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Consider an electrochemical cell with the following half-cell reaction: Cu(s) | Cu2+(aq) || Ag+(aq) | Ag(s). Suppose the concentration of Cu2+ is 2.0 M and the concentration of Ag+ is 1.0 M. Calculate the resistance of the electrochemical cell if the cell potential is 0.60 V at 25°C.

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To calculate the resistance of the electrochemical cell, we first need to determine the cell potential under standard conditions  Ecell  and then use the Nernst equation to find the cell potential under non-standard conditions  Ecell . Finally, we can use Ohm's law to calculate the resistance.1. Determine the standard cell potential  Ecell :The half-cell reactions are:Cu2+ aq  + 2e-  Cu s   E = +0.34 V  reduction Ag+ aq  + e-  Ag s   E = +0.80 V  reduction Since the Cu2+ half-cell is being oxidized, we need to reverse the sign of its potential:Cu s   Cu2+ aq  + 2e-  E = -0.34 V  oxidation Now, we can calculate the standard cell potential  Ecell  by adding the two half-cell potentials:Ecell = E Cu2+/Cu  + E Ag+/Ag  = -0.34 V + 0.80 V = 0.46 V2. Use the Nernst equation to find the cell potential under non-standard conditions  Ecell :Ecell = Ecell -  RT/nF  * ln Q where R is the gas constant  8.314 J/molK , T is the temperature in Kelvin  25C + 273.15 = 298.15 K , n is the number of electrons transferred  2 for Cu2+ and 1 for Ag+; we'll use 2 since it's the lowest common multiple , F is the Faraday constant  96485 C/mol , and Q is the reaction quotient.Q = [Cu2+]/[Ag+] =  2.0 M / 1.0 M  = 2Ecell = 0.46 V -  8.314 J/molK * 298.15 K /  2 * 96485 C/mol   * ln 2 Ecell  0.46 V - 0.0147 V = 0.4453 VHowever, the problem states that the cell potential is 0.60 V. This discrepancy could be due to the presence of a resistance in the cell, which we will now calculate using Ohm's law.3. Use Ohm's law to calculate the resistance:Ohm's law states that V = IR, where V is the voltage, I is the current, and R is the resistance. We can rearrange this equation to solve for the resistance: R = V/IFirst, we need to find the difference in voltage between the given cell potential  0.60 V  and the calculated cell potential under non-standard conditions  0.4453 V :V = 0.60 V - 0.4453 V = 0.1547 VNow, we need to determine the current  I  flowing through the cell. We can use the cell potential under non-standard conditions  Ecell  and the number of electrons transferred  n  to calculate the current using the following equation:I = nFEcellI =  2 * 96485 C/mol  * 0.4453 VI  86000 C/molFinally, we can calculate the resistance  R  using Ohm's law:R = V/I = 0.1547 V / 86000 C/mol  1.80  10^-6 The resistance of the electrochemical cell is approximately 1.80  10^-6 .

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