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Question 78

The ionic mobility of alkali metal ions in aqueous solution is maximum for

Solution

Ionic mobility (or molar conductance at infinite dilution) is the drift velocity of an ion per unit electric field. In aqueous solution it depends mainly on the effective (hydrated) size of the ion, not on the bare ionic radius.

1. Hydration of alkali metal ions
   • Smaller bare ions like $$Li^+$$ possess high charge density, attract more water molecules, and become strongly hydrated.
   • Strong hydration increases the effective (hydrated) radius, so the ion faces larger frictional resistance while moving through water.
   • Conversely, larger bare ions such as $$Rb^+$$ and $$Cs^+$$ hold water molecules less firmly, giving a smaller hydrated radius and lower resistance to motion.

2. Order of hydrated (effective) radii
$$Li^+ \gt Na^+ \gt K^+ \gt Rb^+$$

3. Relation between hydrated radius and mobility
According to Stokes’ law, mobility $$u$$ is inversely proportional to the hydrated radius $$r_h$$ (i.e., $$u \propto \frac{1}{r_h}$$). Therefore, the smaller the hydrated radius, the larger the mobility.

4. Predicted mobility trend
Using the order of hydrated radii we get the reverse order for ionic mobilities:
$$Rb^+ \gt K^+ \gt Na^+ \gt Li^+$$

5. Among the given options, $$Rb^+$$ shows the highest mobility.

Option B which is: $$Rb^+$$

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