Question

The equation that is incorrect is :

• A. \( {\left( {\Lambda _m^0} \right)_{KCl}} - {\left( {\Lambda _m^0} \right)_{NaCl}} = {\left( {\Lambda _m^0} \right)_{KBr}} - {\left( {\Lambda _m^0} \right)_{NaBr}} \)
• B. \( {\left( {\Lambda _m^0} \right)_{NaBr}} - {\left( {\Lambda _m^0} \right)_{NaI}} = {\left( {\Lambda _m^0} \right)_{KBr}} - {\left( {\Lambda _m^0} \right)_{NaBr}} \)
• C. \( {\left( {\Lambda _m^0} \right)_{NaBr}} - {\left( {\Lambda _m^0} \right)_{NaCl}} = {\left( {\Lambda _m^0} \right)_{KBr}} - {\left( {\Lambda _m^0} \right)_{KCl}} \)
• D. \( {\left( {\Lambda _m^0} \right)_{{H_2}O}} = {\left( {\Lambda _m^0} \right)_{HCl}} + {\left( {\Lambda _m^0} \right)_{NaOH}} - {\left( {\Lambda _m^0} \right)_{NaCl}} \)

Hint:

Use Kohlrausch's law of independent migration of ions: \(\Lambda_m^0\) of an electrolyte is the sum of the limiting ionic conductivities of its cation and anion.

Answer 1

The Correct Option is B

Step 1: By Kohlrausch's law, \(\Lambda_m^0(\text{MX}) = \lambda^0_{M^+} + \lambda^0_{X^-}\).
Step 2: Option (A): \(\Lambda(KCl)-\Lambda(NaCl)=\lambda_{K}-\lambda_{Na}\) and \(\Lambda(KBr)-\Lambda(NaBr)=\lambda_{K}-\lambda_{Na}\). Equal, so correct.
Step 3: Option (B): LHS \(=\Lambda(NaBr)-\Lambda(NaI)=\lambda_{Br}-\lambda_{I}\), but RHS \(=\Lambda(KBr)-\Lambda(NaBr)=\lambda_{K}-\lambda_{Na}\). These are different quantities (anion difference versus cation difference), so the equation is incorrect.
Step 4: Option (C): \(\lambda_{Br}-\lambda_{Cl}\) on both sides. Correct.
Step 5: Option (D): \(\Lambda(HCl)+\Lambda(NaOH)-\Lambda(NaCl)=\lambda_H+\lambda_{Cl}+\lambda_{Na}+\lambda_{OH}-\lambda_{Na}-\lambda_{Cl}=\lambda_H+\lambda_{OH}=\Lambda(H_2O)\). Correct.
Answer: (B)