In the Laboratory
The BZ Reaction: Experimental and Model Studies in the Physical Chemistry Laboratory Omar Benini, Rinaldo Cervellati,1 and Pasquale Fetto Dipartimento di Chimica “G. Ciamician”, Università di Bologna, via Selmi 2, 40126 Bologna, Italy In a very recent paper, J. A. Pojman et al. pointed out that oscillating chemical dynamics has been the subject of numerous articles in chemical education journals, but most often these works have focused on the demonstration value of oscillating reactions rather than on actually using them as part of the teaching laboratory (1). The excellent paper of Pojman et al. presents therefore a three-experiment module based on the most widely studied oscillating system, the Belousov–Zhabotinsky (BZ) reaction. In our opinion this represents a landmark in the renewal of physical chemistry laboratory experiments in kinetics. For example, Italian chemistry students perform kinetics experiments during the third or fourth year of a nominally five-year degree course. These experiments consist in general in the quantitative determination of rate constants for simple first- and second-order reactions and of the effect of changes in temperature on the rate constants, and they give some insight into the mechanism of the reactions studied (2). We feel that at this stage and with the acquired knowledge, students are able to try a more advanced kinetic than those mentioned above. Therefore the aims of this work are: • to illustrate integrated chemistry-computational lab experiments at the tertiary level on the “classical” BZ oscillating reaction • to show that the Ce4+/Ce3+ and the Fe(phen)32+(ferroin)/ Fe(phen)33+(ferriin)-catalyzed BZ reactions have different mechanisms
In its classic form the BZ reaction is the metal-ioncatalyzed oxidation of an easily brominated organic substrate by BrO3– in a strongly acid medium (3). The most evident feature of the “classical” BZ system [a solution of malonic acid (MA), bromate ions, and a metal ion or an ion complex as catalyst in dilute sulfuric acid] is the periodic change of color due to the change in the oxidation state of the catalyst. In the Ce4+ /Ce3+-catalyzed system the color changes from yellow (ceric ions) to colorless (cerous ions); while using the Fe(phen)32+/Fe(phen)33+ couple the color changes from red (ferroin) to blue (ferriin). The mechanism of the BZ reaction is very complicated: a recent improved model for the Ce4+/Ce3+-catalyzed reaction contains 80 elementary steps and 26 variable species concentrations (4). However, the early mechanism proposed by Field, Körös, and Noyes (FKN) (5) is still adequate to explain the course of the BZ reaction and how oscillations occur. Teachers can find very good descriptions of the FKN mechanism in an article that appeared in this Journal (6) and in a book by S. K. Scott (7). Experimental Study Students worked in two groups, each group doing one of the two laboratory experiments each week (16
hours per week). A third week was devoted to the model and computational study. The complete work was designed for • studying the behavior of the Ce4+/Ce 3+-catalyzed BZ system • studying the behavior of the Fe(phen)32+/Fe(phen)33+catalyzed BZ system • developing, with the help of the teacher, a kinetic model to interpret the experimental data; students are invited to solve the kinetic equations derived from the model by using numerical methods and a suitable computer program
The kind of integrated chemistry-computational lab experiments described below may be a powerful tool in stimulating student interest and in showing the importance of chemical kinetics in the elucidation of reaction mechanism. We sharpen the focus on the model study because experiments on the BZ system have been the subject of several papers that have appeared in this Journal (1).
Oscillations in the Ce4+/Ce3+-Catalyzed BZ System The following three reagent base solutions and 1 L each of 0.5 M and 1.5 M H2SO4 were prepared: 1. Ceric sulphate: 5 × 10–3 M Ce(SO4) 2?H2O in 0.5 M sulfuric acid; 2. Potassium bromate: 0.180 M in 0.5 M sulfuric acid; 3. Malonic acid (MA): 0.60 M in 0.5 M sulfuric acid.
