Question

What is the current density (in A/cm²) of a copper electrode in contact with a 1 M solution of CuSO₄ at 25°C, assuming that the reduction of Cu²⁺ to Cu has an exchange current density of 10⁻⁶ A/cm² and a concentration overpotential of 20 mV?

Answer 1

To calculate the current density, we can use the Butler-Volmer equation, which relates the current density  i  to the exchange current density  i , the overpotential   , and the transfer coefficient   . The equation is as follows:i = i *  exp  * F *  / R / T  - exp -  1 -   * F *  / R / T  where:i = current density  A/cm i = exchange current density = 10 A/cm = transfer coefficient  assumed to be 0.5 for a one-electron transfer process F = Faraday's constant = 96485 C/mol = overpotential = 20 mV = 0.02 VR = gas constant = 8.314 J/molKT = temperature = 25C = 298.15 KNow, we can plug in the values and calculate the current density:i = 10 *  exp 0.5 * 96485 * 0.02 / 8.314 / 298.15  - exp -  1 - 0.5  * 96485 * 0.02 / 8.314 / 298.15  i  10 *  exp 0.392  - exp -0.392  i  10 *  1.480 - 0.675 i  10 * 0.805i  8.05  10 A/cmSo, the current density of the copper electrode in contact with a 1 M solution of CuSO at 25C is approximately 8.05  10 A/cm.