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Question:

In aqueous solution, the ionization constants for carbonic acid (H₂CO₃) are K₁ = 4.2 × 10⁻⁷ and K₂ = 4.8 × 10⁻¹¹. Select the correct statement for a saturated 0.034 M solution of carbonic acid.

The concentration of CO₂ is 0.034 M.

The concentration of H⁺ is double that of CO₂.

The concentration of H⁺ and HCO₃⁻ are approximately equal.

The concentration of CO₂ is greater than that of HCO₃⁻.

Solution:

A → H₂CO₃⇌H⁺ + HCO₃⁻, K₁ = 4.2 × 10⁻⁷
Since K₁ is much larger than K₂, the second ionization can be ignored. Let x be the concentration of H⁺ and HCO₃⁻ at equilibrium. Then:
K₁ = [H⁺][HCO₃⁻]/[H₂CO₃] ≈ x²/0.034
Solving for x:
x = √(K₁ × 0.034) = √(4.2 × 10⁻⁷ × 0.034) ≈ 1.2 × 10⁻⁴ M
Therefore, [H⁺] ≈ [HCO₃⁻] ≈ 1.2 × 10⁻⁴ M. The concentration of H⁺ and HCO₃⁻ are approximately equal. The correct option is C.