What's It Good For? Physical Chemistry Application Problems David M. Whisnant Wofford College, Spattanburg, SC 29303-3663
As Crosby has noted ( I ) ,many undergraduates regard phvsical chemistrv a s "too hard. too abstract,. and.. worst of esoteric and irrelevant". o n e factor that contributes to the perception of irrelevancv is that students often aren't too k r e what physical chem%Ary is good for. I n a n effort to change this perception, I give my students a series of inclass problems, usually drawn from the recent literature, that illustrate how the material from the course is used. These problems are called "application problems", because they show how physical chemistry is applied. Application problems are posed to students four times during each semester, usually in the lecture period before a n examination. These problems focus on the material assigned for the coming examination, but are not limited to this. They can, and often do, contain topics from previous exams a s well. These are multistev problems that require the students not only to make numerical calculations~but also to request information they need or to decide on a method of measurement before data is furnished. The papers on which the problems are modeled come from journals such a s the Journal of the American Chemical Society or the Journal of Physical Chemistry. The students work on the problems in rl&s in groups ofthree or four I present hen: twu examples to illustrate what they are like. The Interaction of Leghemoglobin wlth Nitrogen Although most of the application problems come from the recent literature, this one is based on a 1972 paper (2). I t was eiven to the class before a first semester examination co;ering phase equilibria, chemical equilibria, and solutions. The problem handout begins with a discussion of leguminous hemoglobin, a respiratory pigment found in the root nodules of most leguminous plants. At the time of the leghemoglobin paper, current evidence indicated that lephemoplobin was not directly involved in nitrogen fixation, bit played a secondary role. There was some evidence, however, of interaction between nitrogen and leghemoglobin. The paper on which this application problem is based reported a study of the reaction between the two compounds.
The students are furnished with values of the equilibrium constant for the fcrrileghemoglobin reaction at hiffrrent temperatures. Thc following - questions then are posed in the handout.
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1.Agraph oflnKvs. UTisnot linear. What does this imply? 2. A common equation describing the temperature dependence of AG is AG = A + BT + CTln T. Given a computer and an equation- solver program (3), solve for the parameters A, B, and C using the equilibrium constant data. 3. What are the values of AH and A3 at 278 K?
Presented at the Svm~osiumon Innovations in Teachino Phvsical Chemistry, 11th ~ienkai~onference on Chemical ~ducai;on,~tlanta, GA, August 6, 1990.
4. Is the reaction exothermic or endothermic? N2 is isoeleetronic with CO, which bonds strongly with hemoglobin in the blood. Does it appear that the binding of nitrogen to leghemoglobin is strong or weak? 5. What about the sign of AS for the reaction? What does this suggest happens to the leghemaglobin molecule when it absorbs a nitrogen molecule? 6. In this experiment, the researchers determined the amount of nitrogen absorbed by the leghemoglobin by measuring how much nitrogen was lost above the solution. The nitroeen - .Dressure also decreased above the solution because it dissdved in water. Calculate the quantny of nitrogen that dtssolves in watrr at 298 K whm the nitrogen pressure is 2.00 atm. Ask far any information you need. 7. The nonlinearity of the plot of h Kvs. Z/T indicates that H for the reaction depends an temperature. Assuming that AH = a + bT, derive the equation far AG in problem 2.
Usine the values ofA. B. and C that thev calculate. the students find that the reaction is endother& with a large positive e n t r o ~ vc h a n ~ eThe . positive heat of reaction supgests t h a t thL-binding of nkrogen to leghemoglobin i s weak. A S is positive. indicatincr that the lezhemo~lobin molecule becomes more d~sorderedduring the absorption of mtropen The students need to realire that rhc solubll~tv of nitrogen in water can be calculated fmm Henry's law. The Henry's law constant is supplied upon request.
Non-KekulB Isomers of Benzene This problem, which i s based on portions of two DaDers . . (4).was .,eiven before the second semester examination on 6pectmscupv The problem has two parts, each on a separate handout. ' f i e second Dart is not distributed until thk first handout has been ~ o & ~ l e t e d . The first handout introduces a stable, free biradical, 2,4dimethvlene-1,3-cyclobutanediyl, which is called a "non~ekul6~molecule" because its unpaired electrons are part of a classical rr-system, but are prevented from forming a n-bond by their location on the molecule. The f r s t handout poses a single problem: "What kind of questions could you ask about this compound, concentrating on theoretical and experimental methods from the second semester of this course?" After some class discussion, questions similar to the following are agreed upon. 1.Why don't the two electrons bond and form a bridge? 2. What are the molecular orbitals of this compound and what
is the ground electronic state like? Is it a singlet or triplet state? 3. The compound is yellow-orange. Is the color due to the ahsorption or emission of radiation? After this discussion, the students are given a second handout t h a t suggests how quantum mechanics and spectroscopy can help answer their questions about the biradical. In a n earlier laboratory experiment, the stud e n t s used Huckel molecular orbital theory to approximate energies for rr-electrons. Repeating these calculations for t h e biradical, they find t h a t the highest occupied molecular energy level has two degenerate, or Volume 69 Number 1 January 1992
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nearly degenerate, nonbonding orbitals, suggesting a t r i ~ l estate. t The students next look a t the absorption and emission spectra of the biradical from the original paper. Comparison of the position of the two bands with a color rosette shows that the color of the com~oundis due to absor~tion. An estimation of its oscillator strength indicates that the absorption transition is spin-allowed but parity-forbidden. This and the mirror-image relationship of the two bands identifies the emission band a s being due to fluorescence. That fact that the 0 tt 0' transition is the strongest peak in both spectra suggests that the two electronic states involved have the same geometry. For the final part of this exercise, the students are supDlied with several values: B for the Hiickel MO calculations; estimated strain energies for the hiradical and its ring-closed isomer; and the bond energy for a G C bond. They are asked to calculate the resonance energy of the biradical and then to estimate the difference in energy between the biradical and the ring-closed isomer. They find that the biradical is slightly more stable than its isomer. These are typical a$plfcation problems that use concepts from physical chemistry to help solve a problem of interest in another field. The problems often blend material assigned for the upcaming examination with topics from previous exams or laboratories. They are long ~roblemsand usuallv. require computers to help students . work them in a 50-min period. An answer sheet is handed out a t the end of class so that students will have answers if the problem is not finished.
