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JEE MainChemistryIonic Equilibrium

For a generic diprotic acid H₂A , the first and second ionization constants are K_ a1 and K_ a2 , respectively. If K_w is the ionic product of water, the equilibrium constant ( K_h ) for the overall hydrolysis reaction of its conjugate base, A²⁻ + 2H₂O H₂A + 2OH^- is given by:

Options

  1. AK_h = K_w K_ a1 K_ a2
  2. BK_h = K_w^2 K_ a1 K_ a2
  3. CK_h = K_ a1 K_ a2 K_w^2
  4. DK_h = K_w^2 K_ a1 K_ a2

Correct answer

B. K_h = K_w^2 K_ a1 K_ a2

Step-by-step solution

The overall hydrolysis of the A²⁻ ion occurs in two sequential steps: Step 1: A²⁻ + H₂O HA^- + OH^- The equilibrium constant for this first hydrolysis step is related to the second ionization constant of the acid: K_ h1 = K_w K_ a2 Step 2: HA^- + H₂O H₂A + OH^- The equilibrium constant for this second hydrolysis step is related to the first ionization constant of the acid: K_ h2 = K_w K_ a1 The overall hydrolysis reaction is the sum of Step 1 and Step 2: A²⁻ + 2H₂O H₂A + 2OH^- When reactions are added, their equili

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