Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: The charge/size ratio of a cation determines its polarising power. Which one of the following sequences represents the increasing order of the polarising power of the cationic species, ${\text{K}}^{+},{\text{Ca}}^{2+},{\text{Mg}}^{2+},{\text{Be}}^{2+}$ ?

The concept of a 100% pure ionic bond is a convenient myth. In reality, the electron cloud of an anion is never perfectly spherical when a cation is nearby. This distortion of the electron cloud is the essence of Fajan's Rule, and understanding it unlocks the secret to predicting the covalent character in ionic compounds.

Fajan's Rule Explained

Imagine a tiny, highly charged cation approaching a large, fluffy anion. The cation acts like a powerful magnet, pulling the anion's loosely held outer electrons towards itself. This ability of a cation to distort the electron cloud of an anion is called its polarising power.

When the electron cloud is pulled towards the cation, the electron density between the two nuclei increases. This sharing of electrons is the very definition of a covalent bond! Therefore, the greater the polarising power of the cation, the greater the covalent character of the bond.

Charge and Size

According to Fajan's rule, the polarising power of a cation depends on two critical factors:

1. Charge of the Cation: A higher positive charge means a stronger electrostatic pull on the anion's electrons. Thus, polarising power is directly proportional to the charge. 2. Size of the Cation: A smaller cation can get closer to the anion, and its positive charge is concentrated over a smaller volume. This creates a more intense electric field. Thus, polarising power is inversely proportional to the size.

Mathematically, we often refer to the ratio of charge to size as the ionic potential ($\varphi$):

We are given four cations: ${\text{K}}^{+}$, ${\text{Ca}}^{2+}$, ${\text{Mg}}^{2+}$, and ${\text{Be}}^{2+}$. Let's break down their polarising power step-by-step.

Step 1: The Charge Factor First, we look at the charges. Potassium (${\text{K}}^{+}$) has a $+1$ charge, while Calcium (${\text{Ca}}^{2+}$), Magnesium (${\text{Mg}}^{2+}$), and Beryllium (${\text{Be}}^{2+}$) all carry a $+2$ charge.

Since polarising power is directly proportional to the charge, the monovalent ${\text{K}}^{+}$ ion will have the weakest pull on an anion's electron cloud. Therefore, ${\text{K}}^{+}$ has the lowest polarising power among the group.

Step 2: The Size Factor Now, we must differentiate between the three isovalent cations: ${\text{Ca}}^{2+}$, ${\text{Mg}}^{2+}$, and ${\text{Be}}^{2+}$. Since their charges are identical, size becomes the ultimate deciding factor.

Notice that Beryllium, Magnesium, and Calcium are all alkaline earth metals belonging to Group 2 of the periodic table. As we move down a group, the number of principal electron shells increases, leading to an increase in ionic radius.

The order of their ionic sizes is:

Because polarising power is inversely proportional to size, the smallest ion will pack the biggest punch. Therefore, the tiny ${\text{Be}}^{2+}$ ion will have the highest polarising power, followed by ${\text{Mg}}^{2+}$, and then the larger ${\text{Ca}}^{2+}$.

Combining our deductions from both charge and size, we can construct the final sequence. Potassium is the weakest due to its low charge. Among the $+2$ ions, Calcium is the weakest because it is the largest, followed by Magnesium, and finally the highly polarising Beryllium.

The increasing order of polarising power is:

This perfectly matches option (c). Understanding these trends not only helps in solving direct questions but also builds a strong foundation for predicting properties like melting points, solubility, and thermal stability of various inorganic compounds.