Find the oxidation potential of a hydrogen electrode placed in a 0.1 M solution of a weak monoprotic acid (HA) with K_a = 10⁻⁵ at 298 K. The pressure of H ₂ gas is maintained at 1 atm. ( Given : 2.303 RT F = 0.059 )

Step-by-step solution

First, calculate the hydrogen ion concentration [ H ⁺] for the weak monoprotic acid using Ostwald's dilution law: [ H ⁺] = K_a C [ H ⁺] = 10⁻⁵ 0.1 = 10⁻⁶ = 10⁻³ M The oxidation half-cell reaction for the hydrogen electrode is: H ₂ (g) 2 H ⁺ (aq) + 2 e ⁻ Using the Nernst equation for the oxidation potential: E = E^ _ H ₂/ H ⁺ - 0.059 n [ H ⁺]^2 P_ H ₂ Given values: E^ _ H ₂/ H ⁺ = 0 V n = 2 [ H ⁺] = 10⁻³ M P_ H ₂ = 1 atm Substituting the values into the Nernst equation: E = 0 - 0.059 2 (10⁻³)^2 1 E = -0.0295 (10⁻⁶)