UPSC Combined Geo-Scientist, Mains · 2022 · Mains Paper I

Q1(d). Carbonate in carbonic acid

Question

Calculate the concentration of carbonate ions in 0.10 M H₂CO₃(aq). (Given: Ka1 = 4.3 × 10⁻⁷, Ka2 = 4.6 × 10⁻¹¹.)

[CO₃²⁻] ≈ Ka2 = 4.6 × 10⁻¹¹ mol L⁻¹.

First dissociation: H₂CO₃ ⇌ H⁺ + HCO₃⁻; Ka1 = [H⁺][HCO₃⁻]/[H₂CO₃].
Since Ka1 ≫ Ka2, the first stage controls the acidity: [H⁺] ≈ [HCO₃⁻] ≈ √(Ka1·C) = √(4.3 × 10⁻⁸) ≈ 2.07 × 10⁻⁴ M.
Second dissociation: HCO₃⁻ ⇌ H⁺ + CO₃²⁻. Hence [CO₃²⁻] = Ka2[HCO₃⁻]/[H⁺].
The ratio is approximately one, giving 4.6 × 10⁻¹¹ M, neglecting water ionisation and the tiny second-stage contribution.

The full model answer

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Coversdiprotic acidcarbonic acidcarbonate ion concentrationKa1 Ka2polyprotic acid equilibria