Chemical Reaction Kinetics
Appendix 4.1 Datasets Used for Examples in This Chapter
TABLE A.4.1 Degradation of 1-Methyladenosine in Heated Milk (Figure 4.11)
Heating Time (s)
at 1358C Concentration
(mmol L1)
0 0.41
2 0.38
12 0.36
31.7 0.35
45 0.29
60.1 0.32
70 0.26
128 0.24
156 0.15
Initial Concentration (mmol L1)
Initial Rate (mmol L1s1) at 1358C
0.41 0.011041
0.53 0.014196
0.64 0.01735
0.71 0.019243
1.18 0.031861
1.19 0.032177
2.35 0.063407
5.92 0.159306
Source: From Schlimme E., Ott F.G., and Kiesner C.
Reaction kinetics of the heat-induced formation of N6-methyladenosine in milk. Int Dairy J 4:617–627, 1994.
Note: The author would like to thank Prof. Schlimme for providing the data.
TABLE A.4.2 Nonenzymatic Browning of Whey Powder during Storage (Figure 4.12)
Time (days)
Optical Density Optical Density Exp. 1, 258C Exp. 2, 258C
0 1.8 1.9
30 4.3 4.1
60 6.3 6.1
90 7.4 7.6
120 9.6 9.8
150 12.0 11.8
180 12.5 12.7
210 14.5 14.8
TABLE A.4.2 (continued) Nonenzymatic Browning of Whey Powder during Storage (Figure 4.12) Time (days)
Optical Density Optical Density Exp. 1, 358C Exp. 2, 358C
0 1.7 1.6
10 5.2 5.0
20 7.9 7.9
30 10.6 10.5
40 13.7 13.8
50 16.3 16.5
60 20.2 20.1
70 23.2 23.4
95 27.8 27.7
Optical Density Optical Density
Time (days) Exp. 1, 458C Exp. 2, 458C
0 1.7 1.7
2 5.2 5.2
4 7.1 7.0
7 22.4 22.4
11 25.2 25.3
18 31.7 31.7
28 44.4 44.2
35 50.7 50.9
Source: From Labuza Th.P. Reaction kinetics and accelerated tests. Simulation as a function of temperature. In: Computer Aided Techniques in Food Technology, Vol. I, Saguy (ed.). New York: Marcel Dekker, 1983, pp. 71–115.
TABLE A.4.3 Degradation of Betanin in Aqueous Solution at 758C (Figure 4.13) Time (min)
Betanin mg L1
0 4.29
10 3.65
20 3.04
25 2.83
35 2.30
40 2.20
50 1.83
60 1.49
90 0.96
100 0.70
Source: From Saguy I., Kopelman I.J., and Mizrahi S.
Thermal kinetic degradation of betanin and betalamic acid. J Agric Food Chem 26:360–362, 1978.
TABLE A.4.4 Lysine Loss in Milk Heated at 1608C (Figure 4.14)
Time (s) Lysine (mg L1in Milk)
0 2.93
50 2.62
100 2.40
200 2.12
350 1.98
600 1.54
1000 1.01
1500 0.84
2000 0.62
Source: From Horak F.P. Über die Reaktionskinetik der Sporenabtötung und chemischer Veränderungen bei der thermischen Haltbarmachung von Milch zur Optimierung von Erhitzungsverfahren, PhD thesis.
Technical University of Munich, Germany, 1980.
TABLE A.4.5 Reduction of Hexacyanoferrate (III) ([B]) by Ascorbic Acid ([A]) at Ionic Strength of 0.0384 M (Figure 4.15)
Time ln(A=B)
0
1.02 3.26967
1.87 3.33875
3.05 3.43085
3.96 3.54598
4.98 3.61506
5.99 3.73019
7.12 3.82229
8.03 3.89137
9.1 3.98347
10.06 4.05255
11.19 4.14465
12.15 4.25978
13.22 4.35189
14.08 4.39794
15.2 4.51307
Source: From Watkins K.W. and Olson J.A. Ionic strength effect on the rate of reduction of hexacyanoferrate (III) by ascorbic acid. J Chem Ed 57:158–159, 1980.
