The reaction involves iron(III) oxide (\(Fe_2O_3\)) and carbon monoxide (\(CO\)). According to the statement, the reaction will produce a metal and carbon dioxide (\(CO_2\)).
Step 2: Determine the Products
From the information given, the metal produced is iron (\(Fe\)), and the byproduct is carbon dioxide (\(CO_2\)).
Step 3: Write the Unbalanced Chemical Equation
The unbalanced chemical equation based on the reactants and products is:
\[ Fe_2O_3(s) + CO(g) \rightarrow Fe(s) + CO_2(g) \]
Step 4: Balance the Chemical Equation
To balance the equation, ensure that the number of atoms of each element is the same on both sides of the equation.
Iron (Fe): There are 2 iron atoms in \(Fe_2O_3\), so we need 2 \(Fe\) on the product side.
Oxygen (O): There are 3 oxygen atoms in \(Fe_2O_3\) and 1 in each \(CO\), so we need 3 \(CO\) to balance the oxygen atoms, resulting in 3 \(CO_2\).
Carbon (C): With 3 \(CO\) on the reactant side, we have 3 carbon atoms, which matches the 3 carbon atoms in 3 \(CO_2\).
The balanced chemical equation is:
\[ Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g) \]
Final Answer
The balanced chemical equation for the reaction is:
\[
\boxed{Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)}
\]