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A galvanic cell consists of a standard hydrogen electrode (SHE) as the cathode and a copper electrode as the anode. The measured potential difference between the two electrodes is 1.23 V. Using Tafel analysis, calculate the anodic and cathodic Tafel slopes for the copper electrode.

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To calculate the anodic and cathodic Tafel slopes for the copper electrode, we first need to determine the standard electrode potential for the copper electrode. The standard hydrogen electrode  SHE  has a potential of 0 V by definition. The measured potential difference between the two electrodes is given as 1.23 V.For a galvanic cell, the overall cell potential  E_cell  is the difference between the cathode potential  E_cathode  and the anode potential  E_anode :E_cell = E_cathode - E_anodeSince the SHE is the cathode and has a potential of 0 V:E_cell = 0 V - E_anodeWe are given E_cell as 1.23 V, so:1.23 V = 0 V - E_anodeSolving for E_anode:E_anode = -1.23 VNow, we can use the Tafel equation to determine the anodic and cathodic Tafel slopes for the copper electrode. The Tafel equation is given by: = b * log10 i / i0 where  is the overpotential, b is the Tafel slope, i is the current density, and i0 is the exchange current density.The Tafel equation can be written separately for the anodic and cathodic reactions:_anodic = b_anodic * log10 i_anodic / i0 _cathodic = b_cathodic * log10 i_cathodic / i0 Since we have the standard electrode potential for the copper electrode  E_anode = -1.23 V , we can use the Nernst equation to relate the overpotential    to the electrode potential  E :E = E_standard +  RT/nF  * ln Q where E_standard is the standard electrode potential, R is the gas constant, T is the temperature, n is the number of electrons transferred, F is the Faraday constant, and Q is the reaction quotient.For the copper electrode, the half-reaction is:Cu + 2e  CuThe number of electrons transferred  n  is 2. Assuming the reaction is at room temperature  298 K , we can use the Nernst equation to calculate the overpotential    for the anodic and cathodic reactions:_anodic = E_anode - E_standard_cathodic = E_cathode - E_standardSince we have the overpotential    and the standard electrode potential  E_standard  for the copper electrode, we can now calculate the anodic and cathodic Tafel slopes  b_anodic and b_cathodic  using the Tafel equation:b_anodic = _anodic / log10 i_anodic / i0 b_cathodic = _cathodic / log10 i_cathodic / i0 However, without the values for the current densities  i_anodic and i_cathodic  and the exchange current density  i0 , we cannot calculate the exact values for the anodic and cathodic Tafel slopes. If these values are provided, the Tafel slopes can be calculated using the equations above.

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