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Consider an electrochemical cell consisting of a zinc electrode in one half-cell and a copper electrode in the other half-cell. The zinc electrode has a surface area of 5 cm² and is placed in a 0.1 M ZnSO₄ solution, while the copper electrode has a surface area of 10 cm² and is placed in a 1.0 M CuSO₄ solution. Calculate the polarization of the cell when a current of 0.5 A is passed through it.

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To calculate the polarization of the cell, we need to determine the overpotential at each electrode. The overpotential is the difference between the actual potential of the electrode and its equilibrium potential. The overpotential can be calculated using the Tafel equation: = b * log i / i where  is the overpotential, b is the Tafel slope, i is the current density, and i is the exchange current density.First, we need to calculate the current density  i  at each electrode. Current density is the current per unit area:i_Zn = I / A_Zni_Cu = I / A_Cuwhere I is the current, A_Zn is the surface area of the zinc electrode, and A_Cu is the surface area of the copper electrode.i_Zn = 0.5 A / 5 cm = 0.1 A/cmi_Cu = 0.5 A / 10 cm = 0.05 A/cmNext, we need to determine the exchange current density  i  for each electrode. The exchange current density can be calculated using the Butler-Volmer equation:i = k * C^nwhere k is the rate constant, C is the concentration of the electrolyte, and n is the reaction order.For simplicity, we will assume that the reaction order  n  is 1 and that the rate constants  k  for the zinc and copper electrodes are 10 A/cm and 10 A/cm, respectively.i_Zn = k_Zn * C_Zn = 10 A/cm * 0.1 M = 10 A/cmi_Cu = k_Cu * C_Cu = 10 A/cm * 1.0 M = 10 A/cmNow we can calculate the overpotential    for each electrode using the Tafel equation. We will assume that the Tafel slope  b  is 0.12 V/decade for both electrodes._Zn = b * log i_Zn / i_Zn  = 0.12 V/decade * log 0.1 A/cm / 10 A/cm  = 0.12 V/decade * 6 = 0.72 V_Cu = b * log i_Cu / i_Cu  = 0.12 V/decade * log 0.05 A/cm / 10 A/cm  = 0.12 V/decade * 4 = 0.48 VFinally, we can calculate the polarization of the cell by summing the overpotentials of the two electrodes:Polarization = _Zn + _Cu = 0.72 V + 0.48 V = 1.20 V

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