One of the goals for students who want to master the challenges of organic chemistry should be to develop the ability to think like an organic chemist. (This will amaze your friends and cause your enemies to cower in awe.) In this topic, we will look at one way in which organic chemists think about molecular structure. Specifically, we will examine one way in which they determine whether two atoms or groups within a molecule are identical. This is an important skill because it goes hand-in-hand with their ability to deduce molecular structures from NMR spectra.
Identifying Identical Atoms and Groups
The most rigorous way to determine whether two atoms within a molecule are identical involves the analysis of the symmetry of the molecule. A less rigorous alternative entails enumeration of the atoms and/or groups that are attached to each of the atoms in question. Since there is a subtle difference bewteeen the analysis of cyclic and non-cyclic molecules by this approach, we will consider these two situations separately.
Note Until you have developed the ability to perform the analyses described below in your head, it is advisable for you to work with molecular models of the compounds.
Consider the case of propane,, for example. Is C1 identical identical to the C2? Is it identical to C3? Table 1 illustrates how to tell.
Getting to Know You
The four groups, G1-G4, attached to C1 of propane are H, H, H, and CH2CH3. These are not the same as the four groups attached to C2. Hence C1 and C2 are not identical. By the same token, C2 and C3 are not identical. However, the four groups attached to C1 are identical to those attached to C3, and these two atoms are identical. Remember-The numbers are used simply to keep track of things. If it is not obvious to you that the group G4 attached to C1 is the same as the group G1 attached to C3, redraw Table 1 but don't include the subscripts on the carbons.
Identifying the groups attached to a particular atom that is part of a cyclic molecule is a bit trickier than for non-cyclic molecules. Consider the case of 1-chlorocyclopropane. The structure of this molecule is shown in Figure 1 where each of the carbon atoms is numbered in order to avoid confusion. Note that the numbering proceeds arbitrarily in a clockwise direction from C1 to C3. The structure could just have easily been numbered in a counter-clockwise direction.
Going Round and Round
Table 2 summarizes the groups that are attached to each carbon in this molecule.
Haven't We Met Before?
Notice that there is a form of "double counting" involving G3 and G4. If you focus on C1, G3 is defined by tracing a path from C1 to C2 to C3 and back to C1. G4 is defined by tracing the same path, but in reverse. The same idea applies to C2 and C3.
Since C1 is the only carbon that is bonded directly to a chlorine atom, it is clearly different than C2 and C3. However, C2 and C3 are identical. Since the numbering in Figure 1 was arbitrary, the group G3 that is attached to C2 is really the same as the group G3 that is attached to C3. This is also true for G4 with C2 and C3. This may be more apparent to you if you remove the numbers that identify the carbons in columns G3 and G4 of Table 2. The conclusion to be derived from this analysis is that there are only two unique carbon atoms in 1-chlorocyclopropane.