Question

Assuming a standard hydrogen electrode is used as the reference electrode and a copper electrode is used as the working electrode in an electrochemical cell, calculate the polarization potential when the current density on the copper electrode is 0.5 mA/cm^2 and the concentration of Cu2+ in the solution is 0.1 M.

Answer 1

To calculate the polarization potential, we need to consider the Nernst equation and the Tafel equation. The Nernst equation is used to determine the equilibrium potential of the copper electrode, while the Tafel equation is used to determine the overpotential due to the current density.First, let's determine the equilibrium potential of the copper electrode using the Nernst equation:E = E -  RT/nF  * ln Q where:E = equilibrium potentialE = standard reduction potential of Cu2+/Cu  0.34 V R = gas constant  8.314 J/molK T = temperature  assuming 298 K n = number of electrons transferred  2 for Cu2+/Cu F = Faraday's constant  96485 C/mol Q = reaction quotient  [Cu2+]/[Cu] Since the copper electrode is solid, its concentration is constant and can be omitted from the reaction quotient. Thus, Q = [Cu2+] = 0.1 M.E = 0.34 -  8.314 * 298 /  2 * 96485   * ln 0.1 E  0.34 - 0.0296 * ln 0.1 E  0.34 + 0.068E  0.408 VNext, let's determine the overpotential using the Tafel equation: = b * log10 j/j0 where: = overpotentialb = Tafel slope  assuming 0.12 V/decade for Cu2+/Cu j = current density  0.5 mA/cm j0 = exchange current density  assuming 10^-6 A/cm for Cu2+/Cu  = 0.12 * log10 0.5 / 10^-6   0.12 * 6.3  0.756 VFinally, we can calculate the polarization potential by adding the equilibrium potential and the overpotential:Polarization potential = E + Polarization potential = 0.408 V + 0.756 VPolarization potential  1.164 V