Walter R. Carmody
Seattle University Seattle 22, Washington
Dynamic Equilibrium: A simple quantitative demonstration
Dynamic chemical equilibrium and the part mass action plays in its attainment are concepts that present some difficulty to the beginning student. The mechanism by which a chemical reaction comes to equilibrium is not apparent to the student when he observes even the simplest of such reactions. It is possible, however, to demonstrate the mechanism by which a physical equilibrium is attained and then the analogy between it and the attainment of a chemical equilibrium can be drawn.' Although it has been criticized by W. Hered2 the author believes that this method is very effective in helping the student visualize the mechanism of a chemical dynamic equilibrium. The rough qualitative demonstration of a physical equilibrium involving the simultaneous transfer of a liquid between two vessels has been described by SorumJ and by K a ~ f f r n a n . ~The containers used for the liquid were large beakers or crystallizing dishes and the transferring "dippers" comprised evaporating dishes or beakers of varying sizes. The author has found that this sort of demonstration can be greatly improved and made quantitative by employing graduated cylinders as containers for the liquids and "homemade" pipets as the dippers. This arrangement permits the taking of data and the preparation of curves to illustrate the course of a single reaction and also that of an equilibrium. Quantitative expressions for the rate and for the equilibrium can be developed, and then the similarity between these expressions and the corresponding expressions for a chemical reaction can be shown. As a result thc analogy brtweeu the nttainment of a chcmical eqnilibrium nnd thc attainment of a physical cquilihrium is clearly drawn. Apparatus
From the 100-ml cylinder stock a pair is selected that have precisely matched graduat.4 scales. These may be used as they are, or they may be cut off to a more convenient height; i.e., a t the SO-ml mark. The
' Tbia demonstration was designed for presentation at the Summer Institute for High School Teachers of Science and Mathematics conducted by Seattle University and sponsored by the NSF. It was voted s "most satisfying" demonstration by the members of the seminar on lecture demonstration. ' HERED,W., J. CHEM.EDUC.,27,542 (1950). a SORUM, C. H., J. CHEM.EDUC.,25,489 (1948). ' KAUFR~AN, G. H., J. CREM.EDUC.,36, 150 (1959).
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"dippers" are pairs of glass tubes that are partially closed a t one end so that they may serve as pipets. When such a pipet is immersed in a liquid so that the end touches the bottom of the container, the volume of the liquid entrapped is directly proportional to the height of the liquid in the container. One 9-mm tube and one 12-mm constitute a suitable pair; also two 10-mm tubes. The relative cross sections of the pipets in each pair may be determined by measuring the volume of liquid dipped by each pipet from a beaker of water kept a t a constant level. To increase the precision of the result the volume supplied to a graduated cylinder by four or five dips may be measured in each case. This may be done before the demonstration, or it may be made a part of the demonstration. Demonstration of the Rate Process
One of the graduated cylinders is filled to the 80-ml mark with colored water, and it is pointed out that the scale reading not only indicates the volume of the liquid but also is a measure of the height of the liquid in the cylinder. A pipet tube (8 to 12 mm in diameter) is dipped to the bottom cylinder, the upper end is closed with a finger, and the containing liquid pipetted out. The volume of the liquid remaining in the cylinder is then read (to the nearest ml) and recorded on a graph of volume versus number of dips drawn on the blackboard. The operation is repeated until there is practically no water remaining in the cylinder. A smooth curve is drawn through the points on the graph, and the relationship between the slope and the height discussed. The equation for the rate of transfer of the liquid is then presented, R, = (h)(a) in which R, represents the volume of liquid transferred per dip of the pipet, h represents the height of the liquid in the cylinder, and a represents the cross-sectional area of the pipet. It is pointed out that the height of the liquid is the variable factor in the equation and that the rate of transfer of the liquid varies with the height and is reduced to zero as the height of the liquid is reduced to zero. The mass action expression for a first order reaction is written, r = (c)(k)
and the significance of each term discussed. The analogy then may he drawn between the two variables, height and concentration, and the cause for the declming rate during the course of a chemical reaction explained.
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Demonstration of Dynamic Equilibrium
The pair of matched graduate cylinders is clamped on the desk in a position most suitable for the simultaneous transfer of liquid from each to the other. One of the cvlinders is filled to the 80-ml mark with colored water. I
1
I
1
I
4
8
12
16
20
J
I 24
Number of Exchanges Figure 2.
Attainment of physical equilibrium.
equilihrium, the pipets are dipped again into the cylinders and the enclosed liquids pipetted into two 10-ml graduate cylinden and the volumes recorded. The results usually are quite convincing to the students. Table 1.
Sample Results of Physical Equilibrium Demonstration
Height, equilibrium (relative) Area of pipet (relative) Product (height)(area) Figure 1.
Simultaneous tronrfer of liquid.
The larger of a pair of immersion pipets is placed in this cyiider and the smaller in the empty cylinder. Closing the tops of the pipets, one trausfers the contents of each simultaneously to the other cylinder (Fig. 1). The volume of liquid in the second cylinder is read, and this is recorded on a graph of volume versus number of exchanges (Fig. 2). The operation is repeated (twenty times or more) until no change in volume can he detected during three or four successive exchanges. A smooth curve is drawn through the points on the graph, and the shape of the curve is explained in terms of the operation of the two variables and their effect on the two opposing rates. The expression for the dynamic equilibrium in terms of the final (equilibrium) relative heights and relative cross sections of the pipets, (hJ(at) = ( h d n d
is developed, and the equality of the two checked using the experimental data. Sample results are shown in the accompanying table. In order to demonstrate more convincingly the equality of the two opposing rates a t
Cylinder no. 1
Cylinder no. 2
25 2.24 56
55 1.03 55
The equality of reaction rates for an analogous chemical equilibrium is written, ( ~ ) (=h(c&4 ) in which c, and c, represent the equilihrium concentrations of the reactant and product respectively. It is to be noted that the heights of the liquids in the cylinders are somewhat greater when the pipets are immersed than they are when the readings are taken. The relative increase in height in the cylinder containing the pipet of larger diameter is slightly greater than that in the other cylinder. As a result the relative rate of transfer as measured by the product (height)(area), is usually slightly larger for the pipet with the larger diameter. If one desires to eliminate this error, one can either record the volume (height) readings each time with the pipets immersed, or one can originally determine the relative cross sections of the pipets by a method that involves their immersion in equal volumes of liquid contained in the two cylinders. The analogy between the variables of the physical equilibrium and those of the chemical are again drawn and the mechanism by which a chemical reaction reaches equilihrium finally elucidated.
U. S. colleges and universities increased their scientific research and development 80 per cent hetween 1954 and 1958, a National Science Foundation study shows. Comparisons with rt 1953-54 study show that Federal expenditures for research and development in colleges and universities proper increased 55 per cent during the same period-from $140.7 million to S217.9 million.
Volume 37, ~ u h b e r6, June 1960
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