Source: Libre Text Notes, Purdue University Organic Chemistry
Difficulty: Introductory to Intermediate
Prerequisites: sp³ hybridization, sigma bonds, and the potential energy curve from Part 1 of these notes.
Tags: sp2 hybridization, sp hybridization, pi bond, double bond, triple bond, ethene, ethylene, ethyne, acetylene, trigonal planar, linear geometry, carbonyl group, formaldehyde, carbocation, restricted rotation, alkene, alkyne, bond length comparison
Part 1 covered sp³ hybridization, which explains single bonds and tetrahedral geometry. But organic chemistry is full of double and triple bonds, and those require different hybridization states. This set of notes covers sp² hybridization (double bonds, trigonal planar geometry) and sp hybridization (triple bonds, linear geometry). It also introduces the pi (π) bond, a second type of covalent bond that sits alongside the sigma bond and is responsible for restricted rotation in alkenes. These ideas are essential for understanding reactivity: nucleophilic additions, electrophilic additions, and the chemistry of carbonyl compounds all depend on how π bonds behave.
Double bonds consist of one σ bond plus one π bond, and the carbons involved are sp² hybridised (trigonal planar, ~120° angles). Triple bonds consist of one σ bond plus two π bonds, with sp hybridised carbons (linear, 180° angles). Pi bonds prevent rotation, which is why alkenes can have cis/trans isomers. Carbocations are sp² hybridised carbons with an empty p orbital.
Pi bond (π bond)
A covalent bond formed by the sideways (lateral) overlap of two parallel p orbitals. The electron density sits above and below the plane of the bonded atoms, not along the bond axis.
Think of it as: a second bond layered on top of a sigma bond, made from the p orbitals that were left out of hybridization.
sp² hybridization
The mixing of one s orbital and two p orbitals to produce three equivalent sp² hybrid orbitals arranged in a trigonal planar geometry (120° apart), with one unhybridized p orbital remaining perpendicular to the plane.
In simple terms, this is what happens at a carbon involved in a double bond. Three orbitals form σ bonds (or hold a lone pair), and the leftover p orbital forms the π bond.
sp hybridization
The mixing of one s orbital and one p orbital to produce two equivalent sp hybrid orbitals arranged linearly (180° apart), with two unhybridized p orbitals remaining perpendicular to each other and to the bond axis.
In simple terms, this is the hybridization at a carbon involved in a triple bond.
Trigonal planar geometry
A molecular shape in which three groups are arranged around a central atom in a flat, triangular arrangement with approximately 120° bond angles.
Linear geometry
A molecular shape in which two groups are arranged on opposite sides of a central atom, giving a 180° bond angle.
Double bond
A bond consisting of one sigma bond and one pi bond between two atoms. The sigma bond comes from head-on overlap of sp² hybrid orbitals; the pi bond comes from sideways overlap of unhybridized p orbitals.
Triple bond
A bond consisting of one sigma bond and two pi bonds. The sigma bond comes from head-on overlap of sp hybrid orbitals; the two pi bonds come from sideways overlap of two pairs of unhybridized p orbitals, oriented perpendicular to each other.
Carbocation
A carbon atom bearing only three bonds and a positive formal charge. It is sp² hybridised with an empty (unoccupied) p orbital perpendicular to the plane of the three bonds.
Think of it as: a carbon that has lost its share of one bonding pair. The empty p orbital is what makes it so reactive, because electron-rich species are attracted to it.
Carbonyl group (C=O)
A functional group consisting of a carbon double-bonded to an oxygen. The carbon is sp² hybridised. Found in aldehydes, ketones, carboxylic acids, esters, and amides.
Three characteristics of ethene (C₂H₄) that any bonding model must explain:
Ethene is a planar (flat) molecule.
Bond angles are approximately 120°, and the C=C bond length is 134 pm, significantly shorter than the 154 pm C–C single bond in ethane.
There is a significant barrier to rotation about the carbon-carbon double bond.
In ethene, each carbon undergoes sp² hybridization:
One 2s orbital and two of the three 2p orbitals mix to form three sp² hybrid orbitals.
