Problem 47 - A Complete Resource Book in Chemistry for JEE Main

Question

The ionic mobility of alkali metal ions in aqueous solution is maximum for (a) \(\mathrm{K}^{+}\) (b) \(\mathrm{Rb}^{+}\) (c) \(\mathrm{Li}^{+}\) (d) \(\mathrm{Na}^{+}\)

Step-by-Step Solution

Answer

The ionic mobility is maximum for \(\mathrm{K}^{+}\).

Step 1: Understanding Ionic Mobility

Ionic mobility refers to how quickly ions can move through a solution under the influence of an electric field. It is influenced by factors such as the size of the ion and its hydration in aqueous solutions.

Step 2: Evaluating Ion Sizes

In aqueous solution, smaller ions tend to be more heavily hydrated, creating a larger effective size. Among the alkali metals, \(\mathrm{Li}^{+}\) is the smallest, which typically would mean larger hydration.

Step 3: Impact of Hydration on Mobility

Greater hydration leads to lower mobility due to increased effective size. Though \(\mathrm{Li}^{+}\) is smallest, it hydrates significantly, while larger ions like \(\mathrm{K}^{+}\) and \(\mathrm{Rb}^{+}\) experience less hydration and thus, have higher mobility.

Step 4: Comparative Conclusion

Comparing the hydrated ionic sizes, \(\mathrm{K}^{+}\) typically shows the highest ionic mobility among the options, due to a balance of size and hydration that allows for faster movement through the solution.

Key Concepts

Alkali Metal Ions

Alkali metal ions are a group of elements found in the first column of the periodic table. These ions include lithium (\(\mathrm{Li}^+\) ), sodium (\(\mathrm{Na}^+\) ), potassium (\(\mathrm{K}^+\) ), rubidium (\(\mathrm{Rb}^+\) ), and cesium (\(\mathrm{Cs}^+\) ). Each of these ions has a single positive charge.
Alkali metals are characterized by having only one electron in their outer shell, which leads to their high reactivity and tendency to form cations by losing this electron.

• These ions play a crucial role in various chemical reactions and are essential in biological processes.
• They are known for their good conductivity and solubility in water.

When in solution, these ions interact with water molecules, leading to the formation of hydrated ions, which affects their movement and reactivity.

Hydration

Hydration refers to the interaction between ions and water molecules in a solution. When an alkali metal ion like \(\mathrm{Li}^+\) is placed in water, it becomes surrounded by water molecules. This interaction results in the formation of a hydration shell.

• The extent of hydration depends on the charge and size of the ion.
• Smaller ions tend to attract more water molecules because of their higher charge density.

This means that ions like \(\mathrm{Li}^+\), despite their small size, end up with a relatively large hydration shell.
The hydration process forms barriers around the ion, affecting both its size and the way it moves through the solution.

Ion Sizes

Ion sizes refer to the effective radius of an ion in a solution. With alkali metal ions, there is a trend of increasing size as you move down the periodic table from lithium (\(\mathrm{Li}^+\) ) to cesium (\(\mathrm{Cs}^+\) ).

• Smaller ions, like \(\mathrm{Li}^+\), have higher charge densities and tend to attract water molecules more strongly, leading to greater hydration.
• Larger ions like \(\mathrm{K}^+\) are less hydrated.

The hydration adds an extra layer around the ion, increasing its 'apparent' size in a solution. Since the smallest ionic size doesn't necessarily correlate with the fastest movement due to the hydration shell, larger ions can often show greater mobility.

Aqueous Solutions

Aqueous solutions are systems where water acts as the solvent. When alkali metal ions are dissolved in water, they interact extensively with the water molecules, forming what are known as hydrated ions.

• The degree of ion hydration alters the properties of the solution, such as its conductivity and ionic mobility.
• Aqueous solutions facilitate various chemical reactions and serve as a medium for the transport of ions.

The nature of the solvent, water in this case, determines many characteristics of the ions, including their mobility. This mobility is crucial in processes like electrolysis and in biological systems where ions conduct electrical signals.