To determine which equation is balanced in an acidic solution, we need to consider the following criteria:
1. The number of atoms of each element must be the same on both the reactant and product sides.
2. Acidic solutions contain H[tex]\(^+\)[/tex] ions and do not contain OH[tex]\(^-\)[/tex] ions on the reactant side.
Let's analyze each equation individually:
### Option A
[tex]\[ SO _4^{2-} + 4 H^+ + 2 e^- \rightarrow SO_2(g) + 2 H_2O(l) \][/tex]
- Reactant Side:
- Sulfur (S): 1
- Oxygen (O): 4 (from SO₄²⁻)
- Hydrogen (H): 4 (from 4H⁺)
- Electrons (e⁻): 2
- Product Side:
- Sulfur (S): 1 (from SO₂)
- Oxygen (O): 4 (2 from SO₂ and 2 from 2H₂O)
- Hydrogen (H): 4 (from 2H₂O)
- Electrons (e⁻): 2 (both are on the reactant side and not required to balance)
This equation is balanced as the number of atoms for each element is equal on both sides. Moreover, it contains H⁺ ions, which is characteristic of an acidic solution, without OH⁻ ions.
### Option B
[tex]\[ SO_4^{2-} + 4 H^+ \rightarrow SO_2(g) + 4 OH^- + 2 H_2O(l) \][/tex]
This equation contains OH⁻ ions on the product side and no balancing of charges with electrons. OH⁻ ions are not present in acidic solutions, so this equation is not balanced for an acidic solution.
### Option C
[tex]\[ SO_4^{2-} + 2 e^- \rightarrow SO_2(g) \][/tex]
- Reactant Side:
- Sulfur (S): 1
- Oxygen (O): 4
- Electrons (e⁻): 2
- Product Side:
- Sulfur (S): 1
- Oxygen (O): 2
This option is not congruent since it doesn't account for the hydrogen atoms or water molecules that are necessary to balance the equation in an acidic solution.
### Option D
[tex]\[ SO_4^{2-} + 2 H_2O + 2 e^- \rightarrow SO_2(g) + 4 OH^- \][/tex]
This also includes OH⁻ ions in the product, which are not permissible in acidic solutions, failing our requirement.
Given this detailed analysis of each option, it is clear that the only equation that fits all criteria for being balanced in an acidic solution is:
Option A:
[tex]\[ SO_4^{2-} + 4 H^+ + 2 e^- \rightarrow SO_2(g) + 2 H_2O(l) \][/tex]
Thus, the correct answer is 1.
