Polyprotic acids Knowledge-Based Practice

Questions

1. 1.

   For a generic weak diprotic acid $\text{H}_2\text{A}$ with stepwise acid dissociation constants $K_{a1}$ and $K_{a2}$, which expression correctly represents the first base dissociation constant, $K_{b1}$, of the divalent conjugate base $\text{A}^{2-}$?

   • A) $K_{b1} = \frac{K_w}{K_{a2}}$
   • B) $K_{b1} = \frac{K_w}{K_{a1}}$
   • C) $K_{b1} = \frac{K_w}{K_{a1} K_{a2}}$
   • D) $K_{b1} = \frac{K_{a2}}{K_w}$
2. 2.

   In an aqueous solution containing a triprotic acid, $\text{H}_3\text{A}$, with successive acid dissociation constants $pK_{a1} = 2.12$, $pK_{a2} = 7.21$, and $pK_{a3} = 12.32$, which chemical species is present in the highest concentration when the solution is maintained at $\text{pH} = 9.50$?

   • A) $\text{H}_3\text{A}$
   • B) $\text{H}_2\text{A}^-$
   • C) $\text{HA}^{2-}$
   • D) $\text{A}^{3-}$
3. 3.

   For an aqueous solution of the sodium salt of an amphiprotic intermediate ion, $\text{NaHA}$, derived from a weak diprotic acid $\text{H}_2\text{A}$, which expression represents the standard approximation for $[\text{H}_3\text{O}^+]$ when the initial concentration of the salt is sufficiently large compared to $K_{a1}$?

   • A) $[\text{H}_3\text{O}^+] \approx \sqrt{K_{a1} \cdot C}$
   • B) $[\text{H}_3\text{O}^+] \approx \frac{K_{a1} + K_{a2}}{2}$
   • C) $[\text{H}_3\text{O}^+] \approx \sqrt{\frac{K_{a1} \cdot K_w}{K_{a2}}}$
   • D) $[\text{H}_3\text{O}^+] \approx \sqrt{K_{a1} K_{a2}}$
4. 4.

   Which statement best explains why the first acid dissociation constant ($K_{a1}$) of a polyprotic acid is consistently significantly larger than its second acid dissociation constant ($K_{a2}$)?

   • A) The conjugate base formed in the initial step completely hydrolyzes, shifting the subsequent equilibrium backward.
   • B) The solvent water molecules become fully coordinated around hydronium ions, inhibiting any subsequent proton transfer.
   • C) Removing a positively charged proton from a negatively charged species requires overcoming a greater electrostatic attraction than removing it from a neutral molecule.
   • D) The central nonmetal atom undergoes reduction during the first dissociation, significantly decreasing the polarity of the remaining O–H bonds.
5. 5.

   For an unbuffered aqueous solution of a weak diprotic acid, $\text{H}_2\text{A}$, where $K_{a1} \gg K_{a2}$ and both dissociations proceed to a minimal extent, which relationship correctly approximates the equilibrium concentration of the divalent conjugate base, $[\text{A}^{2-}]$?

   • A) $[\text{A}^{2-}] \approx [\text{HA}^-]$
   • B) $[\text{A}^{2-}] \approx K_{a2}$
   • C) $[\text{A}^{2-}] \approx \sqrt{K_{a1} \cdot K_{a2}}$
   • D) $[\text{A}^{2-}] \approx 2[\text{H}_3\text{O}^+]$

Answers and step-by-step solutions appear after you finish the test.