In the Classroom
A Way To Predict the Relative Stabilities of Structural Isomers John M. Lyon Department of Chemistry, University of Wisconsin–Green Bay, Green Bay, WI 54311
The structure of molecules and molecular ions is one of the important topics that are presented in any introductory chemistry course. The topic is often developed by first introducing Lewis structures and then showing how VSEPR theory can be used to predict the arrangement of atoms around each central atom in the molecule. An aspect of this topic that is not often developed is the analysis of the relative stability of structural isomers. Here, students should be presented with information that they can use to predict the arrangement of atoms that will produce the most stable structure. In most general chemistry texts this topic is poorly treated. Commonly, the only issue addressed is the choice of the central atom and this is usually treated with the general statement that the least electronegative element is the central atom (1–5). One author went a step further and presented a set of rules for the evaluation of the Lewis structures of structural isomers based upon formal charges (3). Less frequently addressed is the idea of extended structures versus compact or branched structures. I have found this subject addressed only with a statement that the compact structure is preferred (2). The literature of chemical education has some excellent papers dealing with the writing of Lewis structures but it does not address the topic of structural isomers beyond the level that is presented in introductory chemistry textbooks (6–9). While the techniques that are presented in these references usually yield a correct result for the prediction of the most stable structural isomer, I find them to be lacking in a basic physical chemical principle that can be easily sold to students. Moreover, they do not promote the investigation of the relative stability of structural isomers, an important basic chemical concept. In this paper I present a set of rules that can be used to evaluate the relative stabilities of structural isomers and the justification of these rules using basic electrostatic arguments. Background Simple rules can be formulated for the analysis of the relative stabilities of structural isomers using the principles upon which semiempirical molecular orbital calculations are based. In very general terms, semiempirical molecular orbital calculations treat molecules as a collection of valence electrons and core structures. The valence electrons are the electrons that are in the valence orbitals of the atoms of the molecule, and the core structures are the nuclei and the inner-shell electrons of each atom. Semiempirical calculations determine two energy terms. The first deals with the attraction between the electrons and the cores and the repulsion between electrons. This term, often called the electronic energy, can be thought of as the energy that is holding the atoms together. The second energy term deals with the repulsion between the cores. This term is often called the core–core repulsion energy and can be thought of as the energy that is holding the atoms apart. The overall energy of the molecule is the difference between these two terms. In stable species, the magnitude of 364
the electronic energy term is greater than the magnitude of the core–core repulsion term. Within a series of structural isomers, the species with the greatest difference between the magnitudes of these two energies will be the most stable. Rules for Predicting Relative Stabilities Two sets of rules have been identified that, in the majority of cases that I have examined, allow the relative stabilities of structural isomers to be correctly predicted. The application of these rules does not require the initial drawing of a valid Lewis structure or detailed calculations of orbital energies. Use of the rules does require a basic knowledge of electron configuration and of how atomic size varies as a function of position on the periodic table. The first set of rules is used for the analysis of organic compounds and the majority of inorganic compounds. The second set addresses the oxides and halides of the halogens and the noble gases of the third period and higher.
First Set of Rules To apply the first set of rules, begin by assigning the connectivities of the atoms in each isomer you care to explore. In most cases, one would follow the basic rules used for writing Lewis structures that concern the normal valence of hydrogen and the halogens. In cases where these rules are hard to follow, such as with the FHF { anion, any structure can be analyzed. Assign to each atom in each structure its core charge. The following rules are then applied sequentially to the set of structural isomers to determine the relative stabilities of the isomers. 1. The most stable structure has the lowest sum of the products of core charges of connected atoms. 2. When a choice must be made between extended structures and compact structures with equal stability from rule 1, the most compact structure is lower in energy. 3. When a choice must be made between equal structures from rules 1 and 2, the structure with the largest central atom will be most stable.
Application of Rule 1: The Structure of Cyanate Four different structures can be formed with three different atoms. Three of the structures are extended structures that differ by the identity of the central atom of the array, and the fourth structure is cyclic. The possible structures are shown in Figure 1 for the atoms in cyanate. The core charge is written below each atom.
Figure 1. The possible structures for the atoms in cyanate with core charges.
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In the Classroom
The sum of the products of the charges of the cores for connected atoms for the four structures would be 20 plus 30 for 50, 24 plus 30 for 54, 20 plus 24 for 44, and 20 plus 30 plus 24 for 74. Based upon rule 1, the order of stability for the four structures would be NCO, CNO, CON, followed by the cyclic structure. This is the correct order of stabilities for the two species, cyanate and isocyanate, that are known for this formula. Application of Rules 2 and 3: The Structure of SO2Cl2 Two different types of structures that are equal by rule 1 for the atoms in sulfuryl chloride are presented in Figure 2. For each structure the calculated value for the sum of the products of the core charges for connected atoms is 156. The first type of structure is an extended structure with all five atoms in a single chain. The chlorine atoms are on each end of the chain, and the oxygen and the sulfur atoms are arranged in different ways between the chlorine atoms. The second type of structure is branched. Three structures have four atoms in a chain and two structures have three atoms in a chain. When we apply rule 2 to this set of structures we identify one of the structures with the three-atom chains as the most stable compound. When we apply rule 3, the structure with sulfur as the middle atom is identified as the lowest-energy species. Discussion Rules 1 and 3 address different ways to reduce the core– core repulsion energy for a molecule. From classical electrostatic analysis, the core–core repulsion energy is proportional to the sum of the product of the charges of the cores divided by the distance that separates the cores for every possible pairing of atoms in the molecule. Rule 1 minimizes this term by reducing the product of the charges for the pairs of atoms that are closest together. For most systems the reduction of this term for the atoms closest together in the molecule will yield the greatest overall decrease in the core–core repulsion term. Rule 3 minimizes the core–core repulsion term by increasing the distance between cores for a number of the terms in the series. Presented in terms of electrostatics, it should be fairly easy to convince students that the most stable structure would have the atoms arranged in such as way as to minimize the repulsion between the cores. Rule 2 is based upon the observation that the electronic energy for a species increases as the structure becomes more compact. A presentation of the way that molecular orbital calculations determine the electronic energy for molecules is not appropriate for this level of analysis. But, one can present
Figure 2. The possible structures of the atoms in sulfuryl chloride that are equal by rule 1.
