Chemistry: Atoms First 2e · Advanced Theories of Bonding
Multiple Bonds
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In 30 seconds
A single covalent bond forms when two atoms share one pair of electrons through head-on (sigma, σ) overlap of orbitals along the internuclear axis. But many molecules — including the oxygen we breathe and the nitrogen in air — share more than one pair. A multiple bond is a bond in which two atoms share two or three electron pairs. A double bond consists of one σ bond plus one pi (π) bond; a triple bond consists of one σ bond plus two π bonds. Multiple bonds are shorter and stronger than single bonds, lock molecular geometry, and block rotation about the bond axis. This topic shows how valence bond theory explains these properties using σ and π overlap plus the hybridization ideas from the previous topic.
Why this matters
Multiple bonds control the behavior of huge families of molecules. Alkenes (compounds with C=C) and alkynes (compounds with C≡C) are far more reactive than alkanes because π electrons sit exposed above and below the bond, where they are easier for attacking reagents to reach — the basis of addition reactions used to make plastics, medicines, and polymers. Restricted rotation around double bonds produces cis/trans (geometric) isomerism, which explains why unsaturated fats with cis double bonds are liquid at room temperature while saturated fats are solid, and why retinal in your eye isomerizes from cis to trans to trigger vision. The strong triple bond of N₂ explains why nitrogen gas is so unreactive and why industrial nitrogen fixation requires high temperatures, high pressures, and catalysts. Bond length and strength data from multiple bonds also underpin IR spectroscopy and set the stage for molecular orbital theory.
The college version
Core Concepts
σ and π bonds are different kinds of orbital overlap
A σ bond forms by head-on overlap along the line between nuclei (internuclear axis). It can come from s–s (H–H), s–p (H–F), or p–p (F–F) overlap, and it is cylindrically symmetric — the electron density is concentrated directly between the nuclei. Rotation about the bond axis does not disturb a σ bond.
A π bond forms when two p orbitals on adjacent atoms overlap side-by-side, above and below the bond axis. The electron density sits in two lobes (one above, one below the axis, or in front/behind for different orientations), and there is a node — a region of zero electron density — right on the internuclear axis. Because the overlap is less direct, a π bond is weaker than a σ bond between the same two atoms.
In a double bond, the two electron pairs are not equivalent: one pair occupies a σ bond and the other a π bond. In a triple bond, one pair is σ and two pairs are π. This distinction matters for geometry, rotation, and reactivity.
Bond order, bond length, and bond strength
bond order Number of shared electron pairs between two atoms. Full entry → is the number of shared electron pairs between two atoms (1 for single, 2 for double, 3 for triple). Increasing bond order shortens the bond and strengthens it, because more electron density pulls the nuclei closer together. Representative values for carbon–carbon bonds:
| Bond | Bond order | Approximate length (pm) | Approximate bond energy (kJ/mol) |
|---|---|---|---|
| C–C | 1 | 154 | 348 |
| C=C | 2 | 134 | 614 |
| C≡C | 3 | 120 | 839 |
Note that a double bond is not "twice as strong" as a single bond: the π component adds energy but less than the σ component does, because side-by-side p-orbital overlap is poorer than head-on overlap.
Hybridization adapts to multiple bonds
Recall from the previous topic that atomic orbitals mix (hybridize) to form equivalent hybrids with the correct geometry:
- sp³ hybridization: four σ bonds, tetrahedral (~109.5°), e.g., ethane, CH₃CH₃.
- sp² hybridization: three σ bonds, trigonal planar (~120°), with one unhybridized p orbital A p orbital not mixed into hybrids; available for π overlap. Full entry → left over — e.g., ethene, H₂C=CH₂.
- sp hybridization: two σ bonds, linear (180°), with two unhybridized p orbitals left over — e.g., ethyne, HC≡CH.
The unhybridized p orbitals on adjacent atoms overlap side-by-side to form the π bond(s). So a double bond requires sp² or sp carbon (or similar for other elements), never sp³ — an sp³ carbon has no p orbital available for π overlap.
Rotation about multiple bonds is restricted
A σ bond alone allows nearly free rotation (ethane can twist between staggered and eclipsed forms). Rotating a double bond would have to break the π overlap, which costs roughly the π bond energy — effectively forbidden at room temperature. This locked geometry creates geometric isomers: molecules with the same connectivity but different spatial arrangement. In 2-butene, CH₃CH=CHCH₃, the two methyl groups can be on the same side (cis) or opposite sides (trans) of the C=C; these are distinct compounds with different boiling points and different biological effects.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| "A double bond is two equal bonds." | σ + π model | The σ and π components are not equivalent: different overlap, different strength, different reactivity. |
| "A double bond is twice as strong as a single bond." | Real bond energies | C=C ≈ 614 kJ/mol vs C–C ≈ 348 kJ/mol; the π component adds less than a full σ bond’s worth of strength. |
| "Rotation is free around any covalent bond." | Restricted rotation around multiple bonds | σ bonds rotate; π bonds lock the geometry, producing cis/trans isomers. |
| "sp³ carbon can form a double bond." | sp²/sp requirement | sp³ has no unhybridized p orbital; multiple bonds need sp² or sp carbon. |
| "π electron density lies on the internuclear axis." | σ vs π placement | σ density is on the axis; π density is above/below it, with a node on the axis. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Imagine two friends holding hands: that’s a single bond. A double bond is like holding hands and linking arms at the same time — they’re stuck together tighter, closer, and they can’t spin around anymore. A triple bond is like holding both hands and linking both arms: even shorter, even stronger, and locked in a straight line. The “extra” links (the π parts) sit above and below their hands, which is also why these molecules are more eager to react with other things.
