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Atoms in Chemical Reactions: Mastery Test
Iron reacts with oxygen to produce iron oxide (rust). This reaction is represented in an equation as [tex]4 \, \text{Fe} + x \, \text{O}_2 \rightarrow 2 \, \text{Fe}_2\text{O}_3[/tex]. Identify the value of [tex]x[/tex] that will balance the equation.
To balance the chemical equation for the reaction of iron with oxygen to produce iron oxide, we follow these steps:
1. Write the given chemical equation: [tex]\[
4 Fe + x O_2 \rightarrow 2 Fe_2O_3
\][/tex]
2. Determine the number of each type of atom on both sides of the equation: - On the left side of the equation: - Fe atoms: 4 - O atoms: [tex]\(2 \times x\)[/tex] (since [tex]\(O_2\)[/tex] has 2 oxygen atoms per molecule)
- On the right side of the equation: - Fe atoms: [tex]\(2 \times 2 = 4\)[/tex] (since [tex]\(Fe_2O_3\)[/tex] has 2 iron atoms per molecule and we have 2 molecules) - O atoms: [tex]\(3 \times 2 = 6\)[/tex] (since [tex]\(Fe_2O_3\)[/tex] has 3 oxygen atoms per molecule and we have 2 molecules)
3. Set up the equality for the oxygen atoms to ensure the equation is balanced: - The number of oxygen atoms on the left side should be equal to the number of oxygen atoms on the right side. Thus, we get: [tex]\[
2x = 6
\][/tex]
4. Solve for [tex]\(x\)[/tex]: - Divide both sides of the equation by 2: [tex]\[
x = \frac{6}{2}
\][/tex] [tex]\[
x = 3
\][/tex]
5. Conclusion: The value of [tex]\(x\)[/tex] that balances the equation is: [tex]\[
x = 3
\][/tex]
Thus, the balanced chemical equation is: [tex]\[
4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3
\][/tex]
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