Electrochemistry Set-8

Q1. A galvanic cell is constructed from the half-cells $Zn(s)\,/\,Zn^{2+}$ and $Cu^{2+}\,/\,Cu(s)$. The concentrations are $[Zn^{2+}]=1.0\times10^{-3}\,\mathrm{M}$ and $[Cu^{2+}]=1.0\,\mathrm{M}$. At $298\,\mathrm{K}$ the standard cell potential is $E^\circ_{\text{cell}}=1.10\,\mathrm{V}$. Using the Nernst equation, calculate the cell emf $E_{\text{cell}}$ (take $n=2$).

Q2. A silver electrode is immersed in an aqueous solution containing total silver $[\mathrm{Ag}]_{\mathrm{T}}=1.0\times10^{-3}\,\mathrm{M}$ and free cyanide $[\mathrm{CN}^-]=0.10\,\mathrm{M}$. Almost all silver is present as $Ag(CN)_2^-$ with formation constant $\beta_2=\dfrac{[Ag(CN)_2^-]}{[Ag^+][CN^-]^2}=1.0\times10^{18}$. Given $E^\circ(\mathrm{Ag}^+/\mathrm{Ag})=+0.799\,\mathrm{V}$ at $298\,\mathrm{K}$, estimate the electrode potential $E(\mathrm{Ag}^+/\mathrm{Ag})$ (assume activities ≈ concentrations).

Q3. For a redox reaction at $T=350\,\mathrm{K}$ the standard emf is $E^\circ_{\text{cell}}=0.250\ \mathrm{V}$ and $n=2$ electrons are transferred. Calculate the equilibrium constant $K$ for the cell reaction at $350\,\mathrm{K}$. Use $F=96485\ \mathrm{C\,mol^{-1}}$ and $R=8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$.

Q4. Consider two half-cells at $298\,\mathrm{K}$: $Ag(s)\,|\,Ag^+$ with $[Ag^+]=1.0\times10^{-3}\,\mathrm{M}$ and $Fe(s)\,|\,Fe^{3+}/Fe^{2+}$ with $[Fe^{3+}]=0.10\,\mathrm{M}$ and $[Fe^{2+}]=1.0\times10^{-3}\,\mathrm{M}$. Given $E^\circ(\mathrm{Ag}^+/\mathrm{Ag})=+0.799\ \mathrm{V}$ and $E^\circ(\mathrm{Fe^{3+}/Fe^{2+}})=+0.771\ \mathrm{V}$, determine (i) which electrode acts as the cathode when the cell is connected and (ii) the cell emf $E_{\text{cell}}$ (to three significant figures). (Assume $n=1$ for the Fe couple and activities ≈ concentrations.)

Q5. The half-reactions are

In a solution at $298\,\mathrm{K}$ with $[\mathrm{MnO_4^-}]=1.0\times10^{-3}\,\mathrm{M}$, $[\mathrm{Mn^{2+}}]=1.0\times10^{-3}\,\mathrm{M}$, $[\mathrm{Fe^{2+}}]=1.0\times10^{-2}\,\mathrm{M}$ and $[\mathrm{Fe^{3+}}]=1.0\times10^{-3}\,\mathrm{M}$, determine the maximum pH at which $\mathrm{MnO_4^-}$ will oxidize $\mathrm{Fe^{2+}}$ spontaneously (i.e. $E_{\text{cell}}>0$). Assume activities ≈ concentrations.

Q6. Consider the galvanic cell $\mathrm{Zn(s)\,|\,Zn^{2+}(0.10\,M)\ ||\ Cu^{2+}(0.01\,M)\,|\,Cu(s)}$ for which $E^\circ_{\text{cell}}=1.10\ \mathrm{V}$ at $298\ \mathrm{K}$. Using the Nernst equation $E=E^\circ-\dfrac{0.0592}{n}\log Q$ (take $n=2$), the emf $E$ of the cell is closest to:

