Electronegativity scales — Pauling, Mulliken comparison and applications

Question

Compare the Pauling and Mulliken scales of electronegativity. How is electronegativity used to predict bond polarity and the percentage ionic character of a bond? If the electronegativity difference between H and Cl is 0.9 (Pauling scale), what can we conclude about the HCl bond?

(JEE Main + CBSE 11 pattern)

Solution — Step by Step

Pauling defined electronegativity based on bond energies. The extra bond energy of A-B compared to the average of A-A and B-B bonds is attributed to the ionic character:

\chi_A - \chi_B = 0.208\sqrt{\Delta E}

where $\Delta E$ is the extra bond energy in kcal/mol.

Pauling assigned F = 4.0 (most electronegative) as the reference. Values range from Cs = 0.7 to F = 4.0.

Mulliken defined electronegativity as the average of ionisation energy (IE) and electron affinity (EA):

\chi_M = \frac{IE + EA}{2}

This makes physical sense: electronegativity measures both the ability to hold electrons (high IE) and attract new ones (high EA). Mulliken values are in energy units and can be converted to Pauling scale: $\chi_P \approx 0.336(\chi_M - 0.615)$ .

$\Delta\chi = \chi_{Cl} - \chi_H = 3.0 - 2.1 = 0.9$

Rules for bond character:

$\Delta\chi = 0$ : purely covalent
$0 < \Delta\chi < 1.7$ : polar covalent
$\Delta\chi > 1.7$ : predominantly ionic

Since 0.9 falls in the polar covalent range, HCl has a polar covalent bond with partial charges: $\text{H}^{\delta+}\text{Cl}^{\delta-}$ .

Percentage ionic character can be estimated using Hannay-Smith equation:

\% \text{ionic} = 16(\Delta\chi) + 3.5(\Delta\chi)^2 = 16(0.9) + 3.5(0.81) = 14.4 + 2.835 \approx \mathbf{17\%}

flowchart TD
    A["Electronegativity Scales"] --> B["Pauling: based on bond energies"]
    A --> C["Mulliken: (IE + EA)/2"]
    D["Applications"] --> E{"Δχ value?"}
    E -->|"Δχ = 0"| F["Pure covalent"]
    E -->|"0 < Δχ < 1.7"| G["Polar covalent"]
    E -->|"Δχ > 1.7"| H["Predominantly ionic"]
    G --> I["Higher Δχ → more polar"]
    B --> J["Reference: F = 4.0"]
    C --> K["Can convert to Pauling scale"]

Why This Works

Electronegativity quantifies an atom’s tendency to attract shared electrons in a bond. It is not a property of an isolated atom (unlike IE and EA) — it depends on the bonding context. This is why Pauling’s definition uses bond energies: it directly measures the unequal sharing of electrons in a bond.

When two atoms with different electronegativities bond, the shared electrons spend more time near the more electronegative atom. This creates a dipole moment ( $\mu = q \times d$ ). The larger the electronegativity difference, the larger the dipole, and the more ionic character the bond has.

Alternative Method — Allred-Rochow Scale

A third scale defines electronegativity based on the electrostatic force experienced by bonding electrons:

\chi_{AR} = \frac{0.359 \times Z_{eff}}{r^2} + 0.744

where $Z_{eff}$ is the effective nuclear charge and $r$ is the covalent radius in Angstroms. This has a clear physical interpretation: more nuclear pull on bonding electrons = higher electronegativity.

For JEE, the Pauling scale is most commonly used. Memorise the electronegativity order across Period 2: Li (1.0) < Be (1.5) < B (2.0) < C (2.5) < N (3.0) < O (3.5) < F (4.0). Down a group, electronegativity decreases: F > Cl > Br > I. These trends follow directly from atomic size and nuclear charge.

Common Mistake

Students confuse electronegativity with electron affinity. Electron affinity is a measurable property of an isolated atom (energy released when adding one electron). Electronegativity is a relative scale describing the tendency to attract electrons in a BOND — it cannot be directly measured for an isolated atom. Noble gases have electron affinity values but are generally not assigned electronegativity values because they rarely form bonds.

Question

Solution — Step by Step

Why This Works

Alternative Method — Allred-Rochow Scale

Common Mistake

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