Pauling’s scale is based on an empirical relation between the energy of a bond and the electro negativities of bonded atoms.
Consider a bond A-B between two dissimilar atoms A and B of a molecule AB. Let the bond energies of A-A, B-B and A-B bonds be represented as EA-A, EB-B and EA-B respectively. It may be seen that the bond dissociation energy of A-B is almost higher than the geometric mean of the bond dissociation energies of A-A and B-B bonds i.e.,
EA-B ≥ √( EA-A * EB-B)
Their difference (Δ) is related to the difference in the electro negativities of A and B according to the following equation
Δ = EA-B – √( EA-A * EB-B)
= (XA – XB)2
A B = (X −X )
(or) 0.208 √Δ = XA – XB
Here, XA and XB are the electronegativities of A and B respectively.
The factor 0.208 arises from the conversion of Kcals to electron volt.
Considering arbitarily the electro negativity of hydrogen to be 2.1, Pauling calculated electro negativities of other elements with the help of this equation.
Disadvantage of Pauling scale
The disadvantage of Pauling’s scale is that bond energies are not known with any degree of accuracy for many solid elements.