Calculate the extent of polarization for a cell in which a copper electrode is coupled with a silver electrode at 25°C. The copper electrode has a potential of -0.34 V and the silver electrode has a potential of 0.80 V. The initial concentration of copper ions and silver ions in the solution are 0.001 M and 0.01 M, respectively. The total resistance of the cell (including both the electrolyte and the external circuit) is 10 ohms. Assume that the transfer coefficient for both the copper and silver ions is 0.5, and the Faraday constant is 96,485 C/mol.

Question

Calculate the extent of polarization for a cell in which a copper electrode is coupled with a silver electrode at

Answer 1

To calculate the extent of polarization, we first need to determine the cell potential  E_cell  and the current  I  flowing through the cell. Then, we can use the Tafel equation to find the overpotential    for each electrode, which will give us the extent of polarization.1. Calculate the cell potential  E_cell :E_cell = E_Ag - E_CuE_cell = 0.80 V -  -0.34 V E_cell = 1.14 V2. Calculate the current  I  flowing through the cell using Ohm's law:I = E_cell / RI = 1.14 V / 10 ohmsI = 0.114 A3. Calculate the overpotential    for each electrode using the Tafel equation: =  2.303 * R * T  /   * n * F  * log10 I / I0 For the copper electrode:_Cu =  2.303 * 8.314 J/molK * 298 K  /  0.5 * 2 * 96,485 C/mol  * log10 0.114 A / 0.001 M _Cu  0.059 VFor the silver electrode:_Ag =  2.303 * 8.314 J/molK * 298 K  /  0.5 * 1 * 96,485 C/mol  * log10 0.114 A / 0.01 M _Ag  0.029 V4. Calculate the extent of polarization:Polarization = _Cu + _AgPolarization = 0.059 V + 0.029 VPolarization  0.088 VThe extent of polarization for the cell is approximately 0.088 V.