TABLE A.4.6 Heat-Induced Denaturation=
Aggregation ofb-Lactoglobulin at 658C (Figure 4.16) Initial Concentration (g L1) Initial Rate
1.485 9.096e-6
Source: From Roefs S.P.F.M. and de Kruif C.G.
A model for the denaturation and aggregation of b-lactoglobulin. Eur J Biochem 226:883–889, 1994.
Note: The author would like to thank Dr. Roefs for supplying the data.
TABLE A.4.7 Degradation of Chlorophyll A at 1158C (Figure 4.17)
Source: From Canjura F.L., Schwarz S.J., and Nunes R.V.
Degradation kinetics of chlorophylls and chlorophyllides.
J Food Sci 56:1639–1643, 1991.
TABLE A.4.8 Sucrose Hydrolysis at 708C and pH 2.5 (Figure 4.18)
Time (min) Sucrose in g L1, exp. 1 Sucrose in g L1, exp. 2
0 0.76 0.76
20 0.72 0.71
30 0.68 0.66
50 0.61 0.59
70 0.55 0.54
85 0.49 0.50
115 0.48 0.44
140 0.37 0.37
175 0.5 0.32
215 0.27 0.26
260 0.22 0.19
320 0.14 0.12
400 0.08 0.07
535 0.03 0.04
Source: From Pinheiro Torres A., Oliveira R., Silva C.L.M., and Fortuna S.P. The influence of pH on the kinetics of acid hydrolysis of sucrose. J Food Process Eng 17:191–208, 1994.
TABLE A.4.9 Effect of pH on Acid Hydrolysis of a Fructo-Oligomer (Figure 4.25) pH
Log (rate) for Raftilose P95
2 1.6
2.6 2
3 2.7
3.5 3
4 3.7
4.2 4
Source: From Blecker C., Fougnies C., van Herck J.C., Chevalier J.P., and Paquot M. Kinetic study of the acid hydrolysis of various oligofructose samples.
J Agric Food Chem 50:1602–1607, 2002.
TABLE A.4.10 Demethylation Kinetics of Aspartame in aqueous solution at 258C (Figure 4.26)
pH Log k1 Log k2 Log k3
0.28 4.96
0.59 5.31
0.91 5.67
1.33 6.15
1.82 6.60
2.25 7.0
5.82 5.96
TABLE A.4.10 (continued) Demethylation Kinetics of Aspartame in aqueous solution at 258C (Figure 4.26) aspartame and L-phenylalanine methyl ester in aqueous solution. Pharm Res 10:1174–1180, 1993.
TABLE A.4.11 Effect of a-Tocopherol on b-Carotene (Figure 4.28)
Tocopherol 7.5mmol dm3 3.8mmol dm3 0mmol dm3
TABLE A.4.11 (continued) Effect of a-Tocopherol on b-Carotene (Figure 4.28)
Source: From Takahashi, A., Shibasaki-Kitakawa, N., and Yonemoto, T., J. Am. Oil Chem. Soc., 80, 1241, 2003.
TABLE A.4.12 Photodecomposition of Riboflavin in Water and Milk Serum (Figure 4.29)
Time (days) Log c=c0in Water
0 2
Time (days) Log c=c0in Milk Serum
0 2
Bibliography and Suggested Further Reading
About Kinetics
Andraos J. A streamlined approach to solving simple and complex kinetic systems analytically. J Chem Ed 76:1578–1583, 1999.
Baird J.K. A generalized statement of the law of mass action. J Chem Ed 76:1146–1150, 1999.
Clegg R.M. Derivation of diffusion controlled chemical rate constants with the help of Einstein’s original derivation of the diffusion constant. J Chem Ed 63:571–574, 1986.
