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Balance the equation.
$Fe + {O_2} + {H_2}O \to F{e_2}{O_3}$.

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Hint:A balanced equation is dependent on the law of conservation of mass. The number of each atom on either side of the equation will remain the same.

Complete step by step answer:The given reaction is the oxidation of iron in presence of oxygen and water. The product of the reaction is iron oxide. The balancing of an equation follows certain guidelines. The guidelines are as follows:
a. The reactants are placed on the left hand side and the products on the right hand side.
b. The reactions in one direction are shown by a single arrow and those at equilibrium are shown by double arrows.
c. The law of conservation of mass on either side of the equation is satisfied for every element. The law of conservation of mass states that the sum of masses of reactants is equal to the sum of masses of products.
d. The ratios of the components of reactants and products are multiplied by integral numbers called as reaction coefficients.
e. The subscripts must be kept unchanged otherwise the change will result in change of the chemical formula of the respective components.
The given unbalanced equation is:
$Fe + {O_2} + {H_2}O \to F{e_2}{O_3}$
The reaction indicates that the product side lacks the presence of hydrogen molecules. Thus a molecule of hydrogen is added in the product side. The number of iron is increased by one unit in the reactant side so as to make it equal to the product side. The number of oxygen atoms is equal on both sides of the equation. The balanced equation is:
$2Fe + {O_2} + {H_2}O \to F{e_2}{O_3} + {H_2}$

Note:This type of reaction is known as redox reaction. In this reaction the element \[Fe\] acts as an oxidizing agent and the \[{H_2}O\] acts as a reducing agent.