Electrochemistry Set-2

Q1. A concentration cell is set up as Zn(s) | Zn^{2+} (0.10 M) || Zn^{2+} (0.010 M) | Zn(s) at 298 K. Using the Nernst equation (take $n=2$ and $0.0591\ \mathrm{V}$ for $RT/F$ at 298 K), the emf of the cell is:

Q2. A galvanic cell Zn(s) | Zn^{2+} (0.010 M) || Cu^{2+} (x M) | Cu(s) at 298 K has measured emf $E_{\text{cell}}=1.05\ \mathrm{V}$. Given $E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$ and $E^\circ_{\mathrm{Zn^{2+}/Zn}}=-0.76\ \mathrm{V}$, calculate the concentration $x$ of Cu^{2+} (use $0.0591\ \mathrm{V}$ for $RT/F$).

Q3. For the cell reaction Zn(s) + Cu^{2+}(aq) → Zn^{2+}(aq) + Cu(s), the measured emf varies with temperature with slope $dE/dT = -3.0\times10^{-4}\ \mathrm{V\,K^{-1}}$ at 298 K. Calculate the standard entropy change $\Delta S^\circ$ for the cell reaction at 298 K. (Use $F=96485\ \mathrm{C\,mol^{-1}}$ and $n=2$, and express your answer in $\mathrm{J\,K^{-1}\,mol^{-1}}$.)

Q4. A silver–silver chloride electrode is prepared by immersing Ag(s) and AgCl(s) in a solution where $[\mathrm{Cl^-}]=0.010\ \mathrm{M}$ at 298 K. Given $K_{sp}(\mathrm{AgCl})=1.8\times10^{-10}$ and $E^\circ_{\mathrm{Ag^+/Ag}}=+0.7996\ \mathrm{V}$, calculate the electrode potential $E$ vs SHE using $E=E^\circ_{\mathrm{Ag^+/Ag}}+0.0591\log[\mathrm{Ag^+}]$ (assume activity of solids = 1 and that $[\mathrm{Ag^+}]=K_{sp}/[\mathrm{Cl^-}]$).

Q5. An aqueous solution initially contains $0.10\ \mathrm{M}$ CuSO_{4} and $0.10\ \mathrm{M}$ ZnSO_{4}. Using inert electrodes, a constant current of $2.00\ \mathrm{A}$ is passed for $30.0\ \mathrm{min}$. Assume ideal behaviour, no overpotentials, and that reduction occurs according to standard reduction potentials ($E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$, $E^\circ_{\mathrm{Zn^{2+}/Zn}}=-0.76\ \mathrm{V}$). What mass of metal is deposited at the cathode? (Atomic mass of Cu = $63.55\ \mathrm{u}$; you may use $F=96500\ \mathrm{C\,mol^{-1}}$.)

Q6. Consider the galvanic cell at $298\ \mathrm{K}$: $\mathrm{Zn(s)\,|\,Zn^{2+}(0.01\ M)\,||\,Cu^{2+}(0.10\ M)\,|\,Cu(s)}$. Given $E^\circ_{\text{cell}}=1.10\ \mathrm{V}$, calculate the cell potential $E_{\text{cell}}$ (use Nernst at $298\ \mathrm{K}$).

Q7. A galvanic cell at $298\ \mathrm{K}$ uses the half-cells $\mathrm{Ag^+/Ag}$ and $\mathrm{Fe^{3+}/Fe^{2+}}$ with $E^\circ(\mathrm{Ag^+/Ag})=0.80\ \mathrm{V}$ and $E^\circ(\mathrm{Fe^{3+}/Fe^{2+}})=0.77\ \mathrm{V}$. Initially $[\mathrm{Ag^+}]=0.100\ \mathrm{M}$, $[\mathrm{Fe^{2+}}]=0.100\ \mathrm{M}$ and $[\mathrm{Fe^{3+}}]=0.010\ \mathrm{M}$. Assuming equal solution volumes and that the cell reaction proceeds until $E_{\text{cell}}=0$, what is the equilibrium $[\mathrm{Ag^+}]$? (Useful relation: $K=10^{\,nE^\circ/0.0591}$ with $n=1$.)

Q8. An electrochemical cell has unknown emf $E$ and internal resistance $r$. When connected to $R_1=10.0\ \Omega$ the current is $I_1=1.00\ \mathrm{A}$; when connected to $R_2=5.00\ \Omega$ the current is $I_2=1.50\ \mathrm{A}$. Determine $E$ and $r$.

Q9. Assertion (A): Tripling the balanced half-reaction $\mathrm{Fe^{3+} + e^- \rightarrow Fe^{2+}}$ would triple its standard electrode potential from $E^\circ=0.77\ \mathrm{V}$ to $2.31\ \mathrm{V}$.
Reason (R): Standard electrode potential $E^\circ$ is an intensive property independent of the stoichiometric coefficient; only $\Delta G^\circ$ scales with the number of electrons transferred.

Q10. An aqueous solution of total volume $0.50\ \mathrm{L}$ contains $0.020\ \mathrm{M}$ $\mathrm{Ag^+}$ and $0.050\ \mathrm{M}$ $\mathrm{Cu^{2+}}$. Using inert electrodes a current $I=10.0\ \mathrm{A}$ is passed for $t=5.00\ \mathrm{min}$. Assume preferential discharge (more positive $E^\circ$ deposits first). Calculate the mass of copper (in grams) deposited at the cathode. (Take $F=96485\ \mathrm{C\ mol^{-1}}$, atomic mass of Cu $=63.55\ \mathrm{g\ mol^{-1}}$.)