Corradini M.G. and Peleg M. A model of non-isothermal degradation of nutrients, pigments and enzymes. J Sci Food Agric 84:217–226, 2004.
Croce A.E. The application of the concept of extent of reaction. J Chem Ed 79:506–509, 2002.
TABLE A.4.12 (continued) Photodecomposition of Riboflavin in Water and Milk Serum (Figure 4.29)
Time (days) Log c=c0in Water
2.68 1.15
3.18 1.12
3.39 1.07
3.81 1.05
3.9 0.98
Source: From Toyosaki T., Yamamoto A., and Mineshita T. Kinetics of photolysis of milk riboflavin. Milchwiss 43:
143–146, 1988.
TABLE A.4.13 Photodecomposition of Aspartame (Figure 4.30)
0 lx 1100 lx 3300 lx 5500 lx
Time (days) (30.001 M)
0 1.2 1.2 1.2 1.2
2 1.18 1.18 1.16 1.12
4 1.16 1.14 1.09 1.03
6 1.15 1.13 1.02 0.9
8 1.12 1.1 0.96 0.81
10 1.09 1.04 0.92 0.73
Source: From Kim, S.K., Jung, M.Y., and Kim, S.Y., Food Chem., 59, 273, 1997.
TABLE A.4.14 Photosensitization of Ascorbic Acid by Riboflavin (Figure 4.31)
Riboflavin 0 ppm 1.2 ppm 2.4 ppm 3.6 ppm 6.0 ppm
Time (min) (30.0001 M)
0 1.20 1.20 1.21 1.21 1.20
3 1.18 1.00 0.87 0.74 0.60
6 1.18 0.76 0.50 0.31 0.13
9 1.18 0.54 0.23 0.032 0.02
12 1.17 0.35 0.04 0.003 0
15 1.17 0.22 0.004 0 0
Source: From Jung, M.Y., Kim, S.K., and Kim, S.Y., Food Chem., 53, 397, 1995.
Cvitaš T. A new look at reaction rates. J Chem Ed 76:1574–1577, 1999.
Cvitaš T. and Kallay N. A mole of chemical transformations. Ed Chem 17:166–168, 1980.
Davis J.S. Practical aspects of kinetic analysis. Methods Enzymol 210:374–390, 1992.
De Levie R. Stochastics, the basis of chemical dynamics. J Chem Ed 77:771–774, 2000.
Diemente D. A closer look at the addition of equations and reactions. J Chem Ed 75:319–321, 1998.
Dyson R., Maeder M., Puxty G., and Neuhold Y.M. Simulation of complex chemical kinetics.
Inorganic Reaction Mechanisms 5:1–8, 2003.
Eberhart J.G. and Levin E. A simplified integration technique for reaction rate laws of integral order in several substances. J Chem Ed 72:193–195, 1995.
Gellene G.I. Application of kinetic approximations to the A Ð B ! C reaction system. J Chem Ed 72:196–199, 1995.
Laidler K.J. Rate-controlling step: A necessary or useful concept? J Chem Ed 65:250–254, 1988.
Le Vent S. Rate of reaction and rate equations. J Chem Ed 80:89–91, 386, 2003.
Lee J.Y. The relationship between stoichiometry and kinetics revisited. J Chem Ed 78:1283–1284, 2001.
Lin K.C. Understanding product optimization: Kinetic versus thermodynamic control. J Chem Ed 65:857–860, 1988.
Loudon G.M. Mechanistic interpretation of pH-rate profiles. J Chem Ed 68:973–984, 1991.
Puxty G., Maeder M., and Hungerbühler K. Tutorial on thefitting of kinetics models to multivariate spectroscopic measurements with non-linear least-squares regression. Chemometr Intell Lab Sys 81:149–164, 2006.
Pyun C.W. Steady-state and equilibrium approximations in chemical kinetics. J Chem Ed 48:194–196, 1971.
