To calculate the exchange current density i for a copper electrode in contact with a 1M solution of CuSO at 25C, we need to use the Butler-Volmer equation:i = i * exp * n * F * / R / T - exp - 1 - * n * F * / R / T where:i = current densityi = exchange current density = charge transfer coefficient assumed to be 0.5 for a symmetric reaction n = number of electrons transferred in the reaction 2 for the Cu/Cu redox couple F = Faraday's constant 96485 C/mol = overpotential difference between the electrode potential and the equilibrium potential R = gas constant 8.314 J/mol/K T = temperature in Kelvin 25C = 298.15 K First, we need to find the overpotential . The standard electrode potential for the Cu/Cu redox couple is +0.34 V. The electrode potential is given as 0.25 V versus the standard hydrogen electrode. Therefore, the overpotential is: = 0.25 V - 0.34 V = -0.09 VNow, we can use the Butler-Volmer equation to solve for the exchange current density i . Since we are not given the actual current density i , we will assume that the electrode is at equilibrium, which means that the net current density is zero i = 0 . This simplifies the equation to:0 = i * exp * n * F * / R / T - exp - 1 - * n * F * / R / T Rearranging the equation to solve for i:i = - exp - 1 - * n * F * / R / T / exp * n * F * / R / T - 1 Plugging in the values:i = - exp - 1 - 0.5 * 2 * 96485 * -0.09 / 8.314 / 298.15 / exp 0.5 * 2 * 96485 * -0.09 / 8.314 / 298.15 - 1 i 1.15 x 10 A/cmThe exchange current density for a copper electrode in contact with a 1M solution of CuSO at a temperature of 25C and an electrode potential of 0.25 V versus the standard hydrogen electrode is approximately 1.15 x 10 A/cm.