Hydrogenation of CO and CO2 from industrial exhaust gases into CH4 represents a promising method for sustainable chemical energy storage. While iron-based catalysts are in principle suitable for that purpose, the active metal Fe undergoes complex transformation during the chemical reaction process. However, only little is known on the change in catalytically active species under reaction conditions, primarily caused by structural changes in the catalyst material, so far. By using core-shell model-materials, factors that alter the catalyst structure can be excluded, making it possible to observe the direct influence of the reactants on the activity in the present work. Furthermore, stoichiometric analysis is used as a key tool for the evaluation of individual key reactions in the complex reaction network purely from experimental data and thus, makes it possible to draw conclusions about the catalyst state. In the case of CO hydrogenation, the presumed Boudouard reaction and the associated carburization of the catalyst can be quantified and the main reaction (CO methanation) can be determined. The results of CO2 hydrogenation show that here mainly reverse water-gas-shift reaction takes place, but under ongoing change of the catalytic active iron phase. Due to the systematic exchange between CO and CO2 in the reactant gas stream, a mutual influence could also be observed. The results from stoichiometric analysis provide the basis for the development of kinetic models for the key reactions in future work.