The Toppling Box: A Macroscopic Analogy to Single-Step Exothermic Reactions Thomas H. Eberlein Pennsylvania State University-Schuylkill Campus, 200 University Drive, Schuylkill Haven. PA 17972 Energy changes accompany chemical reactions. Energy diamams are quite useful in illustrating these changes on a continuous basis as the reaction proceeds. Terms such as "activation energy" (E,),"transition state" (I),and "enthalpy change" (AH,,) are easy to define by referring to a graph such as Figure 1. Endothermic and exothermic reactions are just as easily defined, according to the sign of AH,,. Students who are unfamiliar with such diagrams may find i t difficult to visualize the energy changes associated with the processes occurring during a reaction. A simple visual analogy of these changes that is particularly easy to demonstrate in the classroom is the toppling of a box that has been h laced on its end (Fig. 2). The similarities hitween the energetics of this process and thoseof a single-step exothermic reaction make box toppling a useful explanatory device. State R (the reactants) is represented by the box standing on its end; a student should he readilv able to see that althouah " the box is in a less stable position than if i t were lying on its side, it will remain standing indefinitely. In order to achieve the lower energy state P (the products), the box must first pass through a state of hieher enerw -- (i, .. the transition state) than either R or P. A more or less gentle tap to the top of the standing box will provide the "activation energy" necessary for the toppling process t o occur. (It can he instructive to give the box several light taps of insufficient energy to knock it over before dealing the blow that ultimately leadson to "products." After all, not every collision between reacting partners or other energy-absorbing process in actual chemical systems yields a chemical reaction.) At this ~ o i n in t the demonstration, the instructor might want to emphasize that although boxes standing on their ends or lvina on their sides are commonly observed, they are never s e i n b a ~ a n c i nsomewhere ~ between these two extremes. Similarly, the transition state for an elementary process is an elusive species that cannot be observed directly: its structure must be inferred. Students should be eucouraged to topple boxes of their own (slowly!) in order to "feel" the transition state, i.e., the point a t which no further ~ u s h i n eis necessarv for the box to fall over. Additionallv. the relative difficulty of the endothermic reverse process (P R) can he easily demonstrated. No amount of light tapping will cause the toppled box to stand back up; one edge of the box must he phvsicallv lifted to provide the activation energy necessary foithis "reaction" take place. For students beyond their first year of study, those in organic chemistry classes for example, the analogy can he extended to illustrate the Hammond postulate: "If two states, as for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearlv the same euerav ... content, their interconversion will involve only a small reorganization of the molecular structure." Implicit in this statement is the notion that the transition state for an exothermic process will more closely resemble (structurally) the reactants than it will the prod-
Products
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Figure 1. An energy diagram for an exothermic reaction,
Fails
-47 BOX after
"
a
"
"
(P)
Figure 2. The energetics of a falling box are similar to those of a single-step exothermic reaction.
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' Hammond, G. S. J. Am. Chem. Soc. 1955, 77,334-338. 26
Journal of Chemical Education
Figure 3. A box toppling from a higbnergy orientation to one of lower energy has a "transition state displacement angle" (6t)of less than 45'.
