Calculate the equilibrium constant $(K_c)$ of the reaction: $Ni_{(s)} + 2Ag_{(aq)}^{+} \rightarrow Ni_{(aq)}^{2+} + 2Ag_{(s)}$; $E_{cell}^{\circ} = 1.05 \ V$. (Given: $\frac{2.303 \ RT}{F} = 0.06$)

For an electrochemical cell
$Sn_{(s)} | Sn^{2+}(aq, 1 \ M) || Pb^{2+}(aq, 1 \ M) | Pb_{(s)}$
the ratio $\frac{[Sn^{2+}]}{[Pb^{2+}]}$ when this cell attains equilibrium is
(Given $E^{0}_{Sn^{2+}/Sn} = -0.14 \ V$,$E^{0}_{Pb^{2+}/Pb} = -0.13 \ V$,$\frac{2.303 \ RT}{F} = 0.06$)

If $E^{\circ}(Ag^{+}_{(aq)} \mid Ag_{(s)}) = +0.80 \ V$,what is the potential developed for $Ag_{(s)} \rightarrow Ag^{+}_{(aq)} (0.01 \ M) + e^{-}$ at $298 \ K$?

Calculate the equilibrium constant for the following reaction: $Ni_{(s)} + Cu_{(aq)}^{2+} \to Cu_{(s)} + Ni_{(aq)}^{2+}$. Given: $E_{Ni^{2+}|Ni}^o = -0.25 \ V$ and $E_{Cu^{2+}|Cu}^o = 0.34 \ V$.

If the standard electrode potential of $Cu^{2+}/Cu$ electrode is $0.34 \, V$,what is the electrode potential of $0.01 \, M$ concentration of $Cu^{2+}$ $(T = 298 \, K)$ (in $, V$)?

For a general redox reaction: $aA + bB \xrightarrow{n e^-} cC + dD$. Derive the Nernst equation.