Derek A. Davenport Purdue University West Lofayette, Indiana 47907
Capillary Flow A versatile analog for chemical kinetics
In order to measure relative viscosities of alcohol/water mixtures and, only partly coincidentally, to find a use for around 3500 surplus Mohr burets, we came up with the simple apparatus shown in Figure 1. A moment's reflection serves to show that the emptying of the buret is a firstorder process, the rate constant for which is, by Poiseuille's Law, inversely proportional to the viscosity of the liquid. While this procedure satisfied our immediate needs it also suggested a number of novel ways in which capillary flow could be used as a mechanical analog for chemical kinetics. The simde first-order analogy is not new for it has been advocated before using sirnil;; experimental set-ups (1-3). Furthermore, several experimental hydrodynamic models have been described which serve to simulate various aspects of chemical equilihrium and chemical kinetics (4-6). A particularly elegant version of these is that of Zandler (7). The present proposals include not only first-order analogs but also zero-, one third- and one half-order cases, firstorder relaxation, and consecutive and simultaneous firstorder reactions with and without equilihrium. Further possibilities, some of Rube Goldbergian (Heath-Robinsonian to our English readers) complexity, will occur to teachers and to the more tortoous-minded student. Since the "rate constant" is governed by the length (or, more perversely, by the radius) of the capillary used, each student may be given a quantitatively unique example. We have found some of these useful as preludes (wet-labbiug?) to proper chemical kinetics experiments since it is our experience that many freshman students are overwhelmed by the concatenation of the conceptual aspects of rate processes with the problems involved in data-gathering and data-processing. In our case the conversion of reactant to product as a function of time is almost simple-mindedly apparent. The parallel between the capillary and the activated complex (or the energy of activation) is probably dangerous but certainly appealing. Certainly capillary flow of liquids is an activated process and for most liquids (water is a notable exception (8))a straight line is obtained when the logarithm of the viscosity is plotted against the reciprocal of the absolute temperature. The present apparatus is not at all suitable for studies of the temperature dependence of viscosity but unused Ostwald and Ubbelohde viscosimeters which have been banished from all fonvard-looking physical chemistry laboratories can often be located.
Figure 1 First-order reaction
Pseudo Zero-Order Kinetics
A sufficient excess pressure, P, applied to the top of the buret will change the natural first-order reaction into one following a zeroth-order rate law. By studying stepwise increase in pressure the transition from first- to pseudo zero-order can be followed. The ratio of P to the barometric height when the reaction is sensibly zeroth-order provides a useful insight into the well-known isolation method of determining reaction order. One Third-Order Kinetics
Fractional orders are not uncommon in complex systems and one third-order kinetics is easily demonstrated by the apparatus shown in Figure 2. A 4-in. funnel is con-
First-Order Kinetics
See Figure 1. The usual Vr versus time, In V , versus time, and Guggenheim (9) plots should he made. The reaction order is good to the last drop and commonly observed scatter in the loa d o t s towards the end can usually he traced to the stat&al approach freshmen bring to evaluating logarithms of numbers less than one. The concept of tGz and the lack of dependence of the rate constant on the initial volume, VO,may also be experimentally confirmed.
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venient and the capillary must be on a line with the apex of the funnel. This experiment is perhaps best given as an unknown, the student merely being told that the rate law is of the form
Some students may find it easier to calculate the order using their "concurrent calculus" and simply confirm their conclusions experimentally. More strength to them for theirs is the kingdom of physical chemistry. They might even tackle the ti,* problem with different initial volumes for the "funnel order" reaction and consider the effect of funnel angle, 8 , (Including the case of 8 = O?). Figure 5. Consecutive first-order reactions with equilibrium
One Half-Order Kinetics
A triangular prism of the type shown in Figure 3 is readily made from sheet plastic. Again this is, perhaps, best used as an unknown.
Consecutive First-Order Reactions
The apparatus is shown in Figure 4. The ratio kilki' may be varied by using appropriate lengths of capillary. If one is much longer than the other the idea of a rate-controlling step is illustrated. The analysis of this reaction scheme is given in standard texts (11). Several burets may of course be connected in series. By using a constant delivery Mariotte bottle (6) the parentldaughter relationships of radioactive decay can readily be shown. Convergent First-Order Kinetics
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400
500
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1100
The rate of change of A, B, and C can he separately monitored. Discussion of a similar experiment is given in reference (6). An application is found in the analysis of copper by neutron activation analysis (12).
Fiaure 3. Prism-order reaction
First-Order Relaxation
The first-order rate constant for a given capillary is first determined. Two burets are then connected together by the horizontal capillary and the rate of approach to equilibrium found for varying displacements in both directions. One limitation is that all equilibrium constants in these experiments are unity, and so the usual k l + k - i (10) reduces to 2kl.
Figure 4. Consecutive first-order reactions.
380 / Journal of ChemicalEducatbn
Figure 6. Michaelis-Menton t y w kinetics.
A formal analoe of this i m ~ o r t a n tclass of kinetic behavior can be achieved with the apparatus shown in Figure 6. Detailed analysis is available in many texts (13). Second-Order Kinetics
This paper would have been submitted several years ago if a simple analog of second-order kinetics using the capillary flow of liquids could have been devised. Coffin ( I ) has described an apparatus where such behavior can be demonstrated for gases, but though one can think of ways of simplifying his equipment the method remains a formidable undertaking for mass use in general chemistry courses. It is possible to design an apparatus (Fig. 7) which would deliver a second-order.analog and to a good approximation this can be, indeed has been, built. But there is something demeaning in programming in desired results in this way. One would like a simple apparatus in which Nature takes her course in a precisely second-order way but such has so far proved chimerical.
Figure 7. Secand-order a p p a r a t u s
~onsecutiveFirst-Order Reactions with Eauilibriurn
A L LB ~ C The apparatus and typical results are shown in Figure 5. Mathematical analysis is fairly complex (11). hut the question of when overshooting of the equilibrium value occurs in B can be studied experimentally by varying the relative lengths of the capillaries ( 5 ) .
Literature Cited (1) (21 (31 (41 IS1 (61
Cof1in.C.C.. J . CHEM.EDUC.25,187~19dS1. Lomiieh, a ,J.CHEM.EDUC.,31,431(19541. Hocht, K.,School Sci. Re"., 41.439 119601 Weigang,O.E., J.CHEM.EDUC.39, 146119621. Lago. R.M., Wei. J.. and Praur. C. D.. J . CHEM. EDUC.. 40,395 (1963). Meinen. H. F. (Editor). "Physic% Demon.tration Elperimentn." Ronald P m s . New York. 1910, Volume 11. p. 124&44. (71 Zandler, M . E.. Abstracts, 167th A.C.S. Nstional Meeting. Laa Aneclcs. 1974. Abstract CHEOP. (8) Eiaonhmg, D., and Kauzmann, "The Structure and R o w d i e s of Water.'' Oxfold University Resa. Near Ynk.1969, p. 223. 191 &naon. S. w.. "The Foundsfions of Chemical Kinetics" McGraa-Hill Book
Michaelis-Menten Type Kinetics kt
k'
A e B A C A-1
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