What is the correct Nernst equation for the following cell? Zn(s)|Zn^…

The correct answer is Option (2) → $E_{cell}=E°_{cell}-\frac{2.303\,RT}{nF}\log\frac{[Zn^{2+}]}{[Ag^+]^2}$

For the cell:

$Zn(s) | Zn^{2+} || Ag^+ | Ag(s)$

Step 1: Write the cell reaction:

$Zn(s) + 2 Ag^+ (aq) -> Zn^{2+} (aq) + 2 Ag(s)$

• n = 2 (number of electrons transferred)

Step 2: General Nernst equation:

$E_\text{cell} = E_\text{cell}^\circ - \frac{0.0591}{n} \log Q$

$Q = \frac{[Zn^{2+}]}{[Ag^+]^2} \quad \text{(products/reactants)}$

$E_\text{cell} = E_\text{cell}^\circ - \frac{0.0591}{2} \log \frac{[{Zn^{2+}}]}{[{Ag^+}]^2} = E_\text{cell}^\circ - \frac{0.0591}{2} \log [{Zn^{2+}}] + 0.0591 \log [{Ag^+}]$

Step 3: Compare with options

$E_\text{cell} = E_\text{cell}^\circ - \frac{2.303 RT}{nF} \log \frac{[{Zn^{2+}}]}{[{Ag^+}]^2}$