FAJAN'S RULE, Ionic compounds

POLARIZING POWER AND POLARIZABILITY (FAJAN'S RULE)

An anions of large size has electron cloud which is less tightly held by nuclus and it is easy for small size cations to distort the electron cloud towards itself and electron density increases between the nuclei is called polarization. Here the power of an ion to distort the other ion is called polarizing power and the tendency of the anion to be distorted is called polarizability.

Fajan's rules point out the factors that favours polarisation and hence covalency. Following are the rules:

1. Small positive ion : The cation with small size have high polarising power because of the concentration of positive charge in small space. For example, BeCl₂and CaCl₂have identical charge on cation but BeCl₂is more covalent than CaCl₂because of smaller size of Be²⁺in comparison with Ca²⁺.
2. Large negative ion : The large anions contains electron cloud which is less strongly held by its nucleus and it is easy for positive ion to distort or polarised it. Example. the covalent character increases from LiF to LiI because the size of anion increases from F^-to I^-. This increases the polarizibility which ultimately increases the covalency.
3. Presence of high charge on either cation or anion or on both: Increase in charge in both cation and anion increases polarising power. For example Na⁺and Ca⁺⁺have almost similar ionic radii but CaCl₂have high covalency than NaCl as higher charge is present on Ca²⁺.
4. Polarisation is favoured by incomplete valence shell configuration than noble gas configuration (ns²np⁶): Due to better shielding effect on noble gas configuration it is less polarised than incomplete configuration. For example, CuCl is more covalent and NaCl is ionic because Cu⁺has greater polarising power than Na⁺.

Dipole moment

The measure of polarity of covalent molecule in terms of magnitude of electric charge in esu and distance between positive and negative charges in angstorm (A⁰) is called dipole moment.

i.e.μ = e\(\times\) d

Since the charge e is of the order of 10^-10esu and d is of the order of 10^-18esu.cm. This unit is called Debye and is represent by 'D'.

Dipole moment is important bacause it can give an idea about the polar character of a molecule. it is a vector quantity. It is represented by arrow with a crossed tial (\(\longmapsto\)). The arrow point to negative charge from positive charge.

Thus molecule of HCl may be represented as

H⁺ \(\longmapsto\) Cl^-

The shape of the molecule affect the dipole moment. For example, in case of carbondioxide (CO₂) and water (H₂O). CO₂has a linear shape and the dipole moment of CO of one side is cancelled by other side of the molecule giving zero dipole moment. In case of H₂O, its structure is bent and the angle between two O-H bond is 104.27 and the dipole moment is found to be 1.84 D.

Also in case of BF₃, there is sp²hybridisation the structure is trigonal planar so the dipole moment is not zero.

Percentage ionic character from dipole moments and electro negativity differences

1. Electronegativity difference and percentage of ionic character:If the electronegativity difference is same between two bonding atoms then it is called covalent bond.However, increase in electronegativity difference between two atom increases the polarity of the bond and it is called polar covalent bond. Some empirical equations have been proposed to calculate the % of ionic character of a covalent bond from the electronegaritivities of the bonding atoms. Two of them are:

The Pauling equation

Pauling derived the following equation for determining the percentage of ionic character of a covalent bond,

% of ionic character = [1 - e^{1/4 (\(\chi_A\) - \(\chi_B\))}]

Where \(\chi_A\) and \(\chi_B\) are the electronegativities of A and B.

The Hannay- Smith-equation

Hannay - Smith proposed the following equation

% of the ionic character = 16 (\(\chi_A\) - \(\chi_B\)) + 3.5(\(\chi_A\) - \(\chi_B\))²

2. Dipole moment and percentage of ionic character: Percentage of ionic charcater can be calculated as:

% ionic character = \(\frac{actual dipole moment}{Theoretical dipole moment (dipole moment of pure ionic compound)}\)

Ionic compounds of type AX (NaCl, CsCl, ZnS)

Structure of sodium chloride (NaCl)

The radius ratio for sodium chloride, NaCl, is 0.52 which points towards the octahedral arrangement. Each Na⁺ion is surrounded by six Cl^-ions at the corners of a regular tetrahdron and similarly each Cl^-ion is surrounded by six Na⁺ions. The coordination is thus 6:6. This structure may be regarded as a cubic close-packed array of Cl^-ions, with Na⁺ions occupying all the octahedral holes.

Structure of CsCl

The radius ratio of CsCl is 0.93 which suggests that body-centred cubic type of arrangement, where each Cs⁺ion is surrounded by eight Cl^-ions, and vice-versa. The coordination thus present is 8:8. It should be noted that this structure is not closed packed, and is not strictly body-centred.

In a body-centred cubic arrangement, the atom at the centre of the cube is identical to those at the corners. This sturcture is found in metals, but in CsCl if the ions at the corners are Cl^-then there will be a Cs⁺ion at the body-centred position, so it is not strictly body-centred cubic. Therefore, the structure of CsCl should described both as body-centred and non body-centred cubic.

Structure of ZnS

The radius ratio of zinc sulphide is 0.40 which indicates the tetrahedral arrangement. Each Zn²⁺ion is tetrahedrally surrounded by four S^2-ions and each S^2-is tetrahedrally surrounded by four Zn²⁺ions. The coordination number of both ions is 4, so this is called a 4:4 structures.

Both the structures may be considered as close-packed arrangements of S^--ions. Zinc blende is related to a cubic close-packed structure while wurtzite is related to a hexagonal close-packed structure. In both structures the Zn²⁺occupy tetrahedral holes in the lattice. Since the number of tetrahedral holes are twice than that of S^2-ions, it follows that to obtain a formula ZnS only half of the tetrahedral holes are occupied by Zn²⁺ions.