Question

A student needs to calculate the activation energy for a reaction that takes place at an electrode with a current density of 2.5 mA/cm² at a temperature of 25°C. The reaction has a transfer coefficient of 0.5 and a standard rate constant of 2.0 × 10⁻⁶ cm/s. The student has access to the necessary thermodynamic data for the reaction. What is the activation energy for this electrochemical reaction?

Answer 1

To calculate the activation energy for the electrochemical reaction, we can use the Tafel equation, which relates the current density  j , the transfer coefficient   , the standard rate constant  k , and the activation energy  Ea  as follows:j = k * exp - * Ea /  RT  where R is the gas constant  8.314 J/molK  and T is the temperature in Kelvin  25C = 298.15 K .We are given the values for j, , k, and T. We need to solve for Ea.2.5 mA/cm = 2.5  10 A/cm  converting from mA to A 2.5  10 A/cm = 2.0  10 cm/s * exp -0.5 * Ea /  8.314 J/molK * 298.15 K  Now, we need to isolate Ea:exp -0.5 * Ea /  8.314 J/molK * 298.15 K   =  2.5  10 A/cm  /  2.0  10 cm/s Take the natural logarithm of both sides:-0.5 * Ea /  8.314 J/molK * 298.15 K  = ln  2.5  10 A/cm  /  2.0  10 cm/s  Ea = -2 *  8.314 J/molK * 298.15 K  * ln  2.5  10 A/cm  /  2.0  10 cm/s  Ea  40,000 J/molThe activation energy for this electrochemical reaction is approximately 40,000 J/mol.