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, K+, Ca2+, Mg2+, Be2+?

To understand the polarizing power of cations, we need to consider two main factors: the charge of the cation and its size. The polarizing power refers to the ability of a cation to distort the electron cloud of an anion. Generally, a higher charge and a smaller size lead to greater polarizing power. Let's break down the cations you've mentioned: K⁺, Ca²⁺, Mg²⁺, and Be²⁺.

Analyzing the Cations

1. **K⁺**: This is a monovalent cation with a relatively large ionic radius. Its low charge and larger size mean it has the least polarizing power among the group.

2. **Ca²⁺**: This cation has a +2 charge and is smaller than K⁺. The increased charge allows it to exert a stronger attractive force on the electron cloud of nearby anions, enhancing its polarizing ability compared to K⁺.

3. **Mg²⁺**: Similar to Ca²⁺, Mg²⁺ also has a +2 charge, but it is smaller in size. The smaller ionic radius combined with the same charge as Ca²⁺ gives Mg²⁺ a higher polarizing power.

4. **Be²⁺**: This cation has the highest charge density due to its +2 charge and very small size. The combination of a high charge and small size results in the greatest polarizing power among the four cations.

Comparative Summary

• K⁺: Lowest polarizing power due to low charge and large size.
• Ca²⁺: Moderate polarizing power; larger than Mg²⁺ but with a +2 charge.
• Mg²⁺: Higher polarizing power than Ca²⁺ due to smaller size.
• Be²⁺: Highest polarizing power because of its small size and high charge density.

Increasing Order of Polarizing Power

Based on the analysis above, the increasing order of polarizing power for the cations is:

K⁺ < K²⁺ < Mg²⁺ < Be²⁺

In conclusion, when comparing the polarizing power of these cations, the sequence from lowest to highest is K⁺, Ca²⁺, Mg²⁺, and Be²⁺. This understanding is crucial in predicting the behavior of these ions in various chemical reactions, especially in ionic compounds and their interactions with anions.