Question

Calculate the overpotential of an electrochemical cell where Zinc metal is used as an anode and Copper metal as a cathode. The concentration of Zinc ions in the half-cell is 1 M and Copper ions in the half-cell is 0.1 M. The temperature of the system is 25°C. (Given: Standard Reduction Potentials - Zn²⁺ + 2e⁻ → Zn(s) = -0.76 V and Cu²⁺ + 2e⁻ → Cu(s) = +0.34 V)

Answer 1

To calculate the overpotential of the electrochemical cell, we first need to find the cell potential  E_cell  using the Nernst equation. The Nernst equation is given by:E_cell = E_cell -  RT/nF  * ln Q where:E_cell = standard cell potentialR = gas constant  8.314 J/molK T = temperature in Kelvin  25C = 298.15 K n = number of electrons transferred  2 for both Zn and Cu redox reactions F = Faraday's constant  96,485 C/mol Q = reaction quotientFirst, we need to find the standard cell potential  E_cell . This can be calculated using the standard reduction potentials given:E_cell = E_cathode - E_anodeE_cell =  +0.34 V  -  -0.76 V E_cell = 1.10 VNext, we need to find the reaction quotient  Q . For the given reaction, Q can be calculated as:Q = [Cu]/[Zn]Now, we can plug in the given concentrations:Q =  0.1 M / 1 M Q = 0.1Now, we can use the Nernst equation to find the cell potential  E_cell :E_cell = 1.10 V -  8.314 J/molK * 298.15 K  /  2 * 96,485 C/mol  * ln 0.1 E_cell = 1.10 V -  0.0257 V  * ln 0.1 E_cell  1.10 V -  -0.0592 V E_cell  1.1592 VFinally, we can calculate the overpotential by subtracting the standard cell potential from the cell potential:Overpotential = E_cell - E_cellOverpotential = 1.1592 V - 1.10 VOverpotential  0.0592 V