Statement I: The conductivity of solutions of different electrolytes in the same solvent and at a gi — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Evaluate Statement I (The conductivity of different electrolytes) Statement I states: *"The conductivity of solutions of different electrolytes in the same solvent and at a given temperature is same."* To evaluate this statement, we look at the definition of conductivity ($\kappa$). Conductivity is the measure of a solution's ability to conduct electricity and is directly proportional to the number of charge carriers (ions) present per unit volume, the charge of each ion, and how fast these ions move: $$\kappa = \sum (c_i \cdot z_i \cdot F \cdot u_i)$$ Where: * $c_i$ represents the concentration of ion $i$ * $z_i$ represents the valence charge of ion $i$ * $F$ is Faraday's constant ($96,500\ \text{C mol}^{-1}$) * $u_i$ is the ionic mobility of ion $i$ Because different electrolytes dissociate to produce ions with highly distinct charges, sizes (hydrated radii), and individual speeds (mobilities), their solutions will exhibit completely different conductivities even when dissolved in the same solvent at identical concentrations and temperatures. For instance, at $298\text{ K}$, a $0.1\ \text{M}$ aqueous solution of hydrochloric acid ($\ce{HCl}$) has a significantly higher conductivity than a $0.1\ \text{M}$ aqueous solution of sodium chloride ($\ce{NaCl}$). This difference arises because the highly mobile hydronium ion ($\ce{H^+}$) moves much faster through water than the sodium ion ($\ce{Na^+}$). Therefore, **Statement I is incorrect**. Step 2 - Evaluate Statement II (Factors affecting conductivity) Statement II states: *"The conductivity depends on the charge and size of the ions, the concentrations of ions and ease with which the ions move under potential gradient."* Let us analyze each of these factors: 1. **Concentration of ions:** A higher concentration of ions provides more charge carriers per unit volume, directly increasing conductivity. 2. **Charge of the ions ($z_i$):** Highly charged ions (such as $\ce{Al^3+}$ or $\ce{SO4^2-}$) carry more electric charge per ion than singly charged ions (such as $\ce{Na^+}$ or $\ce{Cl^-}$). 3. **Size of the ions:** In aqueous solutions, ions are hydrated. Smaller ions with high charge density attract more water molecules, forming a larger hydrated radius. The larger this hydrated sphere, the greater the viscous drag it experiences, which slows its movement. 4. **Ease with which ions move (Ionic Mobility, $u_i$):** This represents the drift velocity of an ion under a unit potential gradient ($1\ \text{V cm}^{-1}$). The more easily an ion moves through the solvent, the higher the rate of charge transfer, which increases conductivity. Since conductivity is directly determined by these physical and chemical parameters, **Statement II is correct**. Step 3 - Determine the Correct Option * Statement I is incorrect. * Statement II is correct. This corresponds to Option (D). $$\text{Correct Option: } \boxed{D}$$