Quick question on single displacements?

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Hydrogen gas does react with hot iron (II) oxide, contrary to the initial assumption that no reaction occurs due to hydrogen's lower activity compared to iron. The correct reaction is H2 + FeO → Fe + H2O, as the removal of water shifts the equilibrium to favor product formation. The presence of heat enhances the reaction's spontaneity, and calculating deltaG could confirm this. The alternative reaction involving H3O+ is irrelevant in this context, as it only applies in acidic, aqueous solutions. Overall, the reaction is feasible under the specified conditions.
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Hydrogen gas is passed over hot iron (II) oxide powder.

My initial answer was that there was going to be no reaction because of the fact that H2 is less active than Fe:

H_{2} + FeO \rightarrow No Reaction

Then, I looked over the web to find the answer to this but encountered two different ones. The first one complies with the rule for the activity series. However, I found this answer to be contradicting with mines since Fe is more active than H2:

H_{2} + FeO \rightarrow Fe + H_{2}O

The other answer I found was the following, which I have no idea how they got:

H_{2} + FeO \rightarrow Fe + H_{3}O^{+}

Which of these equations is the the right one for the problem?
 
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The third reaction is only going to occur in acidic, aqueous solution (since it's the hydronium ion), so that's not going to happen here.

I would calculate deltaG for this reaction to see if it's spontaneous. The entropy term,
T \Delta S
has a temperature dependence, so above a certain temperature, the reaction may be spontaneous.

However, since the problem specifies "hot iron (II) oxide," my hunch would be that the reaction does occur.
 
Note that you are removing produced water - it is being taken out by the gas stream. That shifts equilibrium to the right.
 
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