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

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

Step 1: Understanding Polarizing Power

Polarizing power is the ability of a cation to distort the electron cloud of an anion. It depends on the charge density of the ion, which is the charge to size ratio. The higher the charge and the smaller the size, the greater the polarizing power.

Step 2: Identify Cations and Compare Charges

Identify the cations in the options and consider their charges: - \(\mathrm{Cs}^+\) and \(\mathrm{K}^+\) have charges of +1, - \(\mathrm{Mg}^{2+}\) has a charge of +2,- \(\mathrm{Al}^{3+}\) has a charge of +3. Typically, higher charged cations have greater polarizing power.

Step 3: Consider Ionic Sizes

Next, consider the sizes of these ions. Smaller ions exert stronger forces due to closer proximity to the negatively charged electrons. Among the given ions:- \(\mathrm{Cs}^+\) is larger than \(\mathrm{K}^+\),- \(\mathrm{K}^+\) is larger than \(\mathrm{Mg}^{2+}\),- \(\mathrm{Mg}^{2+}\) is larger than \(\mathrm{Al}^{3+}\). Smaller sizes lead to greater polarizing power.

Step 4: Order the Ions by Polarizing Power

Considering both charge and size, we arrange these ions from least to greatest polarizing power: \(\mathrm{Cs}^+ < \mathrm{K}^+ < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+}\). This order shows that as charge increases and size decreases, polarizing power increases.

Step 5: Select Correct Answer

Among the provided options, option (a) matches the calculated order: \(\mathrm{Cs}^+ < \mathrm{K}^+ < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+}\). Choose option (a) as the correct one.

Key Concepts

Cation Charge

The charge on a cation is an essential factor that influences its polarizing power. A cation with a higher charge can attract the electron cloud of an anion more effectively. This is because a higher positive charge means a stronger electrostatic pull towards negatively charged electrons.
For example, comparing the cations \(\mathrm{Cs}^{+}\), \(\mathrm{K}^{+}\), \(\mathrm{Mg}^{2+}\), and \(\mathrm{Al}^{3+}\):

• \(\mathrm{Cs}^{+}\) and \(\mathrm{K}^{+}\) both have a charge of +1.
• \(\mathrm{Mg}^{2+}\) has a charge of +2.
• \(\mathrm{Al}^{3+}\) has a charge of +3.

As the charge increases from +1 to +3, the cation can distort the anion's electron cloud more. This results in increased polarizing power. Hence, \(\mathrm{Al}^{3+}\), with the highest charge, has the greatest potential to polarize anions.

Ionic Size

The size of a cation plays a crucial role in its polarizing power. Smaller cations are closer to the electron cloud of anions and can exert a stronger pull on these electrons. In essence, cations with smaller ionic radii tend to have higher polarizing power.
In the case of the cations in the exercise:

• \(\mathrm{Cs}^{+}\) is the largest.
• \(\mathrm{K}^{+}\) is smaller than \(\mathrm{Cs}^{+}\).
• \(\mathrm{Mg}^{2+}\) is smaller than both \(\mathrm{K}^{+}\) and \(\mathrm{Cs}^{+}\).
• \(\mathrm{Al}^{3+}\) is the smallest cation.

The smaller the size, the closer the cation can get to the anion's electron cloud. Therefore, it has more influence in distorting it, enhancing its polarizing power. Thus, \(\mathrm{Al}^{3+}\), being the smallest, has the highest polarizing power based on size.

Charge Density

Charge density can be thought of as the concentration of charge within a specific volume. It is calculated as the ratio of the cation's charge to its volume.
A high charge density implies that the cation is either highly charged, very small, or both. This leads to a stronger ability to polarize anions because the charge is concentrated in a small space, creating a more intense electric field. Evaluating charge density:

• \(\mathrm{Cs}^{+}\) and \(\mathrm{K}^{+}\): Low charge density due to their large size and +1 charge.
• \(\mathrm{Mg}^{2+}\): Higher charge density because of a +2 charge.
• \(\mathrm{Al}^{3+}\): Highest charge density with a +3 charge and small size.

Thus, \(\mathrm{Al}^{3+}\) has the highest charge density, leading to the highest polarizing power.

Polarizability

Polarizability refers to the ease with which the electron cloud of an anion or neutral atom can be distorted. While polarizing power focuses on the cation, polarizability is an attribute of the anion. However, it helps us understand how polarizing power works:

• High polarizing power of the cation means it can distort an anion's electron cloud substantially.
• Anions with high polarizability, typically large anions, have more easily distortable electron clouds.

Combining this with the polarizing power of cations, you can see how interactions between ions are determined. Therefore, in polarizing power discussions, both cationic properties like charge and size, and anionic properties like polarizability are significant. The interaction leads to the idea that small, highly charged cations and large, easily polarizable anions often form strong bonds.