How lopsided is a polar bond?
The electronegativity lecture showed that in hydrogen chloride, H–Cl, chlorine pulls the shared pair harder than hydrogen does. So chlorine gets a small negative charge, written δ−, and hydrogen a small positive charge, δ+. The bond is polar.
But how small is "small"? Is chlorine's charge nearly −1, as if it had taken the electron, or is it tiny? That lecture gave a rough guide for naming bonds. This lecture looks inside a polar bond: what the δ means, how big it really is, how chemists draw it, and how Pauling turned bond energies into his electronegativity numbers. The VSEPR lecture promised exactly this step: first see how unevenly each bond shares its electrons, then (in the next lecture) add up the bonds using the shapes. Start with a guess.
In a molecule of hydrogen chloride, about how much charge does the chlorine end carry? (A full electron's charge is −1.)
The size of the partial charge on chlorine in H–Cl. Many students guess −1 or −0.5, but the measured value is much smaller.
Measurements give about −0.18: less than a fifth of an electron's charge. The shared pair is shifted towards chlorine, but it is still shared.
What the δ really means
Electrons in a molecule are not little balls sitting at fixed points. It is better to picture a cloud of negative charge spread around the atoms. In H–H, the cloud of the bonding pair is spread evenly between the two nuclei. In H–Cl, the cloud is pulled towards chlorine. Chlorine's end of the molecule has a little more negative charge than its protons cancel, and hydrogen's end has a little less.
The δ (the Greek letter delta) means "partial". It is a reminder that the charge is a fraction of an electron's charge, not a whole one. How big a fraction can be measured. In an electric field, polar molecules turn to line up, and the strength of that effect, called the dipole moment, can be measured. For hydrogen chloride it is about 1.11 debye, and the bond is 127.5 pm long. Dividing one by the other gives a charge of about 0.18 of an electron's charge on each end (Averill and Eldredge, General Chemistry: Principles, Patterns, and Applications, section 8.9). Chemists say the bond has about 18% ionic character.
That is it. That is the whole idea. A polar bond is still a shared bond. The pair is shifted, not handed over, and δ measures the size of the shift.
Getting 0.18 from a measurement
Where does the figure of 0.18 come from? The dipole moment measures how strongly a molecule is turned by an electric field. For two charges and a distance apart, it equals . So if you know the dipole moment and the bond length, you can find .
For HCl, the dipole moment of 1.11 debye is about C m (one debye is about C m). The bond length is m. Dividing gives C. An electron's charge is C, so is about 0.18 of it. If the electron had been fully transferred, would be the whole electron's charge, and the dipole moment would be more than five times larger. The measurement shows directly that the bond is mostly shared.
A pair of equal and opposite charges a small distance apart is called a dipole ("two poles"). A polar bond is a bond dipole. Chemists draw it with a special arrow: it starts with a small cross at the δ+ end, like a plus sign, and points towards the δ− end. The arrow points the way the electrons have shifted. (Some physics books draw the dipole moment the other way round, from − to +. In chemistry, and in this course, the arrow points to δ−.)
A scale of polarity
The bigger the difference in electronegativity, the further the pair shifts, and the more polar the bond. Using Pauling values to two decimal places, as in the electronegativity lecture:
There are no gaps or jumps on this scale. "Non-polar", "polar" and "ionic" are useful names for regions of one continuous line, not boxes with walls. That is why the boundaries are always given as "about".
In a C–H bond, which atom is δ−, if either?
Show the answer
Carbon, slightly. Carbon's electronegativity is 2.55 and hydrogen's is 2.20, so carbon pulls the pair a little harder. But the difference, 0.35, is small, and in practice C–H bonds are treated as almost non-polar. This matters later: molecules made only of carbon and hydrogen, like the fuels in petrol, mix poorly with water, because they have almost no δ+ and δ− ends to attract water molecules.
Fluorine is the most electronegative element. Is the F–F bond in a fluorine molecule polar?
Show the answer
No. Polarity comes from a difference in pull, not from a strong pull. In F–F, both atoms pull with exactly the same strength, 3.98, so the difference is zero and the pair sits in the middle. The same is true for H–H and Cl–Cl. A bond can only be polar when its two atoms are different elements, and even then only when their electronegativities differ noticeably.
