applications anJ analoqiss
edited by RON DELORENZO Middle Georgia College Cochran, GA31014
A Perfect (Gas) Analogy for Kinetic versus Thermodynamic Control Roger S. Macornber University of Cincinnati Cincinnati, OH 45221 The concept of thermodynamic versus kinetic control of cornpetitivc reactions is one that is introduced in virtually all s%phomore-levelorganic chemistry courses. For example, hydro-bromination of l&butadiene (A) a t low temperature gives predominantly the l,2-addition product B, while 1,4-adduct C is the preferred product at higher temperatures or when longer reaction times are used. (See reaction.)
Reaction Coordinate Figure 1. The reaction profile diagram for the reaction The appropriate definitions are easily memorized. When a reaction is conducted under conditions of thermodynamic control the product ratio BIC is determined solely by the relative free enerdes of B and C. From Fimre 1, we note that C (with lower free energy than B) would predominate at eauilibrium. Bv contrast. under conditions favorine kinetiE control the product ratio BIC is determined solely by the relative rates of formation of B versus C. From Figure 1(which neglects the carbocation intermediate common to both products), we can see that product B (with the lower activation barrier of formation) would predominate in this case. As straightforward as these definitions seem to be, it has been mv exuerience that manv students have difficultv auplying these concepts because they have so little experience with either thermodynamics or kinetics. The physical analogy described below relates to perfect gas behavior with which virtually every student is familiar. It seems to be successful in giving most of them a much better feel for relationship between kinetic and thermodynamic control of a reaction. "
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Imagine three interconnected glass bulbs as shown in Figure 2. Bulb 3 has 10 times the volume of bulb 2, which in turn has nine times the volume of bulb 1. Initially there is 1atm of an inert ideal gas in bulb 1, while bulbs 2 and 3 are evacuated. Furthermire, the diameter of the tube that connects 1with 2 is 10 times that connecting 1to 3 . Thus, under equal pressure differentials, gas will flow 100 times faster from 1to 2 than from 1to 3. For the purposes of our subsequent discussion we will assume that the volumes of the tubes are negligible, and all processes occur isothermally. Most students can correctly predict, a t least qualitatively, what will happen when stopcocks 1-2 and 1-3 are opened simultaneously. In the time it takes for bulbs 1and 2 to equilibrate (giving 0.1 atm in both), only about 1%of the gas will have leaked into bulb 3. If the stopcocks are closed a t this point, the mole ratio of gas in the first two bulbs (211) would be about 911, the same as the ratio of their volumes. The mole ratio 213 would be about 910.1 = 90. This is the result of kinetic control, the outxome having been determined bv the rate of gas flow among the three bulbs.
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Volume 71
Number4 April 1994
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Figure 2. The bulb volumes are:l, 1.OL; 2, 9L; 3, 90L
length of time the stopcocks are open (i.e., the reaction time) determines whether the reaction is subject to kinetic control, thermodynamic control, or some combination of the two. In this analogy, we can equate the volume of each bulb to the negative free energy of the corresponding chemical species in the reaction, and the diameter of the connecting tubes to the rate wnstants km and ~ A (i.e., C the smaller diameter corresponds to the higher activation barrier). Finally, it is useful to remind students that at 25 'C a difference ofjnst 11.3kJlmol(2.7 kcallmol) in activation free energies is enough to provide a 100-fold difference in rate constants. Readers interested in more detailed information regarding triangular kinetic reactions (1,2)and wnsecutive-com~etitivereactions (3-7)mav wish to consult these references. Literature Cited
Now let's re-o~enthe two sto~coeksand wait until complete equilibri&n is attained, i.e.,PI = Pz = P3 = 0.01 atm. At this ~ o i nthe t mole ratio 213 will be 9/90 or 0.1 (the same as the r k o of their volumes), the result of thermodynamic control. The key for the students to realize is that the
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Journal of Chemical Education
1.Mammber,R. S. J. O g Chrm.l911,36,999. 2. Msmmber.8. S. J.Olg Cham. 1918.38.2568. 3. Maamber,%. S.;Bopp,TTSynih. Commun. 1980,10,767. 4.Conatentinides, I.; lourde&ura,M.;Memmber,R. 8.J. Phya. Org C k m
