Electrochemistry Set-9

Q1. A concentration cell at $298\ \text{K}$ is constructed as $\text{Zn(s)}\mid\text{Zn}^{2+}(0.001\ \text{M})\;||\;\text{Zn}^{2+}(0.10\ \text{M})\mid\text{Zn(s)}$. Using the Nernst equation $E=\dfrac{0.0592}{n}\log\!\dfrac{[\text{Zn}^{2+}]_{\text{cathode}}}{[\text{Zn}^{2+}]_{\text{anode}}}$, the emf of the cell is:

Q2. At $298\ \text{K}$ a galvanic cell is: $\text{Fe(s)}\mid\text{Fe}^{2+}(0.005\ \text{M})\;||\;\text{Cu}^{2+}(0.050\ \text{M})\mid\text{Cu(s)}$. Given $E^\circ(\text{Cu}^{2+}/\text{Cu})=+0.34\ \text{V}$ and $E^\circ(\text{Fe}^{2+}/\text{Fe})=-0.44\ \text{V}$, calculate the initial cell emf using $E=E^\circ_{\text{cell}}-\dfrac{0.0592}{n}\log Q$.

Q3. A $0.010\ \text{M}$ solution of acetic acid at $298\ \text{K}$ has molar conductivity $\Lambda_m=15.0\ \text{S cm}^2\text{mol}^{-1}$. Given limiting ionic molar conductivities $\lambda^\circ(\text{H}^+)=350.0\ \text{S cm}^2\text{mol}^{-1}$ and $\lambda^\circ(\text{CH}_3\text{COO}^-)=40.0\ \text{S cm}^2\text{mol}^{-1}$, calculate the degree of dissociation $\alpha$ using $\alpha=\dfrac{\Lambda_m}{\Lambda^\circ}$ and $\Lambda^\circ=\lambda^\circ_++\lambda^\circ_-$.

Q4. A concentration cell at $298\ \text{K}$ uses two silver electrodes. Initially both compartments have $[\text{Ag}^+]=1.0\times10^{-2}\ \text{M}$. To one compartment $1.0\times10^{-2}\ \text{M}$ Cl$^-$ is added and AgCl(s) precipitates. Given $K_{sp}(\text{AgCl})=1.8\times10^{-10}$ and $E=\dfrac{0.0592}{n}\log\!\dfrac{[\text{Ag}^+]_{\text{cathode}}}{[\text{Ag}^+]_{\text{anode}}}$ with $n=1$, the emf of the cell (assume the compartment without Cl$^-$ is the cathode) is approximately:

Q5. A silver electrode is immersed in a solution with total silver $[\text{Ag}]_{\text{total}}=1.0\times10^{-2}\ \text{M}$ and $[\text{NH}_3]=0.10\ \text{M}$ (assume $[\text{NH}_3]$ remains effectively constant). The complex [\text{Ag(NH}_3)_2}]^+ forms with $\beta_2=1.6\times10^{7}$. Given $E^\circ(\text{Ag}^+/\text{Ag})=+0.800\ \text{V}$ at $298\ \text{K}$, and using the relations $[\text{Ag}^+]_{\text{free}}=\dfrac{[\text{Ag}]_{\text{total}}}{1+\beta_2[\text{NH}_3]^2}$ and $E=E^\circ+0.0592\log[\text{Ag}^+]$, the electrode potential is closest to:

Q6. A concentration cell is constructed with copper electrodes: $Cu(s)\,|\,Cu^{2+}(0.01\ \mathrm{M})\,\|\,Cu^{2+}(1.0\ \mathrm{M})\,|\,Cu(s)$ at $25^\circ\mathrm{C}$. What is the emf of the cell?

Q7. Consider the galvanic cell $Zn(s)\,|\,Zn^{2+}(0.001\ \mathrm{M})\,\|\,Ag^{+}(0.01\ \mathrm{M})\,|\,Ag(s)$ at $25^\circ\mathrm{C}$. Given $E^\circ(Ag^{+}/Ag)=+0.80\ \mathrm{V}$ and $E^\circ(Zn^{2+}/Zn)=-0.76\ \mathrm{V}$, what is the emf of the cell?

