COMEDK · Chemistry · 18. Electrochemistry

Identify the correct mathematical expression which represents the variation in molar conductivity of a weak acid having concentration C and ionisation constant \(K_a\)
(\(\lambda_m^\infty\) = molar conductivity at infinite dilution, \(\lambda_m\) = molar conductivity at concentration C)

A \(K_a = \lambda_m^2 C / \lambda_m^\infty(\lambda_m^\infty - \lambda_m)\)
B \(K_a = \lambda_m \lambda_m^\infty - (\lambda_m^\infty)^2 + \lambda_m^2 C\)
C \(\lambda_m + \lambda_m^\infty + K_a C^{\frac{1}{2}} = 0\)
D \(K_a = \lambda_m^2 C / \lambda_m^\infty(\lambda_m^\infty + \lambda_m)\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(K_a = \lambda_m^2 C / \lambda_m^\infty(\lambda_m^\infty - \lambda_m)\)

Step-by-step Solution

Detailed explanation

The degree of dissociation \(\alpha\) for a weak electrolyte is given by: \(\alpha = \dfrac{\lambda_m}{\lambda_m^\infty}\) For a weak acid, the ionisation constant \(K_a\) is given by Ostwald's dilution law: \(K_a = \dfrac{C \alpha^2}{1 - \alpha}\) Substituting the expression…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Identify the correct mathematical expression which represents the variation in molar conductivity of a weak acid having concentration C and ionisation constant \(K_a\)(\(\lambda_m^\infty\) = molar conductivity at infinite dilution, \(\lambda_m\) = molar conductivity at concentration C)

Step-by-step Solution

Identify the correct mathematical expression which represents the variation in molar conductivity of a weak acid having concentration C and ionisation constant \(K_a\)
(\(\lambda_m^\infty\) = molar conductivity at infinite dilution, \(\lambda_m\) = molar conductivity at concentration C)