Visualizing Reaction Progress and the Geometry and Instability of the

Demonstration pubs.acs.org/jchemeduc

Visualizing Reaction Progress and the Geometry and Instability of the Transition State Jeffrey E. Fieberg* Chemistry Program, Centre College, Danville, Kentucky 40422, United States ABSTRACT: Transition state theory (TST), also called activated complex theory, is often discussed in general chemistry and physical chemistry courses when learning kinetics. This demonstration takes the abstract concepts of transition state, activation energy, and reaction progress (reaction coordinate) and makes them more concrete and accessible. The demonstration uses a children’s toy (Hoberman Switch Pitch) to model a chemical reaction that follows a reactant through a transition state before making a product. The reaction progress, activation energy, and specific geometry of the transition state are discussed as part of a question and answer dialogue. The complex, multidimensionality of a reaction coordinate and the inherent instability of a transition state become evident. The demonstration also shows that certain reactions may “go” more readily if the energy of a reactant is in a particular type of internal mode (vibrations or rotations). The preferential partition of a given total energy into internal modes of motion versus translational collision energy may allow a system to access the transition state more easily. The demonstration may also aid in the teaching of isomerization reactions, collision theory, and state-resolved reaction dynamics. KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Demonstrations, Organic Chemistry, Physical Chemistry, Analogies/Transfer, Hands-On Learning/Manipulatives, Constitutional Isomers, Kinetics, Mechanisms of Reactions FEATURE: Tested Demonstration

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energy barrier (Ea) to pass through the transition state (activated complex) to form products. Many students have difficulty grasping the terms “reaction progress” and “transition state”. The multidimensionality of reaction progress, where bond lengths, bond angles, or both change simultaneously, challenges the brightest students. Difficulty may also be encountered by confusing “reaction progress” with “extent of reaction”. Several articles have previously sought to clarify definitions involved in transition state theory.2−4 Other articles described the use of plaster and computer models5 or flipping coins and rolling dice6 to better visualize the reaction progress and transition state, respectively. This demonstration takes the abstract concepts of transition state, activation energy, and reaction progress and makes them more concrete and accessible. The demonstration uses a children’s toy, Hoberman Switch Pitch, to model a chemical reaction that follows a reactant through a transition state before making a product. The reaction progress, activation energy, and specific geometry of the transition state are discussed as part of a question and answer dialogue. The complex multidimensionality of reaction progress and the inherent instability of a transition state become evident. The demonstration also shows that certain reactions may “go” more readily if the energy of a reactant is in a particular type of internal mode (vibrations or rotations). The preferential partition of a given total energy into internal modes of motion (e.g., vibrational) versus translational collision energy

ransition state theory (TST), also called activated complex theory, is often discussed in general chemistry and physical chemistry courses when learning kinetics. This theory of reaction rates was principally pioneered by Henry Eyring in the 1930s.1 A reaction energy diagram is used to follow the progress of the reaction from reactants through a transition state to products (Figure 1). The reaction energy diagram plots the system’s po-

Figure 1. Reaction energy diagram.

tential energy versus reaction progress (or reaction coordinate) and shows that reactant molecules must overcome an activation © 2012 American Chemical Society and Division of Chemical Education, Inc.

Published: June 22, 2012 1174

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allows the system to access the transition state more easily.7−11 It has also recently been shown that mechanical force may be used to direct a reaction pathway via stabilization of a transition state;12 the demonstration provides a way to visualize this phenomenon. This demonstration adds the Switch Pitch to the many previous uses of toys in the classroom,13 including the use of a slap bracelet to teach the concept of activation energy.14 Several toy demonstrations were highlighted during the “Joy of Toys” theme for the 2005 National Chemistry Week.15−17 An annotated bibliography of JCE resources for chemistry and toys was also published.18

The necessity that reactants must overcome an activation energy barrier to proceed to products has already been introduced in the discussion of the Arrhenius equation. Transition state theory, however, explains why the activation energy is needed: bonds in the reactant molecules must stretch and deform to reach the transition state. The elongated bonds (those being broken or formed in the elementary step) are typically rendered with dashed lines in a pictorial of the transition state. Performing the Demonstration

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The 10 min demonstration may be performed in a question and answer format. The Switch Pitch toy is presented. The students are asked to note the color of the ball. The ball is lightly tossed in the air. The students will see that the ball is not rigid; its parts move. Next, the ball is tossed up a little harder so that it inverts and therefore changes color (Figure 3); it may take a few tosses.