Q8. For the redox reaction

at $25^\circ\mathrm{C}$, the standard reduction potentials are $E^\circ(Fe^{3+}/Fe^{2+})=+0.77\ \mathrm{V}$ and $E^\circ(Cu^{2+}/Cu)=+0.34\ \mathrm{V}$. What is the equilibrium constant $K$ for this reaction?

Q9. For the cell reaction

the standard enthalpy and entropy changes are $\Delta H^\circ=-50.0\ \mathrm{kJ\,mol^{-1}}$ and $\Delta S^\circ=-100.0\ \mathrm{J\,K^{-1}\,mol^{-1}}$. Assuming $\Delta H^\circ$ and $\Delta S^\circ$ are temperature independent, at what temperature will the standard emf $E^\circ$ of the cell become zero?

Q10. Consider the cell written as $Ag(s)\,|\,AgCl(s),Cl^{-}(0.100\ \mathrm{M})\,\|\,AgCl(s),Ag(s)$ where the right-hand half-cell is in pure water saturated with $AgCl(s)$. Given $K_{sp}(AgCl)=1.8\times10^{-10}$ at $25^\circ\mathrm{C}$ and using $0.05916\ \mathrm{V}$ for $\dfrac{RT}{F}\ln10$, what is the emf $E_{cell}$ for the cell as written (left to right)?

Q11. A current of $2.5\ \mathrm{A}$ is passed through an aqueous solution of $CuSO_4$ for $30\ \mathrm{min}$. Assuming $100\%$ current efficiency and that the cathodic reaction is $Cu^{2+}+2e^{-}\rightarrow Cu(s)$, what mass of copper (in grams) is deposited at the cathode? (Take $M_{Cu}=63.5\ \mathrm{g\,mol^{-1}}$ and $F=96500\ \mathrm{C\,mol^{-1}}$)

Q12. At $298\ \mathrm{K}$ a galvanic cell is constructed with the following half-cells: $Zn(s)\mid Zn^{2+}(1.0\ \mathrm{M})$ and $Cu^{2+}(0.010\ \mathrm{M})\mid Cu(s)$. Given $E^\circ_{Zn^{2+}/Zn}=-0.76\ \mathrm{V}$ and $E^\circ_{Cu^{2+}/Cu}=+0.34\ \mathrm{V}$, determine the cell emf and identify the anode. Use the Nernst equation $E=E^\circ-\dfrac{0.05916}{n}\log_{10}Q$.

Q13. Two half-cells of a concentration cell are made using silver electrodes; each compartment has volume $V=100\ \mathrm{mL}$. The left compartment initially contains $[Ag^+]=1.00\ \mathrm{M}$ and the right $[Ag^+]=0.010\ \mathrm{M}$. When the cell is allowed to run until concentrations become equal (volume change negligible), how many moles of Ag are deposited on the cathode?

Q14. Assertion (A): In the electrolysis of concentrated $NaCl(aq)$ using inert electrodes, chlorine gas is produced at the anode instead of oxygen even though $E^\circ(\mathrm{O_2/H_2O})=+1.23\ \mathrm{V}$ is lower than $E^\circ(\mathrm{Cl_2/Cl^-})=+1.36\ \mathrm{V}$.
Reason (R): Chlorine formed at the anode hydrolyses with water producing hypochlorous acid and chloride, e.g.

Q15. A cell is made from a copper electrode in $0.010\ \mathrm{M}\ Cu^{2+}$ and a hydrogen electrode in contact with $H_2$ at $0.10\ \mathrm{atm}$ in a solution of pH $3.00$ at $298\ \mathrm{K}$. Given $E^\circ_{Cu^{2+}/Cu}=+0.34\ \mathrm{V}$ and the Nernst equation $E=E^\circ-\dfrac{0.05916}{n}\log_{10}Q$, calculate the cell emf $E_{cell}=E_{cathode}-E_{anode}$ and identify the cathode.