A solution is prepared by mixing two weak monoprotic acids: () and (). Find the total hydrogen ion c — Ionic Equilibrium Chemistry Question
Question
A solution is prepared by mixing two weak monoprotic acids: $0.1 \text{ M } HA$ ($K_a = 5 \times 10^{-5}$) and $0.1 \text{ M } HB$ ($K_a = 4 \times 10^{-5}$). Find the total hydrogen ion concentration $[H^+]$ in the mixture. If the answer is $y \times 10^{-3} \text{ M}$, enter the exact numerical value of $y$.
Answer: 3
💡 Solution & Explanation
For a mixture of two weak acids, the combined $[H^+]$ is approximated by $[H^+] = \sqrt{K_{a1}C_1 + K_{a2}C_2}$. Substituting the known values: $[H^+] = \sqrt{(5 \times 10^{-5})(0.1) + (4 \times 10^{-5})(0.1)} = \sqrt{5 \times 10^{-6} + 4 \times 10^{-6}} = \sqrt{9 \times 10^{-6}} = 3 \times 10^{-3} \text{ M}$. Thus, $y = 3$.
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