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The reaction between Iron and steam in my textbook is given as this:

$$\ce{3Fe + 4H_2O <=> Fe_3O4 + H_2} $$

My question is why these following reactions are not possible or do not happen. $$\ce{Fe + H_2O <=> FeO + H2}$$ $$\ce{2Fe + 3H_2O <=> Fe_2O_3 + 3H2}$$

I mean, how do the atoms know to form iron (II,III) oxide instead of Iron (II) oxide or iron (III) oxide in this reaction?

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Recall that $\ce{Fe3O4}$ is basically just an equimolar mixture of $\ce{FeO}$ and $\ce{Fe2O3}$. So, in that way, both of the reactions that you mentioned do infact happen, and the result is what was mentioned in your textbook.

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