G. G. Giachinol Rensselaer PolVtechnic Institute Troy. New York 12181
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Analw- Comxltet' Simulation of the Methanolysis of Acetal
T h e use of analog computers to obtain the solutions of differential equations such as those encountered in chemical kinetics and quantum mechanics is becoming more common in chemistry, and several articles have appeared in this Journal ( 1 ) on the suhiect. Most of these aoolications have dealt with general rathkr than specific probiems, and often the cornouter has been oroerammed (i.e.. "oatched") hv the instructbr and used as ahlack box by the &dents. ~ l t h b u g h solutions to eeneral oroblems are certainly. very useful, students will appreciate the power of an analog computer more if it is also used on a problem with which they are familiar. The value of the experiment will he increased still further if the student is oermitted to patch the program himself after first being instiucted in the functionsand operation of the comouter's basic components. In this paper we describe an experiment using the anahg wmputcr which inrurporates both at t h v s ~fratures. The prublem investigated is the kinetics ot the methanolvsis of a c d . which the students have oreviouslv examined experimentally by means of gas chromatography. T h e nrocedure for the kinetics exoeriment is essentiallv that given h) duhnston (2),whu mudit'ied the original pnaedure of Juvet and Chiu (:I). In uur laboratories we ~ e r i o r mthe exM periment with a hydrogen ion concentration bf 1.7 X (which corresoonds to one of the concentrations actually used by Juvet and'chiu). The acetal reaction is ~articularlywell suited for this investigation becau~e'althou~h an analytical solution of the kinetics is very complicated, the analog computer program required is extremely simple and does not need any non-linear components of the computer. This latter fact not only makes the program easy to understand by the novice, but places very small demands on the computer itself, so that even the simulest comnuter should be sufficient. Furthermore. this experiment is an excellent springboard for the student who wishes to learn about the more complicated aspects of analog computation, such as scaling or the various non-linear components (multipliers, function generators, etc.)
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Methanolysis of Acetal Before proceeding with a discussion of the experiment, it is desirable to review some of the features of the reaction between methanol and acetal. The overall reaction may he wrltten CH'CH(0Et)2+
k-I
CH3CH(0Me)(0Et) + EtOH
CH3CH(OMe)(OEt)+ MeOH
3 *-. CH&H(OMe)z + EtOH (2)
Juvet and Chiu (3)found the reactions above to he first order in the appropriate acetal, first order in the hydrogen ion catalyst, and independent of the concentration of the alcohols. Therefore, if the hydrogen ion concentration is held constant, the kinetics will be identical to that found for the simple reaction scheme X & Y ~ Z .b.-., .h. k-z it will reach a maximum value and then slowly decrease. A much more stringent test of the program is to examine the value of the equilibrium constants, which for this simple reaction must be merely the ratio of the fonvard and backward rate constants, that is K I , = kllk-I and KZIp= kzlk-2. Thus, if kt = 2k-1, then the equilibrium concentration af Y must be twice that of X, regardless of the values set for kz and k-z (except, of course, when k-z = 0 and kz + 0). Similarly,if kz = k-2, then the equilibrium concentration of Z must equal that of Y, regardless of what k~and k-I ere. It should be noted here that this is also a good exercise in demonstrating that the value of one equilibrium constant is independent of the other, although the individual concentrations change. When the comouter the desired . has been successfullv. oatehed. . output chcmld be cmnrrted to a plurter so rhar che kinpti~imay br exammed more ensilg. Hefore prurceding LO the rmnplete systrm. howesvr, u e find it initrucrivr toexamine thr behavior
