# Pauling Scale: How to Use it to Calculate Electronegativity?

Electronegativity is an atom’s tendency to attract a shared pair of electrons in a bond. In 1955, an American scientist Linus Pauling, who was awarded the Noble prize for both science and peace, described this phenomenon. He deduced the electronegativity of an atom is the property of a nucleus of an atom in a bond. He stated that when a bond is formed, the ability of an atom to attract this shared pair of electrons can be calculated by using its bond dissociation enthalpy. He calculated electronegativities of different elements and its tabulated form is known as the Pauling scale.

The electronegativities calculated are arranged in ascending order to set up a scale known as the Pauling scale of electronegativity. This scale starts from 0.79 for strontium element to the maximum value of 4.0 for fluorine. Initially, hydrogen 2.1 was taken as a reference and changed to 2.2 after experimental corrections.

Significance

Pauling used Bond enthalpies to calculate electronegativity that chemists easily understood. Bond dissociation enthalpies are related with evaluate the power of an atom in a bond to attract electron pairs. Bond energies are distinct to every element and dependent upon the pull of nuclei in the bond. Moreover, the values given by the Pauling scale are dimensionless.

## The concept behind Pauling’s method

Puling’s method is based upon the bond energies of atoms. It is to be noted that the geometric mean of bond energies of atoms with themselves is lesser than the bond energies of different atoms. In other words, the bond present between two similar atoms has a bond energy of EA-A, and the other two atoms EB-B is always less than EA-B. The additional energy leads to ionic resonance.

𝜓AB = a𝜓A-B+ b𝜓A+B + c𝜓AB+  →  (i)

The above equation illustrates the possible interaction during bond formation. If a molecule is made up of identical atoms, is equal to ‘c’ and always significantly less than the ‘a’. The first component shows the pure covalent nature of the bond as if the bond is in a nonionic state. Hence it has more contribution. The second component is the state when electron density is present at B. Similarly, the 3rd one represents the possibility when the electron is near atom A.

For example, the bond dissociation enthalpies of similar bonds i.e H-H and Cl-Cl. on the other hand, H-Cl is considered to calculate the electronegativity difference between hydrogen and chloride. The bond dissociation enthalpy of HCl is greater than that of either H2 or Cl2. The stability of a molecule formed by the atoms of different electronegativity is due to the ionic resonance energy.

The equation (i) shows the wave function of the bond A-B is the sum of three different states. The number of possible structures or canonical forms leads toward stability.

## Calculation of electronegativity by Pauling method

How Pauling calculated electronegativities using bond energies of covalent bonds of similar atoms and different atoms is explained with the help of an example below.

Chlorine reacts with fluorine as,

Cl-Cl + F-F → 2Cl-F

Bond enthalpy of F2= EA-A =158kJ/mol

Bond enthalpy of Cl2= EB-B = 242kJ/mol

Bond enthalpy of = EA-B= 255 kJ/mol

Pauling equation of electronegativity

𝝌A-𝝌B 1/2

𝝌A-𝝌B = (√(EA-B-{EA-A+EB-B}/2)eV-1/2

Where,

“𝝌A is the electronegativity of fluorine

“𝝌B is the electronegativity of chlorine

“Δ”  is the difference between experimental and actual bond dissociation energy

To calculate (EA-A+EB-B )/2

(242 + 152)/2

= 200 kJ/mol → (iii)

By putting the values in equation (ii)

𝝌A-𝝌B = √(255-200)

= √55

Since energy units are in KJ converted into eV by dividing 96.5

=  √(55/96.5)

𝝌A-𝝌B= 0.76

So the range of electronegativities can be easily calculated by using this equation.

## Limitations of the Pauling scale

Inaccurate bond energies of various solid compounds

In the Pauling scale, electronegativity is highly dependent upon bond energy. Therefore, bond energy accuracy is inevitable. Elements found in solid-state sometimes have inaccurate bond energies so we could not calculate their electronegativity with the required precision using this scale.

Reactivity of fluorine

Among halogens, fluorine is the most reactive element, this is due to the minimum bond dissociation energy of F−F bond dissociation energy. Furthermore, fluorine has a peculiar behavior because it is present at the top of the group, and it differs hilariously from other members.​ Hence, It is not suitable for absolute maximum electronegativity.

Hydrogen as a reference

A reference or primary standard should have a fixed value of bond energies but hydrogen forms hydrides and protic compounds e.g mineral acids.

## Other methods to calculate electronegativity

Allred and Rochow

This method is more likely to use as an alternative method. It uses electron densities of both atoms to deduce electronegativity. It can be easily applied on more than 2 no of involved atoms.

The electron density is attracted towards an atom in a chemical bond. It depends upon the charge on the effective nuclear charge(Z*). By coulombs law, the force of attraction is given by

Force = (Z*e)(e)/4πεo

The final equation, adjusted to calculate electronegativity is as follows,

𝝌= 0.359 (Z*/r2) + 0.744

Where,

• Z* is the effective nuclear charge
• r is the distance between electron pair and nucleus of the atom

Allen’s Scale

It is the most recent scale devised to calculate electronegativity. L.C Allen used spectroscopy for the measurements. The ionization enthalpies of s and p orbitals electrons of an atom are calculated through high-resolution spectroscopies.

Allen’s equation of spectroscopic electronegativity is given by

𝝌spec = (m∈p+n∈s)/(m+n)

where,

• m and n are the number of electrons in p and s orbitals
• ands are the averages of ionization enthalpies in different multiplicities

## Concepts Berg

How is electronegativity measured by Pauling?

Electronegativity was measured by Pauling by calculating the geometric mean of energies of both atoms involved.

What is the validity of the Pauling scale of electronegativity?

The Pauling scale is the most widely used method used till date. It is applicable for elements of periods 1 and 2 i.e for the first 25 elements. It depends upon the resonance of the bond pair of electrons between two nuclei. Therefore, the bond energy becomes complex to calculate for higher members of the periodic table.

What is the Mulliken scale of electronegativity?

According to Mulliken, the electronegativity of an atom can be measured by calculating its electron affinity and ionization enthalpy. Though electron attachment enthalpies were not available so a complete-scale can not be formed.

What is the Sanderson scale of electronegativity?

It is the scale for the measurement of electronegativity based on the volume of the atom.

What is the electronegativity of chlorine?

The electronegativity of the chlorine 3.0 at the Pauling scale.

What is the highest electronegativity value?

Fluorine is considered the atom with the highest electronegativity due to the following reasons.

1. Charge density
2. Shielding effect

What is phosphorus electronegativity?

On the Pauling scale, the electronegativity of phosphorus is 1.5.

Why are C-H bonds considered nonpolar?

The electronegativity difference between carbon and hydrogen is only 0.2. If the electronegativity difference is 0.0 to 0.4 the bond would be nonpolar.

Why do smaller atoms have higher electronegativity?

The smaller atoms with greater nuclear charge have more tendency to attract the shared pair of electrons in a bond. This is due to the more negligible shielding effect and shorter distance between electron and nucleus.

Reference books

• General Chemistry Principles and Structure | Third edition, by James E. Brandy (St. John’s University, Jamaica, New York) and Gerard E. Humiston (Widener University, West Chester, Pennsylvania) – [SI version, Prepared by Henry Heikkinen (University of Maryland, USA)]