Variation of molar conductance of an electrolytic solution with temperature is that it — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Define Molar Conductance ($\Lambda_m$) and Its Governing Factors Molar conductance ($\Lambda_m$) is defined as the conducting power of all the ions produced by dissolving exactly $1\text{ mole}$ of an electrolyte in a given volume of solution: $$\Lambda_m = \frac{\kappa \times 1000}{C}$$ Where: * $\kappa$ is the specific conductivity of the solution (in $\text{S cm}^{-1}$). * $C$ is the molar concentration of the solution (in $\text{mol L}^{-1}$). At the microscopic level, the electrical conductance of an electrolytic solution is governed by two key parameters: 1. The **concentration of free ions** (charge carriers) present in the solution. 2. The **ionic mobility** (velocity) of these migrating ions under an applied electric field. Step 2 - Analyze the Physical and Chemical Effects of Temperature When the temperature of an electrolytic solution is increased, several critical thermodynamic and physical changes occur simultaneously: 1. **Decrease in Solvent Viscosity ($\eta$):** Rising temperature increases the kinetic energy of solvent molecules, weakening intermolecular forces (such as hydrogen bonds in water). This leads to a substantial decrease in the viscosity ($\eta$) of the solvent. According to Stokes' Law, the frictional retarding force ($F_d$) acting on an ion of radius $r$ moving with velocity $v$ is: $$F_d = 6\pi \eta r v$$ A decrease in viscosity ($\eta$) directly reduces this frictional drag, allowing ions to migrate much faster. 2. **Increase in Thermal Kinetic Energy and Ionic Mobility ($u$):** Ions acquire greater thermal kinetic energy as temperature rises. The ionic mobility ($u$) is related to the diffusion coefficient ($D$) through the Einstein relation: $$u = \frac{z e D}{k_B T}$$ Because the diffusion rate of ions increases dramatically with temperature, their velocity ($v$) and corresponding mobility ($u$) increase. 3. **Reduction in Interionic Attractions:** For strong electrolytes, higher thermal motion disrupts the stable ion-atmosphere surrounding each ion. This significantly reduces both the electrophoretic effect and the asymmetry (relaxation) effect that otherwise act to retard ionic migration. 4. **Increase in the Degree of Dissociation ($\alpha$) of Weak Electrolytes:** The ionization of weak electrolytes is generally an endothermic process: $$\ce{AB(aq) <=> A^+(aq) + B^-(aq)} \quad \Delta H_{\text{ion}} > 0$$ According to Le Chatelier's principle, an increase in temperature shifts this equilibrium to the right, increasing the degree of dissociation ($\alpha$) and producing a higher concentration of free ions. Step 3 - Determine the Net Variation of Molar Conductance Because the velocity of all ions increases due to reduced viscosity and higher kinetic energy, and because the total number of free ions increases for weak electrolytes, the overall conducting capability of the solution rises. Consequently, the molar conductance ($\Lambda_m$) of any electrolytic solution—whether strong or weak—always increases continuously as the temperature is raised: $$\Lambda_m(T_2) > \Lambda_m(T_1) \quad \text{for } T_2 > T_1$$ Step 4 - Evaluate and Explain the Options * **Option (A) is correct:** As demonstrated, molar conductance increases continuously with an increase in temperature due to enhanced ionic mobility and reduced solvent viscosity. * **Option (B) is incorrect:** Molar conductance does not decrease with temperature. This behavior is opposite to that of metallic conductors, where conductivity decreases with temperature due to increased thermal vibration of the metal kernels (lattice scattering). * **Option (C) is incorrect:** Molar conductance increases monotonically with temperature; there is no thermodynamic mechanism causing it to first increase and then decrease under normal liquid conditions. * **Option (D) is incorrect:** Conductance is highly temperature-dependent, meaning it is strongly affected by changes in temperature. $$\text{Correct Option: } \boxed{\text{A}}$$