The oxidation reaction of Fe is as follows:
2Fe + 3H2O → Fe2O3 + 3H2
i.e, 2 moles of Fe reacts with 3 moles of H2O
Moreover,
18g of steam corresponds to 1 mole of H2O which will react with 2/3 mole of Fe
Molecular mass of Fe2O3 = 55.847 g/mol
Hence,
Mass of Fe reacted = 55.847 x 2/3
= 37.23 g of Fe