Electrochemistry Set-7

Q1. During electroplating from $CuSO_4$ solution a current of $2.0\ \mathrm{A}$ is passed for $30\ \mathrm{min}$. The cathodic half‑reaction is $Cu^{2+} + 2e^- \rightarrow Cu(s)$. Using $F=96500\ \mathrm{C\,mol^{-1}}$ and atomic mass of Cu $=63.5\ \mathrm{g\,mol^{-1}}$, the mass of copper deposited is:

Q2. For the reaction $Cu(s)+2Fe^{3+}(aq)\rightarrow Cu^{2+}(aq)+2Fe^{2+}(aq)$, given $E^\circ(Fe^{3+}/Fe^{2+})=+0.77\ \mathrm{V}$ and $E^\circ(Cu^{2+}/Cu)=+0.34\ \mathrm{V}$ at $298\ \mathrm{K}$, the equilibrium constant $K$ for the reaction is closest to:

Q3. Calculate the emf at $298\ \mathrm{K}$ for the cell $Zn(s)\,|\,Zn^{2+}(0.01\ \mathrm{M})\parallel Cu^{2+}(0.001\ \mathrm{M})\,|\,Cu(s)$. Use $E^\circ(Zn^{2+}/Zn)=-0.76\ \mathrm{V}$ and $E^\circ(Cu^{2+}/Cu)=+0.34\ \mathrm{V}$.

Q4. Assertion (A): A concentration cell made of identical electrodes with the same analytical concentration of $Ag^+$ in both compartments will always show zero emf even if an inert electrolyte (e.g. $KNO_3$) is added to one compartment.
Reason (R): Cell emf depends on ionic activities (effective concentrations); addition of an inert electrolyte can change activity coefficients and thereby can produce a non‑zero emf.

Q5. A galvanic cell at $298\ \mathrm{K}$ is set up as $Cu(s)\,|\,Cu^{2+}(0.010\ \mathrm{M})\parallel$ solution containing total silver $0.010\ \mathrm{M}$ plus $0.10\ \mathrm{M}\ NH_3\,|\,Ag(s)$. Ammonia forms the complex $Ag^{+}+2NH_3 \rightleftharpoons [Ag(NH_3)_2]^+$ with $K_f=1.6\times10^{7}$. Using $E^\circ(Ag^{+}/Ag)=+0.80\ \mathrm{V}$ and $E^\circ(Cu^{2+}/Cu)=+0.34\ \mathrm{V}$, the emf of the cell (to two significant figures) is approximately:

Q6. A concentration cell is constructed as $Cu(s)\,|\,Cu^{2+}(1.0\ \mathrm{M})\,||\,Cu^{2+}(0.01\ \mathrm{M})\,|\,Cu(s)$ at $298\ \mathrm{K}$. Calculate the emf of the cell.

Q7. At $298\ \mathrm{K}$ a galvanic cell is set up as $Pt|H_{2}(g,1\ \mathrm{atm})|H^{+}(aq)\,||\,Cu^{2+}(0.01\ \mathrm{M})|Cu(s)$. The measured emf is $0.340\ \mathrm{V}$ (the copper half-cell acts as the cathode). What is the pH of the hydrogen half-cell?

Q8. For the reaction $2\mathrm{Fe}^{3+} + \mathrm{Sn}^{2+} \rightarrow 2\mathrm{Fe}^{2+} + \mathrm{Sn}^{4+}$, given $E^\circ(\mathrm{Fe}^{3+}/\mathrm{Fe}^{2+})=+0.77\ \mathrm{V}$ and $E^\circ(\mathrm{Sn}^{4+}/\mathrm{Sn}^{2+})=+0.15\ \mathrm{V}$ at $298\ \mathrm{K}$, calculate the equilibrium constant $K$ for the reaction.

Q9. An electrolytic cell with inert Pt electrodes contains an aqueous solution initially of $0.10\ \mathrm{M}$ CuSO$_4$ and $1.0\ \mathrm{M}$ H$_2$SO$_4$ (assume complete dissociation so $[H^+]=2.0\ \mathrm{M}$). A current of $2.0\ \mathrm{A}$ is passed for $30$ minutes. Given $E^\circ(\mathrm{Cu}^{2+}/\mathrm{Cu})=+0.34\ \mathrm{V}$ and $E^\circ(\mathrm{H}^+/\mathrm{H}_2)=0.00\ \mathrm{V}$, identify the species reduced at the cathode and calculate the mass of copper deposited (assume 100% coulombic efficiency). Also state the gas evolved at the anode.

Q10. Assertion (A): For a reversible electrochemical cell at constant pressure, if the standard entropy change $\Delta S^\circ$ of the cell reaction is positive, the cell emf $E$ increases with temperature.
Reason (R): From $\Delta G^\circ = -\,nFE^\circ$ and $\Delta G^\circ=\Delta H^\circ - T\Delta S^\circ$, differentiating with respect to $T$ at constant pressure gives $\displaystyle\left(\frac{\partial E}{\partial T}\right)_p=\frac{\Delta S^\circ}{nF}$.

Q11. A galvanic cell at 298 K is: Zn(s) | Zn^{2+} (0.01 M) || Cu^{2+} (0.10 M) | Cu(s). Given $E^\circ_{Cu^{2+}/Cu}=+0.34\ \text{V}$ and $E^\circ_{Zn^{2+}/Zn}=-0.76\ \text{V}$, calculate the cell potential $E_{\text{cell}}$ using the Nernst equation $E=E^\circ-\dfrac{0.0591}{n}\log Q$ at 298 K.

Q12. A concentration cell is made of hydrogen electrodes: Pt | H$_2$(1 atm) | H$^+$ (10^{-3}\ \mathrm{M}) || H$^+$ (10^{-6}\ \mathrm{M}) | H$_2$(1 atm) | Pt at 298 K. Using the Nernst relation for the hydrogen electrode ($E=0-\dfrac{0.0591}{2}\log\!\dfrac{P_{H_2}}{[H^+]^2}$), what is the emf of the cell (in volts)?

Q13. At 298 K consider the cell Cu(s) | Cu^{2+} (0.010 M) || AgCl(s) | Ag(s) in a solution where $[Cl^-]=0.10\ \mathrm{M}$. Given $E^\circ_{Ag^+/Ag}=+0.80\ \mathrm{V}$, $E^\circ_{Cu^{2+}/Cu}=+0.34\ \mathrm{V}$ and $K_{sp}(AgCl)=1.8\times10^{-10}$, calculate the emf of the cell (assume activities ≈ concentrations and use Nernst equation).

Q14. Assertion (A): For the reduction half-reaction $MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O$, the reduction potential is much more sensitive to changes in pH than to equal-fold changes in $[MnO_4^-]$ at 298 K.
Reason (R): From the Nernst equation $E = E^\circ - \dfrac{0.0591}{5}\log\!\left(\dfrac{[Mn^{2+}]}{[MnO_4^-][H^+]^8}\right)$, a tenfold change in $[H^+]$ changes $E$ by $\dfrac{0.0591\times 8}{5}=0.09456\ \text{V}$, whereas a tenfold change in $[MnO_4^-]$ changes $E$ by only $\dfrac{0.0591}{5}=0.01182\ \text{V}$.

Q15. During electrolysis of concentrated aqueous NaCl using inert electrodes at near-neutral pH, chlorine gas ($Cl_2$) is commonly evolved at the anode even though standard potentials are $E^\circ(Cl_2/Cl^-)=+1.36\ \text{V}$ and $E^\circ(O_2/H_2O)=+1.23\ \text{V}$. Which of the following best explains this observation?