An electrochemical cell is set up at 298 K as follows: Pt(s) | H ₂( g , 1 atm ) | HA (0.1 M ) || Ag ^+ (0.1 M ) | Ag(s) where HA is a weak monoprotic acid. The cell potential is measured to be 0.918 V . Given that the standard reduction potential E^ _ Ag ^+/ Ag = 0.80 V and 2.303 RT F = 0.059 V , the p K_a of the weak acid HA is ________.

Step-by-step solution

The half-cell reactions are: Anode: 1 2 H ₂( g ) H ^+( aq ) + e^- Cathode: Ag ^+( aq ) + e^- Ag(s) Overall cell reaction: 1 2 H ₂( g ) + Ag ^+( aq ) H ^+( aq ) + Ag(s) Here, n = 1 . The standard cell potential is: E^ _ cell = E^ _ Ag ^+/ Ag - E^ _ H ^+/ H ₂ = 0.80 - 0 = 0.80 V Using the Nernst equation: E_ cell = E^ _ cell - 0.059 1 ₁₀ [ H ^+] [ Ag ^+] 0.918 = 0.80 - 0.059 ₁₀ [ H ^+] 0.1 0.118 = -0.059 ₁₀ [ H ^+] 0.1 ₁₀ [ H ^+] 0.1 = -2 [ H ^+] 0.1 = 10⁻² [ H ^+] = 10⁻³ M For the weak monoprotic acid HA of concentr