All materials should be of the highest purity available from commercial sources. Reaction mixtures were prepared by mixing the appropriate amounts of the base solutions 1, 2, 3 and 0.5 M or 1.5 M sulfuric acid. The oscillations of the Ce4+ concentration in the reactant mixture have been followed spectrophotometrically (8–10). Students measured the period of oscillation and the maximum Ce4+ ion concentration reached in the oscillations as a function of the initial concentration of any one of the reactant mixture components: Ce4+, MA, BrO3–, or H +. All measurements were made at 20 °C. An induction period of approximately 2– 10 min is necessary before the oscillations of the Ce4+/ Ce3+ concentration will occur. Plots of the period of oscillation as a function of the initial concentration of any one of the components are then made. A plot of the oscillation period versus the initial Ce 4+ concentration is shown in Figure 1. From Figure 1 it appears that the periods of oscillation became increasingly longer with increased Ce4+ ion concentration. All the experimental data show that at the oscillation peaks the catalyst is at more than 90% in its reduced form (Ce3+). In order to show the presence of radicals in the reaction mixture the suggestion of Pojman et al. (1) has been followed.
1
Author to whom correspondence should be addressed.
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Figure 1. Period of oscillation plotted as a function of the initial concentration of Ce 4+. [BrO 3–] o= 0.03, [MA]o= 0.10, [H+] o= 1.0.
Figure 2. Period of oscillation plotted as a function of the initial concentration of Fe(phen)32+. [BrO3–] o = 0.108, [Br –]o = 1.67×10 –2, [MA]o = 0.125, [H +] o = 1.0.
Oscillations in the Fe(phen)32+/Fe(phen) 33+-Catalyzed BZ System The following base solutions were prepared:
duce the original “Oregonator” model proposed by Field and Noyes (12) for the cerium-catalyzed BZ reaction. A didactic explanation of this model can be found in references 6, 13, and 14. The main features and the importance of the Oregonator as the first model satisfactorily accounting for the behavior of a real oscillating system must be pointed out. However the Oregonator is indifferent to the chemical condition of the conservation of the total cerium-ion concentration: the maximum Ce4+ ion concentration calculated is often greater than the initial one. In order to overcome this problem, the following model was used in our study: A + Y → X + P rate constant k1 (1) X + Y → 2P rate constant k2 (2) (3) A + X → 2W rate constant k3 C+W X + Z rate constants k4 and k{4 (4) 2X → A + P rate constant k5 (5) Z → gY + C rate constant k6 (6)
1. 2. 3. 4.
Sodium bromate: 1.08 M in 0.5 M sulfuric acid Malonic acid (MA): 0.75 M in 0.5 M sulfuric acid Sodium bromide: 1.00 M in 0.5 M sulfuric acid Fe(phen)32+: 1.35×10{3 M (prepared by adding a little excess of 1,10-phenanthroline to the appropriate amount of FeSO4?7H 2O in 0.5 M sulfuric acid) 5. 1 L of H2SO4 0.5 M and 1 L of H2SO4 1.0 M
Reaction mixtures were prepared by mixing the appropriate amounts of the base solutions 1, 2, and 3 and 0.5 M or 1.0 M sulfuric acid. Appropriate amounts of solution 4 were added after the free bromine (brown color) produced by the reaction between BrO3– and Br– had disappeared. Students followed spectrophotometrically the oscillations of the Fe(phen)32+ concentration in the reactant mixture (10, 11). The period of oscillation and the maximum Fe(phen)32+ ion concentration reached in the oscillations were measured as a function of the initial concentration of any one of the reactant mixture components: Fe(phen)32+ , MA, BrO3–, Br – or H +. All measurements were made at 20 °C. A plot of the oscillation period versus the Fe(phen)32+ concentration is shown in Figure 2. In this case the dependence of the oscillation period on the [Fe(phen)32+]o is linear and all the experimental data show that at the oscillation peaks the catalyst is less than 10% in its reduced form [Fe(phen)32+]. These differences may suggest that the two couples catalyze the reaction by different mechanisms.
