Kazimierz Fajans first discussed the idea of partial covalent characteristics of some ionic bonds in 1923, using X-ray crystallography to predict whether a chemical bond would be covalent or ionic. This theory is now known as Fajans’ Rule.

Table of Contents

Postulates of Fajan’s Rule

Explanation of Fazan’s Rule

Fajan’s Rule with Detailed Illustration

Examples on Fajan’s Rule

Summary on Fajan’s Rule

Fajans’ rule is a rule that states that the charge on a cation is proportional to the ratio of the radius of the cation to the radius of the anion.

We classify certain compounds as ionic and other compounds as covalent. Now if we were to ask, amongst the alkali chlorides, which is the most ionic? To answer these kinds of questions, we employ Fajans’ rules as a tool.

Fajan’s Rule states that ionic compounds generally form between a metal and a nonmetal, while covalent compounds generally form between two nonmetals.

Read More

Chemical Bonding

Hybridization

Molecular Orbital Theory

VSEPR Theory

To gain an understanding of Fajans’ rule, let us first become familiar with a few terms:

Polarizing Power

The polarising power of a cation is directly proportional to its charge density. Charge density is the ratio of charge to volume. Therefore, the higher the charge density, the greater the polarising power of the cation.

Polarizability

The extent to which an ion can be polarised is referred to as polarisability. This can also be thought of as the ease with which an ion can be polarised. Polarisation is the process of distorting a spherically symmetric electron cloud to an unsymmetric cloud.

Postulates of Fajans’ Rule

The rule can be stated based on the following three factors:

1. Size of the Ion: The smaller the size of the cation, the larger the size of the anion, the greater the covalent character of the ionic bond.

2. The Charge of Cation: Greater the charge of cation, the more covalent the character of the ionic bond will be.

3. Electronic Configuration: For cations with the same charge and size, those with the electronic configuration of (n-1)dnnso, which is commonly found in transition elements, have a greater covalent character than those with the electronic configuration of ns2np6, which is usually found in alkali or alkaline earth metals. Electronic Configuration

Explanation of Fazan’s Rule

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Rule 1:

The first rule states that the cation has polarizing power, which is determined by its size. If the cation is smaller, then the volume of the ion is less. Consequently, the charge density of the ion would be higher.

The polarising power of the ion would be high due to the high charge density, which makes the compound to be more covalent.

Rule 2:

The second rule states that the larger the anion, the lower the effective nuclear charge on its valence electron. As a result, the valence electron is more loosely bound in large anions and can be more easily polarised by a cation, leading to a more covalent compound.

Rule 3:

The special case is the third rule. Let us use an example to explain this point.

We can explain why we cannot use size as a factor to conclude which compound is more covalent between HgCl2 and Calcium Chloride by employing the third rule. This is because both Hg2+ and Ca2+ are of almost equal size.

The electronic configuration of Hg²⁺ is 6s⁰ 5d¹⁰. This configuration is called pseudo-octet because the d-orbital is fully filled, but the element does not have 8 electrons or an octet.

We know that d orbitals are not good at shielding, so we can say that the anion (Cl–) would be more polarised because the d orbital is poor at shielding making HgCl2 more covalent than CaCl2 because Ca2+ ion has a noble gas configuration.

Now to answer the question that we asked first, which amongst the alkali chlorides is the most covalent?

According to Fajans’ rules, since the anion is the same, we have to compare the cations. The smaller the cation, the more covalent the compound, so LiCl is the most covalent.

Exploring Fajans’ Rule Through a Detailed Illustration

Consider Aluminum Iodide (AlI3)

This is an ionic bond which was formed by transfer of electrons.

The larger size of Iodine means that it has a lower effective nuclear charge, resulting in fewer bonding electrons being attracted to the Iodine nucleus.

On the contrary, the aluminium with its three positive charges pulls the shared pair of electrons towards itself.

This leads to insufficient charge separation for it to be ionic, resulting in the development of covalent character in AlI3.

Aluminium Fluoride (AlF3)

This is an ionic bond, which was formed by the transfer of an electron. Here, due to the smaller size of Fluorine, it attracts the shared pair of electrons more towards itself, leading to sufficient charge separation, thus making it an ionic bond.

Examples of Fajans’ Rule

Illustration 1: Which metal halide is theoretically the most ionic and the most covalent?

Given:

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Solution:

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The smallest metal ion and the largest anion should technically have the strongest covalent bond.

Therefore, LiI is the most covalent.

Therefore, CsF should be the most ionic, due to its combination of the largest cation and the smallest anion.

Illustration 2: Arrange the following according to the increasing order of covalency:

NaF, NaCl, NaBr, NaI

LiF, NaF, KF, RbF, CsF

Given:

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Solution:

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1. Since the cation is the same, compare the anions. Amongst the anions, the larger the size, the greater the covalency. Therefore, the order is: NaF < NaCl < NaBr < NaI.

2. The order of cations from smallest to largest is: LiF < NaF < KF < RbF < CsF, as the smaller the cation, the higher the covalency.

Fajans’ Rule states that:

| Large Cation | Small Cation |

| Small Charge | Large Charge |

Try This: Make a list of the things you need to do today.

1. CuCl is more covalent than NaCl because it has a higher electronegativity difference between the two elements which leads to a stronger attraction between the two ions, creating a stronger covalent bond.

2. LiCl is more soluble in pyridine than in H2O because according to Fajans’ Rule, the larger the difference in electronegativity between two atoms, the more polar the bond between them, and therefore the more soluble the compound is in a polar solvent like pyridine.