Subscriber access provided by UNIVERSITY OF TOLEDO LIBRARIES
Comment: The Principle of Detailed Balancing in Complex Mechanisms and its Application to Iodate Reactions David M. Stanbury J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b01660 • Publication Date (Web): 28 Mar 2018 Downloaded from http://pubs.acs.org on March 28, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Comment: The Principle of Detailed Balancing in Complex Mechanisms and its Application to Iodate Reactions David M. Stanbury* Dept. of Chemistry and Biochemistry Auburn University, Auburn, AL 36842, USA
In this Comment we draw attention to the importance of the principle of detailed balancing and its application in the simulation of complex reaction mechanisms. Specifically, we identify a series of eight publications on iodate (IO3–) reactions in aqueous solution having multistep mechanisms with a subset of three iodine-based reactions that violates the principle of detailed balancing. These publications describe oxidations by iodate of N-acetyl-L-methionine,1 N-acetyl homocysteine thiolactone (NAHT),2 methionine,3 cysteamine,4 N,N’dimethylaminoiminomethanesulfinic acid,5 amidinothiourea,6 2-aminoethanethiolsulfuric acid,7 and aminoiminomethanesulfinic acid (AIMSA).8 Here, a mechanistic alternative is proposed that complies with detailed balancing. The principle of detailed balancing was first developed in the context of molecular collisions by Fowler in 1936,9 and it has become one of the foundations of modern chemical kinetics, earning a position of prominence in most textbooks on the subject. One statement of the principle of detailed balancing is that "when the overall reaction is at equilibrium each simple step must also be at equilibrium, and for each step the rate of the forward reaction equals the rate of the reverse reaction."10 Thus, for each step the equilibrium constant must be equal to the ratio of the forward and reverse rate constants (Keq = kf/kr). This can impose specific relationships among rate constants when there are multiple pathways between reactants and products. The above-cited iodate publications describe reactions in which iodate is reduced, typically to iodide, and consequently the reaction mechanisms include steps involving several intermediate oxidation states of iodine. The mechanisms proposed in these publications all include the following three reversible steps: IO3– + I– + 2H+ –
HIO2 + I + H –
+
IO3 + HOI + H
+
HIO2 + HOI
k1, k–1, K1
(1)
2HOI
k2, k–2, K2
(2)
k3, k–3, K3
(3)
2HIO2
1
ACS Paragon Plus Environment
The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 5
These three reactions are not independent and constitute a reversible cycle, since reaction 1 is equivalent to the sum of reactions 2 and 3. The principle of detailed balancing thus requires that the following relationship be satisfied: k1/k–1 = (k2/k–2)(k3/k–3), or K1 = K2K3
(4)
Four1-4 of the eight publications cited above all use the same set of rate constants for reactions 1, 2, and 3: k1 = 2.8 M–3 s–1, k–1 = 1.44 103 M–1 s–1, k2 = 2.1 108 M–2 s–1, k–2 = 90 M– s , k3 = 8.6 102 M–2 s–1, and k–3 = 2.00 M–1 s–1. Thus, we obtain k1/k–1 = 1.9 10–3 M–2 and
1 –1
(k2/k–2)(k3/k–3) = 1.0 109 M–2. These two results disagree by more than 11 orders of magnitude and therefore demonstrate an extreme violation of the principle of detailed balancing. Three5, 6, 8 other of the eight publications cited above use a value of 2.1 109 M–2 s–1 for k2 instead of 2.1 108 M–2 s–1. This leads to a value of 1.0 1010 M–2 for (k2/k–2)(k3/k–3), which disagrees with the value of k1/k–1 by an additional order of magnitude. One7 other of the eight publications uses k1 = 1.44 103 M–3 s–1, k–1 = 5 10–2 M–1 s–1, and k2 = 2 109 M–2 s–1. Here the results are k1/k–1 = 2.9 104 M–2 and (k2/k–2)(k3/k–3) = 9.6 109 M–2, and the principle of detailed balancing is violated by five orders of magnitude. Reactions 1-3 were also included in simulations of the oxidation of thiocyanate (SCN –) by iodate.11 In this case the rate constants used for reactions 1-3 are quite different from those mentioned above and are in agreement with the principle of detailed balancing. However, as described in the Supporting Information, another set of reactions in the proposed mechanism violates the principle of detailed balancing by a factor of about 10 9. Since any valid reaction mechanism must comply with the principle of detailed balancing, one might hope that a simple adjustment of the rate constants included in all reversible cycles would resolve the issue. Unfortunately, such adjustments can alter the results of the simulations, as is the case when k3 is modified appropriately for the mechanism of the iodate/AIMSA reaction (see Supporting Information). Conceivably, modification of other rate constants in the mechanism could lead to simulations that reproduce the observed results, but it is currently unclear whether a single set of rate constants for reactions 1-3 could lead to acceptable fits to the data for all eight substrates under consideration. Apparently there is difficulty in finding a set of rate constants for reactions 1-3 that fits the data and meets the requirements of detailed balancing. Moreover, although the rate constant for the second-order decomposition of HIO2 (k–3) seems reasonably well established,12 there is little experimental evidence that this decomposition yields the species indicated in eq 3. Alternative mechanisms of iodate oxidations should be considered, such as those in the literature
2
ACS Paragon Plus Environment
Page 3 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
that do not include reaction 3.13-15 As shown in the Supporting Information, such a mechanism is capable of simulating the autocatalytic production of I2 in the reaction of IO3– with NAHT. Although it can be challenging to ensure compliance with the principle of detailed balancing when working with large multistep mechanisms, such compliance is a requirement. DigiSim16 (for electrochemistry) is an example of a kinetic simulation software that automatically enforces detailed balancing by requiring all steps to be reversible and calculating rate constants that are defined by detailed balancing. A similar outcome is achieved for homogeneous reactions with Kintecus17 when it used in the Thermodynamics mode; in this case compliance with detailed balancing is ensured by requiring input of thermodynamic data for all reaction species. ASSOCIATED CONTENT Supporting Information Analysis of detailed balancing in the reaction of SCN– with IO3–. Simulations of the reaction of IO3– with AIMSA. Alternative model of the reaction of IO 3– with NAHT. AUTHOR INFORMATION Corresponding Author *D. M. Stanbury. E-mail:
[email protected] Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for support of this research.