where X ≡ HBrO2, Y ≡ Br- , Z ≡ Ce4+, W ≡ BrO 2?, C ≡ Ce3+ , A ≡ BrO3–, P ≡ HOBr, and g is a stoichiometric factor. This model is a simplification of that proposed by Field and Försterling (15). The introduction of the Ce3+ species guarantees the conservation of cerium ion and the reversibility of step 4 is necessary in order to take into account the behavior of the couple Ce4+/Ce3+. The steps 1–5 can be related to the following chemical reactions in the FKN mechanism: Br–+ BrO3 + 2H+→ HBrO2 + HOBr rate constant k 1, 2.0 M {3s {1 –
Br + HBrO2 + H+→ 2HOBr –
rate constant k2 , 2.0×106 M {2s{1
BrO3–+ HBrO2 + H+→ 2BrO2? + H2O rate constant k 3, 33.0 M {2s {1
Mathematical Model and Computational Study At the beginning of this part the teacher must explain in detail the main reactions of the FKN mechanism (6, 7), focusing on the role of the intermediate spe– cies Br , HBrO2, HOBr, and BrO2? and the reduced and oxidized forms of the catalyst, as well as on the organic substrate. Students must realize that the FKN mechanism is so complicated that in order to reproduce the oscillatory behavior of the BZ system simplified kinetic models are needed. At this point the teacher can intro-
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Ce3++ BrO2?+ H
+
Ce4+ + HBrO2
2HBrO2 → HOBr + BrO3 + H+ –
rate constants k4, k {4, 4 {2 {1 3 {1 {1 6.2×10 M s , 7.0×10 M s rate constant k5, 3.0×103 M{1s{1
for which the experimental values of rate constants (4) are given. The model leads to five differential equations: d[X]/dt = k1[A][Y] – k2[X][Y] – k3[A][X] + k4[W][C] – k-4[Z][X] – 2k5[X]2 d[Y]/dt = –k1[A][Y] – k2[X][Y] + gk6[Z]
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d[Z]/dt = k4[W][C] – k-4[X][Z] – k6[Z] d[W]/dt = 2k3[A][X] – k4[W][C] + k-4[Z][X] d[C]/dt = –k4[W][C] + k-4[X][Z] + k6[Z] For solving these equations a suitable numerical integration program has been written in Quick BASIC for an IBM-compatible PC. The block scheme and the main feature of the program have been clearly discussed with the students. In particular the routine for the numerical integration uses a Runge-Kutta 4 method (16) modified by us. Our modification consists in imposing the steady-state condition for the HBrO2 concentration when it falls near to its minimum value.
Parameterization of k6 Step 6 of the model cannot be related to a single reaction of the FKN mechanism: it is the sum of various reactions in which Ce4+ is reduced and MA is oxidized with production of Br–. For this reason, in all the model studies, k6 has been arbitrarily assumed or adjusted to reproduce the experimental data. The same applies also to the stoichiometric factor g. We have tried to parameterize k6 as a function of the initial concentrations of Ce4+, BrO 3–, MA and H + . By using the experimental data and the computational program we have determined the dependence of k6 on each of the initial concentrations of the above-mentioned components. We have found that each dependence is linear, so the k6 can be parameterized as follows: – + k6 = a[Ce4+] + b[BrO3 ] + c[MA] + d[H ] + e
In order to determine the coefficients a, b, c, d, and e, we have performed a multiple linear regression calculation. The results were: a = –0.138 ± 0.004 b = 20.8 ± 0.2 c = 0.57 ± 0.05 d = 0.602 + 0.004 e = –0.548 + 0.004
Figure 3. (a) Experimental trace of Ce 4+ ion absorbance vs. time. Initial conditions: [Ce4+] o = 8.34×10–4, [BrO3–]o = 0.03, [MA]o = 0.10, [H+ ]o = 0.50. (b) Computed trace.
The parameterized k6 has been introduced into the program.
Typical Results Students performed a number of computations using the values of k 1–k 5 rate constants listed above transformed in k 1–k5, taking into account the acidity effects, g = 0.50, and the values of the initial concentrations of the reactants. The results have shown very good agreement between the calculated and experimental values of the maximum Ce4+ ion concentrations reached in the oscillations peaks, as far as the shape of the oscillations. As an example of this agreement, an experimental trace of Ce4+ ion absorbance vs. time is reported in Figure 3a and the corresponding computed trace is reported in Figure 3b. The agreement between the experimental and computed oscillation periods is not as good as that between the Ce4+ concentrations. The model underestimates the oscillation periods by ~30%. We feel that this is because during the induction period, the BrO3– and MA concentrations decrease as a result of the reaction; therefore, when oscillations commence, these concentrations are different from the initial ones. But the model assumes that oscillations occur at the initial values of BrO3– and malonic acid concentrations, so it appears reasonable to ascribe to these differences the discrepancies between experimental and computed oscillation periods.
Figure 4. (a) Experimental trace of Fe(phen) 32+ ion absorbance vs. time. Initial conditions: [Fe(phen)32+] o = 2.25×10 –4, [BrO3–] o = 0.18, [Br–] o = 1.67×10–2, [MA]o = 0.25, [H+ ]o = 1.0. (b) Computed trace.