Worked example
Example 1: Counting σ and π bonds in ethene and ethyne
Draw (or recall) the Lewis structures: ethene is H₂C=CH₂, ethyne is HC≡CH.
For ethene: four C–H single bonds are 4 σ bonds; the C=C double bond is 1 σ + 1 π. Total: 5 σ bonds and 1 π bond.
For ethyne: two C–H single bonds are 2 σ; the C≡C triple bond is 1 σ + 2 π. Total: 3 σ bonds and 2 π bonds.
Check the pattern: adding π bonds never adds a σ bond, and the number of σ bonds equals the number of "connections" to other atoms. For HCN (H–C≡N): one C–H σ, one C–N σ, two π → 2 σ and 2 π total.
Example 2: Predicting geometry from hybridization
Ethene (C₂H₄): each carbon is bonded to two H atoms and one C atom — three electron domains, so sp² hybridized, trigonal planar, ~120° bond angles, and the whole molecule is flat. The leftover p orbitals overlap to form the π bond perpendicular to the molecular plane.
Ethyne (C₂H₂): each carbon is bonded to one H and one C — two electron domains, so sp hybridized, linear, 180°, and all four atoms lie on a straight line. The two leftover p orbitals per carbon give the two π bonds of the triple bond.
Carbon dioxide (CO₂): O=C=O — the carbon has two double bonds, two domains, sp hybridized, linear (180°), matching the observed shape. Each C=O is 1 σ + 1 π.
Example 3: Why nitrogen gas is so hard to "fix"
Nitrogen, N₂, has a triple bond: 1 σ + 2 π, bond order 3, bond energy ≈ 941 kJ/mol — one of the strongest bonds known. The Haber–Bosch process (N₂ + 3H₂ → 2NH₃) must break that triple bond, which is why industrial ammonia synthesis runs at high temperature (~400–500 °C), high pressure (~150–300 atm), and with an iron catalyst. The same reasoning explains why lightning is one of the few natural ways to convert N₂ into biologically useful compounds.
Key takeaways
- A double bond = 1 σ + 1 π; a triple bond = 1 σ + 2 π. Count them as σ first, then π.
- π electrons lie above and below the bond axis (not on it), making alkenes/alkynes more reactive than alkanes (addition reactions).
- Higher bond order → shorter bond, stronger bond, higher bond energy.
- Multiple bonds require unhybridized p orbitals: sp² (one double bond, trigonal planar, ~120°) and sp (one triple bond or two double bonds, linear, 180°).
- Rotation is restricted around π bonds, which enables cis/trans (geometric) isomerism.
- A node of zero electron density lies on the axis of a π bond — key again in molecular orbital theory.
Check yourself
5 review questions from the chapter. Try each one, then open the answer.
How many σ and how many π bonds are in a C≡C triple bond?
Show answer
One σ bond and two π bonds.
Why is a C=C double bond shorter and stronger than a C–C single bond?
Show answer
More shared electron pairs pull the nuclei closer together (shorter) and hold them more firmly (stronger); the π overlap adds energy even though it is weaker than σ overlap.
What hybridization does a carbon with one double bond have, and what geometry and bond angle result?
Show answer
sp²; trigonal planar with ~120° bond angles.
Why can 2-butene exist as cis and trans isomers, but ethane cannot?
Show answer
2-butene has a C=C double bond whose π overlap blocks rotation, so the methyl groups stay fixed on the same side (cis) or opposite sides (trans); ethane’s σ bond allows free rotation, so such fixed isomers cannot exist.
Which is more reactive toward addition reactions: ethane (CH₃CH₃) or ethene (H₂C=CH₂)? Explain in one sentence.
Show answer
Ethene: its exposed π electrons are far easier for reagents to attack than ethane’s shielded C–H and C–C σ electrons.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- σ (sigma) bond
- Bond formed by head-on orbital overlap along the internuclear axis.
- π (pi) bond
- Bond formed by side-by-side overlap of parallel p orbitals, with density above/below the axis.
- bond order
- Number of shared electron pairs between two atoms.
- geometric (cis/trans) isomer
- Isomers with the same connectivity but different arrangement around a restricted bond.
- sp² / sp hybridization
- Mixing of one s and two (or one) p orbitals to give trigonal-planar (or linear) bonding.
- unhybridized p orbital
- A p orbital not mixed into hybrids; available for π overlap.
- sigma (σ) bond
- Bond from head-on orbital overlap, electron density along the internuclear axis
Sources & references
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
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