Question

Iron oxide ores, commonly a mixture of FeO and \(\mathrm{Fe}_{2} \mathrm{O}_{3},\) are given the general formula \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) . They yield elemental iron when heated to a very high temperature with either carbon monoxide or elemental hydrogen. Balance the following equations for these processes: $$ \begin{array}{c}{\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{O}(g)} \\\ {\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)}\end{array} $$

Short answer

The balanced equations are: 1. \(Fe_3O_4(s) + 4H_2(g) \rightarrow 3Fe(s) + 4H_2O(g)\) 2. \(Fe_3O_4(s) + 3CO(g) \rightarrow 3Fe(s) + 3CO_2(g)\)

Step-by-step solution

Balancing Reaction with Hydrogen gas (H2)

Begin by listing the number of atoms for each element on both sides of the equation: Reactants: Fe (3), O (4), H (2) Products: Fe (1), O (1), H (2) To balance the iron atoms, we need 3 moles of Fe on the product side. So we'll add a coefficient of 3 in front of Fe(s) in the product side: Fe3O4(s) + H2(g) -> 3Fe(s) + H2O(g) Now the iron atoms are balanced, and we have: Reactants: Fe (3), O (4), H (2) Products: Fe (3), O (1), H (2) Next, we'll balance the oxygen atoms by placing a coefficient of 4 in front of H2O(g) in the product side: Fe3O4(s) + H2(g) -> 3Fe(s) + 4H2O(g) Now we have: Reactants: Fe (3), O (4), H (2) Products: Fe (3), O (4), H (8) Finally, we'll balance the hydrogen atoms by placing a coefficient of 4 in front of H2(g) in the reactant side: Fe3O4(s) + 4H2(g) -> 3Fe(s) + 4H2O(g) Now the reaction is balanced, with equal numbers of each atom on both sides.

Balancing Reaction with Carbon Monoxide (CO)

Begin by listing the number of atoms for each element on both sides of the equation: Reactants: Fe (3), O (4), C (1), O (1) Products: Fe (1), C (1), O (2) To balance the iron atoms, we need 3 moles of Fe on the product side. So we'll add a coefficient of 3 in front of Fe(s) in the product side: Fe3O4(s) + CO(g) -> 3Fe(s) + CO2(g) Now the iron atoms are balanced, and we have: Reactants: Fe (3), O (4), C (1), O (1) Products: Fe (3), C (1), O (6) Next, we'll balance the carbon atoms by placing a coefficient of 3 in front of CO(g) in the reactant side: Fe3O4(s) + 3CO(g) -> 3Fe(s) + CO2(g) Now we have: Reactants: Fe (3), O (4), C (3), O (3) Products: Fe (3), C (1), O (6) Finally, we'll balance the oxygen atoms by placing a coefficient of 3 in front of CO2(g) in the product side: Fe3O4(s) + 3CO(g) -> 3Fe(s) + 3CO2(g) Now the reaction is balanced, with equal numbers of each atom on both sides.

Key concepts

Iron Oxide Reduction

Iron oxide reduction is a fascinating process where various forms of iron oxide are converted into elemental iron. This process involves a chemical reaction where iron oxide, like magnetite (\(\mathrm{Fe}_{3}\mathrm{O}_{4}\)), interacts with reducing agents such as carbon monoxide (\(\mathrm{CO}\)) or hydrogen gas (\(\mathrm{H}_{2}\)). In these reactions:

• Iron oxides lose oxygen atoms, becoming pure iron.
• The reducing agents gain oxygen atoms in the process, becoming oxidized themselves.

For example, in the reduction with hydrogen gas, the equation becomes balanced when 4 moles of hydrogen react with one mole of \(\mathrm{Fe}_{3}\mathrm{O}_{4}\), producing 3 moles of iron and 4 moles of water. Similarly, reduction with carbon monoxide involves 3 moles of carbon monoxide reacting with one mole of \(\mathrm{Fe}_{3}\mathrm{O}_{4}\), resulting in 3 moles of iron and 3 moles of \(\mathrm{CO}_{2}\). These balanced equations illustrate how the reduction process meticulously converts iron ore into its elemental form while maintaining atomic balance.

Stoichiometry

Stoichiometry plays a crucial role in balancing chemical equations, ensuring the correct proportions of reactants and products. It involves counting and comparing the number of atoms for each element on both sides of a chemical equation.
In iron oxide reduction, stoichiometry ensures that every atom from the reactants (like \(\mathrm{Fe}_{3}\mathrm{O}_{4}\), \(\mathrm{H}_{2}\) or \(\mathrm{CO}\)) is accounted for in the products (like elemental \(\mathrm{Fe}\) and compounds like \(\mathrm{H}_{2}\mathrm{O}\) or \(\mathrm{CO}_{2}\)).

• Start by listing the number of each atom in the reactants and products.
• Use coefficients to balance the atoms systematically.

For example, by balancing the iron atoms first, then oxygen, and finally hydrogen or carbon, students learn to distribute the atoms evenly across both sides of the equation. With stoichiometry, the principle of conservation of mass is adhered to, ensuring no atom is lost or gained in the reaction.

Redox Reactions

Redox reactions are a class of chemical reactions where the oxidation state of substances changes. In iron oxide reduction, both oxidation and reduction occur simultaneously.

• Reduction refers to the gain of electrons or loss of oxygen atoms.
• Oxidation involves the loss of electrons or gain of oxygen atoms.

For instance, when \(\mathrm{Fe}_{3}\mathrm{O}_{4}\) is reduced:

• Iron is gaining electrons (reduction).
• Hydrogen or carbon monoxide is losing electrons (oxidation) as it bonds with oxygen.

The beauty of redox reactions in the context of iron oxide reduction is that they allow the extraction of pure iron from its oxide forms. Understanding redox reactions enables students to identify which elements are oxidized and which are reduced in a reaction, providing insight into the transfer of electrons and changes in energy states.