Question

Calculate the exchange current density for a metal electrode immersed in a 1 M solution of its corresponding ions. The standard rate constant for the reaction is 6.3 x 10^-5 cm/s and the concentration of the electrons in the electrode is 5 x 10^23 atoms/cm^3. Additionally, assume the temperature is 25°C and the Faraday constant is 96,500 C/mol.

Answer 1

To calculate the exchange current density  i0 , we can use the Butler-Volmer equation. The exchange current density is given by:i0 = n * F * k0 * [Ox] * [Red]where:n = number of electrons transferred in the reaction  assumed to be 1 for simplicity F = Faraday constant  96,500 C/mol k0 = standard rate constant  6.3 x 10^-5 cm/s [Ox] = concentration of oxidized species  1 M [Red] = concentration of reduced species  5 x 10^23 atoms/cm^3 First, we need to convert the concentration of reduced species from atoms/cm^3 to mol/cm^3. To do this, we can use Avogadro's number  6.022 x 10^23 atoms/mol :[Red] =  5 x 10^23 atoms/cm^3  /  6.022 x 10^23 atoms/mol  = 0.83 mol/cm^3Now, we can plug the values into the equation:i0 =  1  *  96,500 C/mol  *  6.3 x 10^-5 cm/s  *  1 M  *  0.83 mol/cm^3 i0 = 5.13 x 10^-2 A/cm^2So, the exchange current density for the metal electrode immersed in a 1 M solution of its corresponding ions is 5.13 x 10^-2 A/cm^2.