Robert T. Alden
Abington High School Abington, Pennsylvania 19001 and Joseph S. Schmuckler Temple University Philadelphia, Pennsylvania 19122
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The Design and Use d an Equilibrium Mathine
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number of analogies and simulators that use water to demonstrate chemical equilibrium OF have appear~d over the years in the JOURNAL CHEMICALEDUCATION( I - ) All are effect,ive in showing the macroscopic effects associated with equilibrium (constant macroscopic properties), but none of the devices is used to determine an equilibrium constant, which in turn can be used to determine quantitatively equilibrium shifts when demonstrating Le Chatelier's Principle. Also, in thc above cited analogies, relations to molecular level considerations and the probabilistic nature of equilibrium are vague or lacking. Ot,her devices (7, 8) which use beads to simulate molecular level effects have been described, but they, too, are not quantitative in nature. An operating model has been developed which does
Figure 1. Design of the model. Ports of the analogy are represented by: 1, the activation energy of the fomord reoction; 2, the net potenti01 energy change far the reversible reactions; ond 3, the activation energy for the reverse reaction. Mechanical p a r h ore: 4 and 5, poddle wheels connected by 6, a rubber belt, propelled by on electric motor, 7.
Reaction Coordinate Figure 2. Potential energy diagram on which the onology ir based. 1, The octivotion energy of the forward reaction; 2, the net potentid energy chonge for the reversible reactions; 3, the activation energy for the reverse reaction.
demonstrate many of the facets missing in the others. The device is simply a Plexiglas container (see Fig. 1 ) that is an analogy based on the potential cnergy diagrams of chemical reactions found in many high school and college texts (see Fig. 2). In Figures 1 and 2 the activation energy for the forward reaction, the net potential energy change for the reversible reactions, and the activation energy for the reverse reaction are labeled 1, 2 , and 3, respect,ively. The device is operated in the following fashion. A predetermined number of plastic beads ( N , ) is loaded into the model. They may be loaded in any fashion desired to show that equilibrium may be approached from either direction. The machine is then turned on. Refer again to Figure 1 . Two paddle wheels (4 and 5 ) are connected to each other with a rubber belt (6) and are propelled at the same velocity by an electric motor (7). This assures that the average kinetic energy imparted to the beads is the same in both chambers. Hence, both chambers are a t the same "temperature." The beads are allowed to equilibrate, which usually takes a few seconds of operation, and the motor is turned off, i.e., the "temperature" is dropped to absolute zero. The beads are then counted and the number of beads in the upper chamber ( N u ) and the number of beads in the lower chamber ( N J are then recorded. Due to the limited number of beads employed at any given time, ten or more trial runs arc taken for a given N L and each consecutive N , and N r are recorded. Finally, the average values for the number of beads in the upper and and flc) are calculated. The lower chambers equilibrium constant (K) is then determined from the expression,'K = iT"/iTL. To test for the constancy of K, the authors experimented with varying numbers of beads in the machine. The table shows the results. The data suggest that the most effective number of beads to use in the apparatus ranges between 150 and 250 beads. K values determined from numbers below 150 fluctuated too widely to be of use. K values determined from numbers above 250 showed a diminishing trend. This indicates, perhaps, that the motor speed was being lowered due to an cxcessive number of beads, causing a "loading effect" on t,he motor. If this is the case, then the effect would be that of lowering the
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' The concentrations of the reactants and products can he used in determining the K value, but the volumes of the chsmhers remain constant, Hence, the volumes have been incorporated in60 the K value, and only the numbers of heads may be used. Volume 49, Number 7, July 1972
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Test of Constoncv
N t = total number of beads in the machine
temperature of the system, which indeed vould change the K value. The average value for K in the useable range is 0.176. A trial run in which 218 beads were loaded into the machin? gave good results. Using 0.176 as the value for K, the average numbers of beads in the upper and lower chambers (R"and RZ) were predicted: Given: R,,/R, = 0.176; let x = flu and (218 - x) = R,;then x/(218 - x) = 0.176; solving, x = 32.6 and (218 -x) = 185.4. Artual experimentation followed and the results for and Rrwere 32.4 and 185.6, respectively. In addition to the propertips already drscrihcd, the apparatus can simulate effects in the K value due to
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temperature changes. This can be done by varying the motor speed. The authors have used a "LahVolt" variable voltage apparatus, the type often found in high school and college chemistry and physics laboratories, to accomplish this. I t can be seen that lowering the temperature of the system favors the exothermic process. Students have readily determined why this is the case. The model clearly shows that lowering the average kinetic energy of the beads in both chambers lessens the probability that the activation energy barrier will be surmounted by beads in the lower chamber to a greater extent than by beads in the upper chamber. Thus, the students realized that a shift of the equilibrium point and the K value is accomplished with temperature changes. Furthermore, they were able to correctly predict the directions in which the equilibrium point will shift and the K value will change. Literature Cited K*nm,G.M.. J.CHEM.EDUC.,4.1431 (1927). K*urmrm. G. B.. J . C m r . Eouo.,36. 150 (1959). R*nea~RAw.N. W.. J. CREM. Eouc.,3,450 (1926). Sanur. C. H.. J. C a m . Eoiic., 25,488 (1948). TUCKER, W. C.. J.CHEM.EDUO., 35,411 (1958). WEIGANO, 0. E.. JR.,J. CHEM.EDUC.,39,146 (1962). ALYEA.H.N.. J. CXGM. E ~ u c . 4l,A458 , (1964). ALYEA,H. N., J. CXEM.EDUE..41, A518 (1964).
