Organic Chemistry · Organic Compounds: Cycloalkanes and Their Stereochemistry
Stability of Cycloalkanes: Ring Strain
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In 30 seconds
Why is cyclohexane the most stable ring, and why is cyclopropane so reactive? The answer is ring strain Extra internal energy from forced geometry Full entry → — the extra internal energy a ring carries when its geometry is forced away from what carbon prefers. Carbon bonded to four single bonds wants tetrahedral geometry (bond angles near 109.5°) and staggered bonds (Chapter 3). A ring forces compromises on both counts, summed as ring strain:
ring strain = angle strain + torsional strain + steric (van der Waals) strain
Cyclopropane pays heavily on all three; cyclohexane, in its chair, pays essentially nothing. Measuring each ring's discomfort tells you its stability and reactivity — and why chemists can do things with cyclopropanes that are impossible with cyclohexanes.
Why this matters
- Reactivity: Strained rings release energy when they open; cyclopropane and its derivatives undergo additions ordinary alkanes never do, because strain makes bond breaking favorable. This drives ring-opening chemistry used throughout the book.
- Conformational foundation: Ring strain is why cyclohexane adopts the chair (next topics).
- Drug design: Many bioactive molecules (some antibiotics, pyrethroid insecticides) exploit strained small rings' rigidity and reactivity.
- Physical organic chemistry: Heats of combustion are the classic route to strain energies.
The college version
Core Concepts
The three components of ring strain
- angle strain Deviation of bond angles from 109.5° Full entry →: deviation of C–C–C bond angles from the ideal sp³ value of 109.5°. For a regular planar polygon with n carbons, the interior angle is:
interior angle = (n - 2) × 180°n
So cyclopropane (n = 3) would have 60° angles (deviation 49.5°), cyclobutane (n = 4) 90° (deviation 19.5°), cyclopentane (n = 5) 108° (deviation 1.5°), and a planar cyclohexane (n = 6) 120° (deviation −10.5°).
- torsional strain Eclipsing penalty between adjacent bonds Full entry →: repulsion between eclipsed bonds. In a perfectly planar small ring, all adjacent C–H bonds are eclipsed — the situation Chapter 3 showed to be unfavorable. Rings pucker to relieve this, trading a little angle strain for much less eclipsing.
- Steric (van der Waals) strain: crowding between nonbonded atoms. In medium and large rings (cycloheptane and larger), hydrogens press across the ring interior — transannular strain Repulsion between atoms across a ring interior Full entry → — which is why the largest rings are not automatically the most stable.
Measuring ring strain: heats of combustion
The classic experiment burns a cycloalkane and measures the heat released; divide by the number of CH₂ units to compare ring sizes fairly. Approximate heats of combustion per CH₂ (kJ/mol):
| Ring | ΔH combustion per CH₂ (kJ/mol) | Deviation from unstrained (~659) |
|---|---|---|
| Cyclopropane | ≈ 697 | +38 |
| Cyclobutane | ≈ 686 | +27 |
| Cyclopentane | ≈ 664 | +5 |
| Cyclohexane | ≈ 659 | ~0 |
| Cycloheptane | ≈ 662 | +3 |
| Cyclooctane | ≈ 664 | +5 |
| Long-chain alkane (reference) | ≈ 659 | 0 |
Because combustion breaks every bond, the heat released per CH₂ reflects stored strain. The resulting total ring strain energies are approximately: cyclopropane 115 kJ/mol, cyclobutane 110 kJ/mol, cyclopentane 26 kJ/mol, cyclohexane 0 kJ/mol, cycloheptane 26 kJ/mol, cyclooctane 40 kJ/mol.
The Baeyer strain theory (1885) — and its failure
Adolf von Baeyer proposed (1885) that cycloalkanes are planar and strain comes purely from angle deviation. His model ranked small rings as strained but predicted cyclopentane (108° angles, nearest 109.5°) would be most stable — wrong. Real cyclobutane puckers, cyclopentane folds into an envelope, and cyclohexane adopts the chair, with every angle 109.5° and every bond staggered. The lesson: molecular shape is three-dimensional, not a flat polygon.
Why cyclopropane is special
Cyclopropane's three carbons are forced planar (a triangle cannot pucker), so its ~49.5° angle deviation and fully eclipsed C–H bonds are unavoidable. Its C–C bonds are bent ("banana") bonds, and the ring reacts like an alkene in some ways (it adds H₂, Br₂, HX under conditions alkanes ignore). Its ~115 kJ/mol of strain is the largest of the common cycloalkanes.
Common Confusions
| Do not confuse | With | Difference |
|---|---|---|
| "Cyclopentane is the most stable ring" | Measured stability | Baeyer predicted it from planar angles; data show the chair is strain-free and most stable |
| Angle strain only | Total ring strain | Strain = angle + torsional + steric; cyclopentane's tiny angle strain hides real torsional strain |
| "Larger rings are more stable" | Strain vs ring size | Strain falls from 3→6 carbons, then rises (cycloheptane 26, cyclooctane 40 kJ/mol) due to transannular strain |
| Heat of combustion per molecule | Per CH₂ group | Always compare per CH₂ — bigger rings burn more overall; per-CH₂ values reveal strain |
| Cyclopropane is a normal alkane | Strained, alkene-like ring | Adds H₂, Br₂, HX under conditions alkanes resist; bent bonds and ~115 kJ/mol strain change its chemistry |
| The 120° angle of a hexagon | Cyclohexane's actual angles | A planar hexagon has 120° angles; the chair bends them to 109.5° |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Imagine fitting kids around a table so each can hold hands with the next. Three forced into a tiny triangle are squeezed and grumpy (cyclopropane); four in a square is awkward; five is close to a circle — pretty good. Six make a perfect circle, everyone comfortable (cyclohexane). The grumpier the kids, the more stored energy — and if let go, they'll gladly break out.
