If and are the first and second ionization constants of and , the incorrect relation(s) is/are — Ionic Equilibrium Chemistry Question
Question
If $K_1$ and $K_2$ are the first and second ionization constants of $\text{H}_2\text{CO}_3$ and $K_1 \gg K_2$, the incorrect relation(s) is/are
💡 Solution & Explanation
Because $K_1 \gg K_2$, the first dissociation dictates $[\text{H}^+]$. Thus, $[\text{H}^+] \approx [\text{HCO}_3^-]$ and $[\text{H}^+] \approx \sqrt{K_1 [\text{H}_2\text{CO}_3]}$, validating (a) and (b). From the second dissociation, $K_2 = \frac{[\text{H}^+][\text{CO}_3^{2-}]}{[\text{HCO}_3^-]}$, and since $[\text{H}^+] \approx [\text{HCO}_3^-]$, $K_2 \approx [\text{CO}_3^{2-}]$, validating (c). Option (d) asserts $[\text{H}^+] = 2[\text{CO}_3^{2-}]$, which assumes complete dissociation of both protons—an impossibility for a weak acid. Thus, (d) is the only incorrect relation. Therefore, correct answer is D.