Relative Stabilities of Organic Compounds Using Benson's Additivity Rules Dale E. Vitale Kean College of New Jersey, Union, NJ 07083
With few exceptions beginning organic chemistry students find the underlying principles of the subject to he elusive. T o many, it at first appears to he a catalog of loosely related, descriptive examples. Perhaps the most pervasive of these principles, the structure-energy relationship ( I ) , could be treated in a more explicit manner than i t traditionally is. In many cases this principle is only alluded to where qualitative arguments are supported by experimental data. While such specific allusions provide students with the "proof" necessary to give them confidence in the arguments, they tend to obscure the generality of the structure-energy principle (SEP). A second point regarding the traditional treatment of the SEP concerns the relationship of organic chemistry to other physical science courses. While in these other cases general principles are often derived from simple precepts, those in organic are usually presented qualitatively. Consequently, students are forced to rely heavily upon qualitative, rather than quantitative, understanding. Although qualitative reasoning is an important part of scientific thinking, this fea'ture of organic instruction leads some students to the difficult task of memorizing the subject when they fail to acquire the requisite understanding. Finally, the empirical approach to the SEP could be presented with more precision than i t is. Although the use of data from specific experiments does add precision to discussions of relative, molecular stabilities, it does not provide students with a general tool for making such comparisons. Specifically, without experimental data they can make only qualitative predictions which, in some cases, may not allow them to reach a conclusion a t all. This is particularly a problem when two influential factors work in opposite directions. While treatment of the SEP in a nonempirical manner (i.e., using quantum mechanics) is urecluded. a t least for beyinnin;st"dents,an efficient method for calculating heats of formation (AH,?)of organic compounds would afford students just the quantitative approa'h alluded to above. More specifically it would: 1) make treatment of the SEP more explicit, 2) make the presentation of this principle more consistent with the way in which similar generalizations are taught in other physical science courses, and 3) afford students a more precise tool for comparing molecular stahilities. Fortunately, such a method has already been developed by Benson et al. (2). Known as Benson's Additivity Rules, this method provides asimple and efficient route to AHp's of even complex organic compounds a t 25 OC in the gas phase. It is based on the concept that AHp for a given compound may be taken as the sum of the AHp's for the "groups" that make up its structure. Here a "group" is defined as a carbon atom plus its ligands. For example the calculation, using Benson's notation, of H p for 2,2-dimethylpropane is illustrated in Figure 1.From tables compiled by Benson et al. the group enthalpies for C-(C)r and C-(C) (HI3are +0.5 kcal mol-' and -10.08 kcal mol-I, respectively. According to the equation in Figure 1the AHp for this alkane is then -39.82 kcal mol, which compares respectably with the experimental value of -40.32 kcal mol-I (3). 304
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Benson et al. have compiled extensive tables of AHp's for the commonly occurring groups (4). In addition to the group enthalpies, these tables include correction factors for gauche interactions, and angle strain in alicyclic compounds, as well as values for compounds containing heteroatoms. This scheme often provides heats of formation that are within a few kcal mol-I of the experimental ones. The examples that follow illustrate how, through the generality of this scheme, the structure-energy principle can be made more explicit to students while providing them with a more precise tool for treating related problems. In addition, these examples show how the use of heats of formation can make the teaching of this principle more consistent with the way similar themes are taught in other physical science courses.
= -39.82 kcal mol-' Figure 1. Heat of formation (kcal mol") of 2.24imethylpropane using Benson's notation (4).
Figure 2. Heats of formation (kcal mol-')of isomeric alkenes
Appllcatlons of Group-Enthalples Relative Stabilities of Alkenes
One of the first places in which beginning organic chemistry students encounter an applicationof the SEP is in studying alkene preparation. In turn, one of the first things that they learn about alkenes is that those with more carbon atoms attached to the doubly bonded carbon atoms are more stable (5).However, what they typically do not learn, at least in an exnlicit wav.. is how stabledkenes are relative to other classes of compounds (e.g., alkanes). Figure 2 shows the structures of five isomeric alkenes and their corresponding heats of formation (kcal mol-I), calculated from Benson's erouo enthal~ies.The use of AHto's ~rovidesa number of adva&ages. First, they give explicit sipport for conclusions about relative alkene stabilities reached on a qualitative basis (i.e., AHf"' Hn0 AHIIIO > AHlp >AHyo) a n d show clearly how significant differences in substitution about the double bond are. This treatment, although still fundamentally empirical, is more consistent with those of other physical science courses and could he accomplished by students without reference to experimental data. Second, the AHro's provide the precision needed to distinguish between compounds like I1 and 111; a distinction that could not he made by most students qualitatively.
