Question

The pair of electrolytes that posses same value for the constant (A) in the Debye - Huckel - Onsagar equation, $\lambda_m = \lambda^0_m - A\sqrt{C}$ is

• A. $MgSO_4, NaSO_4$
• B. $NH_4Cl, NaBr$
• C. $NaBr, MgSO_4$
• D. $NaCl, CaCl_2$

Answer 1

The Correct Option is B

The value of the constant \(A\) in the Debye - Huckel -Onsager equation, \(\lambda_{ m }=\) \(\lambda_{m}^{0}-A \sqrt{C}\) depends on temperature, charges of the ions, the dielectric constant of the solvent and also the viscosity of the solvent. Here, since we are not given the solvent, we will assume that the solvent is the same for each case. Here, the deciding factor is the charge on the ions. Again, in \(NH _{4} Cl\) and \(NaBr\), the charges on the ions are the same.

Hence the pair of electrolytes that will possess the same value for the constant (A) will be \(NH _{4} Cl , NaBr\).

Answer 2

The Debye-Hückel-Onsager equation relates the molar conductivity (\( \lambda_m \)) of an electrolyte solution to its concentration (\( C \)): \[ \lambda_m = \lambda^\circ_m - A \sqrt{C} \] where:
\( \lambda_m \) is the molar conductivity at concentration \( C \),
\( \lambda^\circ_m \) is the limiting molar conductivity (when concentration approaches zero),
\( A \) is a constant that depends on the nature of the electrolyte and the solvent. The constant \( A \) is influenced by the ionic strength of the solution and the type of ions present.

For a given type of solvent (water, in this case), the value of \( A \) is the same for pairs of electrolytes that have the same type of ion (monovalent or divalent). The key observation is that the electrolytes that are pairwise similar in their ion characteristics tend to have similar values of \( A \).

Looking at the options:
MgSO₄ and Na₂SO₄ both have divalent cations (Mg²⁺ and Na⁺), and therefore, the constant \( A \) will be the same for both, as their ionic interactions are similar.

Thus, the correct answer is (B).