Dissociation constants of acids HA and HB are and , respectively. The in the resulting solution obta — Ionic Equilibrium Chemistry Question
Question
Dissociation constants of acids HA and HB are $2.0 \times 10^{-4}$ and $5 \times 10^{-5}$, respectively. The $[H^+]$ in the resulting solution obtained by mixing 20 ml of 0.5 M – HA solution and 30 ml of 0.2 M – HB solution is
💡 Solution & Explanation
The total volume after mixing is $20 + 30 = 50 \text{ ml}$. Concentration of HA in the mixture $C_A = (20 \times 0.5) / 50 = 0.2 \text{ M}$. Concentration of HB in the mixture $C_B = (30 \times 0.2) / 50 = 0.12 \text{ M}$. The total $[H^+]$ for a mixture of weak acids is given by $\sqrt{K_{a1}C_A + K_{a2}C_B} = \sqrt{(2.0 \times 10^{-4})(0.2) + (5 \times 10^{-5})(0.12)} = \sqrt{4.0 \times 10^{-5} + 0.6 \times 10^{-5}} = \sqrt{4.6 \times 10^{-5}} = \sqrt{46 \times 10^{-6}}$. Since $\sqrt{46} \approx 6.78$, $[H^+] = 6.78 \times 10^{-3} \text{ M}$. Therefore, correct answer is B.