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Relative Stability

The relative stability of cycloalkanes depends on their size and hence, on the strain within their rings.

Table of calculated and experimental heats of combustion of cycloalkanes (CH₂)ₙ, total strain and strain per CH₂

From the table of heats of combustion of alkanes one can deduce that every added CH2 group makes the value more negative by 157.4 kcal/mol. We can thus calculate the expected heat of combustion (157.4 x n) of any cycloalkane (CH2)n.

In the case of cyclopropane, the combustion is more exothermic than expected. That means that the CH2 groups of cyclopropane are not 'normal' because forming a three-membered ring makes them higher in energy (less stable) than expected. The energy difference reflects the strain in the cyclopropane ring.

Heat of combustion of cyclopropane: experimental −499.8 versus calculated −472.2 kcal/mol; the difference (27.6) is the ring strain
Heats of combustion of graphite (−94.1 kcal/mol) and hydrogen (−57.8 kcal/mol, to gaseous water) and heat of condensation of water (−10.52 kcal/mol)

We may use the calculation of the heats of formation to compare the relative stability of cyclopropane and propane.

Heats of formation of propane (−24.9 kcal/mol) and cyclopropane (+12.6 kcal/mol)

Propane is more stable (by about 25 kcal/mol) than its separate elements.

In turn, cyclopropane is less stable (by about 13 kcal/mol) than its separate elements. This does not prevent cyclopropane from existing as a stable molecule, but its positive heat of formation again reflects ring strain. This makes it more reactive, since it tends to release the strain by ring opening.

Small cycloalkanes are less stable than expected as compared to 'normal' alkanes. What is the origin of that 'abnormality'?

In an acyclic alkane the bonds form 109.5° angles and the hydrogens are staggered

In an acyclic alkane the head-on overlap of the sp3 orbitals is maximal, giving rise to a C-C bond of high strength (ΔH°C–C = 90 kcal/mol). On the other hand, the hydrogens can easily adopt a staggered conformation where their steric and orbital interactions are minimized.

Imperfect, 'banana' overlap of the sp3 orbitals in cyclopropane

The internal angle in cyclopropane is 60º, much smaller than the natural angle of tetrahedral sp3 orbitals (109.5º). Therefore, the orbital overlap in cyclopropane cannot be truly head-on and is less effective. The experimental lower strength of the C-C bonds in cyclopropane (ΔH°C–C = 65 kcal/mol) is proof of that.

In cyclopropane the internal angle is 60° and the hydrogens are eclipsed

In addition to the distortion in orbital overlapping due to the small size of the ring, the hydrogens on neighboring carbons are inevitably eclipsed. This adds further instability. The combination of the two factors -ring strain and eclipsing strain- explains the difference between the calculated heat of combustion -as if cyclopropane were a 'normal' alkane- and the experimental one.