To balance the chemical equation given:
[tex]\[ \_\_ \text{Al} + \text{H}_2\text{SO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \_\_ \text{H}_2 \][/tex]
We need to determine the correct coefficients (stoichiometric coefficients) for each compound such that the number of atoms of each element is the same on both sides of the equation. Here are the steps to balance the equation:
1. Identify the elements involved:
- Aluminum (Al)
- Sulfur (S)
- Oxygen (O)
- Hydrogen (H)
2. Write the unbalanced equation:
[tex]\[ \_\_ \text{Al} + \_\_ \text{H}_2\text{SO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \_\_ \text{H}_2 \][/tex]
3. Balance Aluminum (Al):
- On the right side, we have [tex]\(\text{Al}_2(\text{SO}_4)_3\)[/tex], which contains 2 Al atoms.
- Therefore, we need 2 Al atoms on the left side as well.
[tex]\[ 2 \text{Al} + \_\_ \text{H}_2\text{SO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \_\_ \text{H}_2 \][/tex]
4. Balance Sulfur (S):
- On the right side, [tex]\(\text{Al}_2(\text{SO}_4)_3\)[/tex] contains 3 sulfate ([tex]\(\text{SO}_4\)[/tex]) groups, which means 3 S atoms.
- Thus, we need 3 [tex]\(\text{H}_2\text{SO}_4\)[/tex] on the left side to provide 3 S atoms.
[tex]\[ 2 \text{Al} + 3 \text{H}_2\text{SO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \_\_ \text{H}_2 \][/tex]
5. Balance Hydrogen (H) and Oxygen (O):
- On the left side, 3 [tex]\(\text{H}_2\text{SO}_4\)[/tex] provide [tex]\(3 \times 2 = 6\)[/tex] H atoms and [tex]\(3 \times 4 = 12\)[/tex] O atoms.
- On the right side, [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex] already balances the oxygen perfectly with 12 O atoms (3 [tex]\(\text{SO}_4\)[/tex]).
- The 6 H atoms on the left side come from 3 [tex]\(\text{H}_2\text{SO}_4\)[/tex], which split into [tex]\(3 \times 2 = 6\)[/tex] H atoms forming hydrogen gas [tex]\(3 \text{H}_2\)[/tex] on the product side.
[tex]\[ 2 \text{Al} + 3 \text{H}_2\text{SO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{H}_2 \][/tex]
So the balanced equation is:
[tex]\[ 2 \text{Al} + 3 \text{H}_2\text{SO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{H}_2 \][/tex]
Hence, the coefficient of [tex]\(\text{H}_2\text{SO}_4\)[/tex] when the equation is correctly balanced is 3.
