or high [HAc] due to the detection limits of the automatic titrator. The instrument did not allow the addition of more than 25 mL of the titrant as preset by the FOS/TAC titration program. Sometimes, even the addition of a small amount of titrant to a depleted FOS and TAC solution would cause the equivalent point to be exceeded, making the calculation of FOS or TAC impossible. Figure 2 shows the experimental sodium bicarbonate concentration determined with [PERSON]'s empirical formula (Equation (3)) at different acetic acid levels against its real concentration. The empirically calculated concentrations of bicarbonate obviously varied linearly with the real values, highly dependent on the acetic acid concentration. For low acetic acid concentrations (i.e., [HAc] = 0, 145, 536 and 1126 mg\(\cdot\)L\({}^{-1}\)), the average error between the [NaHCO\({}_{3}\)] determined by the FOS/TAC method and the real [NaHCO\({}_{3}\)] was less than 3%, whereas for larger [HAc], it was 3138, 5044, 10,315 and 20,472 mg\(\cdot\)L\({}^{-1}\); this discrepancy increased from 26% to 247%. This meant that the higher the acetic acid concentration, the less accurate the bicarbonate determination. The bicarbonate concentration and, thus, the corresponding TAC were systematically overestimated by the [PERSON]'s FOS/TAC formulas. This justified the remark in the previous section that the acetate reacts with the proton during the determination of the bicarbonate alkalinity. This additional consumption of the titrant was taken into account in the TAC calculation and, therefore, distorted the result, especially for the determination of TAC with a high FOS content. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & & **Total TAC (mg CaCO\({}_{3}\)\(\cdot\)L\({}^{-1}\))** & & \\ \cline{3-8}  & & X & **X + 596** & **X + 2979** & **X + 5958** & **X + 11,916** & **X + 17,874** \\ \hline \multirow{4}{*}{**FOS/TAC**} & \multirow{2}{*}{**Y**} & ✓ & & & & ✓ & ✓ \\  & & **Y + 1000** & & ✓ & & & & \\  & & **Y + 5000** & & & ✓ & & & \\  & & **Y + 10,000** & & & & ✓ & & \\  & & **Y + 20,000** & ✓ & & & & ✓ & \\  & & **Y + 30,000** & ✓ & & & & & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tested conditions in degassed digestate for experimental validation of proposed new formulas. Figure 2: Experimental (points) and simulated (lines) sodium bicarbonate concentrations versus true sodium bicarbonate concentrations at different acetic acid concentration levels. Similarly, the [HAc] determined by [PERSON]'s method at different bicarbonate concentrations was compared with the real [HAc] in the solutions. As illustrated in Figure 3A, the average error between the measured [HAc] and the true value in the solution was much smaller than that of the bicarbonate determination. This implied that the presence of bicarbonate had a less significant effect on the determination of [HAc]. Nevertheless, when zooming in on the [HAc] = 0 to 5000 mg HAc\(\cdot\)L\({}^{-1}\) part (see Figure 3B), one can note that a systematic overestimation of [HAc] could also be observed. The difference between the experiment and reality could be as high as 684%. It means bicarbonate concentration also interferes with the determination of FOS, especially when [HAc] (or FOS) is very low and [NaHCO\({}_{3}\)] (or TAC) is much higher. The determination of the sodium bicarbonate and acetic acid concentration by the Nordmann method was highly dependent on each other.