A hydrogen concentration cell is constructed at 298 K as follows: Pt(s) , H ₂( g , 1 bar ) | HA ( aq , 0.1 M ) HCl ( aq , 0.1 M ) | H ₂( g , 1 bar ), Pt(s) where HA is a weak monoprotic acid. If the cell potential is 0.18 V , the p K_a value of the weak acid HA is _____ . (Given: 2.303RT F = 0.06 V and assume HCl is completely dissociated)

Step-by-step solution

For a concentration cell, the standard cell potential E^ _ cell = 0 V . The cell reaction can be represented for one electron transfer as: H ⁺( cathode ) H ⁺( anode ) Here, n = 1 . Using the Nernst equation: E_ cell = - 0.06 1 ( [ H ⁺]_ anode [ H ⁺]_ cathode ) Since HCl is a strong acid and completely dissociates, [ H ⁺]_ cathode = 0.1 M . Substituting the given values: 0.18 = -0.06 ( [ H ⁺]_ anode 0.1 ) -3 = [ H ⁺]_ anode - (0.1) -3 = [ H ⁺]_ anode - (-1) [ H ⁺]_ anode = -4 [ H ⁺]_ anode = 10⁻⁴ M For the weak mono