Problem 4 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following alkali metal ions has the lowest ionic mobility in aqueous solution? (a) \(\mathrm{Na}^{+}\) (b) \(\mathrm{Li}^{+}\) (c) \(\mathrm{Rb}^{+}\) (d) \(\mathrm{Cs}^{+}\)

Step-by-Step Solution

Answer

\( \mathrm{Li}^{+} \) has the lowest ionic mobility in aqueous solution due to its strong hydration.

Step 1: Understand Ionic Mobility

Ionic mobility refers to the speed at which an ion moves through a solvent under the influence of an electric field. In aqueous solutions, smaller ions with higher charge densities bind strongly with water molecules, forming larger hydrated species, which move more slowly.

Step 2: Compare Ionic Sizes

Among alkali metals, as you move down the group in the periodic table, ions become larger. Thus, the ion size increases in the order: \( \mathrm{Li}^{+} < \mathrm{Na}^{+} < \mathrm{Rb}^{+} < \mathrm{Cs}^{+} \).

Step 3: Assess Influence of Hydration

Smaller ions like \( \mathrm{Li}^{+} \) have higher charge densities and attract a large number of water molecules compared to larger ions like \( \mathrm{Cs}^{+} \). This results in a larger effective size (hydrated ion size), reducing mobility.

Step 4: Determine Lowest Ionic Mobility

\( \mathrm{Li}^{+} \) attracts waters of hydration most strongly, resulting in large and more slowly moving hydrated ions compared to larger alkali metal ions.

Key Concepts

Alkali Metal Ions

Alkali metals belong to a unique group in the periodic table, known for their highly reactive nature and the formation of ions. When looking at the alkali metal ions, particularly

• \(\mathrm{Li}^{+}\)
• \(\mathrm{Na}^{+}\)
• \(\mathrm{Rb}^{+}\)
• \(\mathrm{Cs}^{+}\)

we notice they all lose one electron to form a +1 charge. This loss results in a single positive charge common to all these ions, contributing significantly to their chemical behavior.
Each of these ions behaves differently in an aqueous solution, primarily due to differences in ionic size and properties like charge density, which we will explore further in the upcoming sections.

Hydration

Hydration is a critical process for ions in an aqueous solution. It refers to the interaction of water molecules with an ion. Smaller ions, such as \( \mathrm{Li}^{+} \), have a more intense electric field due to their compact positive charges.
This strong field attracts water molecules more effectively, forming a hydrated sphere around the ion.

• A small ion has a large hydration shell
• Its mobility decreases in the solution

The ions that form larger hydration shells move more slowly. Therefore, even though they are minuscule, the water they attract increases their effective volume. This increase in volume limits their speed when moving under an electric field in a solution.

Ion Size

The size of an ion is crucial when discussing ionic mobility. As we look at the alkali metals:

• \( \mathrm{Li}^{+} \) is the smallest
• \( \mathrm{Na}^{+} \) is next in size
• \( \mathrm{Rb}^{+} \) is larger
• \( \mathrm{Cs}^{+} \) is the largest

An important outcome when comparing ion size is its effect on hydration and mobility. Ion size directly influences how tightly an ion can hold onto water molecules. For instance, \( \mathrm{Li}^{+} \)'s small size means a greater charge density that pulls water molecules closer. On the other hand, larger ions like \( \mathrm{Cs}^{+} \) show less intense attraction to water molecules, resulting in smaller hydrate volumes and faster mobility.

Charge Density

Charge density is a concept explaining how much charge is packed into a given volume of an atom. With ions like \( \mathrm{Li}^{+} \), the charge is concentrated into a smaller space, creating high charge density.

• High charge density: strong attraction to water
• Leads to larger hydration shells
• Reduces mobility in a solution

In contrast, larger ions like \( \mathrm{Cs}^{+} \) have lower charge density since they spread over larger volumes, making the attraction to water less strong. This difference in charge density helps determine the extent of hydration and, ultimately, the ionic mobility of each ion in an aqueous environment.