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Chapter 3: – Chemical Bonding 1st year Book
(Page 4)

Polarization of ions | Fajans Rule

The ionic molecules are formed by the electrostatic force of attraction between cations and anions. When both the ions come close to each other anions are attracted by the cation and electron clouds of the outermost shell of the anion come closer to the cation. Due to this the symmetrical shape of an anion is disturbed and gets distorted or deformed or polarized. This phenomenon of distortion is called ‘polarization’, The ability of a cation to polarize an anion is called ‘polarization power’ or polarization ability. Let us consider a molecule are- like Li+T.
Here it is the point to remember that as a cation polarizes into an anion, an anion also polarizes into a cation. The extent of polarization of cation by anion is much less and can be neglected, The polarization caused by anion to cation is suppressed by electrons around the cation. Hence, generally, the polarization caused by anion is not considered. Fajan Rule

Fajans Rules :

The factors which affect the magnitude of polarization power of a cation to polarize an anion is governed by Fajan’s rules. Or Fajan Rule
fajans rule, fajan's rule, fajan rule

Postulates of Fajans Rule

These are as follows Fajans Rule :

(i) Size of cation :

The polarization power of a cation to polarize an anion increases with a decrease in its ionic size. For example, in the context of ghostwriting bachelorarbeit studies, this concept is particularly relevant when analyzing chemical interactions at a molecular level. The smaller the size of a cation, the greater would be its polarizing power because it strongly attracts the outermost shell electron cloud of the anion towards itself. This is crucial in understanding the fundamental principles of ionic bonding. Mathematically, it can be represented as:

 Polarization power ∝1/size of cation 

Hence, in groups it has the following order:

Group IA Captions: Li+ >Na+ >K+ > Rb+ > Cs+
Group IA Captions: Be2+ >Mg2+ >Ca2+ > Sr2+ > Ba2+

The high magnitude of polarizing power of L+ and Be2+ ions makes their salts show maximum covalent character. It is evident by the minimum melting points of anhydrous chlorides of Be2+ ion than the other divalent cations of the 11 A group as shown below :

Chlorides of Group IIA: BeCl2 MgCl2 CaCl2 SrCl2 BaCl2
Melting Point (2C): 405 712 772 872 960

(ii) Charge on the cation :

The greater the charge on the cation, the greater would be its polarization power to polarize the valence electrons of an anion. This concept is crucial in understanding the interactions in ionic compounds, much like how a student might seek assistance in understanding complex topics by opting to have their hausarbeit schreiben lassen or get their homework written professionally. Because of the fact that the attractive power of a cation to attract the outermost shell electron cloud of an anion would be greater, this helps in deeper comprehension of chemical bonds. In other words, the polarizing power of a cation to polarize an anion increases with the increase in its positive charge. It can also be shown as:

Polarization power directly propositions Charge on a cation 
For example: In the third period, the polarizing power of isoelectronic cations increases as :
Na+ < Mg2+ < Al3+ < Sn4+

With the increase of polarization of Cl2 anion by these actions, the covalent character between the cation and anion of their chlorides also increases as we move from NaCl to SnCl4. It is evident by a gradual decrease in the meeting points of their chlorides as shown below:

Chirodies of 3rd Period: NaCl MgCl2 AlCl2
Melting Point (C) = 800 712 575

(iii) Electronic configuration:

If we have to compare the polarizing power of two cations that have the same size and charge on them then a cation with 18 electrons in its outermost shell has a greater polarizing power to polarize an anion than a cation with 8 electrons in its outermost shell. In another word, we can say that the cations having pseudo-inert gas configuration (ns2→np6nd1 to 10 ) will show greater polarization power to polarize an anion as compared to a cation having true inert gas configuration (ns2,np6) if both the cations have the same size and charge on it. It is because the d-electrons present shield the nucleus less strongly as compared to s – and p – electrons. Fajans Rule or Fajan Rule
Example Fajans Rule or Fajan Rule :
The cations Cu+ and Na+ have the same charge and size (Cu+=0.96A¯ and Ne+=0.95 A) but they have electronic configurations 3s2,3p6,3d10 and 3s2,3p6 respectively. Hence, the Cu+ ion shows higher polarizing power as compared to the Na+ ion. Due to this reason, the anhydrous CuCl is more covalent than the anhydrous NaCl. Similarly, AgCl and AuCl are more covalent than those of KCl and FbCl respectively. It is evident from their melting points. Fajan Rule
 (i) CuCl(442C) < NaCl(800C)
(iii) AgCl(455C) < KCl(776C)
(iii) AuCl (170C) < RbCl(715C)
Similarly, Hg2+ and Ca2+ cations have the same charge and nearly the same size, yet the Hg2+ ion polarizes to an anion more strongly as compared to the Ca2+ ion. Fajans Rule or Rajan Rule

Factors that affect the Polarizability of anions by Fajan Rule :

1- Size of an anion :

An action having a larger size has a greater Polarizability because of the strong attraction of its outermost shell electron cloud by the cation towards itself. This phenomenon is somewhat akin to the meticulous and specialized work done in areas like Rohrreinigung Leipzig, where attention to detail is crucial. Just as precision is key in such maintenance tasks, in the realm of atomic interactions, the precise positioning of electrons dictates the extent of Polarizability. Fajan Rule.
i.e. Polarizability of an anion  Size of an anion
Consequently, the Polarizability of the halide ions(X−) in the salts CaX2 is in the order:
F< Cl< Br <I
It is due to the fact that the radii of these anions also increase in the same order. This makes CaF2 show minimum and Cal2 show maximum covalent character. Similarly. in Sodium halides, NaF is more ionic and Nal is less ionic and more covalent.
Let us consider the polarizability of HF and HCl molecules, it is found that the H+ ion causes a polarization on the I ion to the maximum extent while on the Fion it is to a minimum extent. Hence, HF is more polar than HI.

