Problem 28 - A Complete Resource Book in Chemistry for JEE Main

Question

Correct order of polarizing power is (a) \(\mathrm{Cs}^{+}<\mathrm{K}^{+}<\mathrm{Mg}^{2+}<\mathrm{Al}^{3+}\) (b) \(\mathrm{K}^{+}<\mathrm{Cs}^{+}<\mathrm{Mg}^{2+}<\mathrm{Al}^{3+}\) (c) \(\mathrm{Cs}^{+}<\mathrm{K}^{+}<\mathrm{Al}^{3+}<\mathrm{Mg}^{2+}\) (d) \(\mathrm{K}^{+}<\mathrm{Cs}^{+}<\mathrm{Al}^{3+}<\mathrm{Mg}^{2+}\)

Step-by-Step Solution

Answer

Option (a) is correct: \( \mathrm{Cs}^{+} < \mathrm{K}^{+} < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+} \).

Step 1: Understanding Polarizing Power

Polarizing power is the ability of a cation to distort the electron cloud of the anion it is bonded to. It depends primarily on the charge density of the cation, which is the ratio of its charge to its size.

Step 2: Compare Ionic Charges

Higher charges on ions increase polarizing power. Here we compare charges: \( \mathrm{Al}^{3+} \) has a higher charge than \( \mathrm{Mg}^{2+} \), which in turn is greater than \( \mathrm{K}^{+} \) and \( \mathrm{Cs}^{+} \) which both have a charge of +1. Therefore, \( \mathrm{Al}^{3+} > \mathrm{Mg}^{2+} > \mathrm{K}^{+} = \mathrm{Cs}^{+} \) when looking at charge considerations.

Step 3: Compare Ionic Sizes

Smaller positive ions have higher polarizing power due to a higher charge density. \( \mathrm{Al}^{3+} \) and \( \mathrm{Mg}^{2+} \) are smaller than \( \mathrm{K}^{+} \) and \( \mathrm{Cs}^{+} \), which are larger in size.

Step 4: Analyze Options with Combined Charge and Size

Given that \( \mathrm{Al}^{3+} \) is smaller and has the highest charge, it has the highest polarizing power. \( \mathrm{Mg}^{2+} \) comes next due to its higher charge compared to \( \mathrm{K}^{+} \) and \( \mathrm{Cs}^{+} \). Among \( \mathrm{K}^{+} \) and \( \mathrm{Cs}^{+} \), \( \mathrm{K}^{+} \) is smaller hence more polarizing. Thus, the order should be \( \mathrm{Cs}^{+} < \mathrm{K}^{+} < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+} \).

Step 5: Conclusion and Correct Answer Choice

The correct order of polarizing power is option (a) \( \mathrm{Cs}^{+} < \mathrm{K}^{+} < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+} \).

Key Concepts

Charge Density

Charge density plays a vital role in determining the polarizing power of a cation. It is defined as the ratio of the ionic charge to the ionic size. The concept ties directly into how strongly a cation can attract the electron cloud of an anion, influencing the cation's ability to polarize.
When a cation has a high charge density, it means it has either a high charge, a small size, or both. This allows the cation to exert greater electrostatic forces on the anion's electron cloud. Consequently, ions with high charge density can distort the electron cloud more efficiently.
Understanding charge density is crucial because it combines the influences of both ionic charge and ionic size, leading to a fuller picture of an ion's polarizing power. A strong polarizing cation would thus be both significantly charged and relatively small, optimizing its charge density.

Ionic Charge

The ionic charge is a key factor in determining an ion's polarizing power. Primarily, it refers to the net positive or negative charge that an ion carries. Higher ionic charges result in greater electrostatic attractions between the cation and the anion, which then increases the polarizing power.
For example, in the given set of ions:

• Aluminum ion (\(\mathrm{Al}^{3+}\), with a charge of +3) has a greater ionic charge compared to the magnesium ion (\(\mathrm{Mg}^{2+}\), with a charge of +2).
• Both potassium (\(\mathrm{K}^{+}\)) and cesium ions (\(\mathrm{Cs}^{+}\)) carry the same charge of +1.

The higher the charge, the stronger the ion's ability to attract and distort the anion's electron cloud, thereby enhancing polarizing power. Essentially, as the ionic charge increases, so does the ion's influence over nearby electron clouds.

Ionic Size

Ionic size, or ionic radius, is another critical factor influencing an ion's polarizing power. Smaller ions have a higher polarizing power because their nuclear charge is concentrated over a smaller volume. In simple terms, when the size of an ion is reduced, the positive charge is more densely packed, allowing it to exert a more intense electric field.

Consider the sequence of ions analyzed:

• Aluminum ion (\(\mathrm{Al}^{3+}\)) is smaller than magnesium ion (\(\mathrm{Mg}^{2+}\)).
• Both potassium (\(\mathrm{K}^{+}\)) and cesium (\(\mathrm{Cs}^{+}\)) have larger ionic sizes compared to magnesium and aluminum.

The impact of smaller ionic radius becomes evident when comparing potassium and cesium; \(\mathrm{K}^{+}\) is smaller and therefore more polarizing than \(\mathrm{Cs}^{+}\). Therefore, when assessing polarizing power, smaller-sized ions are generally more effective at distorting electron clouds.