ucts, since the reactants are closer to the transition state in energy than are the products (an "early" transition state). Also implied is that the transition state for an endothermic reaction should more closely resemble the products than the reaction (a "late" transition state). By referring to Figure 2, the reader can see that this concept has already been addressed, a t least hy implication. The transition state for toppling the box ( P R) is "struc-
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turally" more like the standing box (R) than it is like the box lying on its side (P). T o be more explicit, consider the standing box to have a "displacement angle" (6) of 0°, and the toppled box to have a 6 of 90' (see Fig. 3). The transition P is achieved a t a displacement state for the process R angle of significantly less than 45', and so it more closely resembles the standine box than it does the tonnled box. If one mentally reverses the order of events'depicted in Figure 2, then the endothermic process P R is represented. As such, the identities of the "reactants" and "products" are reversed. and the transition state for this reaction more closely resembles the product (the standing box) than it does the reactants. Another implication of the Hammond postulate is that if two similar but energetically nonequivalent products can arise bv similar mechanisms from a common intermediate. formation of the more stable product will predomi: th& nate. This is because the transition state leading to the more stable product will be more like the intermediate (and hence of lower energy) than will the transition state leading to the higher energy product. Figure 4 is an energy diagram of just such a case, the formation of two different alkene products
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~
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tee
Figwe 5. A toppling box as an analogue of the reactions shown In Figure 4. Trsdlon State Displacemenl Angles for the Toppllng ol Boxer ol Varlous Dlrnenslona &x Ently
Reactlo"
C~ardinaL~
energy dlagam of the two possible depmtonation mDdes of the Cation derive3 from the ionization d 2-brd-methylbutane. Film 4. An
from a common carbocation. Specifically, Figure 4 illustrates the enerw chanees associated with two ~ossible modes of deprotonation in the rate-determining step of the SimE l elimination of HRr from 2-hromo-3-meth~lbutane.~ ilar results are obtained in theacid-catalyzeddehydrationof 3-methyl-2-b~tanol.~ In these examples, the more highly substituted (and more stable) alkene, 2-methyl-2-butene, is the major product; the less highly substituted alkene, 3methyl-l-butene, is the minor product. The relative energies of the transition states in these reactions correlate with the relative energies of the products, as well they might; the transition state in this, the product-determining step of the reaction. has beeun to take on some double-bond cba~acter.~ To illustrate the situation just described on a macroscopic level. the box toonline analoev can be carried a step further. on its If a box having &ee Gdes of;;lequal lengths is
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McMuny, J. Organic Chemistry, 2nd ed.; Wadsworth: Belmont, CA, 1988; p 358. Footnote 2. p 596.
'Lowry. T. H.; Richardson, K. S. Mechanismand Theory in Organic
Chemisby; Harpar and Row: New York. 1976: p 357. Boxes used should be empty or otherwise uniformly packed. Partially fllled boxes will require "artificially" large displacement angles in order to fall over. The boxes used for gathering the data presented in the table were a filled facial tissue box (entry I), an empty cassettetape case ( e m 2), and an empty cellophane tape box (entry 3). The author makes no claim that the results shown in the table will be fully reproducible for any box of the given dimensions. but the results should be the same on a qualitative basis.
Height
Dimensions (in cm) Len@
Width
6f
@Y
smallest end (state R: see Fie. - 5)... there will be two enereetically nonequivalent exothermic modes by which top&ng can take dace (Fia. 5, mode x and mode v). The box can be toppled toward t h i wider base (mode x ) nr toward the narrower base (mode y). The product of mode x toppling (P,) is more stable than the product of mode y toppling (P,). It should be intuitively obvious that it will he easier to tip the box in the direction that leads to the more stable roduct, i.e., the one with the larger base. Conversely, it ;ill be less easy to tip the box in the direction that leads to the less stable product, i.e., the one with the smaller base. This can be verified bv measurine the anale (69 throuah which various boxes m i s t be tipped in or&r to fall ove;in both the x and .v modes. For example, a filled facial tissue box (see the tab& entry 1) having ihe dimensions 25.1 cm X 12.1 cm X 8.7 em has a value of 6% of 16' for the more exothermic t o n ~ l i n enrocess x (hence 6%. = 16O). ., and a value of 6f of 21° fa; 'the iek exotheimic proeess, mode y (hence 6', = 21°). Thus the transition state for the more exothermic nrocess. R P,, occurs earlier along the reaction coordinate'and mire closelv resembles the reactant (R. . . 6 = 0') than does the transition state for the less exothermic process, R P,. Additional data for uniformlv filled boxes of varvina dimensions are listed in the table.: Note particular~ykntry3, for which toppling mode y involves no net change in energy; the reactant (R) and the product (P,) are standing on bases of identical surface area. Exactly as one would expect, the transition state in this case occurs a t 6 = 4 5 O , which is halfway between R (6 = 0') and P, (6 = 90"). The box-toppling analogy can be extended to include endothermic processes, such as electrophilic additions to alkenes or to benzene derivatives. Doina so, however, involves the lifting of a box from its most stabie orientation into one of its two less stable orientations. Whether there are further extensions of the analogy which can be used to pedagogical advantage is left to the reader's imagination.
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Acknowledgment The author wishes to thank William J. Faenza and Thomas R. Smith for their assistance in the preparation of this manuscript. Volume 67 Number 1 January 1990
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