Up to now, we haven’t given an entirely accurate impression of rings. We have been drawing them all as though they were planar, although this is actually not the case. In this section you will learn how to draw rings more accurately and to understand the properties of the different conformations adopted. If we assume that in fully saturated carbocyclic rings each carbon is sp³ hybridized, then each bond angle would ideally be 109.5°. However, in a planar ring, the carbon atoms don’t have the luxury of choosing their bond angles: internal angle depends only on the number of atoms in the ring. If this angle differs from the ideal 109.5°, there will be some sort of strain in the molecule. This is best seen in the picture below, where the atoms are forced planar. The more strained the molecules are, the more the bonds curve—in a strain-free molecule, the bonds are straight.

Notice how in the smaller rings the bonds curve outwards, whilst in the larger rings the bonds curve inwards. The table gives values for the internal angles for regular planar polygons and an indication of the strain per carbon atom due to the deviation of this angle from the ideal tetrahedral angle of 109.5°. These data are best presented as a graph, and the ring strain per carbon atom in planar rings for ring sizes up to 17 are shown on the next page. Whether the bonds are strained inwards or outwards is not important so only the magnitude of the strain is shown. From these fi gures (represented in the graph on p. 368), note:

• These are calculated data for hypothetical planar rings. As you will see, real rings are rather different.

• The calculated ring strain is largest for three-membered rings but rapidly decreases through a four-membered ring and reaches a minimum for a five-membered ring.

• The calculated ring strain increases again (although less rapidly) as the rings get larger after the minimum at 5. But what we really need is a measure of the strain in actual compounds, not just a theoretical prediction in planar rings, so that we can compare this with the theoretical angle strain. A good measure of the strain in real rings is obtained using heats of combustion. Look at the following heats of combustion for some straight-chain alkanes. What is striking is that the difference between any two in the series is very nearly constant at around –660 kJ mol⁻¹.

If we assume (as is reasonable) that there is no strain in the straight-chain alkanes, then each extra methylene group, –CH₂–, contributes on average an extra 658.7 kJ mol−1 to the heat of combustion for the alkane. A cycloalkane (CH₂) n is simply a number of methylene groups joined together. If the cycloalkane is strain-free, then its heat of combustion should be n × 658.7 kJ mol⁻¹. If, however, there is some strain in the ring that makes the ring less stable (that is, raises its energy) then more energy is given out on combustion. Now, let’s put all this together in a graph showing, for each ring size: (a) angle strain per CH₂ group and (b) heat of combustion per CH₂ group.

Points to notice in graph above:

• The greatest strain by far is in the three-membered ring, cyclopropane (n = 3).

• The strain decreases rapidly with ring size but reaches a minimum for cyclohexane, not cyclopentane as you might have predicted from the angle calculations.

• The strain then increases but not nearly as quickly as the angle calculation suggested:

it reaches a maximum at around n = 9 and then decreases once more.

• The strain does not go on increasing as ring size increases but instead remains roughly constant after about n = 14.

• Cyclohexane (n = 6) and the larger cycloalkanes (n ≥ 14) all have heats of combustion per –CH₂ group of around 658 kJ mol−1, the same value as that of a –CH₂ group in a straight-chain alkane, that is, they are essentially strain-free. You might ask yourself some questions now: Why are six-membered rings and large rings virtually strain-free? Why is there still some strain in five-membered rings even though the bond angles in a planar structure are almost 109.5°? The answer to both these questions, as you may already have guessed, is that the assumption that the rings are planar is simply not correct. It is easy to see how large rings can fold up into many different conformations as easily as acyclic compounds do. It is less clear to predict what happens in six-membered rings.

مواضيع ذات صلة

E1 reactions can be stereoselective

The role of the leaving group

Substrate structure may allow E1

E1 and E2 mechanisms

Size

Elimination happens when the nucleophile attacks hydrogen instead of carbon

Axially and equatorially substituted rings react differently

Steroid

Decalins

What happens with more than one substituent on the ring

Substituted cyclohexanes

The ring inversion (flipping) of cyclohexane