To calculate the cell potential, Ecell, for the given reaction at 298K, we need to use the Nernst equation. The Nernst equation relates the cell potential to the standard cell potential, temperature, and the concentrations of the reactants and products. The Nernst equation is given as follows:
Ecell = E°cell - (RT/nF) ln(Q)
where,
Ecell = cell potential
E°cell = standard cell potential
R = gas constant (8.314 J/K.mol)
T = temperature (298 K)
n = number of electrons transferred in the balanced redox reaction
F = Faraday constant (96,485 C/mol)
Q = reaction quotient
The given reaction is a redox reaction, which involves the transfer of two electrons from Co to Ag+. The balanced half-reactions are as follows:
Co(s) → Co2+(aq) + 2 e-
Ag+(aq) + e- → Ag(s)
The standard reduction potentials for these half-reactions are:
Co2+(aq) + 2 e- → Co(s) E°red = -0.28 V
Ag+(aq) + e- → Ag(s) E°red = +0.80 V
The overall standard cell potential can be calculated by subtracting the standard reduction potential of the anode from that of the cathode:
E°cell = E°red,cathode - E°red,anode
= +0.80 V - (-0.28 V)
= +1.08 V
Now we need to calculate the reaction quotient Q using the concentrations of the reactants and products. According to the given information, [Ag+] = 0.010 M and [Co2+] = 0.015 M.
Q = ([Co2+][Ag+]^2)/([Ag+]^2)
= ([0.015][0.010]^2)/([0.010]^2)
= 0.015 M
Substituting the values in the Nernst equation, we get:
Ecell = E°cell - (RT/nF) ln(Q)
= 1.08 - (8.314 x 298 / (2 x 96485)) ln(0.015)
= 0.829 V
Therefore, the cell potential, Ecell, for the given reaction at 298K is 0.829 V.