Formulas

The composition of a compound is given by its formula. If the compound is an ionic compound it can have only one formula. The ionic compound magnesium chloride has the formula, MgCl₂, which tells us that the compound consists of magnesium and chlorine and that there are two chlorine atoms for every magnesium atom. For the covalent compound benzene, there are a number of formulas. First, the empirical formula CH tells us that the compound contains only carbon and hydrogen and that for every one atom of carbon there is one atom of hydrogen. Second, the molecular formula tells us how many of each type of atom are present in one molecule. For benzene, the molecular formula is C₆H₆, and therefore there are six atoms of carbon and six atoms of hydrogen in one molecule. Notice that the molecular formula is always some multiple of the empirical formula (6 x CH = C₆H₆).

Third, when we are dealing with molecules we would also like to know how the atoms are arranged. This is represented by the structural formula. For a molecule with six carbons and six hydrogens, the atoms could be arranged in the following way:

In fact, there are a number of ways in which the six carbons and six hydrogens could be arranged, but when the structure of benzene was experimentally determined it was found that the carbons were arranged in a ring and that one hydrogen was attached to each carbon:

It may seem that we now know everything we need about the structure of benzene. If you think about the molecule in 3-dimensions, however, you begin to ask questions like: Is the ring planar? What are the angles between the carbon-carbon bonds? Is the ring a perfect hexagon? These questions can be answered by experimental techniques such as x-ray diffraction, and the answers can be given as a series of bond angles and lengths. It is usually more convenient to convey the information as some sort of three dimensional structural formula. Three dimensional formulas usually take one of three forms: a) structural formulas drawn to give a three-dimensional view, b) computer-generated drawing used specifically by x-ray crystallographers and usually called ORTEP diagrams, and c) molecular models, usually generated by computer. Figure 27 shows a three-dimensional structural formula of benzene and the amino acid, alanine.

Figure 27. 3-Dimensional formulas for benzene (computer model) and alanine (wedge and line).

Notice that a wedge is used to indicate that the group extends out of the plane of the page toward the reader, a solid line to indicate a group in the plane of the paper, and a dotted line (or reverse wedge) to indicate a group behind the plane of the paper. When we discuss structure in the next section, the reason for the use of these devices will become clearer. Figure 28 shows a ball and stick model and a space-filling model for alanine.

Figure 28. Ball and stick and space-filling models of alanine.

The structural formulas of organic compounds can be particularly cumbersome. Consider the compound 3-octene which has the molecular formula C₈H₁₆. Figure 29 shows a number of ways of writing the structural formula of 3-octene. In part (a) all of the bonds between the hydrogens and carbons are written out. This formula shows that the third carbon has a double bond joining it to the adjacent carbon. The formula is actually an electron-dot formula, which we will discuss below, but it also clearly shows which atoms are attached to one another. In part (b), the structural formula is condensed somewhat by placing the atoms together in groups. For example, the CH₃ group designates three hydrogens attached to a carbon. This group can also be written as H₃C. In part (c), the structural formula is even more condensed by omitting the carbon and hydrogen atoms. This type of line formula is frequently used by organic chemists because of the complexity of the formulas of many organic compounds.

Figure 29. Formulas for 3-octene.

Because this type of formula is somewhat unusual, let us consider several simple examples. The compound isopropyl alcohol (rubbing alcohol) has the formula (CH₃)₂CHOH, which should be interpreted to mean that two methyl groups, a hydrogen, and an OH group are attached to a carbon:

In line formula notation, isopropyl alcohol would be written:

It is assumed that the reader will recognize that the termination of each line and the junction of one line with another represents a carbon and enough attached hydrogens to provide four bonds around each carbon.

Another example is the compound ethyl acetate, which has the formula CH₃COOCH₂CH₃. This compound contains the carboxyl group (COO) which has one oxygen doubly bonded to the carbon while the other oxygen is singly bonded to the carbon. Thus, the full structural formula showing all the bonds is:

The condensed formula is:

and the line formula is:

Nobel laureate, Roald Hoffmann, a physical chemist with an interest in many diverse topics, says of illustrations, "What are these curious drawings, filling the pages of a scientific paper? I now ask the question from the point of view of an artist or draftsman. They are not isometric projections, certainly not photographs. Yet they're obviously attempts to represent in two dimensions a three-dimensional object for the purpose of communicating its essence to some remote reader.

"It is fascinating to see the chemical structures on the pages of every journal and to realize that from such minimal information people can actually see molecules in their mind's eye. The clues to three-dimensionality are minimal. The molecules float (see below), and you're usually discouraged from putting in a reference set of planes to help you see them (center).

"Some chemists rely so much on the code that they don't draw norbornane as on the left side of the illustration above, but as on the right. What's the difference? One line "crossed" instead of "broken." ...

"The policies of journals, their economic limitations, and the available technology put constraints not only on what is printed but also on how we think about molecules. Take norbornane (see below). Until about 1950 no journal in the world was prepared to reproduce this structure as shown below on the right. Instead you saw it in the journal as illustrated on the left.

Now everyone had known since 1874 that carbon is tetrahedral, meaning that the four bonds to it are formed along the four directions radiating out from the center of a tetrahedron to its vertices. Molecular models were available or could be relatively easily built. Yet I suspect that the icon of norbornane that a typical chemist had in his mind around 1925 was that on the left, not that on the right. He was conditioned by what he saw in a journal or textbook--an image, and a flat one at that. He might have been--I think he often was--moved to act (in synthesizing a derivative of this molecule, for instance) by that unrealistic two dimensional image*."

*Roald Hoffmann, The Same and Not the Same, Columbia University Press, New York, 1995, page 76-78.

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