Factors Governing Polarization And Polarisability (Fajan's Rule)

Chemical Bonding of Class 11


Cation Size: 

Smaller is the cation more is the value of φ and hence more its polarising power. As a result more covalent character will develop. Let us take the example of the chlorides of the alkaline earth metals. As we go down from Be to Ba the cation size increases and the value of φ decreases which indicates that BaCl2 is less covalent i.e. more ionic. This is well reflected in their melting points. Melting points of BeCl2 = 405°C and BaCl2 = 960°C.

Cationic Charge: 

More is the charge on the cation, the higher is the value of φ and higher is the polarising power. This can be well illustrated by the example already given, NaBr and AlBr3. Here the charge on Na is +1 while that of Al is +3, hence polarising power of Al is higher which in turn means a higher degree of covalency resulting in a lowering of melting point of AlBr3 as compared to NaBr.

Noble Gas vs Pseudo Noble Gas Cation:

 A Pseudo noble gas cation consists of a noble gas core surrounded by electron cloud due to filled d-subshell. Since d-electrons provide inadequate shielding from the nuclei charge due to relatively less penetration of orbitals into the inner electron core, the effective nuclear charge (ENC) is relatively larger than that of a noble gas cation of the same period. NaCl has got a melting point of 800°C while CuCl has got melting point of 425°C. The configuration of Cu+ = [Ar] 3d10 while that Na+ = [Ne]. Due to presence of d electrons ENC is more and therefore Cl is more polarised in CuCl leading to a higher degree of covalency and lower melting point. 

Anion Size: 

Larger is the anion, more is the polarisability and hence more covalent character is expected. An e.g. of this is CaF2 and CaI2, the former has meltingpoint of 1400°C and latter has 575°C. The larger size of I ion compared to F causes more polarization of the molecule leading to a lowering of covalency and increasing in melting point. 

Anionic Charge: 

Larger is the anionic charge, the more is the polarisability. A well illustrated example is the much higher degree of covalency in magnesium nitride (3Mg++ N3–) compared to magnesium fluoride (Mg++ 2F). This is due to higher charge of nitride compare to fluoride. 

These five factors are collectively known as Fajan’s Rule.


1. Prediction of degree of covalency in an ionic compound.

2. Tendency of a cation to form complexes can be estimated.

3. Tendency of cations towards solvation.

chemical bonding

E.g.: [Li(H2O)6]+, [Na(H2O)4]+, [Cs(H2O)]+

4. Nature of oxides: Emperically for an oxide of the type chemical bonding

  • √φMn+ < 2.2 basic
  • √φ  lying between 2.2 – 3.2 amphoteric
  • √φ  > 3.2 acidic

i.e. higher is the value of φ greater is acidic nature of oxide.

Case I:

When r+ << r the contribution of the anion to the hydration enthalpy is small so the total ΔHhydration would be dominated by the cation alone. In a series of salts of a large anion, the hydrational enthalpy will decrease in magnitude with increasing cation size. Now how does the lattice energy respond to this changing cation radius? The lattice energy is inversely proportional to (r+ + r). Since r >> r+, the sum will not change significantly as r+ increases. Consequently the lattice energy will not decrease as fast as the hydration energy with increasing cationic size. The more quickly diminishing hydration energy results in a decrease in solubility. 

E.g. Solubility of LiI > NaI > KI…

MgSO4 > CaSO4 > SrSO4 > BaSO4

Case II:

r+ ≈ r

Here the lattice energy decreases with increasing cationic size more rapidly than the hydration energy which therefore results in an enhanced solubility in a series.

E.g. Solubility of LiF < NaF < KF

Mg(OH)2 < Ca(OH)2 < Ba(OH)2

Deviation  from Covalent to Ionic Character:

In the previous section we discussed about those compounds which deviate from fully ionic to some degree of covalency. A similar trend can also be observed with pure covalent molecules which can change to a partially ionic bond.

This happens when the electronegativities of the two atoms which form the covalent bond are not the same. The atom having higher electronegativity will draw the bonded electron pair more towards itself resulting in a partial charge separation. The distribution of the electron cloud in the bond does not remain uniform and shifts towards the more eletronegative one. Such bonds are called polar covalent bonds. For example the bond formed between hydrogen and chlorine or between hydrogen and oxygen in water is of this type. 

chemical bonding

Molecules like HCl, H2O, NH3 i.e. molecules of the type H – X having two polar ends (positive and negative) are known as polar molecules. The extent of polar character or the degree of polarity in a compound is given by it’s dipole moment which is defined as the product of the net positive or negative charge and the distance of separation of the charges i.e. the bond length. The symbol of dipole moment is μ

μ = electronic charge (e) × distance

The unit of dipole moment is Debye (D)

1D = 3.33 × 10–30 Cm = 10–18 esu cm

Dipole moment is indicated by an arrow having a symbol (chemical bonding) pointing towards the negative end. Dipole moment has both magnitude and direction and therefore it is a vector quantity.

To calculate the dipole moment of a molecule we should calculate the net dipole due to all bonds and for lone pair if any. Diatomic molecules like HCl, HF have the dipole moment of the bond (called bond dipole) equal to the molecular dipole as the structure has one bond only. But for poly atomic molecules the net dipole is the resultant of the individual bond dipoles. A compound having a zero dipole moment indicates that the compound is a symmetrical one.

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