Identify the correct equations for the emf of a cell at equilibrium.

1. \(E^0_{cell} = \frac{2.303RT}{nF}logK_c\)
2. \(E^0_{cell} =\frac{\Delta G}{nF}\)
3. \(E_{cell} = E^0_{cell} - \frac{RT}{nF}ln\frac{[Products]}{[Reactants]}\)
4. \(E^0_{cell} = E^0_{left} – E^0_{right}\)

Choose the correct answer from the options given below:

(A) and (C) only

The correct answer is option 1.  (A) and (C) only.

We know the Nernst equation is

\(E_{cell} = E^0_{cell} - \frac{RT}{nF}ln Q\)

\(E_{cell} = E^0_{cell} - \frac{RT}{nF}ln\frac{[Products]}{[Reactants]}\) [Since, \(Q = \frac{[Product]}{[Reactant]}\)]

At equilibrium, \(E_{cell}= 0\) and \(Q = K_c\)

\(E^0_{cell} = \frac{2.303RT}{nF}logK_c\)

\(\Delta G^0 = -nFE^0_{cell}\)

\(E^0_{cell} = E^0_{right} - E^0_{left}\)