Quisenberry K.T. and Tellinghuisen J. Textbook deficiencies: Ambiguities in chemical kinetics rates and rate constants. J Chem Ed 83:510–512, 2006.
Ramachandran B.R. and Halpern A.M. A novel experiment in kinetics: The AÐ B ! C reaction system.
J Chem Ed 74:975, 1997.
Schmitz G. What is a reaction rate? J Chem Ed 82:1091–1093, 2005.
Snadden B. A new perspective on kinetic and thermodynamic control of reactions. J Chem Ed 62:653–655, 1985.
Stumm W. (Ed.) Aquatic Chemical Kinetics. Reaction Rates of Processes in Natural Waters. New York:
Wiley-Interscience, 1990.
Toby S. The relationship between stoichiometry and kinetics. J Chem Ed 77:188–190, 2000.
Villota R. and Hawkes J.G. Reaction kinetics in food systems. Handbook of Food Engineering, Heldman D.R. and Lund D.B. (Eds.), New York: Marcel Dekker, 1992.
Viossat V. and Ben-Aim R.I. Validity of the quasi-stationary-state approximation in the case of two successive reversiblefirst-order reactions. J Chem Ed 75:1165–1169, 1998.
About Radical Reactions
Antunes F., Salvador A., Marinho H.S., Alves R., and Pinto R.E. Lipid peroxidation in mitochondrial inner membranes. 1. An integrative kinetic model. Free Radic Biol Med 21:917–943, 1996.
Brimberg U.I. and Kamal-Eldin A. On the kinetics of the autoxidation of fats: Influence of pro-oxidants, antioxidants and synergists. Eur J Lipid Sci Technol 105:83–91, 2003.
Brimberg U.I. and Kamal-Eldin A. On the kinetics of the autoxidation of fats: Substrates with conjugated double bonds. Eur J Lipid Sci Technol 105:17–22, 2003.
Chen B.H., Chen T.M., and Chien J.T. Kinetic model for studying the isomerization of alpha- and beta-carotene during heating and illumination. J Agric Food Chem, 42:2391–2397, 1994.
Ingold K.U. Kinetic and mechanistic studies of free radical reactions in the 21st century. Pure Appl Chem 69:241–243, 1997.
Karel M. Kinetics of lipid oxidation. In: Physical Chemistry of Foods, Schwartzberg H.G. and Hartel R.W.
(Eds.), pp. 651–668, New York: Marcel Dekker, 1992.
Labuza T.P. Kinetics of lipid oxidation. Crit Rev Food Sci Nutr 2:355–404, 1971.
Minn D.B. and Boff J.M. Chemistry and reaction of singlet oxygen in foods. Comp Rev Food Sci Food Safety 1:58–72, 2002
Takahashi A., Shibasaki-Kitakawa N., and Yonemoto T. A rigorous kinetic model for b-carotene oxidation in the presence of an antioxidant,a-tocopherol. J Am Oil Chem Soc 80:1241–1247, 2003.
Yanishlieva N.V., Kamal-Eldin A., Marinova E.M., and Toneva A.G. Kinetics of antioxidant action of a-andg-tocopherols in sunflower and soybean triacylglycerols. Eur J Lipid Sci Technol 104:262–270, 2002.
About Photochemistry
Hippler M. Photochemical kinetics: Reaction orders and analogies with molecular beam scattering and cavity ring-down experiments. J Chem Educ 80:1074–1077, 2003.
Jung M.Y., Kim S.K., and Kim S.Y. Riboflavin-sensitized photooxidation of ascorbic acid: Kinetics and amino acid effects. Food Chem 53:397–403, 1995.
Kim S.K., Jung M.Y., and Kim S.Y. Photodecomposition of aspartame in aqueous solutions. Food Chem 59:273–278, 1997.
Logan S.R. Does a photochemical reaction have a reaction order? J Chem Educ 74:1303, 1997.
Rae M. and Berberan Santos M.N. A generalized pre-equilibrium approximation in chemical and photophysical kinetics. J Chem Educ 81:436–440, 2004.
