Arrange the electrolytes in increasing order of limiting molar conduc…

The correct answer is Option (3) → (A), (D), (C), (B)

By Kohlrausch’s law, the limiting molar conductivity of an electrolyte is the sum of the limiting molar conductivities of its cation and anion:

    \( \displaystyle \Lambda_m^{\circ}=\lambda_{+}^{\circ}+\lambda_{-}^{\circ} \)

All four electrolytes share the anion \( \ce{Cl^{-}} \), so the order depends only on how fast the alkali metal cation moves:

• Size of the bare ion: \( \ce{Li^{+}} \) < \( \ce{Na^{+}} \) < \( \ce{K^{+}} \) < \( \ce{Cs^{+}} \). The smaller the ion, the higher its charge density.

• Hydration: a high charge density attracts more water molecules. So the hydrated ion is largest for \( \ce{Li^{+}} \) and smallest for \( \ce{Cs^{+}} \): Li⁺(aq) > Na⁺(aq) > K⁺(aq) > Cs⁺(aq).

• Mobility: a larger hydrated ion moves more slowly, so mobility is \( \ce{Li^{+}} \) < \( \ce{Na^{+}} \) < \( \ce{K^{+}} \) < \( \ce{Cs^{+}} \).

The limiting molar conductivities (S cm² mol⁻¹) of \( \ce{Li^{+}} \), \( \ce{Na^{+}} \) and \( \ce{K^{+}} \) are 38.7, 50.1 and 73.5, and \( \ce{Cs^{+}} \) is higher still.

• (A) LiCl: smallest bare cation, most hydrated, least mobile

• (D) NaCl

• (C) KCl

• (B) CsCl: largest bare cation, least hydrated, most mobile

Shortcut: LiCl (A) is the lowest and CsCl (B) the highest. Only Option (3) starts with (A) and ends with (B).