Trying the model on the Fe(phen)32+/Fe(phen)33+-Catalyzed BZ System If the Ce4+/Ce3+-catalyzed and Fe(phen)32+/Fe(phen)33+catalyzed BZ systems proceeded by similar mechanism, the latter could be easily simulated on the basis of the described model. Thus one should simply change the rate constant of step 4 in accordance with the different behavior of the two catalysts. This difference makes step 4 irreversible in the case of the Fe(phen)32+/Fe(phen)33+ couple, with k4 = 109 M–2 s–1 (15), but any attempt to reproduce the oscillations of the Fe(phen)32+ concentration
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is destined to fail. The model shows that instead of oscillating, the Fe(phen)32+ concentration approaches a steady state. As an example, an experimental trace of Fe(phen)32+ ion absorbance vs. time and the corresponding computed trace are illustrated in Figure 4. Discussion The metal ion and metal ion complex catalysts of the BZ system have been classified in two groups (17). The high-reduction potential couple Ce4+ /Ce3+ (E° = 1.44 V) belongs to the former group, whereas the low-potential couple Fe(phen)33+/Fe(phen)32+ (ferriin/ferroin, E° = 1.06 V) belongs to the latter. Noyes (18) pointed out that the couple ferriin/ferroin should not catalyze the BZ reaction by the same mechanism appropriate for the Ce4+/ Ce3+ couple. The results presented here are in agreement with Noyes’ conclusions; in fact the model derived from the FKN mechanism for the cerium-catalyzed reaction fails to account for the ferroin-catalyzed reaction. So this latter system must proceed by a different mechanism. Simple kinetic arguments supporting this conclusion can be found in reference 19.
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Acknowledgment This work was supported by the Italian Ministry of University and Research (MURST). Literature Cited 1. Pojmam, J. A.; Craven, R.; Leard, D. J. Chem. Educ. 1994, 71, 84–90 and references therein; see also Cartwright, H. M.; Farley, H. A. Educ. Chem. 1989, 26, 46–48. 2. Daniels, F.; Williams, J. W.; Bender, P.; Alberty, R. A.; Cornwell, C. D.; Harriman, J. E. Experimental Physical Chemistry; McGraw Hill: New York, 1970; pp 137–155. 3. Field, R. J.; Boyd, P. M. J. Phys. Chem. 1985, 89, 3707–3714. 4. Györgyi, L.; Turànyi, T.; Field, R. J. J. Phys. Chem. 1990, 94, 7162–7170. 5. Field, R. J.; Körös, E.; Noyes, R. M. J. Am. Chem. Soc. 1972, 94, 8649–8664. 6. Field, R. J.; Schneider, F. W. J. Chem. Educ. 1989, 66, 195–204. 7. Scott, S. K. Oscillations, Waves and Chaos in Chemical Kinetics; Oxford Science: Oxford, 1994; pp 26–29. 8. Kasperek, G. J.; Bruice, T. C. Inorg. Chem. 1971, 10, 382–386. 9. Vidal, C.; Roux, J. C.; Rossi, A. J. Am. Chem. Soc. 1980, 102, 1241–1245. 10. Geckle, D. S.; Salmon, J. F. J. Chem. Educ. 1986, 63, 908–909. 11. Kuhnert, L.; Krung, H-J.; Pohlmann, L. J. Phys. Chem., 1985, 89, 2022-2026 12. Field, R. J.; Noyes, R. M. J. Chem. Phys. 1974, 60, 1877–1884. 13. see ref 7, pp 29–30. 14. Shakhashiri, B. Z. Chemical Demostrations: A Handbook for Teachers; University of Wisconsin: Madison, 1985; pp 236–238. 15. Field, R. J.; Försterling, H-D. J. Phys. Chem. 1986, 90, 5400–5407. 16. Norris, A. C. Computational Chemistry. An Introduction to Numerical Methods; John Wiley & Sons: New York, 1981; pp 217–224. 17. Körös, E.; Burger, M.; Friedrich, V.; Ladànyi, L.; Nagy, Zs.; Orbàn, M. Faraday Symp. Chem. Soc. 1974, 9, 28–37. 18. Noyes, R. M. J. Am. Chem. Soc. 1980, 102, 4644–4649. 19. See ref 7, pp 9–10.
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