Give the correct balanced equation for the single replacement reaction of magnesium with aluminum oxide. A $$ \mathrm{Mg}+\mathrm{AlO} \rightarrow \mathrm{MgO}+\mathrm{Al} $$ B $$ \mathrm{Mg}+\mathrm{Al}_{2} \mathrm{O}_{3} \rightarrow \mathrm{MgO}+\mathrm{Al} $$ C $$ 3 \mathrm{Mg}+\mathrm{Al}_{2} \mathrm{O}_{3} \rightarrow 3 \mathrm{MgO}+2 \mathrm{AI} $$ D $$ \mathrm{Mg}+\mathrm{Al}_{2} \mathrm{O}_{3} \rightarrow \mathrm{MgO}_{3}+\mathrm{Al}_{2} $$

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The correct balanced equation for the single replacement reaction between magnesium (Mg) and aluminum oxide (Al₂O₃) is:

**C.** $$ 3\, \mathrm{Mg} + \mathrm{Al}_{2}\mathrm{O}_{3} \rightarrow 3\, \mathrm{MgO} + 2\, \mathrm{Al} $$

**Explanation:**

1. **Identify the Reactants and Products:**
   - **Reactants:** Magnesium (Mg) and Aluminum Oxide (Al₂O₃).
   - **Products:** Magnesium Oxide (MgO) and Aluminum (Al).

2. **Write the Unbalanced Equation:**
   $$
   \mathrm{Mg} + \mathrm{Al}_{2}\mathrm{O}_{3} \rightarrow \mathrm{MgO} + \mathrm{Al}
   $$

3. **Balance the Equation:**
   - **Aluminum (Al):** There are 2 aluminum atoms in Al₂O₃, so you need 2 Al on the product side.
   - **Magnesium (Mg):** For every Al₂O₃, 3 Mg atoms are required to balance the oxygen atoms in 3 MgO.
   - **Oxygen (O):** 3 oxygen atoms in Al₂O₃ are balanced by 3 MgO molecules.

4. **Final Balanced Equation:**
   $$
   3\, \mathrm{Mg} + \mathrm{Al}_{2}\mathrm{O}_{3} \rightarrow 3\, \mathrm{MgO} + 2\, \mathrm{Al}
   $$

**Option C** correctly represents this balanced equation.

**Answer:**  
**C** $$ 3\,\mathrm{Mg} + \mathrm{Al}_2\mathrm{O}_3 \rightarrow 3\,\mathrm{MgO} + 2\,\mathrm{Al} $$
The correct balanced equation is: C. $$ 3\, \mathrm{Mg} + \mathrm{Al}_{2}\mathrm{O}_{3} \rightarrow 3\, \mathrm{MgO} + 2\, \mathrm{Al} $$

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