Lesson 4 · 25 min

Bond polarity and electronegativity

A shared pair is not always shared equally. The electronegativity difference decides which way the electron cloud leans and how far — from H–H to Cs–F, covalent and ionic are ends of one continuum.

In this lesson

Say what electronegativity means and read its trends across the periodic table
Judge bond polarity from the electronegativity difference and mark the partial charges δ+ and δ−
Compute a bond’s ionic character from its dipole moment and length, and compare with Pauling’s empirical formula
Explain why ionic and covalent bonds are two ends of one continuum

In 1932 Linus Pauling noticed something odd. The H–H bond energy is 436 kJ/mol and F–F is 159 kJ/mol; if H–F were “in between”, it should be near 263 kJ/mol (their geometric mean). Yet H–F measures 570 kJ/mol — over 300 kJ/mol more. Where does the extra come from? Pauling’s answer: fluorine pulls the shared electrons harder than hydrogen does, the electron cloud leans toward fluorine, and the bond picks up some ionic character — an extra attraction between opposite charges that strengthens it. From this he defined one of chemistry’s most used numbers: electronegativity.

Predict first

The electronegativity difference in HF is 1.78. Judging from its measured dipole moment, roughly what fraction of an electron does the hydrogen end effectively lose?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

0: the pair is shared equally About 0.4 About 0.9 A whole 1: HF is ionic

Electronegativity: how hard an atom pulls on a shared pair

Electronegativity measures how strongly an atom attracts the shared electrons in a bond. On Pauling’s scale fluorine is highest (3.98) and caesium and francium lowest (about 0.7–0.8). Across the periodic table it rises from left to right (higher effective nuclear charge, smaller atoms) and falls down each group (valence electrons further from the nucleus).

The difference ΔEN between two atoms decides which way the shared electrons lean, and how far. The more electronegative end carries a partial negative charge δ−, the other end δ+; such a bond is polar and has a bond dipole, drawn as an arrow with a “+” tail pointing from δ+ to δ−. The dipole moment is charge times distance, usually quoted in debye (D).

|\chi_\mathrm{A} - \chi_\mathrm{B}| = 0.102\sqrt{E_\mathrm{AB} - \sqrt{E_\mathrm{AA}\,E_\mathrm{BB}}}

Pauling defined electronegativity differences from bond energies (in kJ/mol). For H–F:

0.102\sqrt{570 - 263} = 1.79

, almost exactly the tabulated 1.78.

$\chi_\mathrm{A},\ \chi_\mathrm{B}$: electronegativities of the two atoms
$E_\mathrm{AB}$: bond energy of A–B
$\sqrt{E_\mathrm{AA}E_\mathrm{BB}}$: geometric mean of A–A and B–B: roughly what a purely covalent A–B bond would have

Electronegativity difference · partial charge · ionic character

Bond polarity probe

Main-group elements (numbers: Pauling electronegativity)

Where the bonding pair sits

Difference ΔEN: 2.23
Ionic character (Pauling, empirical): 71%
Rough class: Mostly ionic
Measured dipole moment: 8.97 D
Ionic character from the measured dipole: 79%

Pauling’s formula gives 71 %; the measured dipole gives 79 %.

Covalent to ionic is a continuum

Ionic character versus ΔEN

Pauling’s formula 1 − e^(−ΔEN²/4)
From measured dipoles (gas-phase molecules)

Pick “Atom A” or “Atom B”, then choose an element in the table. Work through H–H, C–H, H–Cl, H–F, Na–Cl and Cs–F: watch the electron cloud lean further and further. Then try Li–I and C–O and read the notes that appear.

Ionic character: from dipole moments to a continuum

If a bond were completely ionic, each end would carry a full charge $e$ and the dipole moment would be $e \cdot r$ . Dividing the measured dipole by that value gives the bond’s ionic character. Pauling also offered an empirical formula that needs only the electronegativity difference. The table puts the two estimates side by side: they broadly agree but are not equal — the empirical value is too high for HF and too low for NaCl.

f_\mathrm{ion} = \frac{\mu}{e\,r_\mathrm{e}},\qquad f_\mathrm{ion} \approx 1 - e^{-(\Delta\chi)^2/4}

Two ways to estimate ionic character: the left uses the measured dipole moment and bond length, the right (Pauling’s empirical formula) only the electronegativity difference. Both are models.

$f_\mathrm{ion}$: ionic character: 0 purely covalent, 1 fully ionic
$\mu$: measured dipole moment (1 D = 3.336 × 10⁻³⁰ C·m)
$e$: elementary charge
$r_\mathrm{e}$: bond length
$\Delta\chi$: electronegativity difference

Ionic character (%) of gas-phase diatomics: Pauling’s formula versus the value from the dipole moment
Bond	ΔEN	Pauling formula	From dipole moment
H–I	0.46	5	6
H–Br	0.76	13	12
H–Cl	0.96	21	18
H–F	1.78	55	41
Na–Cl	2.23	71	79
Li–F	3.00	89	84

Source: Pauling electronegativities (PubChem); dipole moments from NIST CCCBDB and the CRC Handbook; bond lengths from Huber & Herzberg (NIST WebBook). Values computed by the site’s bond-polarity kernel.

Worked example

The ionic character of HBr

HBr has a dipole moment of 0.827 D and a bond length of 141.4 pm. Find its ionic character and compare with Pauling’s formula (Br 2.96, H 2.20).

Concept check

Which of these bonds is the most polar?

C–H N–H O–H S–H

Try the calculation

What is the electronegativity difference of a C–O bond? (C 2.55, O 3.44)

Key takeaways

Electronegativity measures an atom’s pull on shared electrons: it rises across a period, falls down a group, and peaks at fluorine.
The larger ΔEN, the more polar the bond; the more electronegative end is δ−, and the bond dipole points from δ+ to δ−.
Ionic character can be estimated from the dipole moment (μ/er) or from Pauling’s formula; the two agree only roughly.
From H–H to Cs–F, covalent and ionic form one continuum; ΔEN cut-offs are only rough guides.

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Data and references

L. Pauling, “The nature of the chemical bond. IV.”, J. Am. Chem. Soc. 54, 3570 (1932); L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell University Press, 1960).
PubChem Periodic Table of Elements (Pauling electronegativities), National Center for Biotechnology Information.
NIST Computational Chemistry Comparison and Benchmark Database (CCCBDB), Release 22 (2022): experimental dipole moments.
K. P. Huber, G. Herzberg, Constants of Diatomic Molecules (1979), via the NIST Chemistry WebBook (bond lengths).