Difficulty: Intermediate | Prerequisites: Chair conformations (see Part 1 notes), bond angles, hybridisation
Not all ring sizes are created equal. Cyclohexane is strain-free in its chair form, but smaller and larger rings carry varying amounts of strain that make them less stable. This topic covers how we measure that instability (via heats of combustion), the three types of ring strain, and how to handle molecules with two or more rings fused or bridged together. You will also learn Bredt's rule, which restricts where double bonds can sit in small bridged bicyclics. This material builds directly on the chair conformation concepts from Part 1.
Ring strain is the extra energy a cycloalkane has compared to an unstrained reference. It comes from angle strain, torsional strain, or transannular strain. Cyclohexane (six-membered ring) has zero ring strain in the chair. Smaller rings, especially cyclopropane, have a lot. Bicyclic compounds can be bridged or fused, and Bredt's rule says you cannot put a double bond at a bridgehead of a small bridged ring.
Ring strain
The additional energy a cyclic molecule possesses relative to an equivalent strain-free open-chain reference. Think of it as how "unhappy" the ring is compared to a straight chain with the same number of carbons.
Angle strain (Baeyer strain)
Strain that arises when bond angles are forced away from the ideal tetrahedral angle of 109.5°. Cyclopropane, with internal angles of 60°, has extreme angle strain.
Torsional strain
Strain from eclipsing interactions along C–C bonds. In small rings such as cyclopropane and cyclobutane, the hydrogens on adjacent carbons are forced into eclipsed arrangements.
Transannular strain
Strain in medium-sized rings (7+ carbons) where atoms on opposite sides of the ring are pushed close enough across the interior to repel each other. In simple terms, the ring is big enough to fold inward and bump into itself.
Heat of combustion (ΔHₖ)
The enthalpy change when a compound is completely burned in oxygen to produce CO₂ and H₂O. Combustion breaks all bonds, so a higher (more negative) heat of combustion per CH₂ unit indicates more stored energy, i.e. more strain.
Envelope conformation
The preferred shape of cyclopentane, in which four carbons are roughly coplanar and the fifth is bent out of the plane (like the flap of an envelope). This relieves some of the torsional strain that would be present in a flat ring.
Bicyclic compound
A molecule containing two rings that share two or more atoms.
Bridged bicyclic
A bicyclic compound in which the two rings share atoms that are not directly bonded to each other, creating a "bridge" of one or more carbons between the shared atoms (bridgeheads). Example: norbornane, bicyclo[2.2.1]heptane.
Fused bicyclic
A bicyclic compound in which the two rings share an edge (a bond between two adjacent shared atoms). Example: decalin, bicyclo[4.4.0]decane.
Polycyclic compound
A molecule with more than two rings. Examples: cubane, adamantane.
Bridgehead atom
An atom shared between two or more rings in a bridged bicyclic system.
Bredt's rule
In a bridged bicyclic compound, a bridgehead carbon cannot be part of a double bond if the rings are small (≤7 atoms total in the smallest ring containing the bridgehead). The geometry around a double bond (trigonal planar, 120°) introduces too much angle strain at a bridgehead in a small ring.
The preferred bond angle for sp³ carbons is 109.5°, and the preferred conformation around any C–C bond is staggered.
Cyclohexane achieves both perfectly in its chair conformation: zero angle strain, zero torsional strain. It is the most stable common ring size.
Cyclopentane (5-membered) has low angle strain (internal angles ~108°, close to 109.5°) but some torsional strain from near-eclipsing. It relieves this by puckering into the envelope conformation.
Cyclobutane (4-membered) has significant angle strain (90° vs. 109.5°) and torsional strain. Ring strain: ~26 kcal/mol.
Cyclopropane (3-membered) has extreme angle strain (60° vs. 109.5°) and fully eclipsed hydrogens. Ring strain: ~29 kcal/mol. This is the most strained common ring.
Combustion breaks all bonds and forms C=O and O–H bonds (which are stronger). A more strained molecule stores more energy, so it releases more energy per CH₂ on combustion.