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Finally, theuse of AHto's, and Benson's scheme. provides a basis onwhich to contrast alkenes with compounds helongina to other classes. For example, the heat of formation for the alkane corresponding to the carbon skeleton in Figure 2 is -54.02 kcal mol-', about 25 kcal mol-' more stable than even the least enereetic of all the alkenes in Fieure 2. This is general in that allYalkanes are more stable tcan the correspondingalkenes, and this isexemplified by the much higher reactivities of alkenes over alkanes (6). Thus, students are afforded a relationshio. .. based on the SEP. between the two classes of compounds. In addition to the generality, consistency, and precision that this scheme gives to the study of the SEP, it affords rigorousness lacking in a qualitative treatment. For example, most students could predict qualitatively the relative stabilites of the isomeric cycloalkenes shown in Figure 3, based on a knowledge of angle strain (7). Nevertheless, without access to experimental data (e.g., AH-hydrogenation) thev would have onlv an im~reciseunderstandine"of iust . bow large the differences were. However, using Benson's tables the AH& of these compounds (Fig. 3) show immediately that while there is considerable difference in the stabilities of the first and second, that between second and third is minimal. Hence, the student is afforded an understanding of how much "strain" is involved in such a comparison. Aromaticity in Benzenoid Compounds
Figure 3. Heats offwmation (kcal moi-') of tran~3.4dlmethylcyclobuteneB 4. methyicyclopenteneand cyclohexene.
A working definition for "aromatic" that is often used in sophomore organic courses is that aromatic compounds are those cyclic conjugated systems that are more stable than their open-chain analogs (8).This is a simple concept, and therefore attractive. but it is not useful to students unless i t is accompanied by experimental data. Benson's Rules, a t least for henzenoid comoounds, provide an efficient route to such predictions, with& specific experimental data. For example, Figure 4 gives the structures and AHp's (kcal mol-1) for three aromatic henzenoids. Comparison of these values shows that, under the above definition, the cyclic compounds are indeed aromatic. Both the concept and method of calculation are simple. One first writes astructure for the benzenoid comnound. The onen-chain analoe is derived from this by: 1) removing the ring-fusion bonds, 2) removine one sinele bond from the resultiuemonocvcle. The AHHs f i r both compounds are then calc~lated,from the sums of the group enthalpies, and the two values are compared. Thus, under the above definition, the cyclic compounds in Figure 4 are clearly aromatic.
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Keto-Enoi Tautomerism
One of the more obvious applications of Benson's group enthalnies is to the treatment of eauilibria. While there are many examples of equilibria encountered by beginning oreanic students. one of the most i m ~ o r t a n tis between carbony1 compounds and their enols. Figure 5 provides an examole usine cvclohexanone and its enol. The values aiven directly herow- the structures are heats of formation (kcal mol-1). while those in parentheses are entropies of formation (cal mil-' K-l) calcuiated from Benson's group enthalpies and entropies, respectively. The enthalpies indicate clearly that, as is usual, the keto form is considerably more stable than the en01 (9).Thus, a student would be provided with a precise understanding of by how much the keto form is favored in such equilibria and where both compounds rank relative to others in energy (e.g., Fig. 1-4). In addition, should an instructor choose to use them, Benson's tables include values for group entropies affording the option of calculating K., for such equilibria from: AGO = AHo -TASo and A@ =-RTln(K,,). In this case, using AH(% and Sp's from Figure 4, K,,= 2.7 X lo-=, indicating that the ketone is much more highly favored than the enol. Even without the use of Sf%, since their use requires some knowledge of molecular symmetry, students would he. ahle to acquire a useful
Figure 4. Comparison of me heats of formation (kcal mol-') of benzene, naphthalene, and anthracene with the mesponding open-chain compounds.
Figure 5. Heats (kcal mi-') and entropies (cal mol-' K-') of formation of the keto and end forms of cvdohexanone.
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approximation of the positions of such equilibria from AHp's alone (i.e., assuming AH0= AGO). Concluslon Although the use of Benson's additivity rules in sophomore organic chemistry courses would no means provide a panacea for instruction, it would certainly give students a helpful tool. The use of this method would help to make the structure-energy relationship more explicit and would add much precision to the student's ability in evaluating relative molecular stabilities. I t is of value in almost any case where comparison of molecular stabilities has significance and, in particular, where differences are subtle.
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Literature Clted (1) K ~ PD. , s.; vciiaeeio, F. "organic chemistry";wo*
New ~ o r k1980: . p 1053. (2) genaon. S. W. "Thermoehemieal Kinetics", ind ed.: Wiiey-1nteteian"e New York, 1976. C.R.C.Pmaa. (3) Weask, R, C. "C.R.C. Handbook of Physics and Chemistry", ESth d.; I"".: west palrn h h , FL, 1977. "1 C-n~r,B.K."Oeteminstionof OaanicReaaionM~h.nim":Wiiev: NmYorL. 19W. p 221. (5) ~ ~ ~ r iR. ~ To . n; E. ~ . R~:.orgaoic . chemistry", 4th d . ; ~ l l y n a n dBacon N m . MA, 1983; p 301. i8, Soiomana,T. W.0...0.genicCbemisUy..,3dd.~ Wilsv:Nw 1wp135. (7) ~ . ~ h , ~ : ~ ~ d ~ ~ ~ ~ d ~ ~ ~ ~ n i ~ ~ h ~ ~ i . t r y : ~ c p e t i ~ ~ ~ , ~ ~ ~ h a n ~ ed.; McGraw-Hill: New York. 1978: p 116.
Rct 6,
456-
(,, hudon,G. M . ~ O r g a n i e C h r m h ~ A d d i s a n . W ~ i . y : N w York,
