# Polarisability

### Polarisability

#### Lessons

In this lesson, we will learn:

• To understand why theoretical and experimental values for lattice energy are different.
• To explain how polarization leads to ionic bonds with covalent character.
• To understand the factors that affect the polarizability of anions in an ionic compound.
Notes:

• When we calculate lattice energy for a compound, there is an issue to deal with. We can get two different values depending on how we find it.
• An experimental value that comes from Born-Haber cycles, calculated using enthalpy data (e.g. $\triangle H$f , ionization energy, atomization enthalpy) taken from experiments.
• A theoretical value which comes from electrostatic theory that explains how charges interact (Coulombic attraction).

If these values are different, then the theory does not describe the real ‘ionic’ lattice with 100% accuracy. This is because the bonding in the lattice is not 100% ionic!

• When we describe ionic bonding, the ions are often shown:
• Shaped like perfect spheres (or point charges) and
• Not making contact with each other.
However, depending on size and charge of the cation, it can polarize the anion and distort its electron cloud. This gives the bond some covalent bond character as the anion’s negative charge begins to be shared with the cation, just like in a covalent bond. With this, it’s better to think of bonding as a scale, from completely ionic to completely covalent, not a yes or no covalent or ionic compound.
• Remember, the cation polarises and the anion gets polarised, not the other way around!
See the image below; the second diagram shows a negative ion being distorted by the positive ion and their electron cloud beginning to be shared.

There are two properties to know:
• Polarising power: This is the ability of the cation to distort the anion’s electron cloud. This makes the bond more covalent in character and two factors make this effect stronger:
• Charge: the larger the charge, the more polarising the cation will be to any nearby negative ions.
• Ionic radius: the smaller the ionic radius, the higher the charge density which makes the cation’s polarising effect stronger.
To give examples, lithium has much greater polarising power than caesium. This would make lithium chloride (LiCl) much more covalent in nature than caesium chloride (CsCl) because lithium can polarise the chloride electron cloud much more than caesium can, creating a bond more covalent in nature.
• Polarisability: This is how easily the anion has its electron cloud distorted. More distortion creates a bond with more covalent character. Polarisability is affected by:
• Ionic radius: the larger the ionic radius, the greater the polarisability of an ion because electrons are held further from the positive nucleus they’re attracted to.
For example, iodide is more polarisable than fluoride. Iodide is larger, and its charge density much lower, so it is polarised more easily than fluoride which holds its electron cloud extremely tightly. This makes lithium iodide more covalent in nature than lithium fluoride.
The factors that affect these properties are both tied in with electronegativity – a quick guide to “how covalent this ionic compound is” is checking the difference in electronegativity! The smaller the gap, the more covalent in nature the bonding will be.

• This covalent character is seen in the difference between theoretical and experimental values for lattice enthalpy. The theory assumes perfect ionic bonding – the experimental reality, with covalent character, increases the lattice enthalpy. The gap between the two values follows a pattern with the gap in electronegativity between the two given ions in a compound - a gap in electronegativity is what drives ionic bonding in the first place!
• Introduction
Polarisability
a)
Lattice energy: Experiment vs theory.

b)
Ionic bonding with covalent character.

c)
Factors that affect polarisability and covalent character