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+.