Problem 206 - A Complete Resource Book in Chemistry for JEE Main

Question

The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing power of the cationic species, \(\mathrm{K}^{+}, \mathrm{Ca}^{2+}, \mathrm{Mg}^{2+}, \mathrm{Be}^{2+}\) ? [2007] (a) \(\mathrm{Be}^{2+}<\mathrm{K}^{+}<\mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}\) (b) \(\mathrm{K}^{+}<\mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}<\mathrm{Be}^{2+}\) (c) \(\mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}<\mathrm{Be}^{2+}<\mathrm{K}^{+}\) (d) \(\mathrm{Mg}^{2+}<\mathrm{Be}^{2+}<\mathrm{K}^{+}<\mathrm{Ca}^{2+}\)

Step-by-Step Solution

Answer

The correct sequence is option (b): \(\mathrm{K}^{+}<\mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}<\mathrm{Be}^{2+}\).

Step 1: Understand the Concept of Polarizing Power

The concept of polarizing power refers to a cation's ability to distort the electron cloud of an anion. The polarizing power of a cation is dependent on the charge/size ratio. A higher positive charge and a smaller ionic size increase the polarizing power.

Step 2: Determine Charge/Size Ratio

List the charges and estimate the sizes of the given cations: \(\mathrm{K}^{+} (1+), \mathrm{Ca}^{2+} (2+), \mathrm{Mg}^{2+} (2+), \mathrm{Be}^{2+} (2+)\). Now consider the approximate ionic sizes: \(\mathrm{Be}^{2+}\) is smallest, followed by \(\mathrm{Mg}^{2+}\), \(\mathrm{Ca}^{2+}\), and \(\mathrm{K}^{+}\) is the largest.

Step 3: Compare Cation Properties

While they all have different ionic radii, the charges are +1 for \(\mathrm{K}^{+}\) and +2 for the others. Hence, cations like \(\mathrm{Be}^{2+}\), having a small radius with a two-unit charge, possess far greater polarizing power than \(\mathrm{K}^{+}\).

Step 4: Arrange in Increasing Order

Based on polarizing power, order them considering the increasing charge/size ratio: \(\mathrm{K}^{+}\) has the least polarizing power, and \(\mathrm{Be}^{2+}\) the most. The correct order is \(\mathrm{K}^{+} < \mathrm{Ca}^{2+} < \mathrm{Mg}^{2+} < \mathrm{Be}^{2+}\).

Step 5: Select the Correct Option

The sequence from the calculation above corresponds to option (b). Therefore, the increasing order of polarizing power is \(\mathrm{K}^{+}<\mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}<\mathrm{Be}^{2+}\).

Key Concepts

Charge/Size Ratio

The charge/size ratio is a crucial factor in determining the polarizing power of a cation. This ratio is calculated by dividing the charge of the ion by its ionic radius. When a cation has a high charge and a smaller size, it results in a greater charge density. This increased charge density means a higher charge/size ratio, leading to stronger polarizing power.
In simple terms, imagine a small magnet (representing a cation) with a strong magnetic field (high charge) - it will have a great ability to distort nearby objects, like electrons in an anion. This is the concept of polarization. In the exercise,

• the cation Be²⁺ is very small yet has a charge of +2, creating a large charge/size ratio.
• On the other hand, K⁺ , with a larger ionic size and a charge of only +1, has the lowest charge/size ratio and, thus, the least polarizing power.

Polarizing power, therefore, increases as we go from a low charge/size ratio to a high one.

Cation Polarization

Cation polarization is the effect that a cation has on the surrounding electron cloud of an anion. This means that the cation can distort or pull the electron cloud toward itself, resulting in a partially covalent character within what was initially an ionic bond. This happens more prominently if the cation is small and highly charged, as it can attract the electrons more strongly.
The extent of this polarization depends on several factors:

• Charge of the cation: Higher charges mean stronger attraction forces.
• Size of the cation: Smaller cations bring the positive charge closer to the anion’s electron cloud.

For example, in the exercise, all cations except K⁺ have a 2+ charge, but their ability to polarize varies. Be²⁺ , being the smallest, will have the greatest effect on an anion, making it extremely effective at polarizing compared to the other cations listed, like Ca²⁺ and Mg²⁺ .

Ionic Radii

The ionic radius is the measure of an atom's ion in a crystal lattice. It plays a significant role in determining the cation's polarizing power because it influences the charge/size ratio. As a general rule of thumb, cations with smaller ionic radii pack more punch in terms of polarization because they concentrate their charge in a smaller volume.

In the list given:

• K⁺ has the largest ionic radius, making it least polarizing.
• Be²⁺ is the smallest and thus the most polarizing.

This pattern is crucial because a smaller ionic radius with the same charge will result in increased charge density (or charge/size ratio). Consequently, such ions as Be²⁺ are effective at significantly polarizing anions, pulling the electronic cloud towards them strongly.