Molar conductance of an electrolyte increases with dilution according to the equation: ${\Lambda }_m={\Lambda }_m^{\circ }-A\sqrt{c}$. Which of the following statements are true? (A) This equation applies to both strong and weak electrolytes. (B) Value of the constant $A$ depends upon the nature of the solvent. (C) Value of constant $A$ is same for both $\mathrm{BaCl}{}_2$ and $\mathrm{MgSO}{}_4$. (D) Value of constant $A$ is same for both $\mathrm{BaCl}{}_2$ and $\mathrm{Mg}(\mathrm{OH}){}_2$.

Solution & Explanation

\textbf{Answer:} (B) (B) and (D) only \textbf{Solution:} The Debye-H\"uckel-Onsager equation ${\Lambda }_m={\Lambda }_m^{\circ }-A\sqrt{c}$ holds only for strong electrolytes (linear ${\Lambda }_m$ vs $\sqrt{c}$ plot), so statement (A) is false. The slope constant $A$ depends on the nature of the solvent and on the charge type of the electrolyte, so statement (B) is true. $\mathrm{BaCl}{}_2$ is a $2:1$ type electrolyte while $\mathrm{MgSO}{}_4$ is a $2:2$ type, so their $A$ values differ — statement (C) is false. $\mathrm{BaCl}{}_2$ and $\mathrm{Mg}(\mathrm{OH}){}_2$ are both $2:1$ type electrolytes, so they have the same $A$ — statement (D) is true. Hence the correct statements are (B) and (D).