A Bibliography of Chemical Kinetic andEquilibrium Instructional Models

Dean A. WoodHood College

Frederick, Maryland 21701

The study of chemical kinetic and equilibrium processes constitutesa significant portion of introductory college chemistry curricula. TheNational Science Teachers Association Conference of Scientists gaveadditional impetus to the curricular use of these topics by specificallyincluding the two within seven major conceptual schemes deemedto be appropriate for building elementary and secondary curricula.The inclusion of these topics within introductory courses providesinstructional difficulties as kinetic and equilibrium processes appearto many high school and college students as being abstract, highlymathematical and difficult to comprehend. Actual student manipulationof these physical systems within the laboratory as an aid to instructionis therefore highly desirable. Unfortunately, few if any chemicalreaction systems are available that allow introductory students toeasily determine the concentration of all reaction species at any instantof time or to control the reaction by stopping and starting it in orderto more closely examine the state of the system. In addition, manykinetic and equilibrium experimental apparatus are difficult to operateand time consuming for beginning students. For these reasons, teachershave devised alternative methods of instruction that include the useof physical instructional models that are capable of simulating oneor more aspects of the chemical processes. The purpose of this articleis to facilitate the use of the many highly valuable instructional modelsreported in the literature by providing the reader with their briefdescription and summary of characteristics. These instructional modelsare classified below into six categories for simplicity of presentation.

Hydrodynamic Instructional Models

Models that utilize a flow of liquid to simulate various kinetic andequilibrium processes are herein characterized as hydrodynamic in-structional models. These models most commonly incorporate aliquid-containing reservoir connected to a capillary tube or other orifice.The rate of flow of liquid through the orifice is described by Poiseuille’slaw for viscous flow of liquids to be dependent upon the height (H)of the water column. The relationship is represented as

dH��==-kHdt

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Indefinite integration yields

InH^ -kt + K

The above equations are analogous to first-order chemical rate lawswhere "C" represents concentration of reactants.

dC�==-kCdt

lnC= -kt + K

Lemlich (1) reported the development of a model that utilized aburette connected to a length of capillary tubing. The water levelwithin the emptying burette was recorded as a function of time. Themodel simulated first-order rate processes.Hydrodynamic instructional models can easily be inter-coupled to

simulate reversible reaction processes. Liquid expelled from themodel’s first column is transferred to a second column. Similarly,liquid expelled from the second column is transferred back to thefirst column. The attainment of an equilibrium state occurs whenthe amount of liquid in each column remains constant despite continuedtransfer of liquid. Rakestraw (2) reported a model that used an ironpipe containing drilled holes as the orifice, and a power-driven pumpfor transfer of liquid. Karns (3) described a model that utilized astop-cock orifice and air-lift transfer pump. These two models werelater described by Alyea (4). Weigang (5) developed a highly effectivemodel that is particularly worth the reader’s attention that utilizedcentrifugal transfer pumps. Meyer and Glass (6) considered analogousmathematical equations for these models. Interestingly, their ratecalculations were not based upon Poiseuille’s law but rather uponconsideration of energy conservation that yields rate orders of one-half.Escue (7) described a free-flow model that eliminated mechanicalpumping by directing the liquid discharge from one column into alower column* The attainment of an equilibrium state is demonstratedwhen the rate of liquid entering a column is equal to the rate ofliquid leaving the column. However, the model more appropriatelysimulates steady-state processes as the system is not closed. Alyea(8) reported the adaption of this model for the Tested OverheadProjection Series. Tucker (9) described a simple free-flow model fordemonstrating Le Chatelier’s Principle. Two water columns wereconnected at their bases by a horizontal glass tube. A spool, insertedwithin the horizontal tube, acted as a "flag" by moving in the directionof liquid flow. Lago, Wei and Prater (10) reported the development

A Bibliography of Chemical Instructional Models 629

of a more complex model of coupled three-component, first-order,reversible chemical reactions. The reaction scheme is:

A== B\\ //

C

While the mathematical equations describing the flow of liquid dorepresent an equilibrium system, the visual model represents a staticequilibrium as the observable flow of water between cylinders andthus analogous reaction processes, cease at equilibrium.Some hydrodynamic instructional models have been reported that

utilize gas rather than liquid flow. Coffin (11) reported the developmentof a vacuum-pumped multiple-orifice apparatus. He showed that therate-order for the flow of gas into the evacuated apparatus is dependentupon the type of orifice. A pin-hole orifice produces a first-orderescape rate; a capillary orifice produces a second-order escape rate.Kahn (12) described a gas-hydrodynamic model that utilized a hollowstop-cock to obtain incremental volume transfers. The model wasshown to simulate isotopic exponential exchange rates. Kahn (13)also described a model designed to simulate consecutive first-orderreactions and transient equilibrium in a secular system.Sorum (14) and Kauffman (15) described the utilization of students

working at cross-purposes to transfer liquids between containers. Theattainment of an equilibrium state occurs when the amount of liquidin each of two containers remains constant though both students areconstantly transferring liquid. Carmody (16) developed a similar modelusing graduated cylinders capable of quantitatively simulating equilib-rium processes.

Vibrating Bead Instructional Models

Models that utilize rapidly and randomly moving particles to simulatekinetic molecular motion are herein characterized as vibrating beadinstructional models. A model was described by Stoekel (17) in 1918that used evaporating mercury vapor to agitate finely-crushed material.The model was used by Taylor (18) to teach chemical kinetic theory.Bockhoff (19) described a model that utilized a test tube containingbeads. By directing an air stream into the test tube in a mannersuch that only a few beads are in motion at any given instance,liquid-vapor equilibrium processes are simulated. Alyea (20) adaptedthis model for the Tested Overhead Projection Series.

Dainton and Fisher (21) reported the development of a "windmachine" that utilized a centrifugal fan to agitate ping-pong balls.The model was constructed as a box divided into two sections by

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a movable barrier. The ping-pong balls, upon receiving sufficient"activation" energy, mov^ up and across the vertical barrier intothe opposite section of the box. The attainment of an equilibriumstate occurs wh^n the forward and reverse transfer rates are equal.Wulf (22), Leiy (23), Hildebrand (24), Arenson (25), Woolley and

McLachlan (26), Slabaugh (27) and more recently the ChemicalEducation Material Study film Gas Pressure and Molecular Collisions,collaborated by J. Arthur Campbell, reported the development ofmodels that use mechanical vibrators for bead agitation. Fiekers andGibson (28) developed an accessory apparatus for simulating chemicalequilibrium. The apparatus is constructed as a vibrating frame dividedinto two sections by a "gate" or barrier. An equilibrium state isattained when the rate of bead movement through the barrier is equalin both directions. Alyea (29) reported the adaption of Slabaugh’smodel for the Tested Overhead Projection Series. Plumb (30) developeda refined vibrating bead instructional model that used a loudspeakerdriver to agitate polished borosilicate glass beads. A glass plate withcenter depression and beveled edges is used to simulate equilibriumprocesses. An equilibrium state is attained when a constant numberof beads remain in the beveled area of higher potential (gravitational)energy. Plumb (31) has also developed a model that is commerciallyavailable as the Molecular Dynamics Simulator. Also commerciallyavailable is the E.M.E. Molecular Motion Demonstrator (32) thatutilizes plastic and metal spheres of varying sizes agitated by a vibratingmetal frame. Both the Molecular Dynamics Simulator and the Molecu-lar Motion Demonstrator are intended for use in conjunction withan overhead projector. Alden and Schmuckler (33) have reported thedevelopment of an equilibrium machine that uses paddles for beadagitation and produces quantitative data analogous to equilibriumconstants.

Verbal and Mathematical Instructional Models

Stories and mathematical exercises that represent analogies to kineticand equilibrium processes are herein characterized as verbal andmathematical instructional models. Caldwell (34) reported stories thatincluded: "Boy Walking on Moveable Stairway," "CavalrymenMounting and Dismounting Horses," and "Dance Floor Analogy."Lewis (35) reported stories that included "Wild Horse Analogy" and"The Bridge Analogy."A mathematical procedure was developed by Fedorow (36) to

illustrate the attainment of equilibrium by a system with given initialconcentrations and rate constants. Dow (37) devised a geometricillustration to explain that the concentration of reactants must be

A Bibliography of Chemical Instructional Models 631

raised to a power, within the equilibrium constant expression, equalto the reactants coefficient in the given equation.