For a strain-free CH₂ unit, adding one CH₂ to an open chain raises ΔHₖ by about 157 kcal/mol.
For cyclopropane (3 CH₂ units), the predicted ΔHₖ would be 3 × 157 = 471 kcal/mol. The actual value is 500 kcal/mol. The difference (500 – 471 = 29 kcal/mol) is the ring strain.
Cyclohexane has a per-CH₂ combustion value of about 157 kcal/mol, matching the strain-free reference: ring strain = 0.
Angle strain: bond angles compressed or expanded away from 109.5°. Dominant in 3- and 4-membered rings.
Torsional strain: C–C bonds forced into eclipsed (or near-eclipsed) arrangements. Present in flat or nearly flat rings where hydrogens cannot stagger. This is why cyclopentane prefers the envelope.
Transannular strain: only significant in rings of 7 or more carbons. The ring folds inward, and hydrogens across the ring collide.
A perfectly flat cyclopentane would have all C–H bonds eclipsed. By bending one carbon out of the plane (the "envelope flap"), the ring reduces torsional strain substantially.
The flap moves around the ring rapidly (pseudorotation), so no single carbon stays bent out for long.
Bicyclic compounds are named bicyclo[a.b.c]alkane, where a, b, and c are the number of carbons in each bridge (listed largest to smallest), and the total carbon count determines the parent alkane name.
Example: bicyclo[4.3.1]nonane has bridges of 4, 3, and 1 carbon(s), totalling 8 bridge carbons + 2 bridgeheads = 10 carbons, so nonane would be wrong here, it is actually decane. (Always count all carbons in the ring system for the parent name.)
Fused bicyclics have one bridge of length 0: bicyclo[4.4.0]decane (decalin).
If two rings share exactly two adjacent atoms (one bond), the compound is fused.
If the shared atoms are separated by at least one carbon in every path around either ring, the compound is bridged.
A bridgehead atom in a small bicyclic ring (≤7 atoms in the smallest ring containing the bridgehead) cannot be part of a double bond.
A double bond requires trigonal planar geometry (120°). At a bridgehead in a small ring, the geometry is locked tetrahedral by the ring constraints, making a double bond geometrically impossible.
In larger rings, the bridgehead has enough flexibility for a double bond, and Bredt's rule no longer applies.
Two fused rings can be joined cis (both bridgehead hydrogens on the same face) or trans (on opposite faces).
For small fused rings, only cis fusion is possible because the trans arrangement would introduce too much strain.
For larger rings (e.g. decalin), both cis and trans fusion occur, but trans-fused decalin is more stable because it avoids gauche-type interactions present in the cis form.
There is no chair interconversion in fused bicyclics because flipping one ring would break the fusion geometry.
Ring strain from heats of combustion
\text{Ring strain} = \Delta H_{c}^{\text{actual}} - (n \times 157 \text{ kcal/mol})where n = number of CH₂ groups in the ring and 157 kcal/mol is the strain-free increment per CH₂.
Heats of combustion and ring strain by ring size
Ring size | ΔHₖ (kcal/mol) | ΔHₖ per CH₂ | Ring strain (kcal/mol) |
|---|---|---|---|
3 (cyclopropane) | –500 | 167 | 29 |
4 (cyclobutane) | –656 | 164 | 26 |
5 (cyclopentane) | –794 | 159 | 7 |
6 (cyclohexane) | –945 | 157.5 | ~0 |
7 (cycloheptane) | –1108 | 158 | 6 |
Cyclohexane sits at the sweet spot: virtually zero ring strain. Cyclopentane and cycloheptane carry modest strain. Three- and four-membered rings are significantly strained.
Open-chain reference heats of combustion
Compound | ΔHₖ (kcal/mol) | Increment per added CH₂ |
|---|---|---|
Propane | –530 | – |
Butane | –688 | 158 |
Pentane | –845 | 157 |
Hexane | –1002 | 157 |
Heptane | –1160 | 158 |
The per-CH₂ increment converges to ~157 kcal/mol for unstrained open chains.
