Animated Solution for Chemistry - s and p-Block Elements: The ionic mobility of alkali metal ions in aqueous soluton is maximum for

A Deceptive Beginning

When we look at the alkali metals in Group 1 of the periodic table, their sizes follow a very predictable and intuitive trend. As we move down the group from Lithium ($Li$) to Rubidium ($Rb$), the number of electron shells increases. Consequently, the size of the gaseous ions also increases.

We can write the order of their gaseous ionic radii as:

If the question had asked about their mobility in a vacuum or a gaseous state, the smallest ion, $L{i}^{+}$, would naturally be the fastest. However, chemistry is rarely that straightforward. The environment changes everything. The question specifically asks for their mobility in an aqueous solution.

The Hydration Effect

When these ions are dropped into water, they don't just float around naked. Water molecules are highly polar, meaning they have a partial negative charge on the oxygen atom and a partial positive charge on the hydrogen atoms. The positively charged alkali metal ions act like magnets, attracting the partially negative oxygen ends of the water molecules. This process of water molecules surrounding an ion is called hydration.

But here is the catch: not all ions attract water equally. The degree of hydration depends entirely on a property called charge density.

Since all alkali metal ions have the same $+1$ charge, the charge density is inversely proportional to their volume. Lithium ($L{i}^{+}$) is the smallest ion, which means its $+1$ charge is packed into a tiny, highly concentrated space. This massive charge density exerts a powerful pull on the surrounding water molecules, dragging a huge number of them into its orbit.

As a result, the effective size of the Lithium ion in water—its hydrated radius—becomes enormous!

Conversely, Rubidium ($R{b}^{+}$) is a large ion. Its $+1$ charge is spread out over a much larger volume, resulting in a low charge density. It can only weakly attract a few water molecules. Therefore, its hydrated radius remains relatively small.

The order of hydrated ionic radii is exactly the reverse of their gaseous radii:

Ionic Mobility

Now, let's talk about ionic mobility, which is simply the speed at which an ion can move through the solution under an electric field.

Imagine you are trying to run a race. If you are wearing a massive, heavy, water-soaked winter coat (like the hydrated $L{i}^{+}$ ion), you are going to face a lot of resistance and move very slowly. On the other hand, if you are wearing a light, aerodynamic jacket (like the hydrated $R{b}^{+}$ ion), you can sprint through the crowd with ease.

Mathematically, ionic mobility is inversely proportional to the hydrated size:

Because the hydrated Rubidium ion ($R{b}^{+}(aq)$) is the smallest among the given options, it experiences the least resistance from the surrounding water. Therefore, it zips through the solution the fastest, giving it the maximum ionic mobility.

The final order of ionic mobility in aqueous solution is:

Thus, the correct answer is $R{b}^{+}$.