Q7. A concentration cell is made with two silver electrodes: left electrode in $0.010\ \mathrm{M}\ \mathrm{AgNO_3}$ and right electrode in a solution containing $0.100\ \mathrm{M}\ \mathrm{Cl^-}$ in equilibrium with solid $\mathrm{AgCl(s)}$. Given $K_{sp}(\mathrm{AgCl})=1.8\times10^{-10}$ and using $E=\dfrac{0.0592}{n}\log\dfrac{[\mathrm{Ag^+}]_{\text{cathode}}}{[\mathrm{Ag^+}]_{\text{anode}}}$ at $298\ \mathrm{K}$, the emf of the cell is approximately:

Q8. For the reversible concentration cell $\mathrm{Zn(s)\,|\,Zn^{2+}(0.05\,M)\ ||\,Zn^{2+}(0.005\,M)\,|\,Zn(s)}$ at $298\ \mathrm{K}$, if $1.00\ \mathrm{mol}$ of $\mathrm{Zn}$ is oxidized at the anode, the maximum electrical work obtainable (use $E=\dfrac{0.0592}{n}\log\dfrac{[\mathrm{Zn^{2+}}]_{\text{cathode}}}{[\mathrm{Zn^{2+}}]_{\text{anode}}}$, $W_{\max}=nFE$, $F=96485\ \mathrm{C\,mol^{-1}}$) is about:

Q9. Assertion (A): In the concentration cell $\mathrm{M(s)\,|\,M^{z+}(a_1)\ ||\ M^{z+}(a_2)\,|\,M(s)}$ with $a_1<a_2$, the electrode in contact with the lower activity $a_1$ acts as the anode.
Reason (R): This is because the electrode with lower activity has a higher standard electrode potential.

Q10. The overall redox reaction at $298\ \mathrm{K}$ is $\mathrm{Cr_2O_7^{2-} + 14H^+ + 3Cu(s)\rightarrow 2Cr^{3+} + 7H_2O + 3Cu^{2+}}$. Given $E^\circ(\mathrm{Cr_2O_7^{2-}/Cr^{3+}})=+1.33\ \mathrm{V}$ and $E^\circ(\mathrm{Cu^{2+}/Cu})=+0.34\ \mathrm{V}$, the equilibrium constant $K$ for the reaction (use $E^\circ=\dfrac{0.0592}{n}\log K$) is closest to:

Q11. A galvanic cell is constructed with Zn(s) | Zn^{2+} (0.010 M) || Cu^{2+} (1.00 M) | Cu(s) at 298 K. Given $E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$ and $E^\circ_{\mathrm{Zn^{2+}/Zn}}=-0.76\ \mathrm{V}$, calculate the cell emf using the Nernst equation.

Q12. A concentration-type silver cell is made: left half-cell is Ag(s)|AgCl(s)|Cl^- with $[\mathrm{Cl}^-]=0.010\ \mathrm{M}$ (saturated AgCl), right half-cell is Ag(s)|Ag^+ with $[\mathrm{Ag}^+]=1.0\times10^{-4}\ \mathrm{M}$. Given $K_{sp}(\mathrm{AgCl})=1.8\times10^{-10}$ and $E^\circ_{\mathrm{Ag^+/Ag}}=+0.80\ \mathrm{V}$ at $298\ \mathrm{K}$, calculate the cell emf (assume activities ≈ concentrations, $n=1$).

Q13. A plating bath contains $[\mathrm{Ag}^+]=1.0\times10^{-3}\,\mathrm{M}$ and $[\mathrm{Cu}^{2+}]=1.0\times10^{-2}\,\mathrm{M}$. Given $E^\circ_{\mathrm{Ag^+/Ag}}=+0.80\ \mathrm{V}$ and $E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$ at $298\ \mathrm{K}$ (neglect overpotentials), which metal will be preferentially deposited on the cathode when current is passed?

Q14. For the cell reaction

given $E^\circ_{\mathrm{Fe^{3+}/Fe^{2+}}}=+0.77\ \mathrm{V}$ and $E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$ at $298\ \mathrm{K}$, calculate the equilibrium constant $K$ for the reaction.

Q15. Assertion (A): In the industrial electrolysis of concentrated aqueous NaCl (brine), chlorine gas is evolved at the anode rather than oxygen.
Reason (R): Because the standard oxidation potential for $\mathrm{Cl^-}\rightarrow \tfrac{1}{2}\mathrm{Cl_2}$ is lower than that for $\mathrm{H_2O}\rightarrow \tfrac{1}{2}\mathrm{O_2}$.