EQUIPMENT Two Switch Pitch balls by Hoberman Toys19 are needed and are available with teaching instructions from Educational Innovations (pair of Hoberman Switch Pitch Balls) or Flinn Scientific (Visualizing the Transition State Model Kit). Alternatively, the Switch Kick by Hoberman Toys, which is more durable and foamy but also more expensive, can be used.

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CLASSROOM DEMONSTRATION FOR TRANSITION STATE THEORY

Material Presented before the Demonstration

In the class leading up to the demonstration, the Arrhenius equation (k = A e−Ea/RT) and collision theory have been discussed. Therefore, the students know that only a collision with energy greater than the activation energy, Ea and the correct molecular orientation will lead to products. Before the demonstration is performed, background into TST is given. A reaction energy diagram (Figure 2)

Figure 3. Switch Pitch modeling a chemical reaction from reactant to product through a transition state.

To view the action of a Hoberman Switch Pitch, please see the video in ref 19. The students are then asked how they may relate the demonstration to a reaction energy diagram that models an actual chemical reaction. The students are guided as needed to the answers given here: • The initial color of the ball represents a reactant molecule (R). • The final color of the ball represents a product molecule (P). • The activation energy for the reaction is related to how high the ball must be thrown to convert from R → P (which is related to the force imparted to the ball). • This activation energy is supplied by collisions with other molecules. • The configuration of the transition state is when the Switch Pitch is fully expanded, at the top of its arc. The Switch Pitch must expand to achieve the geometry of the transition state (energy must be put into the system). • The bond lengths of the transition state are longer than those in R or P. • The transition state is unstable. Here is one way to demonstrate the instability of a transition state: after manually pulling the Switch Pitch apart to be fully expanded (in the TS), place it on the desk; it will collapse back to R or P. If the reaction has proceeded to the transition state, it must then either go forward to become products or else return to reactants. And if the reaction has proceeded through the transition state, products will form. • Reaction progress involves movement within the entire “molecule”. Reaction progress is complicated and multidimensional, involving changes in bond lengths and angles, as well as molecular volume. Toggling on the action of the Switch Pitch in ref 19 allows the students to probe the entire reaction progress.

Figure 2. Reaction energy diagram for 2BrNO → 2NO + Br2.

is presented on the chalkboard or via PowerPoint. The reaction of 2BrNO → 2NO + Br2 is one example that may be used. Several aspects of TST are then discussed over a 10 min period: • Reaction progress may include changes in interatomic distances and bond angles (those bonds being broken and new bonds being formed). • The species at the top of the activation energy barrier is the transition state (TS) or activated complex. • Some bond lengths of the TS are much longer than those in a stable molecule. • The TS is highly unstable. • Once the reaction has proceeded through the transition state, products are quickly formed as the reaction advances steeply downhill. 1175

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• Because the Switch Pitch reaction is isoenergetic, the reaction energy diagram must be redrawn so that the potential energy of reactants and products are equal (Figure 4).

having one Switch Pitch stationary while dropping or throwing the other. The class predicts under what conditions reactants will most efficiently convert to products. Possible variables include: • total energy of collision is tested by increasing the velocity of the thrown Switch Pitch. Similar to an actual chemical reaction, a certain threshold energy (activation energy) must be reached before products form (one or both Switch Pitches change colors). • impact parameter, b (defined as the perpendicular distance between the parallel velocity vectors (u1 and u2) of two molecules25 (Figure 5). If the Switch Pitches collide head-

Figure 5. Collision geometry and impact parameter, b. The arrows display the parallel velocity vectors (u1, u2). Figure 4. Reaction energy diagram for the Switch Pitch reaction.

The Switch Pitch may also be used to introduce or reinforce isomerization reactions. After discussing the TST aspects of the demonstration, the students may be asked whether the Switch Pitch models a bimolecular reaction that produces multiple species (such as the 2BrNO → 2NO + Br2 example). Once the students realize that the Switch Pitch “product” represents a rearrangement of the “atoms” in the reactant “molecule”, they are able to determine that the Switch Pitch reaction instead models an isomerization reaction. If desired, at this point more information may be given about a specific isomerization reaction; the demonstration could serve as an introduction to a computational study of the isomerization of hydrogen cyanide to hydrogen isocyanide previously described in this Journal.20 Because the reaction modeled by the Switch Pitch, however, is isoenergetic, more appropriate examples of isomerization are conversions between stereoisomers, for example, between the conformers of butane where the energy differences are 0−2 kcal/mol;21 here the activation energy is the barrier to rotation. Another interesting example of an almost isoenergetic reaction is the cis−trans conversion of the amino acid, proline.22 The cis−trans conversion of proline residues is slow due to a relatively large activation energy (80−100 kJ/mol) that may inhibit protein folding.23,24

