Which of the following chemical equations is balanced?

To determine which chemical equation is balanced, we need to count the number of atoms for each element on both the reactant and product sides of each equation. A balanced equation has an equal number of atoms of each element on both sides.

Let's analyze each option:

• A) $2\text{Ca(OH)}_2 + 3\text{H}_2\text{SO}_4 \rightarrow \text{CaSO}_4 + 4\text{H}_2\text{O}$

  • Reactants:
    • Ca: $2 \times 1 = 2$
    • O: $(2 \times 2) + (3 \times 4) = 4 + 12 = 16$
    • H: $(2 \times 2) + (3 \times 2) = 4 + 6 = 10$
    • S: $3 \times 1 = 3$
  • Products:
    • Ca: $1 \times 1 = 1$
    • O: $(1 \times 4) + (4 \times 1) = 4 + 4 = 8$
    • H: $4 \times 2 = 8$
    • S: $1 \times 1 = 1$
  • This equation is not balanced (e.g., Ca: 2 vs 1).

• B) $\text{Ca(OH)}_2 + 2\text{H}_2\text{SO}_4 \rightarrow \text{Ca(HSO}_4\text{)}_2 + 4\text{H}_2\text{O}$

  • Reactants:
    • Ca: $1 \times 1 = 1$
    • O: $(1 \times 2) + (2 \times 4) = 2 + 8 = 10$
    • H: $(1 \times 2) + (2 \times 2) = 2 + 4 = 6$
    • S: $2 \times 1 = 2$
  • Products:
    • Ca: $1 \times 1 = 1$
    • O: $(2 \times 4) + (4 \times 1) = 8 + 4 = 12$
    • H: $(2 \times 1) + (4 \times 2) = 2 + 8 = 10$
    • S: $2 \times 1 = 2$
  • This equation is not balanced (e.g., O: 10 vs 12).

• C) $2\text{Ca(OH)}_2 + \text{H}_2\text{SO}_4 \rightarrow 2\text{CaSO}_4 + 2\text{H}_2\text{O}$

  • Reactants:
    • Ca: $2 \times 1 = 2$
    • O: $(2 \times 2) + (1 \times 4) = 4 + 4 = 8$
    • H: $(2 \times 2) + (1 \times 2) = 4 + 2 = 6$
    • S: $1 \times 1 = 1$
  • Products:
    • Ca: $2 \times 1 = 2$
    • O: $(2 \times 4) + (2 \times 1) = 8 + 2 = 10$
    • H: $2 \times 2 = 4$
    • S: $2 \times 1 = 2$
  • This equation is not balanced (e.g., O: 8 vs 10).

• D) $\text{Ca(OH)}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{CaSO}_4 + 2\text{H}_2\text{O}$

  • Reactants:
    • Ca: $1 \times 1 = 1$
    • O: $(1 \times 2) + (1 \times 4) = 2 + 4 = 6$
    • H: $(1 \times 2) + (1 \times 2) = 2 + 2 = 4$
    • S: $1 \times 1 = 1$
  • Products:
    • Ca: $1 \times 1 = 1$
    • O: $(1 \times 4) + (2 \times 1) = 4 + 2 = 6$
    • H: $2 \times 2 = 4$
    • S: $1 \times 1 = 1$
  • This equation is balanced. All atoms are equal on both sides.

The correct option is D.