Relationship between E1 and E2 for DANIEL cell

Introduction: DANIEL cell is an electrochemical cell that consists of a Zn electrode in contact with ZnSO4 solution and a Cu electrode in contact with CuSO4 solution. The redox reaction that occurs in the cell is Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s).

Emf of DANIEL cell: At 298K, the emf of the DANIEL cell is E1 = E°cell = E°Cu/Cu2+ - E°Zn/Zn2+ = 0.34V - (-0.76V) = 1.10V, where E°Cu/Cu2+ and E°Zn/Zn2+ are the standard reduction potentials of Cu2+ and Zn2+ ions, respectively.

Effect of concentration: The emf of the cell changes with the change in concentration of the electrolytes. According to the Nernst equation, Ecell = E°cell - (RT/nF)lnQ, where R is the gas constant, T is the temperature, n is the number of electrons transferred in the redox reaction, F is the Faraday constant, and Q is the reaction quotient.

Relationship between E1 and E2: When the concentration of ZnSO4 is increased to 1.0M and that of CuSO4 is decreased to 0.01M, the emf of the cell changes to E2. The relationship between E1 and E2 can be obtained by using the Nernst equation.

E1 = E°cell - (RT/nF)lnQ1
E2 = E°cell - (RT/nF)lnQ2

Since E°cell is constant for a given temperature, we can subtract E1 from E2 to obtain:

E2 - E1 = (RT/nF)ln(Q2/Q1)

At constant temperature, R, n, and F are constant, therefore, the difference in emf between the two cells is proportional to the natural logarithm of the ratio of the reaction quotients.

Conclusion: The relationship between E1 and E2 can be obtained by using the Nernst equation, which relates the emf of the cell to the concentration of the electrolytes. The difference in emf between the two cells is proportional to the natural logarithm of the ratio of the reaction quotients.