To determine which chemical equation is balanced, we must ensure that the same number of each type of atom is present on both the reactant and product sides of the equation. Let’s examine each option one by one.
### Option A:
[tex]\[ 2NaCl + H_2SO_4 \rightarrow HCl + NaSO_4 \][/tex]
Reactants:
- [tex]\( \text{Na}: 2 \)[/tex]
- [tex]\( \text{Cl}: 2 \)[/tex]
- [tex]\( \text{H}: 2 \)[/tex]
- [tex]\( \text{S}: 1 \)[/tex]
- [tex]\( \text{O}: 4 \)[/tex]
Products:
- [tex]\( \text{Na}: 1 \)[/tex]
- [tex]\( \text{Cl}: 1 \)[/tex]
- [tex]\( \text{H}: 1 \)[/tex]
- [tex]\( \text{S}: 1 \)[/tex]
- [tex]\( \text{O}: 4 \)[/tex]
Some of the atoms do not match (e.g., Na and Cl), so this equation is not balanced.
### Option B:
[tex]\[ 2Na + S \rightarrow 2NaS \][/tex]
Reactants:
- [tex]\( \text{Na}: 2 \)[/tex]
- [tex]\( \text{S}: 1 \)[/tex]
Products:
- [tex]\( \text{Na}: 2 \)[/tex]
- [tex]\( \text{S}: 2 \)[/tex]
The number of sulfur atoms on the reactant and product sides does not match (reactant: 1, product: 2). Therefore, this equation is not balanced.
### Option C:
[tex]\[ NH_3 + H_2O \rightarrow 2NH_4OH \][/tex]
Reactants:
- [tex]\( \text{N}: 1 \)[/tex]
- [tex]\( \text{H}: 5 \)[/tex]
- [tex]\( \text{O}: 1 \)[/tex]
Products:
- [tex]\( \text{N}: 2 \)[/tex]
- [tex]\( \text{H}: 10 \)[/tex]
- [tex]\( \text{O}: 2 \)[/tex]
The numbers of nitrogen, hydrogen, and oxygen atoms do not match between reactants and products. Thus, this equation is not balanced.
### Option D:
[tex]\[ KOH + H_2SO_4 \rightarrow KHSO_4 + H_2O \][/tex]
Reactants:
- [tex]\( \text{K}: 1 \)[/tex]
- [tex]\( \text{O}: 5 \)[/tex]
- [tex]\( \text{H}: 3 \)[/tex]
- [tex]\( \text{S}: 1 \)[/tex]
Products:
- [tex]\( \text{K}: 1 \)[/tex]
- [tex]\( \text{O}: 5 \)[/tex]
- [tex]\( \text{H}: 3 \)[/tex]
- [tex]\( \text{S}: 1 \)[/tex]
The same counts of potassium, oxygen, hydrogen, and sulfur atoms are present on both sides of the equation. Therefore, this equation is balanced.
So, the correct answer is:
[tex]\[ \boxed{\text{D}} \][/tex]
