Statement I: Specific conductance decreases with dilution while molar conductance increases. Stateme — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Define Specific Conductance and Analyze its Behavior on Dilution Specific conductance (also known as conductivity, denoted by the Greek letter kappa, $\kappa$) is defined as the conductance of a unit volume (specifically, $1\ \text{cm}^3$) of an electrolytic solution. When a solution is diluted by adding more solvent: * The total volume of the solution increases. * The total number of ions remains constant (for strong electrolytes) or increases slightly (for weak electrolytes), but these ions are now dispersed over a much larger volume. * Consequently, the number of current-carrying ions per unit volume (per $\text{cm}^3$) decreases. Since conductivity is directly proportional to the concentration of ions per unit volume, **specific conductance ($\kappa$) always decreases with dilution** for both strong and weak electrolytes. Step 2 - Define Molar Conductance and Analyze its Behavior on Dilution Molar conductance ($\Lambda_m$) is defined as the conducting power of all the ions produced by dissolving exactly one mole of an electrolyte in a given volume of solution. It is mathematically related to specific conductance by the formula: $$\Lambda_m = \kappa \times V$$ Where $V$ is the volume of the solution (in $\text{cm}^3$) containing one mole of the electrolyte. When a solution is diluted: * The specific conductance ($\kappa$) decreases. * However, the volume ($V$) containing one mole of the electrolyte increases. * The increase in volume ($V$) is much more pronounced and mathematically dominates over the decrease in specific conductance ($\kappa$). As a result of this dominant volume expansion, the product $\kappa \times V$ increases, meaning **molar conductance ($\Lambda_m$) always increases with dilution**. This trend is true for both strong and weak electrolytes. Thus, **Statement I is correct**. Step 3 - Evaluate Statement II for Weak and Strong Electrolytes Statement II states: "On dilution, number of ions per unit volume decreases but total number of ions increases considerably." Let us analyze the two assertions in this statement: 1. **"number of ions per unit volume decreases":** This assertion is correct for all types of electrolytes because dilution increases the volume, which disperses the ions. 2. **"but total number of ions increases considerably":** This assertion is not universally true: * For **weak electrolytes** (like acetic acid, $\ce{CH3COOH}$), dilution shifts the dissociation equilibrium to the right according to Ostwald's dilution law, significantly increasing the degree of dissociation ($\alpha$) and thus the total number of ions. * For **strong electrolytes** (like sodium chloride, $\ce{NaCl}$), the electrolyte is already completely dissociated ($\alpha \approx 1$) even at high concentrations. Therefore, dilution does not cause any further dissociation, and the total number of ions does not increase. The increase in molar conductivity for strong electrolytes is instead due to a decrease in interionic attractions as the ions move farther apart. Since Statement II is presented as a general rule for all electrolytes but fails to hold true for strong electrolytes, **Statement II is incorrect**. Step 4 - Determine the Correct Option * Statement I is correct. * Statement II is incorrect. This matches option (C): "Statement I is correct but Statement II is incorrect." $$\text{Correct Option: } \boxed{C}$$