Toby S. Does a photochemical reaction have a kinetic order? J Chem Educ 82:37–38, 2005.
About Kinetics and Mass Transport
Cutler A.H., Antal M.J., and Maitland J. Jr. A critical evaluation of the plugflow idealization of tubular flow reactor data. Ind Eng Chem Res 27:691–697, 1988.
Haas C.N., Joffe J., Heath M.S., and Jacangelo J. Continuousflow residence time distribution function characterization. J Environ Eng ASCE 123:107–114, 1997.
Heppell N.J. Comparison of the residence time distributions of water and milk in an experimental UHT sterilizer. J Food Eng 4:71–84, 1985.
Hill C.G. An Introduction to Chemical Engineering Kinetics and Reactor Design. New York: Wiley, 1977.
Jung A. and Fryer P.J. Optimising the quality of safe food: Computational modelling of a continuous sterilisation process. Chem Eng Sci 54:717–730, 1999.
Levenspiel O. Chemical Reaction Engineering, 2nd ed., New York: Wiley, 1972.
Malcata F.X. Modelling of a series of continuously stirred tank reactors for thermal processing of liquid foods. Int J Food Sci Technol 26:535–546, 1991.
Ramaya S.V. and Antal M.J. Evaluation of systematic error incurred in the plug flow idealization of tubularflow reactor data. J Energy Fuels 3:105–108, 1989.
Sancho M.F. and Rao M.A. Residence time distribution in a holding tube. J Food Eng 15:1–21, 1992.
Missen R.W., Mims C.A., and Saville B.A. Introduction to Chemical Reaction Engineering and Kinetics.
New York: John Wiley & Sons Inc., 1999.
General Textbooks
Atkins P.W. Physical Chemistry, 6th edn. Oxford: Oxford University Press, 1999.
Cussler E.L. and Moggridge G.D. Chemical Product Design. Cambridge, UK: Cambridge University Press, 2001.
Damodaran S., Parkin K.L., and Fennema O.R. Fennema’s Food Chemistry, 4th edn. Food Science and Technology, p. 1144. Taylor & Francis, Boca Raton, FL, 2008.
Gardiner W.C. Rates and Mechanisms of Chemical Reactions. New York: WA Benjamin Inc., 1969.
Fennema O.R. (Ed.) Food Chemistry, 3rd edn. New York: Marcel Dekker, 1996.
Hill C.G. An Introduction to Chemical Engineering Kinetics and Reactor Design. New York: John Wiley &
Sons, 1977.
Laidler K.J. Chemical Kinetics, 3rd edn. New York: Harper & Row, 1987.
Marangoni A.G. Enzyme Kinetics. A Modern Approach. Hoboken, NJ: Wiley Interscience, 2003.
Maskill H. The Physical Basis of Organic Chemistry. Oxford: Oxford University Press, 1985.
Moore W.J. Physical Chemistry. London: Longman, 1972.
Olmsted III J. and Williams G.M. Chemistry, the Molecular Science. Dubuque, IA: Wm.C. Brown, 1997.
Raff L.M. Principles of Physical Chemistry. Upper Saddle River, NJ: Prentice-Hall Inc., 2001.
Tinoco T., Sauer K., and Wang J.C. Physical Chemistry: Principles and Applications in Biological Sciences, 3rd edn. Englewood Cliffs, NJ: Prentice-Hall International, 1995.
Sutton R., Rockett B., and Swindells P. Chemistry for the Life Sciences. London: Taylor & Francis, 2000.
Voet D. and Voet J.G. Biochemistry, 2nd edn. New York: Wiley & Sons, 1995.
Walstra P. Physical Chemistry of Foods. New York: Marcel Dekker, 2003.
Westphal G., Buhr H., and Otto H. Reaktionskinetik in Lebensmitteln (Reaction Kinetics in Foods, in German). Berlin: Springer-Verlag, 1996.