Factors governing polarization and polarisability in Fazans Rule

FACTORS GOVERNING POLARIZATION AND POLARISABILITY (FAJAN’S RULE)

Cation Size: Smaller is the cation more is the value of charge density (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 on Al in +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 of 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 melting point 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⁺⁺ 2N^3–) 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.

Example:

The melting point of KCl is higher than that of AgCl though the crystal radii of Ag⁺and K⁺ ions are almost same.

Solution:

Now whenever any comparison is asked about the melting point of the compounds which are fully ionic from the electron transfer concept it means that the compound having lower melting point has got lesser amount of ionic character than the other one. To analyse such a question first find out the difference between the 2 given compounds. Here in both the compounds the anion is the same. So the deciding factor would be the cation. Now if the cation is different, then the answer should be from the variation of the cation. Now in the above example, the difference of the cation is their electronic configuration. K⁺ = [Ar]; Ag⁺ = [Kr] 4d¹⁰. This is now a comparison between a noble gas core and pseudo noble gas core, the analysis of which we have already done. So try to finish off this answer.

Example: AlF₃ is ionic while AlCl₃ is covalent.

Solution: Since F^– is smaller in size, its polarisability is less and therefore it is having more ionic character. Whereas Cl being larger in size is having more polarisability and hence more covalent character.

Example:

Which compound from each of the following pairs is more covalent and why? 

(a) CuO or CuS                 (b) AgCl or AgI

(c) PbCl₂ or PbCl₄              (d) BeCl₂ or MgCl₂

Solution:

(a) CuS                           (b) AgI

(c) PbCl₄                         (d) BeCl­₂