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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

Expert verified
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

01

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.
02

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Consider the following unbalanced equation: $$ \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{CaSO}_{4}(s)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q) $$ What masses of calcium sulfate and phosphoric acid can be produced from the reaction of 1.0 \(\mathrm{kg}\) calcium phosphate with 1.0 \(\mathrm{kg}\) concentrated sulfuric acid \(\left(98 \% \mathrm{H}_{2} \mathrm{SO}_{4} \text { by mass)? }\right.\)

A compound contains only carbon, hydrogen, and oxygen. Combustion of 10.68 \(\mathrm{mg}\) of the compound yields 16.01 \(\mathrm{mg}\) \(\mathrm{CO}_{2}\) and 4.37 \(\mathrm{mg} \mathrm{H}_{2} \mathrm{O}\) . The molar mass of the compound is 176.1 \(\mathrm{g} / \mathrm{mol} .\) What are the empirical and molecular formulas of the compound?

With the advent of techniques such as scanning tunneling microscopy, it is now possible to "write" with individual atoms by manipulating and arranging atoms on an atomic surface. a. If an image is prepared by manipulating iron atoms and their total mass is \(1.05 \times 10^{-20} \mathrm{g},\) what number of iron atoms were used? b. If the image is prepared on a platinum surface that is exactly 20 platinum atoms high and 14 platinum atoms wide, what is the mass (grams) of the atomic surface? c. If the atomic surface were changed to ruthenium atoms and the same surface mass as determined in part b is used, what number of ruthenium atoms is needed to construct the surface?

You take 1.00 g of an aspirin tablet (a compound consisting solely of carbon, hydrogen, and oxygen), burn it in air, and collect 2.20 \(\mathrm{g} \mathrm{CO}_{2}\) and 0.400 \(\mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) You know that the molar mass of aspirin is between 170 and 190 \(\mathrm{g} / \mathrm{mol}\) . Reacting 1 \(\mathrm{mole}\) of salicylic acid with 1 mole of acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) gives you 1 mole of aspirin and 1 mole of acetic acid \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\right)\) Use this information to determine the molecular formula of salicylic acid.

When the supply of oxygen is limited, iron metal reacts with oxygen to produce a mixture of \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3} .\) In a certain experiment, 20.00 \(\mathrm{g}\) iron metal was reacted with 11.20 \(\mathrm{g}\) oxygen gas. After the experiment, the iron was totally consumed, and 3.24 \(\mathrm{g}\) oxygen gas remained. Calculate the amounts of \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) formed in this experiment.

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