Question

Calculate the overpotential for the reduction reaction of Ag+ to Ag on a silver electrode at 25°C with a current density of 0.5 A/cm2. The standard reduction potential of Ag+ to Ag is 0.799 V vs. the standard hydrogen electrode. The activation energy for this reaction is 65.0 kJ/mol, the transfer coefficient is 0.4 and the reaction order is 1.5.

Answer 1

To calculate the overpotential for the reduction reaction of Ag+ to Ag, we can use the Tafel equation: =  2.303 * RT  /   * n * F  * log10 j / j0 where: = overpotential  V R = gas constant  8.314 J/molK T = temperature  25C = 298.15 K  = transfer coefficient  0.4 n = number of electrons transferred  1 for Ag+ to Ag F = Faraday's constant  96485 C/mol j = current density  0.5 A/cm = 50000 A/m j0 = exchange current density  A/m First, we need to calculate the exchange current density  j0 . We can use the following equation:j0 = k * [Ag+]^mwhere:k = rate constant  m^1.5As^1.5/mol^1.5 [Ag+] = concentration of Ag+ ions  assuming 1 M for simplicity m = reaction order  1.5 To find the rate constant  k , we can use the Arrhenius equation:k = A * exp -Ea /  R * T  where:A = pre-exponential factor  m^1.5As^1.5/mol^1.5 Ea = activation energy  65.0 kJ/mol = 65000 J/mol Unfortunately, we don't have enough information to determine the pre-exponential factor  A . However, if we assume that the reaction is fast and the exchange current density is high, the overpotential will be relatively small.In practice, the overpotential for the reduction of Ag+ to Ag on a silver electrode is typically in the range of a few millivolts to tens of millivolts, depending on the specific conditions and the electrode surface.