Polarity is not just a label. It changes how substances behave. Hydrogen chloride gas dissolves very readily in water, and in solution its polar bond breaks to give ions: this is hydrochloric acid. Methane, whose C–H bonds are almost non-polar, hardly dissolves in water at all. The δ+ hydrogen of H–Cl is attracted by the δ− oxygen of water molecules, and that attraction helps pull the bond apart. A non-polar C–H bond offers water nothing to hold on to.
Where Pauling's numbers came from
Electronegativity values look like they were simply invented. They were not. Linus Pauling worked them out, in 1932, from the energies of bonds. His idea is worth following, because it shows why polar bonds are special. This is the hardest part of the lecture. Read it slowly.
Imagine an H–Cl bond in which the two atoms pulled equally. Its strength would be expected to lie between the strengths of H–H and Cl–Cl. Pauling compared real bond energies with that "fair sharing" average. Here is the comparison, step by step, using one table of average bond energies (the same table as in the covalent bonds lecture).
Press Next to add one step. Read the reason before you go on.
Each step of Pauling's method for H–Cl, in a simplified form, with the reason it is allowed.
- H–H: 436 kJ/mol. Cl–Cl: 242 kJ/mol. Two bonds with perfectly equal sharing.
- Fair-sharing estimate for H–Cl: (436 + 242) ÷ 2 = 339 kJ/mol. If H and Cl pulled equally, the bond strength would be about the average.
- Real H–Cl: 431 kJ/mol. The real bond is stronger than the estimate.
- Extra energy: 431 − 339 = 92 kJ/mol. This extra comes from the attraction between the δ+ and δ− ends.
- 92 kJ/mol ≈ 0.95 eV per bond. Pauling measured energies in electronvolts; 1 eV per bond = 96.5 kJ/mol.
- √0.95 ≈ 0.98. Pauling's rule: the difference in electronegativity is the square root of the extra energy in eV.
- Compare: 3.16 − 2.20 = 0.96. The estimate from bond energies is very close to the difference in the table.
This simplified version of Pauling's method uses the plain average. He and later chemists refined it, and modern tables are fitted to many bonds at once, so a single calculation will not match the table exactly. But the idea is the one that matters: polar bonds are usually stronger than fair sharing would predict, and the extra strength grows with the difference in electronegativity. A bond is more than its shared pair. The attraction between its δ+ and δ− ends adds to it.
Worked examples
For each bond: find the difference in electronegativity, name the δ− atom (the more electronegative one), and draw the arrow towards it.
O: 3.44. H: 2.20. Difference: . Each O–H bond is clearly polar, with oxygen δ− and each hydrogen δ+.
Draw an arrow on each O–H bond, starting at hydrogen and pointing to oxygen. Whether these two bond dipoles add up to make the whole molecule polar depends on water's bent shape. That is the next lecture's question.
O: 3.44. C: 2.55. Difference: . Each C=O bond is polar, with oxygen δ− and carbon δ+.
A double bond has two shared pairs, but the polarity is still described for the bond as a whole: one arrow from carbon towards each oxygen. Both bonds are polar. Whether the molecule is polar is, again, for the next lecture.
Put these bonds in order of increasing polarity: N–H, C–H, O–H, C–Cl.
Differences: C–H ; C–Cl ; N–H ; O–H .
Order: C–H < C–Cl < N–H < O–H. Notice that in C–Cl, carbon is δ+ (chlorine pulls harder), while in C–H, carbon is slightly δ−. The same atom can be δ+ in one bond and δ− in another. It depends on its partner.
Label the partial charges in chloromethane, CH₃Cl, where carbon is bonded to three hydrogens and one chlorine.
C–Cl: difference 0.61, so chlorine is δ− and carbon δ+. C–H: difference 0.35, almost non-polar. So the important dipole is in the C–Cl bond: chlorine δ−, carbon δ+.
This one fact predicts much of chloromethane's chemistry. Particles with a negative charge or a lone pair are attracted to the δ+ carbon, and many reactions of molecules like this begin exactly there. Later organic chemistry lectures build on this.
Which is more polar, a C–O bond or an N–H bond?
C–O: . N–H: . The C–O bond has the slightly larger difference.
But a gap of 0.05 is smaller than the differences between electronegativity tables. The honest answer is that the two bonds are about equally polar. Use electronegativity to compare bonds whose differences are clearly apart, and be careful about drawing strong conclusions from tiny gaps.