One 2p orbital on each carbon remains unhybridized.
The three sp² orbitals lie in a plane at 120° to each other (trigonal planar).
The unhybridized p orbital is perpendicular to that plane.
Bond formation in ethene:
One sp² orbital on each carbon overlaps head-on to form the C–C σ bond.
The remaining sp² orbitals overlap with hydrogen 1s orbitals to form C–H σ bonds.
The two unhybridized p orbitals (one on each carbon) overlap sideways to form the C–C π bond.
A double bond = 1 σ bond + 1 π bond.
Pi bonds do not have cylindrical symmetry (unlike sigma bonds).
Pi bonds cannot rotate freely. Rotation would break the sideways overlap of the p orbitals, destroying the π bond.
This restricted rotation locks the molecule in a planar configuration and is the reason alkenes can exhibit cis/trans (E/Z) isomerism.
In any molecule containing a C=C double bond, the two carbons of the double bond and all four atoms directly attached to them lie in the same plane.
Substituents on either side of the double bond are locked in position relative to each other.
The same bonding pattern appears in carbonyl compounds (C=O).
Example: formaldehyde (CH₂O).
Carbon is sp² hybridised: three sp² orbitals form two C–H σ bonds and one C–O σ bond.
The unhybridized p orbital on carbon overlaps sideways with a p orbital on oxygen to form the C=O π bond.
Oxygen retains two lone pairs.
Geometry around carbon: trigonal planar.
A carbocation is a carbon with only three bonds and a formal positive charge.
The carbon is sp² hybridised with a trigonal planar geometry.
The key feature: one p orbital on the carbon is completely empty.
Example: the methyl carbocation (CH₃⁺).
Three sp² orbitals form three C–H σ bonds in a plane.
The empty p orbital sits perpendicular to that plane.
Carbocations are highly reactive electrophiles because the empty p orbital readily accepts electrons from nucleophiles.
A triple bond consists of 1 σ bond + 2 π bonds.
Example: ethyne (acetylene, C₂H₂), the simplest alkyne.
Each carbon undergoes sp hybridization: one 2s and one 2p orbital mix to form two sp hybrid orbitals arranged linearly (180°).
Two 2p orbitals on each carbon remain unhybridized.
The sp + sp overlap between the two carbons forms the C–C σ bond.
The sp + 1s overlaps form the C–H σ bonds.
The two pairs of unhybridized p orbitals overlap sideways to form two π bonds, oriented perpendicular to each other.
Geometry: linear. H–C≡C–H is a straight line.
The more s character in a hybrid orbital, the shorter and stronger the bond it forms:
sp³ has 25% s character
sp² has 33% s character
sp has 50% s character
Consequence: bonds involving sp orbitals are shorter and stronger than those involving sp², which in turn are shorter and stronger than sp³.
C–C bond lengths reflect this: single bond (sp³–sp³) = 154 pm, double bond (sp²–sp²) = 134 pm, triple bond (sp–sp) = 120 pm.
General rule: the longer the bond, the weaker it is.
C=C double bond length (ethene): 134 pm
C–C single bond length (ethane): 154 pm
C≡C triple bond length (ethyne): ~120 pm
sp² bond angle: ~120° (trigonal planar)
sp bond angle: 180° (linear)
Double bond composition: 1 σ + 1 π
Triple bond composition: 1 σ + 2 π
s character: sp³ = 25%, sp² = 33%, sp = 50%
Restricted rotation around double bonds is why your body distinguishes between cis and trans fats. Both have the same molecular formula, but cis double bonds introduce a kink in the hydrocarbon chain while trans double bonds keep it straight. This geometric difference changes how fat molecules pack together, which affects melting point and (controversially) health outcomes. Carbonyl chemistry is similarly everywhere: the C=O group drives the reactivity of sugars, amino acids, pharmaceuticals, and most synthetic organic reactions.
"A double bond is just two sigma bonds." A double bond is one σ bond plus one π bond. They are different types of orbital overlap with different symmetry and different properties.
