## 3 Results
### Redox Principle  
Figure 3 presents the temporal relative mass change or the reduction and oxidation fractions of the pellet sample S1 over three successive redox cycles (reduction+oxidation) at 700 \({}^{\circ}\)C and a reactive gas flow rate of 250 mL/min with the concentrations ro\({}_{4}\) (cf. Table 2). After the first redox cycle, a relative mass change of 3.2% is observed. Cycles 2 and 3 show, however, a reversible relative mass change of \(\approx\)23.8%. The obtained relative mass reduction/increase represents, indeed, the mass of oxygen removed or gained upon reduction or oxidation of the iron mass in the pellet, respectively. The raw sample S1, before the very first reduction, consists of \(\approx\)90% of Fe\({}_{2}\)O\({}_{3}\), which is reduced to Fe. In the subsequent reaction, Fe is oxidized, however to Fe\({}_{3}\)O\({}_{4}\), as explained by Equation (3).  
According to Equation (5), the difference between the mass of the same number of moles (12 Fe) included in 4 Fe\({}_{3}\)O\({}_{4}\) or 6 Fe\({}_{2}\)O\({}_{3}\) corresponds to the mass of one mole of oxygen.  
\[4\text{Fe}_{3}\text{O}_{4}+\text{O}_{2}\to 6\text{Fe}_{2}\text{O}_{3} \tag{5}\]  
Recalling that the mole mass of Fe\({}_{2}\)O\({}_{3}\) and Fe\({}_{3}\)O\({}_{4}\) amounts to 159.69 g/mol and 231.53 g/mol, respectively, the relative mass reduction of Fe\({}_{2}\)O\({}_{3}\) upon changing to Fe\({}_{3}\)O\({}_{4}\) equals 31.999 g, which is the mole mass of O\({}_{2}\). Being divided by the mass of six moles of Fe\({}_{2}\)O\({}_{3}\) results in a relative mass change of 3.34%. With an \(\approx\)90%-wt. ratio of Fe\({}_{2}\)O\({}_{3}\) inside the raw pellets, the net relative change of mass expected shall be in the order of 3%. The obtained experimental results in Figure 3, namely a relative mass change of about 3.2% between the first and the subsequent redox cycles, puts in evidence that Fe\({}_{2}\)O\({}_{3}\) disappears after the first reduction and that the reversible reactions taking place afterwards are those defined by Equations (2) and (3).  
As depicted in Figure 3, after the first oxidization of Fe to Fe\({}_{3}\)O\({}_{4}\), the two successive redox cycles exhibit exactly the same relative mass change based on Equations (2) and (3). Figure 4 is introduced to give further evidence that Fe\({}_{2}\)O\({}_{3}\) cannot be formed again under the experimental boundary conditions chosen in this work. It illustrates the oxygen's partial pressure limits needed for the different reduction/oxidation reactions at different temperatures [41; 42]. The upper solid line shows the oxygen partial pressure levels needed  
Figure 3: Reaction behavior of Sample 1 (S1) at 700 \({}^{\circ}\)C and 250 mL/min with the gas concentration ro\({}_{4}\) as defined in Table 2.  
for the transition between Fe\({}_{3}\)O\({}_{4}\) and Fe\({}_{2}\)O\({}_{3}\), which lies completely outside the oxygen partial pressure limit curves (dashed lines), which correspond to the limit concentrations of the reactive gas mixtures (cf. Table 2). Accordingly, Fe cannot be oxidized back to Fe\({}_{2}\)O\({}_{3}\) under the investigated boundary conditions.  
The relative mass change between 3 Fe in Fe\({}_{3}\)O\({}_{4}\) and 3 Fe according to Equations (2) and (3) amounts to the mass of two oxygen moles or 63.998 g. The expected relative mass change shall be 27.64% in case the pellets are made of 100% Fe\({}_{2}\)O\({}_{3}\). Again with \(\approx\)90%-wt. of Fe\({}_{2}\)O\({}_{3}\) in the pellets, a relative mass change upon reduction/oxidation is expected to be in the order of 24.88%. Figure 3 proves with a 23.8% relative mass change that the redox reactions after the first cycle do follow Equations (2) and (3). The obtained mass change of 23.8% corresponds to a volumetric hydrogen ESD of 2.8 kWh/(L bulk), based on the investigated S1 pellet geometry and a packed bed porosity of 36%. This ESD matches exactly with the estimated value in Table 1 based on the redox Equations (2) and (3).