Identifying Unique Atoms and Groups

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.

Non-Cyclic Molecules

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.

Table 1

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.

Cyclic Molecules

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.

Figure 1

Going Round and Round

Table 2 summarizes the groups that are attached to each carbon in this molecule.

Table 2

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.