Analog Computer Instructional Models

Models that act as electrical analogs to the systems being simulatedare herein characterized as analog computer instructional models.Analog computers operate on variables that represent continuous ratherthan discrete data. Analog computers have been used as instructionalaids, both for lecture-demonstrations and laboratory experiments.Osburn (38), Corrin (39) Tabbutt (40), Griswold and Haugh (41)

and Lordi (42) have described the utilization of analog computerinstructional models for the simulation of kinetic and equilibriumprocesses. Typically, differential equations are written for the desiredsimulated process, analogous electrical circuits are constructed andsolutions are obtained as time dependent concentration parameters.Analog computers are particularly useful for the quantitative simulationof macroscopic parameters. Vickner (43) has developed an "Equilib-rium System Simulator" that demonstrates Le Chatelier’s Principlethrough the use of a Wheatstone bridge. Equilibrium conditions arerepresented by analog voltages being balanced within each branchof the bridge circuit.

Digital Computer Instructional Models

Models that operate upon variables expressed as data in discreteform and perform arithmetic and logic operations on these data areherein characterized as digital computer instructional models. Typical-ly, digital computer models solve simultaneous equations that havebeen written for the system under study; initial guesses are madefor the problem solutions and systematic trial-and-error or iterativeprocedures are utilized to approximate answers within some givenerror allowance. Computer solutions are usually recorded as printeddata. Casanova and Weaver (44), Emery (45), Bard and King (46),Zajicek (47) and Detar (48), (49) have described the application ofthese models to the solution of problems involving kinetic andequilibrium processes.

Monte Carlo Instructional Models

Models that utilize random sampling techniques to obtain statisticalapproximations to the solution of mathematical or physical problemsare herein characterized as Monte Carlo integration models. Slabaugh(50) described a method of illustrating kinetic and equilibrium processesby the use of blocks to analogously represent reacting molecules.If, for example, a bimolecular mechanism involving two species is

632 School Science and Mathematics

to be illustrated, reaction possibilities are considered for variouscombinations of the two kinds of blocks. It is not clearly indicatedby Slabaugh that random methods for block selection is used.

Castillo and Ward (51) described a method for illustrating first orderrate decay. Sugar cubes are marked on one of six possible; sides,randomly shaken and deposited on a flat surface. All sugar cubeslanding on the marked side up, are removed and the process is repeated.Each repeative operation is counted as one unit of time. A plot of"concentration" of sugar cubes versus time yields a first order rateequation.An interesting model was shown in the Chemical Education Material

Study film Equilibrium, collaborated by G. C. Pimentel. Two fishbowls are connected by a cylindrical pathway in which fish can swim.An equilibrium state is attained when the number of fish in eachbowl remains approximately constant, even though fish continue toswim between bowls.Schaad (52) devised a Monte Carlo computer technique for solving

complex differential rate equations. The technique was developedas a chemical research tool rather than as an instructional modeland is dependent upon the use of modern high-speed digital computerprocessing techniques. Rabinovitch (53) has developed a techniquethat adapts Schaad’s method for use by students with pencil andpaper. His technique utilized a grid matrix rather than computer storageand students performed the required manipulation of digits. Rabino-vitch’s model has been shown to be of equal versatility to Schaad’smethod but more time consuming and less accurate for simulatingvarious types of reaction processes.Wood (54) has developed the "Monte Carlo Integration Computer"

that combines the instructional advantages of both the Schaad andRabinovitch models. This model was designed as a special purposedigital computer.

LITERATURE CITED

1. LEMLICH, R., J. Chem. Educ., 31, 431 (1954).2. RAKESTRAW, N. W., J. Chem. Educ., 3, 450 (1926).3. KARNS.G. M., J. Chem. Educ., 4, 1431 (1927).4. ALYEA, H. N., J. Chem. Educ., 35, A215 (1958).5. WEIGANG, 0. E.,JR., J. Chem. Educ., 39, 146 (1962).6. MEYER, E. F., and GLASS, E., J. Chem. Educ., 47, 646 (1970).7. ESCUE, R. B., JR., J. Chem. Educ., 37, A678 (1960),8. ALYEA, H. N., J. Chem. Educ., 44, A461 (1967).9. TUCKER, W. C., JR., J. Chem. Educ., 35, 411 (1958).10. LAGO, R. W., WEI, J., and PRATER, C. D., J. Chem. Educ., 40, 395 (1963).11. COFFIN, C. C., J. Chem. Educ., 25, 167 (1948).12. KAHN, M., J. Chem. Educ., 32, 177 (1955).13. KAHN, M., J. Chem. Educ., 34, 148 (1957).14. SORUM, C. H., J. Chem. Educ., 25, 489 (1948).

