Electrochemistry Set-4

Q1. A galvanic cell at $298\ \text{K}$ is set up as $\text{Zn(s)}\;|\;\text{Zn}^{2+}(0.010\ \text{M})\;||\;\text{Cu}^{2+}(0.100\ \text{M})\;|\;\text{Cu(s)}$. Given $E^\circ_{\text{Cu}^{2+}/\text{Cu}}=+0.34\ \text{V}$ and $E^\circ_{\text{Zn}^{2+}/\text{Zn}}=-0.76\ \text{V}$, calculate the cell potential $E_{\text{cell}}$ using the Nernst equation $E=E^\circ-\dfrac{0.0591}{n}\log Q$.

Q2. Two compartments, each of volume $50.0\ \text{mL}$, contain AgNO$_3$ solutions: left $0.100\ \text{M}$ and right $0.010\ \text{M}$. A concentration cell is formed: $\text{Ag(s)}|\text{Ag}^+(\text{left})||\text{Ag}^+(\text{right})|\text{Ag(s)}$ at $298\ \text{K}$. Assuming only the Ag/Ag$^+$ redox occurs and the cell runs until equilibrium (both compartments reach the same [Ag$^+$]), calculate (i) the total electric charge passed through the external circuit and (ii) the mass of Ag plated on the cathode. (Take $F=96485\ \text{C mol}^{-1}$, $M_{\text{Ag}}=107.87\ \text{g mol}^{-1}$.)

Q3. Consider a redox reaction under standard conditions with $\Delta H^\circ=0$ and standard cell potential $E^\circ=0.500\ \text{V}$ at $T=298\ \text{K}$.
Statement A: The standard cell potential $E^\circ$ increases with increasing temperature.
Statement R: From $\Delta G^\circ=-nFE^\circ$ and $\Delta G^\circ=\Delta H^\circ-T\Delta S^\circ$, with $\Delta H^\circ=0$ we get $\Delta S^\circ=\dfrac{nFE^\circ}{T}>0$, so $\left(\dfrac{\partial E^\circ}{\partial T}\right)_p=\dfrac{\Delta S^\circ}{nF}>0$, implying $E^\circ$ rises with $T$.

Q4. A cell at $298\ \text{K}$ is: $\text{Ag(s)}|\text{AgCl(s)}|\text{Cl}^- (0.010\ \text{M})\;||\;\text{H}^+ (\text{?})|\text{H}_2(1\ \text{atm})|\text{Pt}$ and the measured emf (with the Ag/AgCl electrode as cathode) is $E_{\text{cell}}=0.518\ \text{V}$. Given $E^\circ(\text{AgCl(s) + e}^-\to\text{Ag(s)+Cl}^-) = +0.2223\ \text{V}$ and using $0.0591\ \text{V}$ as the Nernst constant at $298\ \text{K}$, calculate the pH of the hydrogen electrode compartment.

Q5. $250.0\ \text{mL}$ of aqueous $\text{CuSO}_4$ (initial concentration $0.200\ \text{M}$) is electrolyzed with inert electrodes at $25^\circ\text{C}$ using a constant current of $1.50\ \text{A}$. How long must electrolysis continue to reduce $[\text{Cu}^{2+}]$ to $0.120\ \text{M}$? Assume 100% current efficiency for the reduction $\text{Cu}^{2+}+2e^-\to\text{Cu(s)}$ and take $F=96485\ \text{C mol}^{-1}$.

Q6. A Daniell-type cell is constructed as Zn(s) | Zn^{2+} (1.0 M) || Cu^{2+} (0.010 M) | Cu(s) at 298 K. Given $E^\circ_{\mathrm{Cu}^{2+}/\mathrm{Cu}}=+0.34\ \mathrm{V}$ and $E^\circ_{\mathrm{Zn}^{2+}/\mathrm{Zn}}=-0.76\ \mathrm{V}$, calculate the cell emf $E_{\mathrm{cell}}$ using $E=E^\circ-\dfrac{0.0592}{n}\log Q$.

Q7. For the cell corresponding to the net reaction $2\mathrm{Ag}^+(0.001\ \mathrm{M})+\mathrm{Cu}(s)\rightarrow2\mathrm{Ag}(s)+\mathrm{Cu}^{2+}(0.10\ \mathrm{M})$ at 298 K, given $E^\circ_{\mathrm{Ag}^+/\mathrm{Ag}}=+0.80\ \mathrm{V}$ and $E^\circ_{\mathrm{Cu}^{2+}/\mathrm{Cu}}=+0.34\ \mathrm{V}$, calculate the cell emf $E_{\mathrm{cell}}$ (in V). Use $E=E^\circ-\dfrac{0.0592}{n}\log Q$.

Q8. An aqueous solution containing $\mathrm{Cu}^{2+}$ is electrolysed using inert electrodes with a constant current of $2.0\ \mathrm{A}$ for $30.0\ \mathrm{min}$. Assuming the cathodic reaction is $\mathrm{Cu}^{2+}+2e^-\rightarrow\mathrm{Cu}(s)$ and $\mathrm{Cu}^{2+}$ is not depleted, calculate the mass of copper deposited (in g). Take $M_{\mathrm{Cu}}=63.5\ \mathrm{g\,mol^{-1}}$ and $F=96485\ \mathrm{C\,mol^{-1}}$.

Q9. A concentration cell is set up: $\mathrm{Ag}(s)\mid\mathrm{AgCl}(s)\mid\mathrm{Cl}^-(0.010\ \mathrm{M})\parallel\mathrm{AgCl}(s)\mid\mathrm{Ag}(s)$ (right compartment saturated with AgCl) at 298 K. The measured emf is $0.0592\ \mathrm{V}$. Assuming activity coefficients ≈ 1, calculate the solubility product $K_{sp}$ of AgCl.