about 16 students with no logistical problems, but a larger class would require one or more assistants. The biggest limitation may be the availability of computers. At least noups, two computers are necessary for every three . and one computer for each groupis preferable. Finally, is this approach effective? Students do seem to enjoy the sessions,-and they do take the problems seriously. At least one question on the next examination is drawn &om each appliEation problem, so there is an incentive to understand the problem. There is anecdotal evidence that the anolication uroblems do helo the material seem less esoteric and irrelevant. For instance, more than one student has told me that the problems make the course seem more real, one of them saying, "the problems gave some feeling that the stuff I was struggling with back in my room at 3 a.m. was worthwhile." One added advantage of these problems is that they furnish a wntext that allows the introduction of topics not always included in the first year of physical chemistry. Some of the other problems that have been used are below.
Discussion A number of auestions mav come to mind about these problems. First, kuld they be used as out-of-class assignments? This is possible, although without immediate feedback from thebrofessor, multipart problems can be difficult. The opportunities for class discussion afforded by this approach also would be lost if the problems were assigned to be handed in. Finally, there may be an advantage to students workine together on ~roiectssuch as this. Tobias has commentld 0; the comp&itfon and lack of communitv in manv science classrooms (5).Collaborative problehs such a: these can further a sense of cooperation in the class. If application problems are added to Iectures, what is left out? Actuallv. verv little lecture material must be omitted. Topics can bk moved, for instance, either to laboratory handouts (some electrochemistry, conductivity, and Hiickel MO theory), or to other courses (group theory to inorganic chemistly). The use of spreadsheet templates as in-class examples (6)also can reduce time-consuming work on the board and streamline the lectures. Finally, because the application problems are themselves exan&es, the number of problems worked in class can be reduced. What does the teacher do during the period? He or she circulates around the class watching what the groups are doing, checking answers, and giving hints if needed. The hardest part for the teacher may be remaining quiet during the exercises. There is a great temptation to help a group along instead of letting them puzzle the solution out. What about class size? My classes are small, usually eight to twelve students, so there are at most three groups working simultaneously. One person could handle up to
In working these problems, students have been introduced to ion clusters, high-pressure mass spectrometry, the torsion-effusion method for determining vapor pressure. resonance Raman s ~ e c t r o s c o ~flash v. ~hotolvsis. . . photbelectron s p e c t r o s ~ o g~ a~ ~, - ~ h &protin-transfer e kinetics, applications of FT-NMR spectrometry, and more. In summary, these problems are meant to give physical chemistry students experience with applications of the course. I think they accomplish this because the problems use realistic examples from the research literature that are related to subjects such as planetary atmospheres, the oeone-depletion problem, anticancer drugs, nitrogen iixation, andscanning tunneling microscopy. I plan to continue these problems in the future and may add similar but simpler problems in some lower-level classes.
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Journal of Chemical Education
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1. Thermodynamic properties of gas-phase clusters (71, 2. HN03/H20solution vapor pressures and their application to polar stratospheric clouds (8), 3. Temperature studies of the O(3P)+ pH3 reaction and their implications for planetary atmospheres (9), 4. Infrared and Raman study of matrix-isolatedCuo(ethylene
complexes) (lo), 5. lg5I'tNMR kinetic study of the binding of cisplatin and its
trans isomer to DNA (111, and 6. The hand strength of ethylene (12)
Literature Cited 1. Essays in Physlml chemistry;Lippineott, W. T,Ed.; American Chemical Society: Washington. D.C.,1988; p 5. 2. EaA205. 4. (a)Snyder G. J.; Dough* D. A. J. Am. Cham. Soc. 1984. 111, 3927.3942; (bl Snyder, G.J.;Dougherty, O.A. J.Am. C h m . Soe. 1989,111,39423954. 5. Tobias, S. T h w h Not Dumb, Thoy'm Dlffemnf; Research Corporation: Tucson, Arizona. 1990 o 81. ~~
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6. Whisnant. D. & k~chem. i Edur I W , 6 6 , A 6 2 A S 3 7. (a1Csstleman,A. W ,Jr;HoIland,PM.:Lind6ay.D. M.;Peterson.K I. JAm. Cham. Soc. 1978, 100. 603WC45: (b) Caetle-, A. W , Jr: Keesee. R. G.Cham &u 1986,86,589618;(e)Guo,B.G.:ConWin,B. J:Caatleman,A.W.,Jr.J.h.Cham.
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I I Rdl.rron 11 P . I ~ ~ . ~ . c . A : I . ~ J~ J~ ., ~A ~chenl ~. s 1m.mWM)6871 I? Fnsn. K \I Cmm rr. S , Fhr..,w. S E G d l n LI K . l l m s o n , n 8 : . Rcrbaum. \' \ I . IhPuy C H l.#!sl~urmr. W ( ' . Ellaon C H d Am Chem Sn 1990. 112. i750d759
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