on, b = 0. As the Switch Pitches collide further off-center, b increases to a maximum value of the sum of the molecular radii (bmax = r1 + r2). For b > bmax, the molecules do not collide. In hard-sphere collision theory, for a fixed relative kinetic energy, a reaction with b = 0 has a higher probability of reaction than b > 0. In a head-on collision, the molecules come to a stop; therefore, all of the relative kinetic energy is available to overcome the activation energy barrier. The effect of impact parameter may be tested by dropping one Switch Pitch directly over the other (b = 0), then dropping it at a more glancing blow (larger impact parameter). For the b = 0, it is best to catch the Switch Pitch following the collision, as it reaches its zenith (or else it may collide again with larger impact parameter). For the Switch Pitch reaction (as opposed to hard-sphere collision theory), a larger impact parameter leads more readily to products as the Switch Pitches are not hard spheres. When the impact parameter changes, the entire reaction energy diagram changes: the reaction proceeds along a dif ferent reaction coordinate with different activation energy. In the Switch Pitch reaction, a reaction with a larger impact parameter has a smaller activation energy barrier, that is, less energy is needed to surmount the activation barrier to make products. • angular momentum is tested by varying the amount of rotational energy of one or both Switch Pitches; the “stationary” Switch Pitch may be spun in place. The more rotational energy is in the reactants, the more facile is the Switch Pitch reaction. These results show some of the complexities of gas-phase reaction dynamics, namely, that reaction rates depend on (i) collision energy, (ii) impact parameter, (iii) orientation, and (iv) internal energy of reacting molecules.

Molecular Reaction Dynamics

Control of Chemical Reactions

Switch Pitches may also be used to reinforce collision theory and introduce molecular reaction dynamics. In hard-sphere collision theory, molecules must collide with a collisional energy greater than the activation energy to react. At this point in the demonstration, two students may participate in colliding two Switch Pitches together. The collisions are most easily carried out by

Internal Energy. During the demonstration, one aspect that becomes evident is that if one or both “molecules” have extra rotational energy, products form more readily. This conclusion can also easily be shown by throwing one Switch Pitch into the aira very small quantity of rotational energy changes the color of the ball, compared to a larger quantity of translational energy

The above description is typically how the Switch Pitch is used in general chemistry courses. The Switch Pitch may also be used to aid in the teaching of isomerization reactions, collision theory, and state-resolved reaction dynamics, as outlined below.

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CLASSROOM DEMONSTRATION FOR MORE ADVANCED CHEMISTRY CONCEPTS

Isomerization Reactions

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I thank Kenneth Lyle of Duke University and James Maynard of the University of WisconsinMadison for organizing the Demo Grand Prix at the 19th Biennial Conference on Chemical Education, where I first publicly displayed this demonstration. I thank Educational Innovations, Flinn Scientific, and the Associated Chemistry Teachers of Texas (ACT 2) for their enthusiastic support of the demonstration. I also thank Educational Innovations for supplying the picture of the Switch Pitch used in Figure 3.

needed to change the color of the ball (thrown straight up with no spinning). This conclusion mimics some chemical reactions that “go” more readily if, for a given total quantity of energy, it is partitioned into internal modes of motion versus translational energy.7−10 The preferential partition of a given total energy into internal modes of motion versus translational collision energy may allow a system to access the transition state more easily. For example, excitation of the C−H stretching vibration in CHD3 leads to preferential C−H bond cleavage in two reactions: (i) abstraction of H by an attacking Cl atom or (ii) dissociative adsorption on a nickel surface.26 Reaction probabilities have also been shown to depend on preparation of reactants in particular rotational states;11 interestingly, preferential excitation into rotational motion has been shown to hinder the dissociative adsorption of methane on a nickel surface.27 Mechanical Force. Recently, the use of mechanical force has also been shown to initiate and control a chemical reaction.12 The induced force (tension by sonication) stabilized a diradical transition state of a polymer by stretching it. The polymer could then isomerize to an energetically less-favored product. The Switch Pitch demonstration may be used to show how mechanical force may be used to initiate and control a chemical reaction. Assume that the transition state represented by the reaction coordinate of the Switch Pitch is not easily accessible via typical means such as heat. To mimic the force of sonication, the ball may be manually stretched to its transition state. Once in the transition state, the reaction may proceed to a product that could not have been accessed if not for the applied force. The level of discussion of the Switch Pitch demonstration may be further raised to the detail presented in a physical chemistry course. The demonstration may be related to reaction mechanisms (specifically the Lindemann mechanism for unimolecular reactions28), attractive and repulsive potential energy surfaces,10 and more advanced reaction dynamics.9

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HAZARDS Although the materials used in this demonstration are considered nonhazardous (children’s toys), all normal classroom safety guidelines should be observed. Do not throw the Switch Pitches at or near anyone in the room.

