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POLARITY AND FAJAN'S RULE:

IONIC CHARACTER IN COVALENT COMPOUNDS:
(1) Pauling used dipole moment for depicting percentage of polarity and ionic character of the bond. According to Pauling, a bond can never be 100% ionic.
ILLUSTRATIVE EXAMPLE (1): Calculate the % of ionic character of a bond having length = 0.83 Å and 1.82 D as its observed dipole moment?

SOLUTION: To calculate μ considering 100% ionic bond
                      = 4.8 × 10–10 × 0.83 × 10–8esu cm
                      = 4.8 × 0.83 × 10–18 esu cm = 3.984 D
                          % ionic character = 1.82/3.984 × 100 = 45.68%

(2) When electronegativity difference between two atoms is 2.1, there is 50% ionic character in the bond.
(3) When electronegativity difference is zero (identical atoms), the bond will be 100% covalent.
HANNEY AND SMITH EQUATION:
According to Haney and Smith, the percentage of ionic character of a polar covalent bond can be calculated with help of the following expression.
%ionic character:

POULING EQUATION:

ILLUSTRATIVE EXAMPLE (2) : Calculate the & ionic character in H-X bond of
Halogen acids. Given that electronegativity of  H ,F, Cl, Br. and I  are 2.1, 4.0, 3.0, 2.8,
and 2.5 respectively.



FAJAN'S RULE:

Consider an ionic bond formed between two oppositely charged ions of unequal size of A+  and
B-. In this bond cation and anion remains bonded by electrostatic force of attraction by the valence electrons of larger anion (B-) are attracted by small cation (A+) and so the shape of valence shell is deformed and electron cloud of valence shell of anion remains no longer symmetrical. This process is called Polarisation of anion by cation. The ability of cation to polarise anion is called polarising power and the tendency of anion to get polasied, is called polarisability.

Due to polarisation of anion, an ionic bond acquires some partial covalent character and
greater is the extent of polarisation, more is the covalent character incorporated in ionic bond.
The magnitude of polarization depends upon following factors :

(1)SIZE OF THE CATION: Polarization of the anion increases as the size of the cation decreases i.e., the electrovalent compounds having smaller cations show more of the covalent nature. For example, in the case of halides of alkaline earth metals, the covalent character decreases as we move down the group. Hence melting point increases in the order of

                  BeCl2 < MgCl2 < CaCl2 < SrCl2 < BaCl2 
  
(2)SIZE OF ANION: The larger the size of the anion, more easily it will be polarized by the cation i.e., as the size of the anion increases for a given cation, the covalent character increases. For example, in the case of halides of calcium, the covalent character increases from F anion to I anion i.e. increasing covalent character
                               CaF2 < CaCl2 <CaBr2 < CaI2
Similarly, in case of trihalides of aluminum, the covalent character increases with increase in size of halide anion i.e.
                                  AlF3 <AlCl3< AlBr3 < AlI3
Covalent character increases as the size of halide ion increases

(3) CHARGE ON EITHER OF THE IONS: As the charge on the cation increases, its tendency to polarize the anion increases. This brings more and more covalent nature in the electrovalent compound. Whereas with the increasing charge of anion, its ability to get polarized, by the cation, also increases. For example, in the case of NaCl, MgCl2 and AlCl3 the polarization increases, thereby covalent character becomes more and more as the charge on the cation increases. Similarly, lead forms two chlorides PbCl2 and PbCl4 having charges +2 and +4 respectively. PbCl4 shows covalent nature. Similarly among NaCl, Na2S, Na3P, the charge of the anions are increasing, therefore the increasing order of
Covalent character.  NaCl < Na2S < Na3P

(4) NATURE OF THE CATION: Cations with 18 electrons (s2 p6 d10) in outermost shell polarize an anion more strongly than cations of 8 electrons (s2 p6) type. The d electrons of the 18 electron shell screen the nuclear charge of the cation less effectively than the s and p electrons of the 18- electron shell. Hence the 18-electron cations behave as if they had a greater charge. Copper (I) and Silver (I) halides are more covalent in nature compared with the corresponding sodium and potassium halides although charge on the ions is the same and the sizes of the corresponding ions are similar. This illustrates the effect of 18- electron configuration of Cu+ (3s2 3p6 3d10) and Ag+ (4s2, p6, d10) ions.
ILLUSTRATIVE EXAMPLE:
The decomposition temperature of Li2CO3 is less than that of Na2CO3. Explain.
SOLUTION: As Li+ ion is smaller than Na+ ion, thus small cation (Li+) will favour more covalent character in Li2CO3 and hence it has lower decomposition temperature than that of Na2CO3.
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