To balance the given chemical equation for the oxidation of aluminum,
[tex]\[ \text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3 \][/tex]
we need to make sure that the number of atoms of each element is the same on both sides of the equation.
Step-by-Step Solution:
1. Identify the elements involved: The elements in the equation are aluminum (Al) and oxygen (O).
2. Write the unbalanced equation:
[tex]\[ \text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3 \][/tex]
3. Balance the aluminum (Al) atoms:
- On the right side, we have 2 aluminum atoms in [tex]\(\text{Al}_2\text{O}_3\)[/tex].
- Therefore, we need 2 aluminum atoms on the left side.
- Place a coefficient of 2 in front of Al:
[tex]\[ 2 \text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3 \][/tex]
4. Balance the oxygen (O) atoms:
- On the right side, in [tex]\(\text{Al}_2\text{O}_3\)[/tex], there are 3 oxygen atoms.
- On the left side, oxygen is in the form of [tex]\(\text{O}_2\)[/tex], so we need [tex]\(\frac{3}{2}\)[/tex] [tex]\(\text{O}_2\)[/tex] molecules to have 3 oxygen atoms:
[tex]\[ 2 \text{Al} + \frac{3}{2} \text{O}_2 \rightarrow \text{Al}_2\text{O}_3 \][/tex]
- To avoid using fractions, multiply every coefficient by 2 to get whole numbers:
[tex]\[ 4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3 \][/tex]
5. Verify the balance:
- Left side: 4 aluminum atoms, 6 oxygen atoms
- Right side: 4 aluminum atoms (2 [tex]\(\text{Al}_2\text{O}_3\)[/tex]), 6 oxygen atoms (2 [tex]\(\times\)[/tex] 3)
Hence, the balanced equation is:
[tex]\[ 4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3 \][/tex]
The sequence of coefficients is:
[tex]\[ 4, 3, 2 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{4, 3, 2} \][/tex]
