DIPOLE MOMENT: HOW IT IS CALCULATED AND EXAMPLES - CHEMISTRY - 2025

The dipole moment is a chemical property that indicates how heterogeneously electric charges are distributed in a molecule. It is expressed in Debye units, 3.33 · 10 ^-30 C · m, and generally its values ​​range from 0 to 11 D.

Highly polar compounds tend to have large dipole moments; while the apolar ones, small dipole moments. The more polarized the electric charges are in a molecule, the greater its dipole moment; that is, there must be a region rich in electrons, δ-, and another poor in electrons, δ +.

The two-color eraser serves as an analogy to two poles, positive and negative, of a molecule with a marked dipole moment. Source: Pexels.

The dipole moment, μ, is a vector quantity, so it is affected by the angles of the bonds and, in general, by the molecular structure.

When the molecule is linear, it can be compared to a two-color eraser. Its negative end δ-, would correspond to the color red; while the positive, δ +, would be blue. As the magnitudes of the negative charges at the δ- pole increase, and the distance that separates it from δ +, the dipole moment increases.

Chemically, the above means that the greater the difference in electronegativity between two atoms, and the longer the distance that separates them, the greater the dipole moment between them.

How is the dipole moment calculated?

It is considered a covalent bond between two atoms, A and B:

AB

The distance between the positive and negative partial charges is already defined by the length of their bond:

A ^{δ +} -B ^δ-

Because protons and electrons have the same magnitude of electric charge but with opposite signs, 1.6 · 10 ^-19 C, this is what is taken into account when evaluating the dipole moment between A and B using the following equation:

μ = δd

Where μ is the dipole moment, δ is the charge of the electron without the negative sign, and d is the length of the bond expressed in meters. For example, assuming that d has a value of 2 Å (1 · 10 ^-10 m) the dipole moment, μA-B will be:

μA-B = (1.6 10 ^-19 C) (2 10 ^-10 m)

= 3.2 10 ^-29 C m

But since this value is very small, the Debye unit is used:

μ = (3.2 · 10 ^-29 C · m) · (1 D / 3.33 · 10 ^-30 C · m)

= 9.60 D

This value of μA-B could give to suppose that the bond AB is more ionic than covalent.

Examples

Water

Dipole moment of a water molecule. Source: Gabriel Bolívar.

To calculate the dipole moment of a molecule, all the dipole moments of their respective bonds must be added vectorially, considering the bond angles and a bit of trigonometry. This in the beginning.

Water has one of the largest dipole moments that could be expected for a covalent compound. In the upper image we have that hydrogen atoms have positive partial charges, δ +, while oxygen carries the negative partial charge, δ-. The OH bond is quite polar (1.5D), and there are two of them in an H ₂ O molecule.

Usually, a vector is drawn that is directed from the least electronegative atom (H) to the most electronegative one (O). Although they are not drawn, on the oxygen atom there are two pairs of unshared electrons, which "concentrate" the negative region even more.

Due to the angular geometry of H ₂ O, the dipole moments add in the direction of the oxygen atom. Note that the sum of the two μO-H would give 3D (1.5 + 1.5); but it's not like that. The dipole moment of water has an experimental value of 1.85D. The effect of the near 105 ° angle between the HOH bonds is shown here.

Methanol

Dipole moment of a methanol molecule. Source: Gabriel Bolívar.

The dipole moment of methanol is 1.69D. It is less than that of water. Therefore, the atomic masses do not have much influence on the dipole moment; but their atomic radii are. In the case of methanol, we cannot say that its HO bond has a μ equal to 1.5D; since, the molecular environments are different in CH ₃ OH and H ₂ O.

This is why the length of the HO bond in methanol would have to be measured in order to calculate μO-H. What can be said is that μO-H is larger than μC-O, since the electronegativity difference between carbon and oxygen is less than between hydrogen and oxygen.

Methanol is listed as one of the most polar solvents that can be found along with water and ammonia.

Ammonia

Dipole moment of an ammonia molecule. Source: Gabriel Bolívar.

The HN bonds are quite polar, so nitrogen, due to its higher electronegativity, attracts electrons towards itself (upper image). In addition to this, on it we have an unshared pair of electrons, which contribute their negative charges to the δ- region. Therefore, electric charges predominate on the nitrogen atom of ammonia.

Ammonia has a dipole moment of 1.42D, less than that of methanol. If both ammonia and methanol could be transformed into erasers, it would be seen that the methanol eraser has more defined poles compared to the ammonia eraser.

Ethanol

In the case of ethanol, CH ₃ CH ₂ OH, its dipole moment is very close to that of methanol, but it tends to have lower values. As there are more carbon atoms making up the δ + region, the oxygen atom representing δ- begins to lose some of its "relative negative intensity".

Carbon dioxide

Dipole moment of a carbon dioxide molecule. Source: Gabriel Bolívar.

Carbon dioxide has two polar bonds, C = O, with their respective dipole moments μO-C. However, as can be seen in the image above, the linear geometry of CO ₂ causes the two μO-C to cancel each other vectorly, even when the carbon has a positive partial charge and the oxygens have negative partial charges.

For this reason, carbon dioxide is an apolar molecule, since μCO ₂ has a value of 0D.

Methane

Dipole moment for a methane molecule. Source: Gabriel Bolívar.

Both methane and carbon dioxide share something in common: They are highly symmetric molecules. In general, the more symmetric a molecule is, the smaller its dipole moment.

If we look at the CH ₄ molecule, its CH bonds are polar, and the electrons are directed towards the carbon atom as it is slightly more electronegative. One might think that carbon would have to be a highly negative δ- region; like an eraser with its deep red center and bluish ends.

However, by dividing the CH ₄ in half we would obtain two HCH halves, one on the left and the other on the right, similar to the H ₂ O molecule. Thus, the dipole moment resulting from adding these two μC-H would cancel with the other half. And therefore, μCH ₄ has a value of 0D.

References

1. Whitten, Davis, Peck & Stanley. (2008). Chemistry (8th ed.). CENGAGE Learning.
2. Walter J. Moore. (1963). Physical Chemistry. In Chemical kinetics. Fourth edition, Longmans.
3. Ira N. Levine. (2009). Principles of physicochemistry. Sixth edition, pp. 479-540. Mc Graw Hill.
4. Helmenstine, Anne Marie, Ph.D. (January 29, 2020). Dipole Moment Definition. Recovered from: thoughtco.com
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6. LaRita Williams. (2020). Dipole Moment: Definition, Equation & Examples. Study. Recovered from: study.com
7. Wikipedia. (2020). Bond dipole moment. Recovered from: en.wikipedia.org