Electrochemistry Set-6

Q1. A galvanic cell is constructed as $\mathrm{Zn}(s)\;|\;\mathrm{Zn^{2+}}(1\ \mathrm{M})\;||\;\mathrm{Ag^{+}}(1\ \mathrm{M})\;|\;\mathrm{Ag}(s)$. Given standard reduction potentials $E^\circ_{\mathrm{Ag^+/Ag}}=+0.80\ \mathrm{V}$ and $E^\circ_{\mathrm{Zn^{2+}/Zn}}=-0.76\ \mathrm{V}$, the standard emf $E^\circ_{\mathrm{cell}}$ equals:

Q2. Calculate the emf of the cell at 298 K for $\mathrm{Zn}(s)\;|\;\mathrm{Zn^{2+}}(0.01\ \mathrm{M})\;||\;\mathrm{Cu^{2+}}(0.10\ \mathrm{M})\;|\;\mathrm{Cu}(s)$. Given $E^\circ_{\mathrm{Zn^{2+}/Zn}}=-0.76\ \mathrm{V}$ and $E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$, use $E=E^\circ-\dfrac{0.0591}{n}\log Q$.

Q3. For the cell $\mathrm{Cu}(s)\;|\;\mathrm{Cu^{2+}}(1\ \mathrm{M})\;||\;\mathrm{Ag^{+}}(1\ \mathrm{M})\;|\;\mathrm{Ag}(s)$ at 298 K, the cell reaction is $2\mathrm{Ag^+}+\mathrm{Cu}\rightarrow 2\mathrm{Ag}+\mathrm{Cu^{2+}}$. Given $E^\circ_{\mathrm{Ag^+/Ag}}=+0.80\ \mathrm{V}$ and $E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$, the equilibrium constant $K$ for the reaction is approximately:

Q4. Consider two silver–silver chloride electrodes immersed in separate solutions with different chloride ion concentrations at 298 K. P: The emf of the concentration cell formed depends only on the ratio of chloride concentrations and is independent of the solubility product $K_{sp}(\mathrm{AgCl})$. Q: AgCl is a sparingly soluble salt, so its $K_{sp}$ has a small numerical value.

Q5. Two half-cells contain copper electrodes with solutions: Left — $100.0\ \mathrm{mL}$ of $0.0100\ \mathrm{M}\ \mathrm{Cu^{2+}}$; Right — $100.0\ \mathrm{mL}$ of $0.1000\ \mathrm{M}\ \mathrm{Cu^{2+}}$. The electrodes are connected and the cell operates reversibly until no emf remains. Calculate the total electric charge (in coulombs) that flows through the external circuit during this process. (Take $F=96485\ \mathrm{C\ mol^{-1}}$ and reaction $\mathrm{Cu^{2+}}+2e^-\rightarrow\mathrm{Cu}$.)

Q6. A galvanic cell at $298\ \mathrm{K}$ is set up as $\mathrm{Zn(s)} \mid \mathrm{Zn^{2+}}(0.01\ \mathrm{M}) \;||\; \mathrm{Cu^{2+}}(1.00\ \mathrm{M}) \mid \mathrm{Cu(s)}$. Given $E^\circ_{\mathrm{Zn^{2+}/Zn}}=-0.76\ \mathrm{V}$ and $E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$, calculate the cell EMF $E_{\mathrm{cell}}$ at $298\ \mathrm{K}$ using the Nernst equation $E=E^\circ-\dfrac{0.05916}{n}\log Q$ (assume activities = concentrations).

Q7. At $298\ \mathrm{K}$, two half-cells are prepared: $\mathrm{Ag^+}(0.010\ \mathrm{M})\mid\mathrm{Ag(s)}$ and $\mathrm{Cu^{2+}}(1.0\times10^{-4}\ \mathrm{M})\mid\mathrm{Cu(s)}$. Given $E^\circ_{\mathrm{Ag^+/Ag}}=+0.80\ \mathrm{V}$ and $E^\circ_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$, determine which metal will be oxidised (act as anode) and the EMF of the cell at $298\ \mathrm{K}$ (to three significant figures).

Q8. A $0.010\ \mathrm{M}$ solution of acetic acid at $298\ \mathrm{K}$ has molar conductivity $\Lambda_m=36.9\ \mathrm{S\ cm^{2}\ mol^{-1}}$. The molar conductivity at infinite dilution is $\Lambda_m^0=390\ \mathrm{S\ cm^{2}\ mol^{-1}}$. Assuming $\Lambda_m=\alpha\Lambda_m^0$ and $K_a=\dfrac{\alpha^2 c}{1-\alpha}$, calculate the degree of dissociation $\alpha$ and the acid dissociation constant $K_a$.

Q9. Assertion (A): A concentration cell made with the same redox couple in both compartments (for example $\mathrm{Cu}\mid\mathrm{Cu^{2+}}(c_1)\;||\;\mathrm{Cu^{2+}}(c_2)\mid\mathrm{Cu}$) will give the EMF predicted by the Nernst equation only if the supporting electrolytes in the two compartments are identical; if different supporting electrolytes are used a non‑zero extra potential may be measured even when $c_1=c_2$.
Reason (R): Different supporting electrolytes have ions with unequal mobilities, producing liquid junction potentials at interfaces which, if not equal and opposite, do not cancel and thus add to the measured EMF.

