To calculate the activation energy for the oxidation of hydrogen gas at a Pt electrode, we can use the Tafel equation, which relates the overpotential to the exchange current density i0 and the current density i for an electrochemical reaction: = 2.303 * RT / * n * F * log i / i0 where: = overpotential 100 mV = 0.1 V R = gas constant 8.314 J/molK T = temperature assuming room temperature, 298 K = charge transfer coefficient assumed to be 0.5 for a one-electron transfer process n = number of electrons transferred for hydrogen oxidation, n = 2 F = Faraday's constant 96485 C/mol i = current density 0.5 mA/cm = 5 A/m i0 = exchange current density unknown First, we need to solve for i0:0.1 V = 2.303 * 8.314 J/molK * 298 K / 0.5 * 2 * 96485 C/mol * log 5 A/m / i0 0.1 V = 2.303 * 8.314 J/molK * 298 K / 0.5 * 2 * 96485 C/mol * log 5 A/m / i0 Now, we can solve for i0:log 5 A/m / i0 = 0.1 V * 0.5 * 2 * 96485 C/mol / 2.303 * 8.314 J/molK * 298 K log 5 A/m / i0 0.1 V * 96485 C/mol / 2.303 * 8.314 J/molK * 298 K log 5 A/m / i0 4.475 A/m / i0 = 10^4.47i0 5 A/m / 10^4.47 3.37 10 A/mNow that we have the exchange current density i0 , we can calculate the activation energy Ea using the Arrhenius equation:Ea = - * n * F * d ln i0 / d 1/T Assuming the activation energy is constant over the temperature range of interest, we can approximate the derivative as:Ea = - * n * F * ln i0_2 - ln i0_1 / 1/T_2 - 1/T_1 Unfortunately, we do not have enough information to calculate the activation energy Ea directly, as we would need the exchange current density i0 at a second temperature T_2 to determine the temperature dependence of the reaction.