A polar bond is not a polar molecule: carbon dioxide against water

Where a polar bond comes from

In a covalent bond two atoms share a pair of electrons, and the two need not pull on that pair equally hard. The difference between them is described by electronegativity, an atom’s power, relative to other atoms, to draw the electrons of a bond towards itself. Its scale and values are set out in chemical bonding; here only the comparison between the two atoms of one bond matters.

When those two atoms differ in electronegativity, the more electronegative one attracts the shared pair more strongly, and the electrons are not shared equally. The pair sits nearer that atom. Such a bond is a polar bond: its centre of negative charge no longer lies at the same point as its own centre of positive charge. This is a statement about one bond only; the molecule around it is a separate question.

The shift leaves each end of the bond slightly charged. The more electronegative end carries a partial negative charge, written δ−, and the other end a partial positive charge, written δ+. Between two identical atoms the pull is the same from both sides. The pair is then shared exactly evenly, both charge centres fall halfway between the nuclei, and the bond is not polar.

The bond dipole: a size and a direction

A separation of electric charge is called an electric dipole, and a polar bond is one: a δ+ end and a δ− end, one bond length apart. The dipole of a single bond is its bond dipole. Its size is the charge displaced multiplied by the bond length, so it grows with the charge shifted and with the distance between the two ends. Two identical atoms displace no charge, so their bond has no bond dipole.

A bond dipole also has a direction. It is drawn as an arrow along the bond, with its head at the negative end. That makes it a vector, a quantity with both a size and a direction. Two bond dipoles of equal size can therefore still differ, because they can point different ways.

In a molecule of only two atoms there is a single bond, and its bond dipole is the whole story, since nothing else is present to combine with it. In a two-atom molecule such as hydrogen chloride, whatever bond dipole its one bond has is the molecule’s whole charge separation. A molecule with two or more polar bonds carries several arrows at once, and they have to be combined.

One arrow for the whole molecule

Being vectors, bond dipoles combine by size and direction together, so the result depends on the geometry of the molecule. Two arrows that meet at an angle, rather than lying along one line, do not cancel; their combination still points somewhere. Two arrows of the same size pointing in exactly opposite directions cancel, and nothing is left. The same two polar bonds can therefore leave a molecule with a charge separation or with none.

That combined arrow is the molecular dipole moment: the vector combination of a molecule’s bond dipoles, one dipole for the whole molecule. Lone pairs, pairs of outer electrons on an atom that take part in no bond, can contribute to it as well, as water’s do. Polar bonds may give a molecule a dipole moment, but they need not. It is not uncommon for a molecule built from polar bonds to have no dipole moment at all.

The two outcomes have names. A polar molecule is one whose dipole moment is not zero; it acts as an electric dipole and can interact with an electric field. A nonpolar molecule is one whose dipole moment is zero. The molecule of nitrogen, N₂, is nonpolar because its one bond joins identical atoms and has no bond dipole. Carbon dioxide is nonpolar although each of its bonds has one.

Dipole moments are measured. Between two oppositely charged plates, polar molecules tend to line up along the field, the orientation that lowers their potential energy. The capacitance of the gas or solution then gives the dipole moment’s size.

Carbon dioxide against water

Carbon dioxide, CO₂, has three atoms and two C=O double bonds. Carbon’s electronegativity is 2.55 and oxygen’s 3.44, and each bond is polar. The two bonds lie 180° apart, so the molecule is straight, a shape derived in the article on VSEPR (valence-shell electron-pair repulsion) shapes. Whichever way each bond dipole points, the two lie along one line in opposite directions, and, the two bonds being alike, equal in size. They cancel: carbon dioxide’s dipole moment is zero, a nonpolar molecule built from two polar bonds.

The arrows and their cancelling are not drawn, but their line is: in the viewer, carbon dioxide appears as O=C=O on one straight line.

Water, H₂O, also has three atoms and two polar bonds, here two O–H single bonds, and its oxygen carries two lone pairs. Hydrogen’s electronegativity is 2.2 against oxygen’s 3.44. Oxygen pulls the electrons of each O–H bond towards itself, so both bond dipoles point at oxygen. The angle between the two bonds is 104.5°, and the molecule is bent. Two arrows meeting at 104.5° cannot cancel: they combine into a dipole moment with its negative end at oxygen.

The negative charge gathers at the oxygen end for two reasons: oxygen’s nuclear charge pulling on both bonds, and the two lone pairs, which also contribute to the dipole moment. Water appears in the viewer as a bent H–O–H, the shape in which its two bond dipoles cannot cancel; the lone pairs and the arrows are not drawn.

Each molecule has three atoms and two polar bonds, and what decides whether their bond dipoles cancel is the shape. On carbon dioxide’s straight line the two arrows cancel; in water’s bend they add.

Where the prediction bends

Electronegativity values are predictors of where the electrons of a bond will go, not measurements of it. Bonds to other atoms, multiple bonds and lone pairs can each make that prediction less reliable for a given bond. In a molecule with lone pairs or multiple bonds, the electronegativity difference may even give the wrong direction for a bond.

Carbon monoxide is the case in point. Oxygen’s electronegativity, 3.44, is higher than carbon’s, 2.55, so the prediction puts the partial negative charge on oxygen. In carbon monoxide it sits on carbon instead, the less electronegative of the two atoms. Its one bond is a triple bond, the kind of multiple bond that weakens the prediction.

None of this touches carbon dioxide. Whichever way its two equal bond dipoles point, they point in opposite directions and cancel, and its zero dipole moment is measured rather than predicted.

What dipole moments do between molecules, where they help hold liquids and solids together, belongs to the forces that act between molecules, a subject of its own.