To balance the chemical equation [tex]\( \text{Ga} + \text{H}_2\text{SO}_4 \rightarrow \text{Ga}_2\left(\text{SO}_4\right)_3 + \text{H}_2 \)[/tex], follow these steps:
1. Identify the atoms involved on both sides of the equation:
- Ga (Gallium)
- H (Hydrogen)
- S (Sulfur)
- O (Oxygen)
2. Write down the initial counts for each atom on both sides of the equation:
- Reactants:
- Ga: 1
- H: 2
- S: 1
- O: 4
- Products:
- Ga: 2
- H: 2
- S: 3
- O: 12
3. Balance Gallium (Ga):
- On the reactant side: 1 Ga
- On the product side: 2 Ga
- To balance, put a coefficient of 2 in front of Ga:
[tex]\[
2 \text{Ga} + \text{H}_2\text{SO}_4 \rightarrow \text{Ga}_2\left(\text{SO}_4\right)_3 + \text{H}_2
\][/tex]
4. Balance Sulfur (S) and Oxygen (O):
- Sulfur (S): On reactant side: 1 S in [tex]\(\text{H}_2\text{SO}_4\)[/tex], and on product side: 3 S in [tex]\(\text{Ga}_2\left(\text{SO}_4\right)_3\)[/tex]
- To balance, put a coefficient of 3 in front of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]:
[tex]\[
2 \text{Ga} + 3 \text{H}_2\text{SO}_4 \rightarrow \text{Ga}_2\left(\text{SO}_4\right)_3 + \text{H}_2
\][/tex]
5. Balance Hydrogen (H):
- On the reactant side: [tex]\(3 \times 2 = 6\)[/tex] H atoms in [tex]\( 3 \text{H}_2\text{SO}_4 \)[/tex]
- On the product side: 2 H atoms in [tex]\( \text{H}_2 \)[/tex]
- To balance, put a coefficient of 3 in front of [tex]\( \text{H}_2 \)[/tex]:
[tex]\[
2 \text{Ga} + 3 \text{H}_2\text{SO}_4 \rightarrow \text{Ga}_2\left(\text{SO}_4\right)_3 + 3 \text{H}_2
\][/tex]
Hence, the coefficients in order are:
[tex]\[2,3,1,3\][/tex]
So the correct answer is:
[tex]\[2,3,1,3\][/tex]