a model that qualitatively looks at the forces of attraction between an electron and a set of nuclei. We will use the idea that the amount of energy required to remove an electron from a set of nuclei is directly proportional to the forces that the electron is exerting on the nuclei to hold them together. When we have a nucleus and an electron in a given region of space, the electron experiences a force of attraction to the nucleus due to their opposite charges. When we add a second nucleus to that region of space we increase the attraction of the electron to the region of space. This is due to the increase in the total positive charge of the region. As the number of nuclei that are in the given region of space increases, the forces of attraction holding the electron within that region of space continue to increase. This idea of adding nuclei to a given region of space is analogous to making the molecule more compact. This model therefore predicts that the isomer with the greatest amount of attractive forces between electrons and nuclei will be the isomer that has the nuclei pack together most tightly.
Second Set of Rules The second set of rules addresses two groups of compounds in which the relative importance of the rules as stated above is altered. These compounds are the isomers of the oxides and halides of the halogens and noble gases. For example, by the method presented above the structural isomer for the atoms in chlorate, ClO3{, with oxygen as the central atom is predicted to be more stable than the isomer with chlorine as the central atom. The rules above will always predict the isomer with oxygen as a central atom to be more stable than the isomer with a halogen as the central atom. For the compounds with fluorine and oxygen the prediction would be correct. But for the compounds with the other halogens, unknown species are often predicted as the most stable isomer. In compounds such as those containing ClO3{, the isomer with chlorine as the central atom would have a lower core–core repulsion term than the isomer with oxygen as the central atom because of the larger size of the chlorine atom compared to that of an oxygen atom. With these compounds, the size of the central atom is more important than the sum of the products of the core charges of connected atoms. We could then restate the rules for the oxides and the halides of the halogens and the noble gases that are of the third period or greater as: 1. The compact structure is more stable than the extended structure. 2. The structure with the largest central atom is the most stable.
While I have not performed an exhaustive analysis, I have found that these rules work for most simple organic compounds. Based upon rule 1, alcohols are predicted to be more stable than ethers, primary amines more stable than secondary amines, and the keto form more stable than the enol form of aldehydes and ketones. Based upon rule 2, the branched isomers are predicted to be more stable than the linear isomers for the alkanes. Problems arise with compounds that contain strain energies or have electronic stabilization due to conjugation. For example, this method incorrectly predicts that methylcyclopropane is more stable than cyclobutane and it predicts the same stability for acetamide and aminoethanal. Additional rules could be added to extend this method of analysis to
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include these types of systems. But, I would prefer to keep the analysis as simple as possible and to say that like most simple methods it has limitations. I recommend that this method be used as a starting point for the analysis of the relative stability of structural isomers and that refinements to the method be introduced when the topics of strain energy and electronic stabilization due to conjugation are presented. Conclusions The ideas presented here for the analysis of the relative energies of structural isomers are not being put forward as an alternative to Lewis structures. With this analysis you do not explicitly treat electrons; therefore, it is not possible to predict molecular shapes, Lewis acid and base behavior or any of the other properties that can be predicted from Lewis structures (10). What you can do, in most cases, is predict the most stable structural isomer for a set of atoms. You can do this without using general statements about the arrangement of atoms and without complete Lewis structures and formal
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charges. In addition, the predicted relative stabilities of the structural isomers can be justified using a bonding model that is based upon the fundamentals of electrostatics, an easy-tounderstand basic principle of science. Literature Cited 1. Kotz, J. C.; Treichel, P. Jr. Chemistry & Chemical Reactivity, 3rd ed.; Saunders: Fort Worth, TX, 1996; pp 402–414. 2. Hill, J. W.; Petrucci, R. H. General Chemistry, Prentice Hall: Upper Saddle River, NJ, 1996; pp 330–341. 3. Ebbing, D. D. General Chemistry, 4th ed.; Houghton Mifflin: Boston, 1996; pp 347–358. 4. Whitten, K. W.; Davis, R. E.; Peck, M. L. General Chemistry, 5th ed.; Saunders College Publishing: Fort Worth, 1996; pp 254–266. 5. Olmsted, J. III; Williams, G. M. Chemistry, the Molecular Science; Mosby-Year Books: St. Louis, 1994; pp 329–344. 6. Ahmad, W.-Y.; Omar, S. J. Chem. Educ. 1992, 69, 791–792. 7. McGoran, E. C. J. Chem. Educ. 1991, 68, 19–23. 8. Packer, J. E.; Woodgate, S. D. J. Chem. Educ. 1991, 68, 456–458. 9. Pardo, J. Q. J. Chem. Educ. 1989, 66, 456–458. 10. Reed, J. L. J. Chem. Educ. 1994, 71, 98–100.
Journal of Chemical Education • Vol. 76 No. 3 March 1999 • JChemEd.chem.wisc.edu