"Pi bonds are stronger than sigma bonds." Pi bonds are generally weaker than sigma bonds because sideways overlap is less effective than head-on overlap. The overall double bond is stronger than a single bond, but that is because it contains two bonds (σ + π), not because the π bond alone is strong.
"Rotation around a double bond is just harder, not impossible." At room temperature, rotation around a typical C=C double bond does not occur. It would require breaking the π bond (~264 kJ/mol for ethene), which is far more energy than thermal motion provides.
"sp hybridization means the atom forms fewer bonds." sp hybridization produces two σ bonds, but the two remaining unhybridized p orbitals form two π bonds. An sp carbon in a triple bond is still involved in four bonds total (for example, one C–H σ and one C≡C consisting of σ + 2π).
⚠️ Be prepared to identify the hybridization of every carbon (and heteroatom) in a given structure. Count the number of σ bonds plus lone pairs on the atom: 4 = sp³, 3 = sp², 2 = sp.
⚠️ Know the composition of double bonds (1σ + 1π) and triple bonds (1σ + 2π). Exam questions frequently ask you to count the total number of σ and π bonds in a molecule.
⚠️ Understand why restricted rotation around double bonds leads to geometric (cis/trans) isomers. This will be tested directly and also appears in stereochemistry chapters.
⚠️ Carbocations are a recurring exam topic. Know that they are sp² with an empty p orbital, trigonal planar, and electrophilic.
⚠️ The relationship between s character, bond length, and bond strength is a favourite for multiple-choice and short-answer questions. More s character = shorter, stronger bond.
Fill in the blank: A double bond consists of ___ sigma bond(s) and ___ pi bond(s).
True or false: An sp² hybridised carbon has one unhybridized p orbital. ___
Fill in the blank: The geometry around an sp hybridised carbon is ___.
True or false: Pi bonds allow free rotation. ___
Fill in the blank: A carbocation is sp² hybridised and has an empty ___ orbital.
Answers: 1. One sigma, one pi. 2. True. 3. Linear. 4. False (π bonds prevent rotation). 5. p orbital.
Q: How many sigma bonds and how many pi bonds are in ethyne (C₂H₂)?
A: Three sigma bonds (one C–C and two C–H) and two pi bonds (both in the triple bond).
Q: Explain why ethene is a flat molecule.
A: Each carbon in ethene is sp² hybridised. The three sp² orbitals lie in a plane at 120° angles, and the π bond formed by the unhybridized p orbitals requires these p orbitals to be parallel, which locks all six atoms (2C + 4H) into the same plane.
Q: A carbocation has a formal positive charge. What is the orbital basis for this charge?
A: The carbon is sp² hybridised with three bonds in a trigonal planar arrangement. The remaining p orbital is completely empty (no electrons). The positive charge reflects the fact that the carbon has one fewer electron than a neutral carbon atom.
Q: Rank the following bonds from shortest to longest: C–C (sp³–sp³), C=C (sp²–sp²), C≡C (sp–sp).
A: Shortest to longest: C≡C (~120 pm) < C=C (134 pm) < C–C (154 pm). Higher s character means shorter and stronger bonds.
Q: Why does formaldehyde (CH₂O) have a trigonal planar geometry around carbon?
A: Carbon in formaldehyde is sp² hybridised. It forms two C–H σ bonds and one C–O σ bond using its three sp² orbitals, which are arranged at 120° in a plane. The unhybridized p orbital forms the C=O π bond with oxygen.
Restricted rotation around double bonds leads directly into stereochemistry (cis/trans and E/Z nomenclature, covered in Chapter 5 of most organic texts). Carbocations are central to SN1 reactions, E1 eliminations, and electrophilic addition to alkenes. The carbonyl group (sp² carbon double-bonded to oxygen) is the most important functional group in organic chemistry and drives the reactivity of aldehydes, ketones, carboxylic acids, and their derivatives across multiple chapters. The bond-length trend (sp < sp² < sp³) also connects to acidity: C–H bonds with more s character are shorter and stronger, and the resulting carbanions are more stable, explaining why terminal alkynes are weakly acidic.
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