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The freezing point of a 0.1 M aqueous solution of formic acid (HCOOH) is -0.2046 deg C. Find the equilibrium constant for the reaction: HCOO-(aq) + H2O(l) -> HCOOH(aq) + OH-(aq) Given: Kf(H2O) = 1.86 K kg mol⁻¹. Assume the solution is very dilute.

1. 1.1 * 10⁻³ M
2. 9 * 10⁻¹² M
3. 9 * 10⁻¹³ M
4. 1.1 * 10⁻¹¹ M

Correct answer: 9 * 10⁻¹² M

Solution

The van't Hoff factor i = 1.1 gives a degree of ionization alpha = 0.1, from which Ka = c*alpha²/(1-alpha) = approx 1.11*10⁻³. The hydrolysis constant Kb = Kw/Ka = 10⁻¹⁴ / 1.11*10⁻³ = 9*10⁻¹².

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