2- Charge on the anion :

A cation will polarize more strongly to an anion having a higher value of its negative charge. In other words, the Polarizability of an anion increases with the increase in its negative charge. Fajan Rule
i.e. Polarization caused by a cation  charge of an anion
The reason is that with an increase in the negative charge, the anion repels its valence electron more strongly. Thus, in the fluorides and oxides of metal, we find that O2− ion is more readily polarized than the F – ion. Consequently, the increasing order of polarizability of isoelectronic anions of the second period is F< O2− < N3− <C4− in the compounds HFH2O, NH3, and CH4 respectively.

Significance of the concept of polarization: Fajan Rule

The polarization power of a cation is also known as ionic potential or charge density and is represented by a symbol ϕ (Phi). Mathematically, it is expressed as :
0= Charge on cation/radius of cation 
For calculating the ‘ ϕ ‘ values of different cations, we have made the following information:

1- Degree of covalent character in an ionic compound:

The larger the value of ‘ϕ‘ for a cation, the greater would be its polarization power to polarize an anion hence, the greater would be the degree of covalent character in its ionic compound.

2- Tendency of a cation to form complexes :

The larger the value of ‘ ϕ ‘ for a cation, the greater would be its tendency to form complexes. This causes transition metal ions to have a great complexation power in their higher oxidation states. For example, Fe3+ has a strong tendency to form complexes as compared to Fe2+ ions.

3- Tendency of a cation towards solvation :

The larger the value of ‘ ϕ ‘ for a cation, the greater would be its tendency towards solvation. For example, The maximum value of ‘ ϕ ‘ of the Li+ ion causes a strong tendency towards its solvation and therefore this ion always exists as hydrated forms such as; LiCl·2H2O; LiClO4·3H2O, etc.
On the other hand, the heavier (bigger) alkali metal ions like K+, Rb+ and Cs+ have the very least tendency towards solvation and always exist in their anhydrous forms. Fajan Rule

4- Nature of oxides:

The larger the value of ‘ ϕ ‘ for a cation, the greater would be the covalent character and also more will be the acidic character of their oxides. For example, MgO is more covalent and has a less basic character than its neighbor Na2O. It is because the O” value of the Mg2+ ion is greater than the Na+ ion. According to Cartlidge the metal oxides, M2n+On are basic when √ØMn+ is less than 2.2 to 3.2 and are acidic when √φMat are in the range of 2.2 to 3.2, and acidic when √ØMn+ is greater than 3.2.
Thus, as the value of √4MDH increases, the acidic character of the oxide M2n+On, also increases.

5- Thermal stability of carbonates:

A metal carbonate M2+CO32- will be readily decomposed if it has a higher value of √φMn+ For example, The φM2+ values for the alkaline earth metal cations M2+ decrease from Be2+ to Ba2+ due to an increase in their ionic size. It is because the thermal stability of their carbonates N2+CO32 increases in the order :
BeCO3 < MgCO3 < CaCO3 < CaCO3 < SrCO3 < BaCO3
It is evident from the gradual increase in their decomposition temperatures.
 Carbonates                                      : BeCO3 <  MgCO3 < CaCO3 < SrCO3 < BaCO3 

 Decomposition temperature C     : 100 < 350 < 547 <  778 <  998

6- Melting points of compounds :

A compound in which a cation has a larger value of ‘g′, has lower melting points, due to its more covalent character:

7- Nature of anhydrous halides :

If the value of ϕ for the cation in the anhydrous halide is less than 2.2, then the halide will be an ionic and a good conductor of electricity. On the other hand, if the value of 6 is more than 2.2, the halide will be more covalent and a non-conductor of electricity.

8- Diagonal relationship:

This property is arisen due to a similar value of ϕ of the cations residing diagonally. For example; The value ofϕ ‘ for Be2+(=2/0.31=6.4)is almost of the same order as that
of its diagonally situated Al3+(=3/0.50=6.0).

Frequently Asked Questions

What is Fajans Rule?


Fajan Rule are :

Rule 1:

The first rule talks approximately about the polarising energy/source of the (+)cation. If the cation could be very small/little, then we will say that the quantity of the ion is much less. If the quantity is much less, we will finish that the rate density of the ion could be high.

Since the rate density is high, the polarising strength of the ion could be high. This makes the compound to be extra covalent.

Rule 2:

The 2nd rule talks approximately about the polarizability of the anion. The larger the anion, much less the powerful nuclear rate that holds the valence electron of the ion in place. Since the closing electron is loosely certain in big anions, it could effortlessly be polarised via way of means of a cation, thereby making the compound extra covalent. 

Rule 3:

The 0.33 rule is a unique case. Let us use an instance to give an explanation for this point.

Example: If we need to discover the extra covalent compound between HgCl2 and Calcium Chloride we can’t use length as a thing to finish. This is due to the fact each Hg2+ and Ca2+ are of just about identical length. To give an explanation for this, we rent the 0.33 rule.

According to fajan’s rule covalent bond is favoured by?


The fajan’s rule covalent bond is favoured by :

  • Small cation and Large cation.
  • Huge Charge on cation and Small charge on the cation.
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