ROBERT LEMLICH University of Cincinnati, Cincinnati, Ohio
INTEACHING chemical kinetics, the conducting of a suitable quantitative demonstrative experiment is often something of a problem. Preliminary preparation of solutions, standardization, and carefully timed titrations are usually required. To circumvent these difficulties an analogous kinetic experiment involving a physical process can be performed which is much simpler and yet which clearly demonstrates the principles involved in a first-order reaction. The analogy is based on Poiseuille's law for the viscous flow of fluids. According to this relationship the rate of flow for a given liquid a t constant temperature through a capillary of given dimensions is proportional to the pressure drop across the capillary. Where this pressure drop is due solely to gravity head in a reservoir of constant horizontal cross section, the rate of fall in height, - d H / d r for the liquid level in the reservoir, becomes proportional to the height of the level itself, or,
Rearranging and integrating without limits yields Equations 1 and 2 are exactly analogous to those for a firstorder irreversible chemical reaction where the rate of decrease in the concentration of the reactant - d c / d s is proportional to the concentration itself, or,
A similar integration of equation 3 without limits yields The similarity between the two sets of equations, and therefore the analogy between the two types of kinetic phenomena, is obvious. The gravity-head driving
JOURNAL OF CHEMICAL EDUCATION
force in the first set corresponds t o the concentration driving force in the second set. Thus a simple demonstration involving a falling liquid level can be employed to illustrate a kinetic "reaction." The equipment required consists of an ordinary 50ml. buret, clamped vertically in the usual manner, with a 6-inch length of capillary tubing connected to its tip with rubber tubing. The capillary is clamped in position so that its free end is a t the same level as the 50 ml. mark on the buret, as shown in Figure 1. The buret is filled with water a t room temperature, partially drained to force out air, and refilled above the 0 ml. mark. The stopcock is then opened wide and the liquid level allowed to fall. The time is noted as the level passes half a dozen or so well-spaced ml. marks. By subtracting these ml. readings from 50 ml. a measure of the height of the liquid level is obtained for various instants. Plotting these heights against the elapsed time on semilogarithmic coordinates yields a straight 3
u
0
1
Fi-
2
2.
3 4 Time in minutes
5
6
7
Rate of Change in Xquid L-1
line from which k ' may be determined, thus demonstrating the validity of equations 1 and 2 and therefore by analogy also equations 3 and 4. Figure 2 shows a plot of such experimental data. The analogy may be extended even further. For example, the temperatnre of the water may he increased, thus decreasing its viscosity and in turn iucreasing k'. For moderate changes in temperature, the logarithm of the viscosity is linear with the recipre cal absolute temperature 1/T. By combining this fact with Poisenille's law it can he shown that the logarithm of k ' itself is linear with 1/T. This is analogous to the situation for a chemical reaction where, according to the integrated form of the Arrhenius equation for moderate changes in temperatnre, the logarithm of the velocity constant k is also linear with 1/T. I n this manner the effect of temperatnre on reaction rate may be demonstrated. Another extension of the principle involves the use of two burets in series, the first feeding the second, and the second feeding the receiver. This represents two consecutive chemical reactions. The initial rise, attainment of a niaximum, and subsequent fall of the liquid level in the second buret is analogous t o the initial increase, attainment of a maximum, and subsequent decrease in the concentration of the intermediate compound. Thus the principles involved in a series reaction may he demonstrated. I n conclusion, it might be pointed out that these experiments not only aid in the teaching of chemical kinetics as such, but serve t o introduce the student to some aspects of the fundamental similarities between the kinetics of chemical and physical processes.
