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A battery consists of a Zinc electrode and a Copper electrode. Calculate the exchange current density at the Zinc electrode if the concentration of Zinc ion in its solution is 0.1 M and the potential difference between the electrodes is 1.5 V. The standard electrode potential for Zinc is -0.76 V and the transfer coefficient for the electrode reaction is 0.5.

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To calculate the exchange current density at the Zinc electrode, we will use the Butler-Volmer equation, which relates the current density  i  to the electrode potential  E  and the standard electrode potential  E0 .The Butler-Volmer equation is given by:i = i0 *  exp  * n * F *  E - E0  /  R * T   - exp - * n * F *  E - E0  /  R * T   where:i0 = exchange current density = transfer coefficient  0.5 n = number of electrons transferred in the reaction  for Zinc, n = 2 F = Faraday's constant  96485 C/mol E = electrode potential  1.5 V E0 = standard electrode potential for Zinc  -0.76 V R = gas constant  8.314 J/mol K T = temperature  assuming room temperature, T = 298 K First, we need to find the overpotential    which is the difference between the electrode potential  E  and the standard electrode potential  E0 : = E - E0 = 1.5 V -  -0.76 V  = 2.26 VNow, we can rewrite the Butler-Volmer equation in terms of overpotential:i = i0 *  exp  * n * F *  /  R * T   - exp - * n * F *  /  R * T   We need to find the exchange current density  i0 . To do this, we can use the Tafel equation, which relates the exchange current density to the concentration of the species involved in the reaction:i0 = A *  c^n where:A = a constant  depends on the electrode material and the reaction c = concentration of Zinc ion  0.1 M n = number of electrons transferred in the reaction  2 Unfortunately, we don't have enough information to determine the value of A. However, if we had the value of A, we could calculate i0 and then use the Butler-Volmer equation to find the current density  i  at the Zinc electrode.

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