Calculate the concentration in an aqueous mixture containing () and (). — Ionic Equilibrium Chemistry Question
Question
Calculate the $[H_3O^+]$ concentration in an aqueous mixture containing $0.1 \text{ M } CH_3COOH$ ($K_a = 1.8 \times 10^{-5}$) and $0.01 \text{ M } HCOOH$ ($K_a = 1.8 \times 10^{-4}$).
Answer: A
💡 Solution & Explanation
For a mixture of two weak monoprotic acids, $[H^+] = \sqrt{K_{a1}C_1 + K_{a2}C_2}$. Substituting the values: $[H^+] = \sqrt{(1.8 \times 10^{-5})(0.1) + (1.8 \times 10^{-4})(0.01)} = \sqrt{1.8 \times 10^{-6} + 1.8 \times 10^{-6}} = \sqrt{3.6 \times 10^{-6}} = 1.89 \times 10^{-3} \text{ M}$ (since $\sqrt{3.6} \approx 1.897$).
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