Worked example
Example 1: Computing cyclopropane's ring strain from combustion data
Formula first: ring strain = (ΔH per CH₂ of ring − ΔH per CH₂ of reference) × number of CH₂ units.
Step 1 — data: cyclopropane ≈ 697 kJ/mol per CH₂; unstrained reference ≈ 659; cyclopropane has 3 CH₂ units.
Step 2 — substitute and compute:
strain = (697 - 659) kJ mol-1 × 3 = 38 kJ mol-1 × 3 = 114 kJ mol-1
(Unit check: kJ mol⁻¹ × unitless count = kJ mol⁻¹ ✓)
Step 3 — interpret: about 115 kJ/mol of stored strain — enough that ring-opening or addition reactions become thermodynamically favorable. The same arithmetic for cyclohexane gives (659 − 659) × 6 = 0 kJ/mol.
Example 2: Percent excess heat of combustion
Formula first: percent excess = [(ring ΔH per CH₂ − reference ΔH per CH₂) / reference ΔH per CH₂] × 100%.
Step 1 — cyclopropane:
697 - 659659 × 100% = 38659 × 100% ≈ 5.8%
(Unit check: kJ/mol ÷ kJ/mol = unitless, then ×100% ✓)
Step 2 — cyclobutane:
686 - 659659 × 100% = 27659 × 100% ≈ 4.1%
Step 3 — interpret: cyclopropane releases about 5.8% more heat per CH₂ than an unstrained alkane — a small percentage yet a large absolute strain, which is why combustion data can detect strain that casual inspection misses.
Example 4: Which ring opens more easily?
Setup: compare cyclopropane and cyclohexane under conditions that can add H₂ across the ring.
Prediction using strain: cyclopropane carries ~115 kJ/mol of strain, so ring opening relieves that energy; cyclohexane has none. Cyclopropane therefore adds H₂ (ring opens to propane) far more readily than cyclohexane.
Key takeaways
- Ring strain = angle strain + torsional strain + steric strain; cyclohexane (chair) has essentially zero of all three.
- Interior angle of a regular n-gon: (n - 2) × 180°/ n. Cyclopropane 60°, cyclobutane 90°, cyclopentane 108°, planar cyclohexane 120° — the chair avoids this with 109.5° angles.
- Approximate heats of combustion per CH₂ (kJ/mol): cyclopropane 697, cyclobutane 686, cyclopentane 664, cyclohexane 659 (= unstrained reference), cycloheptane 662, cyclooctane 664.
- Approximate ring strain energies (kJ/mol): cyclopropane 115, cyclobutane 110, cyclopentane 26, cyclohexane 0, cycloheptane 26, cyclooctane 40.
- Stability order: cyclohexane > cyclopentane ≈ cycloheptane > cyclooctane > cyclobutane > cyclopropane.
- Cyclopropane is planar with bent bonds and reacts like an alkene in some ways; medium/large rings suffer transannular strain — bigger is not automatically better.
Check yourself
4 review questions from the chapter. Try each one, then open the answer.
Write the three components of ring strain and state which ring size minimizes all three.
Show answer
Angle strain + torsional strain + steric (van der Waals) strain. Cyclohexane's chair has ≈109.5° angles, all-staggered bonds, and no crowding — zero strain on all three.
Cyclopropane burns at ≈697 kJ/mol per CH₂ and the unstrained reference at ≈659. What is the ring strain per molecule?
Show answer
(697 − 659) kJ/mol × 3 CH₂ = 114 kJ/mol ≈ 115 kJ/mol.
Why did Baeyer's planar-ring theory predict the wrong "most stable" ring?
Show answer
He assumed planar rings and angle strain only. Cyclopentane's 108° angles look best on paper, but cyclohexane avoids the planar hexagon's 120° angles by puckering into a chair with 109.5° angles and staggered bonds.
Rank cyclobutane, cyclohexane, cyclopropane, and cyclopentane from most to least stable.
Show answer
Cyclohexane (0) > cyclopentane (26) > cyclobutane (110) > cyclopropane (115 kJ/mol), using approximate strain energies.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- ring strain
- Extra internal energy from forced geometry
- angle strain
- Deviation of bond angles from 109.5°
- torsional strain
- Eclipsing penalty between adjacent bonds
- steric/van der Waals strain
- Crowding of nonbonded atoms
- heat of combustion
- Heat released when a compound burns completely
- transannular strain
- Repulsion between atoms across a ring interior
- bent (banana) bond
- Cyclopropane C–C bond with electron density off the internuclear axis
- Baeyer strain theory
- 1885 model assuming planar rings and pure angle strain
Sources & references
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