Calculate the cell potential for the reaction between a silver electrode and a copper electrode, given that the silver electrode is immersed in a 0.1 M AgNO3 solution and the copper electrode is immersed in a 1.0 M CuSO4 solution at 25°C. (Standard electrode potentials of Ag and Cu electrodes are +0.80 V and +0.34 V, respectively. Carry out the calculation in steps and provide the final answer with appropriate units.)

Question

Calculate the cell potential for the reaction between a silver electrode and a copper electrode, given that the silver electrode is immersed in a 0.1 M AgNO3 solution and the copper electrode is immersed in a 1.0 M CuSO4 solution at 25°C. (Standard electrode potentials of Ag and Cu electrodes are +0.80 V and +0.34 V, respe

Answer 1

To calculate the cell potential for the reaction between a silver electrode and a copper electrode, we will use the Nernst equation:E_cell = E_cell -  RT/nF  * ln Q where:E_cell = cell potentialE_cell = standard cell potentialR = gas constant  8.314 J/molK T = temperature  25C = 298.15 K n = number of electrons transferred in the redox reactionF = Faraday's constant  96,485 C/mol Q = reaction quotientFirst, we need to determine the balanced redox reaction:Ag aq  + e  Ag s   E = +0.80 V  reduction half-reaction Cu aq  + 2e  Cu s   E = +0.34 V  reduction half-reaction Since we want the reaction between a silver electrode and a copper electrode, we need to reverse the copper half-reaction to make it an oxidation half-reaction:Cu s   Cu aq  + 2e  E = -0.34 V  oxidation half-reaction Now, we can add the two half-reactions to get the overall redox reaction:Ag aq  + Cu s   Ag s  + Cu aq Next, we need to calculate the standard cell potential  E_cell :E_cell = E_reduction + E_oxidation =  +0.80 V  +  -0.34 V  = +0.46 VNow, we need to determine the number of electrons transferred  n  in the redox reaction:n = 1  from the balanced redox reaction Now, we can calculate the reaction quotient  Q :Q = [Cu]/[Ag] =  1.0 M / 0.1 M  = 10Now, we can plug all the values into the Nernst equation:E_cell = E_cell -  RT/nF  * ln Q E_cell = 0.46 V -   8.314 J/molK  *  298.15 K  /  1 * 96,485 C/mol   * ln 10 E_cell = 0.46 V -  0.0257 V  * ln 10 E_cell  0.46 V - 0.0592 VE_cell  0.4008 VThe cell potential for the reaction between a silver electrode and a copper electrode is approximately 0.4008 V.