To calculate the equilibrium constant K for the reaction, we can use the Nernst equation:E = E - RT/nF * ln Q Where:E = cell potential 0.21 V E = standard cell potentialR = gas constant 8.314 J/molK T = temperature 25 C = 298 K n = number of electrons transferredF = Faraday's constant 96,485 C/mol Q = reaction quotientFirst, we need to determine the balanced redox reaction. The half-reactions for nickel and copper are:Ni + 2e Ni reduction Cu + 2e Cu reduction Since we are given that the nickel electrode is placed in a solution containing both nickel and copper ions, the nickel will be oxidized, and the copper will be reduced. The balanced redox reaction is:Ni + Cu Ni + CuNow, we need to find the standard cell potential E . The standard reduction potentials for the half-reactions are:Ni + 2e Ni, E = -0.25 VCu + 2e Cu, E = +0.34 VSince nickel is being oxidized, we need to reverse the sign of its standard reduction potential:Ni Ni + 2e, E = +0.25 VNow, we can calculate the standard cell potential E for the overall reaction:E = E reduction - E oxidation = 0.34 V - 0.25 V = 0.09 VNext, we need to find the reaction quotient Q . For the reaction:Ni + Cu Ni + CuQ = [Ni]/[Cu] = 1.0/1.0 = 1Now, we can use the Nernst equation to solve for the equilibrium constant K :0.21 V = 0.09 V - 8.314 J/molK * 298 K / 2 * 96,485 C/mol * ln K Rearrange the equation to solve for K:ln K = 0.21 V - 0.09 V * 2 * 96,485 C/mol / 8.314 J/molK * 298 K ln K = 0.12 V * 192,970 C/mol / 2,471 J/molK ln K = 9.37Now, take the exponent of both sides to solve for K:K = e^9.37 1.17 10^4The equilibrium constant K for the reaction is approximately 1.17 10^4.