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Calculate the polarization of a copper electrode immersed in a 0.1 M CuSO4 solution at 25°C when it is coupled to a hydrogen electrode with a hydrogen pressure of 1 atm. Given that the standard reduction potential of Cu2+|Cu electrode is 0.34 V and the standard reduction potential of H+|H2 electrode is 0 V at 25°C.

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To calculate the polarization of the copper electrode, we need to determine the cell potential  E_cell  of the electrochemical cell formed by the Cu2+|Cu electrode and the H+|H2 electrode. We can use the Nernst equation to find the cell potential:E_cell = E_cell -  RT/nF  * ln Q Where:E_cell is the standard cell potentialR is the gas constant  8.314 J/molK T is the temperature in Kelvin  25C = 298 K n is the number of electrons transferred in the redox reaction  2 for Cu2+ + 2e- -> Cu F is the Faraday constant  96485 C/mol Q is the reaction quotient, which is equal to [Cu2+]/[H+]^2 for this reactionFirst, we need to find the standard cell potential  E_cell . Since the standard reduction potential of Cu2+|Cu electrode is 0.34 V and the standard reduction potential of H+|H2 electrode is 0 V, the standard cell potential is:E_cell = E_Cu2+|Cu - E_H+|H2 = 0.34 V - 0 V = 0.34 VNext, we need to find the reaction quotient  Q . Since the CuSO4 solution is 0.1 M, the concentration of Cu2+ ions is 0.1 M. The hydrogen electrode has a hydrogen pressure of 1 atm, which means the concentration of H+ ions is also 1 M  assuming 1 atm pressure corresponds to 1 M concentration . Therefore, Q = [Cu2+]/[H+]^2 = 0.1/1^2 = 0.1.Now we can plug these values into the Nernst equation:E_cell = 0.34 V -  8.314 J/molK * 298 K /  2 * 96485 C/mol   * ln 0.1 E_cell = 0.34 V -  0.0129 V  * ln 0.1 E_cell  0.34 V + 0.029 VE_cell  0.369 VThe polarization of the copper electrode is the difference between the standard reduction potential and the cell potential:Polarization = E_Cu2+|Cu - E_cell = 0.34 V - 0.369 V = -0.029 VSo, the polarization of the copper electrode is -0.029 V.

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