Electrochemistry Set-3

Q1. A concentration cell is formed by two copper half‑cells at $298\ \mathrm{K}$: one contains $[Cu^{2+}]=1.0\ \mathrm{M}$ and the other contains $[Cu^{2+}]=1.0\times10^{-2}\ \mathrm{M}$. Using the Nernst relation for the half‑reaction $Cu^{2+}+2e^{-}\rightleftharpoons Cu(s)$ and $E=\dfrac{0.0592}{n}\log\!\left(\dfrac{[Cu^{2+}]_{\text{cathode}}}{[Cu^{2+}]_{\text{anode}}}\right)$ at $298\ \mathrm{K}$, calculate the emf of the cell (in V). (Assume electrons flow from the lower‑concentration compartment to the higher‑concentration compartment.)

Q2. Consider the redox reaction $2Fe^{3+}(aq)+Cu(s)\rightarrow 2Fe^{2+}(aq)+Cu^{2+}(aq)$ at $298\ \mathrm{K}$. Given standard reduction potentials $E^\circ(Fe^{3+}/Fe^{2+})=+0.77\ \mathrm{V}$ and $E^\circ(Cu^{2+}/Cu)=+0.34\ \mathrm{V}$, calculate the equilibrium constant $K$ for this reaction using $E^\circ=\dfrac{0.0592}{n}\log K$ (base 10).

Q3. A galvanic cell at $298\ \mathrm{K}$ is constructed from $Zn(s)\mid Zn^{2+}(0.010\ \mathrm{M})$ and $Ag(s)\mid Ag^{+}(0.0010\ \mathrm{M})$. Given $E^\circ_{Ag^{+}/Ag}=+0.80\ \mathrm{V}$ and $E^\circ_{Zn^{2+}/Zn}=-0.76\ \mathrm{V}$, calculate the cell emf $E$ for the spontaneous reaction $Zn(s)+2Ag^{+}(aq)\rightarrow Zn^{2+}(aq)+2Ag(s)$ using $E=E^\circ-\dfrac{0.0592}{n}\log Q$ with $Q=\dfrac{[Zn^{2+}]}{[Ag^{+}]^{2}}$.

Q4. Assertion (A): Two silver–silver chloride half‑cells, one containing solid $AgCl(s)$ in pure water (saturated with $AgCl$) and the other containing solid $AgCl(s)$ in a $0.010\ \mathrm{M}$ $Cl^{-}$ solution, will produce a non‑zero emf at $298\ \mathrm{K}$ when connected.
Reason (R): In each half‑cell the silver electrode potential follows $E=E^\circ_{Ag^{+}/Ag}+0.0592\log[Ag^{+}]$, and because $[Ag^{+}]$ is set by $K_{sp}(AgCl)$ together with the local $[Cl^{-}]$, the two electrodes have different $E$ values.

Q5. A galvanic cell consists of $Zn(s)\mid Zn^{2+}(0.010\ \mathrm{M})\parallel Cu^{2+}(0.100\ \mathrm{M})\mid Cu(s)$; both compartments contain $1.00\ \mathrm{L}$ of solution. The spontaneous discharge is $Zn+Cu^{2+}\rightarrow Zn^{2+}+Cu$. If $19300\ \mathrm{C}$ of charge passes through the external circuit, what are the final molar concentrations $[Zn^{2+}]$ and $[Cu^{2+}]$? (Use $F=96500\ \mathrm{C\ mol^{-1}}$.)

Q6. For the galvanic cell $Zn(s)\mid Zn^{2+}(0.001\ \text{M})\parallel Cu^{2+}(0.10\ \text{M})\mid Cu(s)$ at $298\ \text{K}$, $E^\circ_{\text{cell}}=1.10\ \text{V}$. Using the Nernst equation $E=E^\circ-\dfrac{0.05916}{n}\log Q$, the cell potential $E$ is closest to:

Q7. A concentration cell is built with silver electrodes. Left half-cell: $[Ag^+]=1.0\times10^{-3}\ \text{M}$. Right half-cell: $0.010\ \text{M}$ AgNO$_3$ in $0.100\ \text{M}$ NH$_3$. The complexation $Ag^+ + 2\,NH_3 \rightleftharpoons [Ag(NH_3)_2]^+$ has $K_f=1.7\times10^7$. At $298\ \text{K}$ (assume activities $\approx$ concentrations and $n=1$), the emf of the cell is approximately:

Q8. A galvanic cell with emf $1.10\ \text{V}$ is connected across an external resistor $5.0\ \Omega$. The cell discharges for $1.0\ \text{h}$ and copper is deposited at the cathode via $Cu^{2+}+2e^-\rightarrow Cu(s)$. Assuming $100\%$ current efficiency and $F=96485\ \text{C mol}^{-1}$, the mass of Cu (in grams) deposited is nearest to:

Q9. Assertion (A): In a concentration cell $Ag(s)\mid Ag^+(c_1)\parallel Ag^+(c_2)\mid Ag(s)$ at $298\ \text{K}$ the EMF computed as $E=\dfrac{0.05916}{n}\log\!\dfrac{c_1}{c_2}$ may differ from the actual EMF if the activity coefficients $\gamma_1$ and $\gamma_2$ are unequal (since $a=\gamma c$). Reason (R): Because both half-cells contain the same ionic species, $\gamma_1$ and $\gamma_2$ must be equal and activities therefore always cancel, so concentrations alone always suffice to compute EMF.

Q10. Consider the concentration cell $Zn(s)\mid Zn^{2+}(0.100\ \mathrm{M})\parallel Zn^{2+}(0.010\ \mathrm{M})\mid Zn(s)$ at $298\ \mathrm{K}$. If $0.100\ \mathrm{M}$ KNO$_3$ (an inert electrolyte) is added only to the compartment containing $0.010\ \mathrm{M}$ Zn$^{2+}$, qualitatively how will the measured cell emf change? (Use $a=\gamma c$ and assume $\gamma$ for Zn$^{2+}$ decreases when ionic strength increases.)