Which of the following statements is/are correct? — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Analyze the Conductivity of Molten \ce{NaCl} In solid sodium chloride (\ce{NaCl}), the sodium ions ($\ce{Na^+}$) and chloride ions ($\ce{Cl^-}$) are bound tightly in a rigid, three-dimensional crystal lattice by strong electrostatic forces of attraction. * When \ce{NaCl} is heated above its melting point to form molten \ce{NaCl}, the intense thermal energy overcomes the lattice energy, collapsing the crystal structure. * In this molten state, the $\ce{Na^+}$ and $\ce{Cl^-}$ ions are no longer held in fixed positions and become highly mobile. * Upon applying a potential difference across the melt, these free ions physically migrate toward their respective oppositely charged electrodes ($\ce{Na^+}$ to the cathode and $\ce{Cl^-}$ to the anode). This migration of free ions carries the electric current. Thus, Statement (A) is correct. Step 2 - Analyze the Conductivity of Solid \ce{NaCl} In solid \ce{NaCl}, the constituent $\ce{Na^+}$ and $\ce{Cl^-}$ ions are locked in fixed positions within the face-centered cubic lattice. * Because the ions are immobile and cannot move to carry an electrical charge, and there are no free electrons available in the ionic crystal structure, solid \ce{NaCl} behaves as an electrical insulator. Thus, Statement (B) is incorrect. Step 3 - Analyze the Conductivity of Molten Sodium Metal Sodium ($\ce{Na}$) is an alkali metal. According to the "electron sea" model of metallic bonding: * A metal consists of a regular array of positive metal ions (kernels) immersed in a highly mobile sea of shared valence electrons. * When sodium metal is melted, the crystalline structure is deformed, but the metallic bonds remain intact, and the valence electrons remain highly mobile. * When a potential difference is applied, these free, mobile valence electrons easily drift through the molten metal to carry the electric current. This makes molten sodium a highly efficient conductor of electricity (metallic conduction). Thus, Statement (C) is correct. Step 4 - Analyze the Definition of Resistivity Let us mathematically define resistivity ($\rho$) and molar conductivity ($\Lambda_m$): * **Resistivity ($\rho$):** Resistivity is defined as the reciprocal of **specific conductance** (also known as conductivity, $\kappa$): $$\rho = \frac{1}{\kappa}$$ * **Molar Conductivity ($\Lambda_m$):** Molar conductivity represents the conducting power of all the ions produced by dissolving one mole of an electrolyte in a solution of concentration $C$: $$\Lambda_m = \frac{\kappa}{C}$$ * Therefore, the reciprocal of molar conductivity is: $$\frac{1}{\Lambda_m} = \frac{C}{\kappa}$$ This clearly shows that resistivity ($\rho = \frac{1}{\kappa}$) is the reciprocal of specific conductance ($\kappa$), not of molar conductivity ($\Lambda_m$). Thus, Statement (D) is incorrect. Step 5 - Conclusion From our physical and chemical evaluation: * Statement (A) is **correct**. * Statement (B) is **incorrect**. * Statement (C) is **correct**. * Statement (D) is **incorrect**. $$\text{Correct Options: } \boxed{\text{A, C}}$$