A Bibliography of Chemical Instructional Models 633

15. KAUFFMAN, G. B., J. Chem. Educ., 36, 150 (1959).16. CARMODY, W. R., J. Chem. Educ., 37, 312 (1960).17. STOEKEL, E. R., Science, 48, 475 (1918).18. TAYLOR, J. N., School Science and Mathematics, 20, 514 (1920).19. BOCKHOFF, F. J., J. Chem. Educ., 37, A295 (1960).20. ALYEA, H. N., J. Chem. Educ., 41, A458 (1964).21. DAINTON, F. S., and FISHER, D. G., Education in Chemistry, 6, 217 (1969).22. WULF, T., Z. Physik. Chem. Unterricht, 34, 5 (1921).23. LELY, U. P., Nederland Tijdschr. Natuurkunde., 20, 241, (1935).24. HILDEBRAND, J. H., Science, 90, 2, (1939).25. ARENSON, S. B., J. Chem. Educ., 18, 169 (1941).26. WOOLLEY, R. H., and MCLACHLAN, D., JR., J. Chem. Educ., 27, 187 (1950)27. SLABAUGH, W. H., J. Chem. Educ., 30, 68 (1953).28. FIEKERS, B. A., and GIBSON, G. S., J. Chem. Educ., 22, 305 (1945).29. ALYEA, H. N., J. Chem. Educ., 41, A518 (1964).30. PLUMB, R. C., J. Chem. Educ., 43, 648 (1966).31. PLUMB, R. C., "Molecular Dynamics Simulator (A Manual of Operation)" Holt,

Rinehart and Winston, Inc., New York, 1969 (received).32. TURNER, A. M., "E.M.E. Molecular Motion Demonstrator Study Guide," Educa-

tional Materials and Equipment Company, Bronxville, N.Y., (1969)33. ALDEN, R. T., and SCHMUCKLER, J. S., J. Chem. Educ., 49, 509 (1972).34. CALDWELL, W. E., J. Chem. Educ., 9, 2079 (1932).35. LEWIS, J. R., J. Chem. Educ., 10, 627 (1933).36. FEDOROW, A. S., J. Chem. Educ., 11, 617 (1934).37. Dow, W. A., J. Chem. Educ., 17, 439 (1940).38. OSBURN, J. 0., J. Chem. Educ., 38, 462 (1961).39. CORRIN, M. L., J. Chem. Educ., 43, 579 (1966).40. TABBUTT, F. D., J. Chem. Educ., 44, 64 (1967).41. GRISWOLD, R., and HAUGH, J. F., J. Chem. Educ. 45, 576 (1968).42. LORDI, N. G., J. Chem. Educ. 46, 861 (1969).43. VICKNER, E. H., JR., "Development and Field Testing of a Model to Simulate

a Demonstration of Le Chatelier’s Principle Using the Wheatstone Bridge Circuit,"(Dissertation) Temple University, Philadelphia, (1972).

44. CASANOVA, J., and WEAVER, E. R., J. Chem. Educ. 42, 137 (1965).45. EMERY, A. R., J. Chem. Educ. 42, 131 (1965).46. BARD, A. J., and KING, D. M., J. Chem. Educ. 42, 127 (1965).47. ZAJICEK, 0. T., J. Chem. Educ. 42, 622 (1965).48. DETAR, D. F., J. Chem. Educ. 44, 193 (1967).49. DETAR, D. F., J. Chem. Educ. 44, 191 (1967).50. SLABAUGH, W. H., J. Chem. Educ. 26, 430 (1949).51. CASTILLO, R., and WARD, R., The Science Teacher, 35, 83 (1968).52. SCHAAD, L. J., J. Amer, Chem. Soc., 85, 3588 (1963).53. RABINOVITCH, B., J. Chem. Educ., 46, 262 (1969).54. WOOD, D. A., ’The Monte Carlo Integration Computer as an Instructional Model

for the Simulation of Equilibrium and Kinetic Chemical Processes: The Developmentand Evaluation of a Teaching Aid," (Dissertation) Temple University, Philadelphia,(1971).

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