Question

Iron oxide ores, commonly a mixture of \(\mathrm{FeO}\) 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. $$\begin{aligned}\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{H}_{2}(g) & \rightarrow \mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{O}(g) \\ \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}(g) & \rightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)\end{aligned}$$

Short answer

The balanced equations for the reduction of iron oxide ores with hydrogen gas and carbon monoxide gas are: \[ \begin{aligned} \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + 8\mathrm{H}_{2}(g) & \rightarrow 3 \mathrm{Fe}(s) + 4\mathrm{H}_{2}\mathrm{O}(g) \\ \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + 2\mathrm{CO}(g) & \rightarrow 3 \mathrm{Fe}(s) + 2\mathrm{CO}_{2}(g) \end{aligned} \]

Step-by-step solution

Identify reactants and products

In this equation, the reactants are iron oxide (Fe3O4) and hydrogen gas (H2), and the products are elemental iron (Fe) and water (H2O).

Balance iron atoms

There are three Fe atoms on the left side, so there should be three Fe atoms on the right side of the equation. This gives us the following balanced equation for iron atoms: $$ \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + \mathrm{H}_{2}(g) \rightarrow 3 \mathrm{Fe}(s) + \mathrm{H}_{2}\mathrm{O}(g) $$

Balance oxygen atoms

There are four O atoms on the left side and only one O atom on the right side. Therefore, we need to ensure there are four O atoms on the right side. This gives us the following balanced equation for oxygen atoms: $$ \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + \mathrm{H}_{2}(g) \rightarrow 3 \mathrm{Fe}(s) + 4\mathrm{H}_{2}\mathrm{O}(g) $$

Balance hydrogen atoms

On the right side of the equation, we now have eight H atoms from the water molecules. We need to have eight H atoms as reactants on the left side. This gives us the final balanced equation: $$ \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + 8\mathrm{H}_{2}(g) \rightarrow 3 \mathrm{Fe}(s) + 4\mathrm{H}_{2}\mathrm{O}(g) $$ #Equation 2: Balancing Iron Oxide Reduction with Carbon Monoxide#

Identify reactants and products

In this equation, the reactants are iron oxide (Fe3O4) and carbon monoxide gas (CO), and the products are elemental iron (Fe) and carbon dioxide gas (CO2).

Balance iron atoms

As in the first equation, there are three Fe atoms on the left side, so there should be three Fe atoms on the right side of the equation: $$ \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + \mathrm{CO}(g) \rightarrow 3 \mathrm{Fe}(s) + \mathrm{CO}_{2}(g) $$

Balance oxygen atoms

There are four O atoms on the left side, but only two O atoms on the right side. We need two CO2 molecules on the right side to have equal oxygen atoms. This gives us: $$ \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + \mathrm{CO}(g) \rightarrow 3 \mathrm{Fe}(s) + 2\mathrm{CO}_{2}(g) $$

Balance carbon atoms

Now that there are two CO2 molecules on the right side with two carbon atoms, we need two CO molecules on the left side. This gives us the final balanced equation: $$ \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + 2\mathrm{CO}(g) \rightarrow 3 \mathrm{Fe}(s) + 2\mathrm{CO}_{2}(g) $$ The balanced equations for the reduction of iron oxide ores with hydrogen gas and carbon monoxide gas are: $$ \begin{aligned} \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + 8\mathrm{H}_{2}(g) & \rightarrow 3 \mathrm{Fe}(s) + 4\mathrm{H}_{2}\mathrm{O}(g) \\ \mathrm{Fe}_{3}\mathrm{O}_{4}(s) + 2\mathrm{CO}(g) & \rightarrow 3 \mathrm{Fe}(s) + 2\mathrm{CO}_{2}(g) \end{aligned} $$

Key concepts

Iron Oxide Reduction

When it comes to the reduction of iron oxide, the term refers to a chemical process wherein iron oxide is converted into elemental iron using a reducing agent.

In the given exercise, iron oxide in the form of Fe_{3}O_{4} reacts with two different reducing agents - hydrogen (H_{2}) and carbon monoxide (CO). This reduction process can be viewed in two predominant chemical reactions that take place at high temperatures. It involves breaking the bonds between iron (Fe) and oxygen (O), with the reducing agent taking on the oxygen atoms to form water (H_{2}O) when hydrogen is used, and carbon dioxide (CO_{2}) when carbon monoxide is used.

The actual balancing process accounts for the conservation of mass, ensuring that the number of atoms for each element is the same on both sides of the reaction equation. This process is critical for accurately representing chemical reactions and for subsequent calculations in stoichiometry, as it pertains to iron's extraction from its ore.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the conservation of mass and the law of definite proportions,

Through stoichiometry, one can determine the relative quantities of substances consumed and produced in a reaction, which is essential for creating the balanced equation. In the example provided, stoichiometry helps us determine that 3 moles of iron (Fe) will be produced for every 1 mole of Fe_{3}O_{4} reacted, and that the amounts of the reducing agents (H_{2} or CO) required are 8 moles and 2 moles respectively for the complete reduction of iron oxide.

To correctly balance a chemical equation, one must align the number of moles of each compound or element based on the reactions' stoichiometry. The balanced equations then provide crucial information for further practical applications, such as industrial chemistry and engineering.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are a fundamental class of chemical reactions where the oxidation states of atoms are changed.

In the context of the exercise, the reduction of iron oxide is a redox reaction. Iron oxide is reduced (its oxidation state decreases) as it loses oxygen to form elemental iron, while the reducing agents (hydrogen or carbon monoxide) are oxidized as they gain the oxygen from the iron oxide to form water and carbon dioxide respectively.

• In the reaction with hydrogen, Fe_{3}O_{4} is reduced to Fe, and the hydrogen is oxidized to H_{2}O.
• In the reaction with carbon monoxide, Fe_{3}O_{4} is reduced to Fe, and the carbon monoxide is oxidized to CO_{2}.

The ability to identify which elements are oxidized and which are reduced is crucial for balancing redox reactions. This also involves keeping track of the electron transfers, though in the given exercise, balancing is done more straightforwardly by matching the number of atoms of each element on both sides of the equation.

Understanding redox reactions is essential for fields beyond basic chemistry, including electrochemistry, biochemistry, and environmental science, as they play a key role in energy production and the transformation of matter.