Question

The value of 'A' in the equation \( \lambda_m = \lambda_m^0 - A\sqrt{C} \) is same for the pair

• A. NaCl and CaCl₂
• B. CaCl₂ and MgSO₄
• C. NaCl and KBr
• D. MgCl₂ and NaCl

Hint:

The constant 'A' remains the same for electrolytes like NaCl and KBr due to their similar dissociation and ionic properties.

Answer 1

The Correct Option is C

To solve the question of identifying the value of 'A' in the given equation \( \lambda_m = \lambda_m^0 - A\sqrt{C} \), we need to understand the Kohlrausch's Law of Independent Migration of Ions. 

This law states that the molar conductivity of an electrolyte at infinite dilution (i.e., when the concentration approaches zero) is equal to the sum of the ionic conductivities of the cations and anions. In this context, the equation can be interpreted for comparing the molar conductivity at infinite dilution for different ionic compounds, denoted as \( \lambda_m^0 \), and its relationship with concentration \( C \).

In the given options:

• NaCl and CaCl₂ - These are different types of ions with different charges, and their constant 'A' would differ due to ionic size and interaction differences.
• CaCl₂ and MgSO₄ - Again, these have different cationic compositions and charge differences.
• NaCl and KBr - Both are halide salts with the same type of anions, similar ionic radii, and similar cationic charge (+1), hence they are expected to have the same 'A' value due to comparable ionic mobility.
• MgCl₂ and NaCl - Different charge states and ionic interactions.

 

The constant 'A' is the ion-specific parameter that reflects the ion's effect on molar conductivity. When comparing NaCl and KBr, both have monovalent cations (Na⁺ and K⁺) and monovalent anions (Cl^- and Br^-), which leads to the same influence on the molar conductivity in the equation, making 'A' the same for them.

Considering these explanations, the correct answer is NaCl and KBr because they both have similar ionic characteristics and behavior in a solution that affects the parameter 'A' equally.