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The first and second ionization constants of a weak dibasic acid H₂ A are 8.1 10⁻⁸ and 1.0 10⁻¹³ respectively. 0.1 mol of H₂ A was dissolved in 1 L of 0.1 M HCl solution. The concentration of HA^- in the resultant solution is:

Options

  1. A0.1 M
  2. B9.53 10⁻⁶ M
  3. C8.1 10⁻⁸ M
  4. D1.0 10⁻¹³ M

Correct answer

C. 8.1 10⁻⁸ M

Step-by-step solution

Given: Weak dibasic acid H₂A with K_ a1 = 8.1 10⁻⁸ and K_ a2 = 1.0 10⁻¹³ Initial concentration: [H₂A]₀ = 0.1 M The solution also contains 0.1 M HCl , which dissociates completely to give [H^+]₀ = 0.1 M . The main source of HA^- is the first dissociation: H₂A H^+ + HA^- Let x be the amount of H₂A that dissociates. Then at equilibrium: [H₂A] = 0.1 - x [H^+] = 0.1 + x [HA^-] = x Applying the equilibrium expression: K_ a1 = [H^+][HA^-] [H₂A] 8.1 10⁻⁸ = (0.1 + x)(x) 0.1 - x Since K_ a1 is very small and the common H^+ i

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