To determine which chemical equation is balanced, we need to check each equation and confirm that the number of atoms for each element is the same on both sides of the equation.
### Option A: [tex]\(2 Na + S \rightarrow 2 NaS\)[/tex]
- Left side: [tex]\(2\)[/tex] sodium (Na) atoms, [tex]\(1\)[/tex] sulfur (S) atom
- Right side: [tex]\(2\)[/tex] sodium (Na) atoms, [tex]\(2\)[/tex] sulfur (S) atoms (because [tex]\(2 NaS\)[/tex] means [tex]\(2 (Na + S)\)[/tex])
This equation is not balanced because the number of sulfur atoms is different on both sides.
### Option B: [tex]\(NH_3 + H_2O \rightarrow 2 NH_4OH\)[/tex]
- Left side: [tex]\(1\)[/tex] nitrogen (N) atom, [tex]\(3\)[/tex] hydrogen (H) atoms from [tex]\(NH_3\)[/tex], [tex]\(2\)[/tex] hydrogen (H) atoms from [tex]\(H_2O\)[/tex], [tex]\(1\)[/tex] oxygen (O) atom from [tex]\(H_2O\)[/tex]
- Total hydrogen atoms on left: [tex]\(3 (from NH_3) + 2 (from H_2O) = 5\)[/tex]
- Right side: [tex]\(2\)[/tex] nitrogen (N) atoms, [tex]\(2 \times 4 = 8\)[/tex] hydrogen (H) atoms ([tex]\(4H\)[/tex] from each [tex]\(NH_4OH)\)[/tex], [tex]\(2\)[/tex] oxygen (O) atoms
This equation is not balanced because the numbers of nitrogen and hydrogen atoms on both sides are different.
### Option C: [tex]\(2 NaCl + H_2SO_4 \rightarrow HCl + NaSO_4\)[/tex]
- Left side: [tex]\(2\)[/tex] sodium (Na) atoms, [tex]\(2\)[/tex] chlorine (Cl) atoms, [tex]\(1\)[/tex] sulfur (S) atom, [tex]\(4\)[/tex] oxygen (O) atoms
- Right side: [tex]\(1\)[/tex] hydrogen (H) atom, [tex]\(1\)[/tex] chlorine (Cl) atom, [tex]\(1\)[/tex] sodium (Na) atom, [tex]\(1\)[/tex] sulfur (S) atom, [tex]\(4\)[/tex] oxygen (O) atoms. However this should be [tex]\(2 HCl + Na_2SO_4\)[/tex] and sodium and hydrogen are not balanced.
This equation is not balanced because the number of atoms of sodium and chlorine is different on both sides.
### Option D: [tex]\(KOH + H_2SO_4 \rightarrow KHSO_4 + H_2O\)[/tex]
- Left side: [tex]\(1\)[/tex] potassium (K) atom, [tex]\(1\)[/tex] oxygen (O) atom from [tex]\(KOH\)[/tex], [tex]\(1\)[/tex] hydrogen (H) atom from [tex]\(KOH\)[/tex], [tex]\(2\)[/tex] hydrogen (H) atoms from [tex]\(H_2SO_4\)[/tex], [tex]\(1\)[/tex] sulfur (S) atom, [tex]\(4\)[/tex] oxygen (O) atoms from [tex]\(H_2SO_4\)[/tex]
- Right side: [tex]\(1\)[/tex] potassium (K) atom, [tex]\(1\)[/tex] sulfur (S) atom, [tex]\(4\)[/tex] oxygen (O) atoms (including the oxygen in [tex]\(H_2O)\)[/tex], [tex]\(2\)[/tex] hydrogen (H) atoms (from [tex]\(H_2O\)[/tex])
This equation is balanced. The number of atoms for each element (K, O, H, S) is the same on both sides.
Thus, the correct answer is:
D. [tex]\(KOH + H_2SO_4 \rightarrow KHSO_4 + H_2O\)[/tex]
