<p>In the following article the authors want to express a caveat on the use of complex equilibrium software, especially with respect to the incorporation of ideal solutions as a user defined “on the fly” option into such calculations. The background is the analysis of the phase behavior of the overall composition Fe₂O₃ + x H₂ in the Fe–H–O system as a function of temperature. The different phase respectively species distributions resulting from variation of x, the molar amount of H₂ relative to one mole of hematite, are investigated. Thermodynamically clearly inconsistent results in recent publications are discussed and consistent results are given to fully understand the reduction paths of Fe₂O₃ for different temperatures and hydrogen amounts. For a series of x values the paths are integrated into the T vs x_O (Type 2) phase diagram of the Fe–O system, i.e. navigation in the phase diagram is provided (see the Graphical Abstract).</p> Graphical Abstract <p></p>