The molar conductance of a strong electrolyte at infinite dilution — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Define Molar Conductance and Infinite Dilution Molar conductance ($\Lambda_m$) represents the conducting power of all the ions produced by dissolving exactly $1\text{ mole}$ of an electrolyte in a given volume ($V$) of solution. Mathematically, it is expressed as: $$\Lambda_m = \frac{\kappa \times 1000}{C}$$ Where: * $\kappa$ is the specific conductance (conductivity) in $\text{S cm}^{-1}$ * $C$ is the molar concentration of the solution in $\text{mol L}^{-1}$ **Infinite dilution** is a limiting state where a solution is diluted with an extremely large volume of solvent such that the concentration of the electrolyte approaches zero ($C \to 0$ or $V \to \infty$). At this state, the ions are separated by infinite distances, and interionic interactions become completely negligible. Step 2 - Analyze the Behavior of Strong Electrolytes with Dilution For a strong electrolyte (e.g., $\ce{NaCl}$, $\ce{KCl}$, $\ce{HCl}$), ionization is virtually complete ($100\%$) at all practical concentrations (the degree of dissociation, $\alpha \approx 1$). Therefore, dilution does not increase the number of ions in the solution. Instead, the change in molar conductance with dilution is governed by interionic attractions: * **At higher concentrations:** Cations and anions are closely packed. Strong interionic attractive forces (ion-atmosphere drag, electrophoretic effect, and asymmetry effect) hinder the free movement of these ions, keeping the molar conductance relatively low. * **As dilution increases (concentration $C$ decreases):** The average distance between ions increases, causing interionic attractions to decrease rapidly. Consequently, the ionic mobility (speed of ions) increases, which leads to a steady increase in the molar conductance ($\Lambda_m$). Step 3 - Examine the Debye-Hückel-Onsager Relationship The relationship between molar conductance and concentration for strong electrolytes is quantitatively described by the **Debye-Hückel-Onsager equation**: $$\Lambda_m = \Lambda_m^\circ - A\sqrt{C}$$ Where: * $\Lambda_m^\circ$ is the limiting molar conductance at infinite dilution. * $A$ is a constant depending on the nature of the solvent, viscosity, and temperature. * $C$ is the molar concentration. As the concentration approaches zero ($C \to 0$): $$\lim_{C \to 0} \Lambda_m = \Lambda_m^\circ$$ Since $\Lambda_m$ increases continuously as the concentration decreases, the limiting value at infinite dilution ($\Lambda_m^\circ$) represents the **maximum finite value** that the molar conductance can achieve. Thus, this finite limiting value is always strictly above the molar conductance measured at any higher concentration ($C > 0$). Step 4 - Evaluate and Explain the Options * **Option (A) is correct:** At infinite dilution, the molar conductance of a strong electrolyte reaches a maximum finite limiting value ($\Lambda_m^\circ$), which is strictly above its value at any higher concentration. * **Option (B) is incorrect:** The value at infinite dilution is the maximum value, so it can never be below the value at higher concentrations. * **Option (C) is incorrect:** Molar conductance increases to a maximum limiting value ($\Lambda_m^\circ$) at infinite dilution; it does not tend to zero. Only the specific conductance ($\kappa$) tends to zero because the number of ions per unit volume decreases with dilution. * **Option (D) is incorrect:** The molar conductance at infinite dilution is significantly higher than that at high concentration because high concentrations suffer from severe interionic retarding forces. $$\text{Correct Option: } \boxed{\text{A}}$$