Molar conductance of an electrolyte increase with dilution according to the equation ${\mathrm{\lambda }}_{\mathrm{m}}={\mathrm{\lambda }}_{\mathrm{m}}^0-\mathrm{A}\sqrt{\mathrm{C}}$.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 solvent.

(C) Value of the constant A is same for both BaCl₂ and MgSO₄

(D) Value of the constant A is same for both BaCl₂ and Mg(OH)₂

Choose the most appropriate answer from the options given below.

The equation for molar conductance, λ_m = λ_m⁰ - A C, describes the variation of molar conductance with dilution. This equation can be applied to both strong and weak electrolytes, but there are important distinctions to consider when analyzing the constants and behavior of different electrolytes in solution.

Correct Statements:

• (B) Value of the constant A depends upon the nature of the solvent.

The constant 'A' in the equation for molar conductance depends on several factors, including the solvent and temperature. It is influenced by the type of electrolyte (whether it's a strong or weak electrolyte) and the nature of the ions formed during dissociation. In particular, the charge on the ions (cation and anion) and the size of these ions can significantly affect the value of 'A'. Therefore, the solvent's properties are crucial in determining the value of this constant.

• (D) Value of the constant A is same for both BaCl₂ and Mg(OH)₂.

The molar conductance of electrolytes like BaCl₂ and Mg(OH)₂ can be analyzed by the equation for molar conductance. For these electrolytes, the constant 'A' is similar because both BaCl₂ and Mg(OH)₂ dissociate into ions that behave similarly in solution, leading to comparable values of 'A'. The dissociation of BaCl₂ and Mg(OH)₂ produces 1-2 electrolytes, which contributes to the similarity in their behavior.

Incorrect Statements:

• (A) This equation applies to both strong and weak electrolytes.

While the equation λ_m = λ_m⁰ - A C applies well to strong electrolytes, weak electrolytes follow a different behavior. For strong electrolytes, the molar conductance follows this equation with a constant A, but for weak electrolytes, we need to apply Kohlrausch’s Law of independent migration of ions, which gives a different relationship. Therefore, this equation is not universally applicable to both types of electrolytes.

• (C) Value of the constant A is same for both BaCl₂ and MgSO₄.

This statement is incorrect because the nature of the ions produced by BaCl₂ and MgSO₄ is different. BaCl₂ dissociates into Ba²⁺ and 2Cl^-, while MgSO₄ dissociates into Mg²⁺ and SO₄^2-. The dissociation behavior of these electrolytes leads to different values of 'A'. Therefore, the constant 'A' is not the same for these two electrolytes.

Summary:

To summarize, molar conductance depends on the electrolyte type, ionization, and the solvent in which the electrolyte is dissolved. The equation λ_m = λ_m⁰ - A C is useful in understanding how molar conductance changes with concentration, especially for strong electrolytes. However, for weak electrolytes, Kohlrausch's Law provides a better description of their behavior. Therefore, the correct answers are (B) and (D) because they account for the influence of the solvent and ion dissociation on the value of the constant A, respectively.