Question

What is the exchange current density (in A/cm2) for the reaction 2H+ + 2e- ⇌ H2 at a temperature of 298 K and a concentration of 0.1 M H+? Given that the standard potential of the half-cell reaction is 0 V, and the Tafel slope is 60 mV/decade.

Answer 1

To calculate the exchange current density  i0  for the reaction 2H+ + 2e-  H2 at a temperature of 298 K and a concentration of 0.1 M H+, we need to use the Butler-Volmer equation:i = i0 *  exp  a * F *   /  R * T   - exp  -c * F *   /  R * T   where:i = current density  A/cm2 i0 = exchange current density  A/cm2 a = anodic charge transfer coefficient  dimensionless c = cathodic charge transfer coefficient  dimensionless F = Faraday's constant  96485 C/mol  = overpotential  V R = gas constant  8.314 J/molK T = temperature  K At equilibrium, the net current density  i  is zero, and the overpotential    is also zero. Therefore, the Butler-Volmer equation simplifies to:i0 = i0 *  exp 0  - exp 0  i0 = i0 *  1 - 1 i0 = 0This result indicates that we cannot determine the exchange current density  i0  directly from the Butler-Volmer equation at equilibrium. Instead, we need to use the Tafel equation to relate the exchange current density to the Tafel slope  b  and the overpotential   : = b * log10 i / i0 where:b = Tafel slope  mV/decade Given the Tafel slope  b  of 60 mV/decade, we can rewrite the Tafel equation as: = 60 * log10 i / i0 However, without additional information about the current density  i  or the overpotential    at a specific point on the polarization curve, it is not possible to determine the exchange current density  i0  for the reaction 2H+ + 2e-  H2 at a temperature of 298 K and a concentration of 0.1 M H+.