Q10. At $298\ \mathrm{K}$ the following concentration cell is assembled: $\mathrm{Ag(s)}\mid \mathrm{AgCl(s)}\mid\mathrm{Cl^-}(0.010\ \mathrm{M})\;||\;\mathrm{AgCl(s)}\mid\mathrm{Ag(s)}$ (right compartment is saturated with $\mathrm{AgCl}$). The measured EMF is $E_{\mathrm{cell}}=0.02958\ \mathrm{V}$. Calculate the solubility product $K_{sp}$ of $\mathrm{AgCl}$.

Q11. For the concentration cell $\,\mathrm{Zn(s)}\big|\mathrm{Zn^{2+}}(0.01\ \mathrm{M})\ ||\ \mathrm{Zn^{2+}}(1.00\ \mathrm{M})\big|\mathrm{Zn(s)}\,$ at $298\ \mathrm{K}$ (with $n=2$), calculate the emf $E_{\text{cell}}$ (use $E=\dfrac{0.05916}{n}\log\!\dfrac{[\text{lower conc.}]}{[\text{higher conc.}]}$).

Q12. Consider the cell $\,\mathrm{Cu(s)}\big|\mathrm{Cu^{2+}}(0.001\ \mathrm{M})\ ||\ \mathrm{H^{+}}(\text{pH}=\ ?)\big|\mathrm{H_2}(1\ \mathrm{atm})\big|\mathrm{Pt}\,$ at $298\ \mathrm{K}$. Copper electrode acts as cathode. Given $E^\circ(\mathrm{Cu^{2+}/Cu})=+0.34\ \mathrm{V}$ and $E(\mathrm{H^{+}/H_2})=-0.05916\times\mathrm{pH}$, the measured cell emf is $0.50\ \mathrm{V}$. The pH of the hydrogen half-cell is:

Q13. A galvanic cell at $298\ \mathrm{K}$ is set up as $\,\mathrm{Ni(s)}\big|\mathrm{Ni^{2+}}(0.100\ \mathrm{M})\ ||\ \mathrm{Ag^{+}}(0.01000\ \mathrm{M})\big|\mathrm{Ag(s)}\,$. Each half-cell contains $1.00\ \mathrm{L}$ of solution. Given $E^\circ(\mathrm{Ag^{+}/Ag})=+0.80\ \mathrm{V}$ and $E^\circ(\mathrm{Ni^{2+}/Ni})=-0.25\ \mathrm{V}$, a steady current of $0.200\ \mathrm{A}$ flows, converting Ni to $\mathrm{Ni^{2+}}$ and $\mathrm{Ag^{+}}$ to Ag. How long (nearest minute) will it take for the cell emf to decrease to $0.80\ \mathrm{V}$? (Use $F=96500\ \mathrm{C\,mol^{-1}}$ and $n=2$.)

Q14. Calculate the electrode potential $E$ (at $298\ \mathrm{K}$) for the half-cell $\,\mathrm{Cu(s)}\big|\mathrm{Cu^{2+}}\,$ when the total copper concentration $[\mathrm{Cu}]_{\text{tot}}=0.0100\ \mathrm{M}$ exists as free $\mathrm{Cu^{2+}}$ and the complex $\mathrm{Cu(NH_3)_4^{2+}}$ in a solution with $[\mathrm{NH_3}]=0.400\ \mathrm{M}$. Given $K_f=\dfrac{[\mathrm{Cu(NH_3)_4^{2+}}]}{[\mathrm{Cu^{2+}}][\mathrm{NH_3}]^4}=1.0\times10^{12}$ and $E^\circ(\mathrm{Cu^{2+}/Cu})=+0.34\ \mathrm{V}$; assume only the $1:4$ complex forms and $n=2$. The electrode potential $E$ is approximately:

Q15. Metals A and B undergo 2-electron reductions with $E^\circ(\mathrm{A^{2+}/A})=+0.45\ \mathrm{V}$ and $E^\circ(\mathrm{B^{2+}/B})=+0.60\ \mathrm{V}$ (vs SHE). Initially $[\mathrm{A^{2+}}]=1.00\ \mathrm{M}$ and total metal B (free $\mathrm{B^{2+}}$ plus complex $\mathrm{BL}$) is $1.00\ \mathrm{M}$. Ligand $L$ forms a 1:1 complex: $\mathrm{B^{2+}}+L\rightleftharpoons\mathrm{BL}$ with $K_f=1.0\times10^{6}$. What minimum initial concentration $[L]$ is needed so that the reaction $\mathrm{B(s)}+\mathrm{A^{2+}(aq)}\rightarrow\mathrm{B^{2+}(aq)}+\mathrm{A(s)}$ becomes spontaneous at $298\ \mathrm{K}$? (Take $n=2$ and assume mass balance: $[\mathrm{B}]_{\text{tot}}=[\mathrm{B^{2+}}]+[\mathrm{BL}]=1.00\ \mathrm{M}$.)