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SUMMARY A children’s toy, the Hoberman Switch Pitch, models a chemical reaction and allows students to visualize the difficult concepts of reaction progress and geometry and instability of the transition state. The demonstration also may be used to aid in the teaching of isomerization reactions, collision theory, and state-resolved reaction dynamics.

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REFERENCES

(1) Eyring, H. J. Chem. Phys. 1935, 3, 107−115. (2) Anonymous. J. Chem. Educ. 1987, 64, 208. (3) Laidler, K. J. J. Chem. Educ. 1988, 65, 540−542. (4) Bauer, S. H.; Wilcox, C. F. J. Chem. Educ. 1995, 72, 13−16. (5) Hulse, J. E.; Jackson, R. A.; Wright, J. S. J. Chem. Educ. 1974, 51, 78−82. (6) Kuntzleman, T. S.; Swanson, M. S.; Sayers, D. K. J. Chem. Educ. 2007, 84, 1776−1778. (7) Sinha, A.; Hsiao, M. C.; Crim, F. F. J. Chem. Phys. 1991, 94, 4928− 4935. (8) Annesley, C. J.; Berke, A. E.; Crim, F. F. J. Phys. Chem. A 2008, 112, 9448−9453. (9) Houston, P. L. Chemical Kinetics and Reaction Dynamics; McGrawHill: Boston. MA, 2001; pp 281−286. (10) Atkins, P. de Paula, J. Physical Chemistry, 9th ed.; W. H. Freeman and Company: New York, 2010; pp 852−856. (11) Gostein, M.; Sitz, G. O. J. Chem. Phys. 1997, 106, 7378−7392. (12) Lenhardt, J. M.; Ong, M. T.; Choe, R.; Evenhuis, C. R.; Martinez, T. J.; Craig, S. L. Science 2010, 329, 1057−1060. (13) Ziegler, G. R. J. Chem. Educ. 1977, 54, 629. (14) Kramer, F. A. J. Chem. Educ. 1993, 70, 1002. (15) Sarquis, J. L.; Sarquis, M. A. J. Chem. Educ. 2005, 82, 1450−1453. (16) Harris, J.; Kehoe, S. J. Chem. Educ. 2005, 82, 1458−1460. (17) Holmes, J. L. J. Chem. Educ. 2006, 83, 1104. (18) Jacobsen, E. K. J. Chem. Educ. 2005, 82, 1443−1446. (19) Hoberman Toys. http://hoberman.com/fold/Switchpitch/ switchpitch.htm (accessed Jun 2012). (20) Halpern, A. M. J. Chem. Educ. 2006, 83, 69−76. (21) Compton, D. A. C.; Montero, S.; Murphy, W. F. J. Phys. Chem. 1980, 84, 3587−3591. (22) Schmid, F. X. Eur. J. Biochem. 1982, 128, 77−80. (23) Brandts, J. F.; Halvorson, H. R.; Brennan, M. Biochemistry 1975, 14, 4953−4963. (24) Pappenberger, G.; Aygün, H.; Engels, J. W.; Reimer, U.; Fischer, G.; Kiefhaber, T. Nat. Struct. Biol. 2001, 8, 452−458. (25) McQuarrie, D. A. Simon, J. D. Physical Chemistry: A Molecular Approach; University Science Books: Sausalito, CA, 1997, p 1235. (26) Crim, F. F. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 12654−12661. (27) Juurlink, L. B. F.; Smith, R. R.; Utz, A. L. Faraday Discuss. 2000, 117, 147−160. (28) Lindemann, F. A. Trans. Faraday Soc. 1922, 17, 598−606.

AUTHOR INFORMATION

Corresponding Author

*E-mail: jeff.fi[email protected]. Notes

The author declares no competing financial interest. J. Charles Williamson (Chemistry Department, Willamette University, Salem, OR 97301) checked this demonstration.

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ACKNOWLEDGMENTS I thank my parents, Jeanette and Robert Fieberg, for purchasing a Switch Pitch as a gift to their grandchildren. Without this gift, this chemical analogy demonstration and article would not exist. 1177

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