Baeyer’s strain theory

Baeyer’s strain theory : To compare stability of cycloalkanes

When we carefully look over the cyclic saturated compounds, we find that each atom is sp3  hybridized.  The ideal bond angle 109028’ but in cycloalkanes this angle is mathematically 180-(360/n) where n is the number of atoms making ring.

for example Cyclopropane, angle is 600; in Cyclobutane it is 900 and so on.

Angle Strain : This difference in ideal bond angle and real bond angle, is called angle strain and it causes strain in bond which affects the stability of molecule.

Greater is the deviation from the theoretical angle, greater is the Angle strain ; lesser the stability.

To calculate the distortion or angle strain in cycloalkane we assume the atoms of ring in a plane, such as in cyclopropane, all the 3 carbon atoms occupy one corner of an equilateral triangle with bond angle 60o. As two corners bent themselves to form bond so strain too is divided equally. So strain in cyclopropane will be ½ (109o28’ – 600) = 24044’.

Deviation of bond angle in cyclopropane from normal tetrahedral angle

Distortion or strain = ½ (109028’ bond angle of ring). So angle strains in some cycloalkanes are listed in the table below.

 Compound No. of C in the ring Angle between the C atoms Distortion or strain Cyclopropane 3 600 24o44’ Cyclobutane 4 900 9o44’ Cyclopentane 5 108o 0o44’ Cyclohexane 6 120o -5o16’ Cycloheptane 7 128o34’ -9o33’ Cyclooctane 8 135o -12o62’

From the table it is clear that cyclopropane has the maximum distortion, so it is highly strained molecule and consequently more reactive than any of one monocylic alkanes, which is clear from the reaction that ring can be opened very easily to relieve strain on reaction with Br2, HBr or H2/Ni at high temperature.

In contrast, cyclopentane & cyclohexane have least strain so they are found more readily and are very stable as compared to cyclopropane.

Baeyer strain theory satisfactorily explains the typical reactivity and stability of smaller rings (from C3 to C5) i.e. Stability order follows : Cyclopropane < Cyclobutane < Cyclopentane

But not valid for cyclohexane onwards because the strain again increases with the increase in number of carbon atom but actually large rings are more stable. So molecular orbital theory is also considered according to which covalent bond is formed by coaxial overlapping of atomic orbitals. The greater is the extent of overlap the stronger is the bond formed. In case of sp3 carbon, C – C bond will have maximum strength if the C-C-C bond have the angle 109o28’. If cyclopropane is an equilateral triangle then the bond angle of each C-C-C bond would be 60o. Therefore it was proposed by Couson that in cyclopropane the sp3 hybridized orbitals are not present exactly in one straight line due to mutual repulsion of orbital of these bonds resulting thereby loss of overlap. This loss of overlap weakens the bond and is responsible for its instability and strain in molecule. Similarly, in case of cyclobutane, there is also loss of overlap but the loss is less than in cyclopropane, so cyclobutane is more stable than cyclopropane. Overlapping of orbitals in large ring compound (5 more carbon atoms) is however much better which accounts for the greater stability of such compound.

It is natural that when a molecule has strain within it, it will affect the stability of molecule. The stability of molecules can be calculated easily by measuring heat of combustion which will give the measure of total strain and thermochemical stability which can be calculated mathematically.

Total strain = (No of C atom is the ring × observed heat of combustion/CH2) observed heat of combustion/CH2 for n alkane.

Experimental data of total strain for different cycloalkanes*

 No. of C in the ring Heat of combustion kJ per CH2 group Total strain in kJ 3 697 115 4 686 109 5 664 27 6 659 0 7 662 27 8 663.8 42 9 664.6 54

* data from Organic chemistry solomons & Fryhle

From the data above it is clear that strain decreases from C3 to C6i.e. stability increases, but stability again deteriorates from C7 to C9 ring system.

According to this theory, the carbon atoms in 5 membered and smaller rings can lie in one plane as explained by Baeyer but Sachse suggested that in six membered and higher rings the carbon atoms are non planar . In this way the ideal angle 109028’ is retained and the ring is free from angle strain. Thus Sachse proposed that cyclohexane exist in two puckered forms as boat and chair form. These forms are readily inter-convertible through half chair and twist boat forms simply by rotation about the single bonds.