Three classic mistakes
In chemistry, the dipole arrow points from δ+ to δ−, towards the more electronegative atom: the way the electrons have shifted. The cross on its tail marks the positive end. Drawing it from δ− to δ+ reverses the meaning.
δ− on chlorine in HCl is about −0.18, not −1. A polar bond is still a shared bond. Writing H⁺ and Cl⁻ for gaseous hydrogen chloride describes ions, which the molecule does not contain.
Every bond in CO₂ is polar, but this does not decide whether the molecule as a whole is polar. Bond dipoles can add up or cancel, depending on the shape. Describe the bonds in this lecture; judge the molecule in the next.
Use Pauling values: H 2.20, C 2.55, N 3.04, O 3.44, S 2.58, F 3.98, Cl 3.16, Br 2.96, I 2.66.
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Put H–F, H–Cl, H–Br and H–I in order of increasing bond polarity, and explain the order using the position of the halogens in the periodic table.
Hint 1
Subtract 2.20 from each halogen's value.
Hint 2
Electronegativity falls down a group.
Full answer
Differences: H–I 0.46, H–Br 0.76, H–Cl 0.96, H–F 1.78. Order: H–I < H–Br < H–Cl < H–F. Down Group 17 the atoms get larger, so the shared pair is further from the nucleus and better shielded. The halogen's pull falls, the shift of the pair falls, and the bond becomes less polar.
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Mark δ+ and δ− on each bond, or say that it is almost non-polar: (a) C–O (b) N–H (c) S–H.
Hint 1
Work out each difference.
Hint 2
A difference below about 0.4 is treated as almost non-polar.
Full answer
(a) 0.89: C δ+, O δ−. (b) 0.84: H δ+, N δ−. (c) : almost non-polar, with sulfur very slightly δ−. This is one reason why H₂S behaves so differently from H₂O, even though the molecules have the same shape.
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Tetrachloromethane, CCl₄, has four C–Cl bonds. Describe the polarity of each bond, and say which atom is δ+.
Hint 1
The difference is .
Hint 2
Chlorine is the more electronegative atom.
Full answer
Each C–Cl bond has a difference of 0.61, so each is polar, with chlorine δ− and carbon δ+. Four arrows point from carbon outwards to the four chlorines. (Whether these four bond dipoles cancel in the tetrahedral shape is the next lecture's question.)
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Use Pauling's simplified method on the O–H bond. Bond energies (same table): O–H 467, H–H 436, O–O 146 kJ/mol. Compare your answer with the table difference, 1.24, and suggest why the match is less close than for H–Cl.
Hint 1
Fair-sharing estimate . Extra energy = 467 minus that.
Hint 2
Divide the extra energy by 96.5 to get eV, then take the square root.
Full answer
Estimate kJ/mol. Extra kJ/mol eV. . The table gives 1.24, so the simple method is about 0.1 too high. There are two reasons. The O–O single bond is unusually weak, because the lone pairs on the two oxygens repel; this pulls the plain average down and makes the "extra" look too big. And modern values are fitted to many bonds at once, not taken from one. The method gives the right size and order, not exact values.
A bond dipole is a tiny separation of charge, but it shapes almost everything about how molecules meet each other. δ+ ends attract δ− ends of neighbouring molecules, which is the start of the forces between molecules. When the δ+ atom is a hydrogen bonded to oxygen, nitrogen or fluorine, the attraction is especially strong, and it is called hydrogen bonding. In proteins, the δ− oxygen of a C=O group attracts the δ+ hydrogen of an N–H group further along the same chain. Many such attractions help hold the chain in its folded shape.
First, though, one question remains. A molecule with several polar bonds may or may not be polar as a whole. The next lecture adds up bond dipoles, using the shapes from VSEPR, to find out.
- In a polar bond, the shared pair is shifted towards the more electronegative atom, which becomes δ−, while the other atom becomes δ+.
- Partial charges are fractions of an electron's charge, about 0.18 for each end of H–Cl, so a polar bond is still a shared bond.
- A bond dipole is drawn as an arrow with a cross at the δ+ end, pointing towards the δ− end.
- Bond polarity grows smoothly with the difference in electronegativity, and "non-polar", "polar" and "ionic" are regions of one scale.
- Pauling based electronegativity on bond energies: polar bonds are usually stronger than fair sharing predicts, and the extra energy grows with the difference.