The calomel electrode is reversible with respect to — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Structural Composition of the Calomel Electrode The calomel electrode is a widely used metal-insoluble salt reference electrode. Structurally, it consists of: 1. A pool of pure liquid mercury ($\ce{Hg}$) at the bottom. 2. A paste of sparingly soluble mercurous chloride ($\ce{Hg2Cl2}$, commonly known as calomel) in contact with the liquid mercury. 3. An aqueous solution of potassium chloride ($\ce{KCl}$) of a known concentration (often saturated, $1.0\text{ M}$, or $0.1\text{ M}$) which provides a stable concentration of chloride ions ($\ce{Cl^-}$). 4. A platinum wire sealed in a glass tube to make electrical contact with the liquid mercury. The cell notation for the calomel half-cell is represented as: $$\ce{Pt(s) \mid Hg(l) \mid Hg2Cl2(s) \mid Cl^-(aq)}$$ Step 2 - Primary Redox Equilibrium At the core of the electrode, the actual potential-determining reduction reaction occurring at the surface of the liquid mercury involves the dimerized mercury(I) cation, known as the mercurous ion ($\ce{Hg2^2+}$): $$\ce{Hg2^2+(aq) + 2e^- <=> 2Hg(l)}$$ Since this is the fundamental electrochemical redox half-reaction where electrons are transferred directly between the metal ($\ce{Hg}$) and its dissolved ions ($\ce{Hg2^2+}$), the electrode is thermodynamically and directly **reversible with respect to mercurous ions ($\ce{Hg2^2+}$)**. Step 3 - The Role of the Solubility Equilibrium Because mercurous chloride ($\ce{Hg2Cl2}$) is a sparingly soluble salt, it dissolves slightly to establish a fast and reversible dynamic solubility equilibrium in the aqueous solution: $$\ce{Hg2Cl2(s) <=> Hg2^2+(aq) + 2Cl^-(aq)}$$ The solubility product constant ($K_{sp}$) for this equilibrium is given by: $$K_{sp} = [\ce{Hg2^2+}][\ce{Cl^-}]^2$$ From this, the concentration of free mercurous ions in the solution is regulated by the concentration of chloride ions: $$[\ce{Hg2^2+}] = \frac{K_{sp}}{[\ce{Cl^-}]^2}$$ Step 4 - Derivation of the Electrode Potential Using the Nernst equation for the primary redox reaction at $298\text{ K}$ ($25^\circ\text{C}$): $$E = E^\circ_{\ce{Hg2^2+|Hg}} - \frac{0.0591}{2} \log \left(\frac{1}{[\ce{Hg2^2+}]}\right)$$ By substituting $[\ce{Hg2^2+}] = \frac{K_{sp}}{[\ce{Cl^-}]^2}$ into the Nernst equation: $$E = E^\circ_{\ce{Hg2^2+|Hg}} - \frac{0.0591}{2} \log \left(\frac{[\ce{Cl^-}]^2}{K_{sp}}\right)$$ $$E = \left( E^\circ_{\ce{Hg2^2+|Hg}} + \frac{0.0591}{2} \log K_{sp} \right) - 0.0591 \log [\ce{Cl^-}]$$ Since the terms inside the parentheses are constants, we can define a new standard potential $E^\circ_{\ce{Hg2Cl2|Hg, Cl^-}}$: $$E = E^\circ_{\ce{Hg2Cl2|Hg, Cl^-}} - 0.0591 \log [\ce{Cl^-}]$$ This shows that while the calomel electrode's potential can be practically adjusted and maintained constant using a fixed concentration of chloride ions ($\ce{Cl^-}$), the direct electron transfer and primary chemical reversibility of the metallic phase at the interface is with the mercurous ions ($\ce{Hg2^2+}$). Step 5 - Explanation of Options * **Option (A) is correct:** As shown by the primary redox half-reaction $\ce{Hg2^2+(aq) + 2e^- <=> 2Hg(l)}$, the electrode is directly reversible with respect to mercurous ($\ce{Hg2^2+}$) ions. * **Option (B) is incorrect:** The potential is independent of $\ce{H^+}$ ion concentration (pH) under normal operating conditions. Electrodes like the glass electrode or quinhydrone electrode are reversible to $\ce{H^+}$. * **Option (C) is incorrect:** Calomel utilizes mercury in its $+1$ oxidation state as a dimer ($\ce{Hg2^2+}$), not the mononuclear mercuric ion ($\ce{Hg^2+}$) which represents the $+2$ oxidation state. * **Option (D) is incorrect:** Although the potential depends on the activity of chloride ions as a secondary reference electrode, the primary electrode reaction that maintains redox equilibrium with the metallic mercury is that of the mercurous cation. $$\text{Correct Option: } \boxed{\text{A}}$$