A half-cell is prepared by dipping a platinum electrode in a solution containing MnO₄^- ( 0.01 M), Mn²⁺ ( 0.1 M), and a weak monobasic acid HA ( 0.1 M). The measured reduction potential of this half-cell is 1.215 V. If the standard reductio

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A half-cell is prepared by dipping a platinum electrode in a solution containing MnO₄^- ( 0.01 M), Mn²⁺ ( 0.1 M), and a weak monobasic acid HA ( 0.1 M). The measured reduction potential of this half-cell is 1.215 V. If the standard reduction potential E^ _ MnO₄^-/Mn²⁺ is 1.51 V, the pK_a of the weak acid HA is ________. (Nearest Integer) Given: 2.303RT F = 0.059 V

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Correct answer: 5

The balanced half-reaction for the reduction of permanganate in acidic medium is: MnO₄^- + 8H^+ + 5e^- Mn²⁺ + 4H₂O Here, n = 5 . Using the Nernst equation: E = E^ - 0.059 5 [Mn²⁺] [MnO₄^-][H^+]^8 Substitute the given values: 1.215 = 1.51 - 0.059 5 0.1 0.01 [H^+]^8 1.215 - 1.51 = - 0.059 5 10 [H^+]^8 -0.295 = - 0.059 5 ( 10 - 8 [H^+]) 0.295 5 0.059 = 1 + 8 pH 25 = 1 + 8 pH 8 pH = 24 pH = 3 So, the hydrogen ion concentration is [H^+] = 10⁻³ M. For a weak monobasic acid HA, the dissociation is given by Ostwald's dilut

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