Ring strain is why cyclopropane rings appear in certain reactive natural products and pharmaceuticals: the stored energy makes them selectively reactive under mild conditions. Bicyclic terpenes (camphor, norbornane derivatives) are abundant in nature, and understanding their naming and strain is essential in natural product chemistry and fragrance chemistry.
Students often think "more carbons = more ring strain." Ring strain actually peaks at 3 and 4 carbons, drops to near zero at 6, and rises modestly again for medium rings (8–12) due to transannular strain. Very large rings are essentially strain-free.
Students confuse ring strain with total energy. A larger molecule has a more negative heat of combustion simply because it has more bonds to break. Ring strain is the excess per-CH₂ energy above the strain-free reference.
Students sometimes think Bredt's rule forbids all double bonds in bicyclic compounds. It only restricts double bonds at bridgehead positions in small bridged rings. Fused bicyclics and large bridged bicyclics can have bridgehead double bonds.
Students sometimes assume fused rings can always adopt both cis and trans fusion. For small fused rings, only cis is geometrically feasible.
⚠️ Calculating ring strain from heats of combustion is a classic exam problem. Know the method: predicted = n × 157, then subtract from the actual value.
⚠️ Be able to identify all three types of ring strain and say which ones dominate for a given ring size.
⚠️ Naming bicyclic compounds using the bicyclo[a.b.c]alkane system is commonly tested. Remember to list bridge sizes largest to smallest and count all carbons for the parent name.
⚠️ Bredt's rule: expect a question asking which of several bicyclic structures can or cannot support a double bond at the bridgehead.
Q: Which common ring size has zero ring strain?
A: Cyclohexane (6-membered ring in the chair conformation).
Q: True or false: transannular strain is the main type of strain in cyclopropane.
A: False. Cyclopropane suffers primarily from angle strain and torsional strain. Transannular strain only applies to rings of 7 or more carbons.
Q: Fill in the blank: cyclopentane adopts the ________ conformation to reduce torsional strain.
A: Envelope.
Q: True or false: in bicyclo[4.4.0]decane, the bridge of length 0 means the compound is fused, not bridged.
A: True.
Q: The actual heat of combustion of cyclobutane is –656 kcal/mol. Calculate its ring strain.
A: Predicted = 4 × 157 = 628 kcal/mol. Ring strain = 656 – 628 = 28 kcal/mol (some sources round to 26 depending on the reference value used).
Q: Why does cyclopentane not stay flat?
A: A flat cyclopentane would have all C–H bonds eclipsed, causing significant torsional strain. By puckering one carbon out of the plane (envelope conformation), the ring reduces eclipsing and lowers its energy.
Q: Explain why trans-fused decalin is more stable than cis-fused decalin.
A: In trans-decalin, both rings can adopt fully staggered chair conformations with no gauche-type interactions between them. In cis-decalin, the ring junction forces some gauche interactions, raising the energy. Also, trans-decalin is conformationally rigid (no ring flip), while cis-decalin can flip.
Q: A student proposes a bridged bicyclic compound with a double bond at the bridgehead, where the smallest ring has 6 atoms. Is this allowed?
A: No. Bredt's rule says the bridgehead cannot support a double bond when the smallest ring containing it has ≤7 atoms. A 6-atom ring is too small.
This connects to chair conformations (Part 1 of these notes): cyclohexane's zero strain comes from the chair. It also connects to stereochemistry of disubstituted cyclohexanes and addition reactions (Part 3 of these notes), where ring geometry determines stereochemical outcomes. Ring strain is revisited when studying the reactivity of epoxides (3-membered rings containing oxygen) and in radical and carbene additions to form cyclopropanes.
Ring strain, angle strain, Baeyer strain, torsional strain, transannular strain, heat of combustion, cyclopropane, cyclobutane, cyclopentane, cyclohexane, envelope conformation, pseudorotation, bicyclic compound, polycyclic, bridged bicyclic, fused bicyclic, decalin, norbornane, bicyclo nomenclature, Bredt's rule, bridgehead, cis-fused, trans-fused, organic chemistry chapter 7