3
ACS Paragon Plus Environment
The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
References (1)
Chipiso, K.; Mbiya, W.; Morakinyo, M. K.; Simoyi, R. H. Oxyhalogen-Sulfur Chemistry: Kinetics and Mechanism of Oxidation of N-Acetyl-L-methionine by Aqueous Iodine and Acidified Iodate. Aust. J. Chem., 2014, 67, 626-635.
(2)
Sexton, A.; Mbiya, W.; Morakinyo, M. K.; Simoyi, R. H. Kinetics and Mechanism of the Oxidation of N-Acetyl Homocysteine Thiolactone with Aqueous Iodine and Iodate. J. Phys. Chem. A, 2013, 117, 12698-12702.
(3)
Chikwana, E.; Davis, B.; Morakinyo, M. K.; Simoyi, R. H. Oxyhalogen-Sulfur Chemistry Kinetics and Mechanism of Oxidation of Methionine by Aqueous Iodine and Acidified Iodate. Can. J. Chem., 2009, 87, 689-697.
(4)
Chanakira, A.; Chikwana, E.; Peyton, D. H.; Simoyi, R. H. Oxyhalogen-Sulfur Chemistry Kinetics and Mechanism of the Oxidation of Cysteamine by Acidic Iodate and Iodine. Can. J. Chem., 2006, 84, 49-57.
(5)
Otoikhian, A.; Simoyi, R. H.; Petersen, J. L. Oxidation of a Dimethylthiourea Metabolite by Iodine and Acidified Iodate: N,N'-Dimethylaminoiminomethanesulfinic Acid (1). Chem. Res. Toxicol., 2005, 18, 1167-1177.
(6)
Chikwana, E.; Simoyi, R. H. Oxyhalogen-Sulfur Chemistry: Kinetics and Mechanism of Oxidation of Amidinothiourea by Acidified Iodate. J. Phys. Chem. A, 2004, 108, 10241032.
(7)
Mundoma, C.; Simoyi, R. H. Oxyhalogen-Sulfur Chemistry. Oxidation of 2aminoethanethiolsulfuric acid by iodate in acidic medium. J. Chem. Soc., Faraday Trans., 1997, 93, 1543-1550.
(8)
Mambo, E.; Simoyi, R. H. Kinetics and Mechanism of the Complex Oxidation of Aminoiminomethanesulfinic Acid by Iodate in Acidic Medium. J. Phys. Chem., 1993, 97, 13662-13667.
(9)
Fowler, R. H. Statistical Mechanics, 2nd ed., Cambridge University Press: London, 1936; pp 659-663.
(10) Moore, J. W.; Pearson, R. G. Kinetics and Mechanism, Wiley: New York, 1981; p 307. (11) Simoyi, R. H.; Manyonda, M.; Masere, J.; Mtambo, M.; Neube, I.; Patel, H.; Epstein, I. R.; Kustin, K. Kinetics and Mechanism of the Oxidation of Thiocyanate by Iodate. J. Phys. Chem., 1991, 95, 770-774. (12) Schmitz, G.; Furrow, S. D. Kinetics of Iodous Acid Disproportionation. Int. J. Chem. Kinet., 2013, 45, 525-530. (13) Horváth, V.; Epstein, I. R.; Kustin, K. Mechanism of the Ferrocyanide-Iodate-Sulfite Oscillatory Chemical Reaction. J. Phys. Chem. A, 2016, 120, 1951-1960. 4
ACS Paragon Plus Environment
Page 4 of 5
Page 5 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
(14) Valkai, L.; Horváth, A. K. Compatible Mechanism for a Simultaneous Description of the Roebuck, Dushman, and Iodate-Arsenous Acid Reactions in an Acidic Medium. Inorg. Chem., 2016, 55, 1595-1603. (15) Xie, Y.; McDonald, M. R.; Margerum, D. W. Mechanism of the Reaction between Iodate and Iodide Ions in Acid Solutions (Dushman Reaction). Inorg. Chem., 1999, 38, 3938-3940. (16) Rudolph, M.; Feldberg, S. W., DigiSim 3.03b, 2013, https://www.basinc.com/products/ec/digisim. (17) Ianni, J. C., Kintecus 6.01, 2017, http://www.kintecus.com.
5
ACS Paragon Plus Environment
