To determine which equation is balanced for both charge and atoms, let's analyze each provided option step-by-step.
### Option A:
[tex]\[ S (s) + 2 e^{-} \rightarrow H_2 S (g) \][/tex]
#### Atoms:
- Reactants: 1 Sulfur (S), 2 Electrons (e^-)
- Products: 2 Hydrogen (H), 1 Sulfur (S)
The atoms are not balanced because we have Hydrogen on the product side but none on the reactant side.
#### Charge:
- Reactants: -2 (from 2 electrons)
- Products: 0 (neutral molecule H₂S)
The charge is also not balanced.
### Option B:
[tex]\[ S (s) + 2 H^{+} + 2 e^{-} \rightarrow H_2 S (g) \][/tex]
#### Atoms:
- Reactants: 1 Sulfur (S), 2 Hydrogen (H), 2 Electrons (e^-)
- Products: 2 Hydrogen (H), 1 Sulfur (S)
The atoms are balanced: 1 S atom on both sides, 2 H atoms on both sides.
#### Charge:
- Reactants: \(2(+1) + 2(-1) = 0\) (From 2 hydrogen ions and 2 electrons)
- Products: 0 (neutral molecule H₂S)
The charge is balanced: 0 on both sides.
### Option C:
[tex]\[ S (s) + 2 H^{+} \rightarrow H_2 S (g) + 2 e^{-} \][/tex]
#### Atoms:
- Reactants: 1 Sulfur (S), 2 Hydrogen (H)
- Products: 2 Hydrogen (H), 1 Sulfur (S), 2 Electrons (e^-)
The atoms are balanced: 1 S atom on both sides, 2 H atoms on both sides.
#### Charge:
- Reactants: \(2(+1) = +2\)
- Products: \(2(-1) = -2\) (2 electrons)
The charge is not balanced, since +2 ≠ -2.
### Option D:
[tex]\[ S (s) + 2 H^{+} \rightarrow H_2 S (g) \][/tex]
#### Atoms:
- Reactants: 1 Sulfur (S), 2 Hydrogen (H)
- Products: 2 Hydrogen (H), 1 Sulfur (S)
The atoms are balanced: 1 S atom on both sides, 2 H atoms on both sides.
#### Charge:
- Reactants: \(2(+1) = +2\)
- Products: 0 (neutral molecule H₂S)
The charge is not balanced, since +2 ≠ 0.
### Conclusion:
Based on our analysis, Option B is the only equation that is balanced for both charge and atoms.
Therefore, the equation balanced for both charge and atoms is:
[tex]\[ \boxed{\text{B}} \][/tex]
As a final step, returning to the context of the numerical result provided earlier (result of 2), we can affirm that:
[tex]\[\boxed{2}\][/tex]
is indeed the correct choice, corresponding to Option B.
