Polarity of Bonds

Polarity of Bonds

A chemical bond is formed when two atoms share a pair of electrons. But what happens when the two atoms are different? Do they pull on the shared electrons with equal strength? The answer is no — and this unequal tug-of-war is the root of bond polarity.

The Concept of Electronegativity

Electronegativity is the measure of the tendency of an atom in a molecule to attract the shared pair of electrons towards itself. It is a relative property — we compare atoms to each other. The most commonly used scale is the Pauling scale, where fluorine (the most electronegative element) is assigned a value of 4.0.

When two atoms of the same element bond (like H–H or Cl–Cl), they have identical electronegativities. The shared electron pair is pulled equally by both nuclei. The bond is non-polar — the electron cloud is symmetrically distributed, and there is no separation of charge.

When two different atoms bond, the atom with higher electronegativity pulls the shared electrons closer to itself. This creates an uneven distribution of charge: the more electronegative atom acquires a partial negative charge (δ–), and the less electronegative atom acquires a partial positive charge (δ+). The bond is now polar.

Dipole Moment — A Quantitative Measure of Polarity

The extent of polarity in a bond is measured by a quantity called the dipole moment. It is defined as the product of the magnitude of the charge (q) and the distance (d) between the two charge centres.

Here, μ (the Greek letter mu) is the dipole moment, q is the charge (in coulombs, C), and d is the distance (in metres, m). The dipole moment is a vector quantity — it has both magnitude and direction. By convention, the direction of the dipole moment is from the positive end towards the negative end (or, in some notations, from δ+ to δ–).

The SI unit of dipole moment is the coulomb-metre (C m). However, for molecular-scale measurements, a more convenient unit is the Debye (D), named after the physicist Peter Debye.

For example, the dipole moment of hydrogen chloride (HCl) is 1.07 D. This tells us that the H–Cl bond is significantly polar — chlorine is more electronegative than hydrogen, so the electron pair is shifted towards Cl, giving H a δ+ and Cl a δ–.

The Crossed-Arrow Convention

In chemistry a bond dipole is drawn as a crossed arrow ($\times\!\!-\!\!\rightarrow$) laid along the bond: the cross sits on the $\delta^+$ end and the arrowhead points at the $\delta^-$ end, so the symbol pictures the electron shift — in HF the arrow runs from H towards F.

Cancellation in BeF$_2$ and BF$_3$

In linear BeF$_2$ the two Be–F bond dipoles are equal and point in opposite directions, summing to zero. In trigonal planar BF$_3$ the three B–F dipoles at $120^\circ$ likewise add vectorially to zero. Symmetric geometry, not absent bond polarity, is what makes such molecules nonpolar.

The Marquee Comparison — NH$_3$ versus NF$_3$

Both molecules are trigonal pyramidal with a lone pair on nitrogen, yet $\mu(\text{NH}_3) = 4.90 \times 10^{-30}$ C m while $\mu(\text{NF}_3)$ is only $0.80 \times 10^{-30}$ C m. In NH$_3$ the orbital dipole of the lone pair points the same way as the resultant of the N–H bond dipoles and reinforces it; in NF$_3$ the N–F bond dipoles point toward the highly electronegative fluorines, opposing the lone-pair dipole. Partial cancellation leaves NF$_3$ with the much smaller moment.

Water's Net Dipole

Bent H$_2$O adds its two O–H bond dipoles at $104.5^\circ$ to a resultant of $6.17 \times 10^{-30}$ C m — i.e. 1.85 D, the value in Table 4.5.

How Dipole Moment Reveals Molecular Geometry

The dipole moment is not just about individual bonds — it is a molecular property. A molecule may contain several polar bonds, yet its overall dipole moment could be zero. This happens when the bond dipoles are arranged symmetrically and cancel each other out.

Consider carbon dioxide, CO₂. Each C=O bond is polar (oxygen is more electronegative than carbon). But the molecule is linear: O=C=O. The two bond dipoles point in opposite directions — one from C to O on the left, and one from C to O on the right. They are equal in magnitude but opposite in direction, so they cancel. The net dipole moment of CO₂ is zero. This tells us that CO₂ is a linear molecule.

Now consider water, H₂O. The O–H bonds are polar. If water were linear (H–O–H), the two bond dipoles would cancel, and the net dipole moment would be zero. But experimentally, water has a dipole moment of 1.85 D. This can only happen if the molecule is bent — the two bond dipoles do not point in opposite directions; they add up vectorially to give a net dipole. The measured dipole moment confirms that water has a bent shape with a bond angle of about 104.5°.

Percentage Ionic Character

No bond is 100% ionic or 100% covalent — there is always some degree of sharing. The dipole moment gives us a way to estimate how ionic a bond is.

If a bond were completely ionic (say, H⁺ Cl⁻ with full unit charges separated by the bond length), we could calculate the theoretical dipole moment using μ = q × d, where q is the charge of an electron (1.602 × 10⁻¹⁹ C) and d is the bond length. For HCl, the bond length is 1.27 Å (1.27 × 10⁻¹⁰ m). The theoretical dipole moment for a fully ionic H–Cl bond would be:

Converting to Debye:

But the actual dipole moment of HCl is only 1.07 D. The ratio of the actual dipole moment to the theoretical ionic dipole moment gives the percentage ionic character:

For HCl:

This means that the H–Cl bond is about 17.6% ionic and roughly 82% covalent. In other words, the electron pair is not fully transferred to chlorine — it is shared, but with a strong bias towards chlorine.