Consecutive, irreversible first‐order reactions. Ambiguities and practical aspects of kinetic analyses

Jackson, W. G.; Harrowfield, J. M.; Vowles, PD

doi:10.1002/kin.550090404

Cited by 30 publications

(8 citation statements)

References 12 publications

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“…Second-order rate constants were obtained from the slopes of plots of k obs vs PAr 3 (Figures S4 and S5). Absorbance vs time data for reactions of tri- o -tolylphosphite were fit by nonlinear least squares to the expression characteristic of successive irreversible pseudo-first-order reactions, with k 1(obs) , k 2(obs) , and the extinction coefficients of the three species being allowed to vary. In each case, it was found that k 1(obs) was greater than k 2(obs) , as the alternative solution gave rise to unreasonably large extinction coefficients for the equilibrium mixture of monophosphite and trans -bis(phosphite) complexes (as judged by comparison to the analogous phosphine complexes).…”

Section: Methodsmentioning

confidence: 99%

Amphiphilicity in Oxygen Atom Transfer Reactions of Oxobis(iminoxolene)osmium Complexes

et al. 2021

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Oxobis(iminoxolene)osmium(VI) compounds ( R ap) 2 OsO ( R ap = 2-(4-RC 6 H 4 N)-4,6-t Bu 2 C 6 H 2 O) are readily deoxygenated by phosphines and phosphites to give five-coordinate ( R ap) 2 Os(PR′ 3 ) or six-coordinate ( R ap) 2 Os(PR′ 3 ) 2 . Structural data indicate that this net two-electron reduction is accompanied by apparent oxidation of the iminoxolene ligands due to their greater ability to engage in π donation to the reduced deoxy form of the osmium complex. In ( R ap) 2 Os(PR′ 3 ) 2 , the HOMO is a ligand-based combination of the iminoxolene redox-active orbitals, while the LUMO is a highly covalent metal-iminoxolene π* orbital. In the trans isomer, the HOMO is required to be ligand-localized by symmetry, while in the cis isomer, the ligands adopt a conformation that minimizes metal−ligand π* interactions in the HOMO. Kinetic studies indicate that the deoxygenations involve the ratedetermining attack of the phosphorus(III) reagent on the five-coordinate oxo complexes. Varying the substituents of the aryl groups on the iminoxolene ligands or on the triarylphosphines has little effect on the rate of oxygen atom transfer, with the best correlation shown between oxygen atom transfer rates and the HOMO−LUMO gap of the oxo complexes. This suggests that the osmium oxo group shows a balance between electrophilic and nucleophilic character in its oxygen atom transfer reactions with phosphorus(III) reagents.

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Section: Methodsmentioning

confidence: 99%

Amphiphilicity in Oxygen Atom Transfer Reactions of Oxobis(iminoxolene)osmium Complexes

et al. 2021

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“…In Table III, on the example of consecutive firstorder reactions, we observe a pattern, which we have previously described as the slow-fast ambiguity [5,6,8,9], the internal factor of equivalency of the kinetic schemes. Mathematical formalization of the pattern will allow us to establish formula dependencies among the global solutions, thus greatly reducing the computational expense of conducting a nonlinear least squares fit of a model [11].…”

Section: Resultsmentioning

confidence: 99%

“…The phenomenon of equivalency of the consecutive first‐order reactions has been extensively studied earlier . Jackson and co‐workers were among the first to show that the phenomenon of equivalency of the kinetic schemes arises from the incomplete nature of the experimental data . They show that the slow–fast ambiguity does directly depend on inability to isolate intermediate species in the experiment.…”

Section: Introductionmentioning

confidence: 99%

Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Петров

Dergachev

2017

Int. J. Chem. Kinet.

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The same experimental data can often be equally well described by multiple mathematically equivalent kinetic schemes. In the present work, we investigate several model‐fitting algorithms and their ability to distinguish between mechanisms and derive the correct kinetic parameters for several different reaction classes involving consecutive reactions. We have conducted numerical experiments using synthetic experimental data for six classes of consecutive reactions involving different combinations of first‐ and second‐order processes. The synthetic data mimic time‐dependent absorption data as would be obtained from spectroscopic investigations of chemical kinetic processes. The connections between mathematically equivalent solutions are investigated, and analytical expressions describing these connections are derived. Ten optimization algorithms based on nonlinear least squares methods are compared in terms of their computational cost and frequency of convergence to global solutions. Performance is discussed, and a preferred method is recommended. A response surface visualization technique of projecting five‐dimensional data onto the three‐dimensional search space of the minimal function values is developed.

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“…These two challenges are respectively known in the literature as the distinguishability and identifiability problems 43–54. They raise the fundamental questions of the uniqueness of the specific attributes of a kinetic problem and whether there may be ambiguity in the reaction model even with a good fit between the experimental data and the chosen model.…”

Section: Resultsmentioning

confidence: 99%

Photophysics and kinetics of naphthopyran derivatives, part 2: Analysis of diarylnaphthopyran kinetics. Degeneracy of the kinetic solution

Maafi¹,

Brown²

2005

Int J of Chemical Kinetics

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The photocoloring and fading kinetics of the photochromic 3,3-diphenyl-3H-naphtho[2,1-b]pyran (NPY) have been analyzed using a kinetic treatment for three related species recently developed by us (Int J Chem Kinet 2005, 37(3), 162). The concepts of identifiability and distinguishability are developed with respect to the elucidation of the NPY kinetics. We find that neither set of kinetic data on its own, nor the two data sets combined, allow the true mechanism to be distinguished. In addition, even for a chosen mechanism, there exist degenerate sets of parameters i.e. the solutions are also unidentifiable. A discussion of the limits and uniqueness of the results' interpretation is presented. C 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: [717][718][719][720][721][722][723][724][725][726][727] 2005

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Consecutive, irreversible first‐order reactions. Ambiguities and practical aspects of kinetic analyses

Abstract: The general problem of eliciting reliable rate constants from experimental data is considered in detail for consecutive reactions. Practical aspects are emphasized.

Cited by 30 publications

References 12 publications

Amphiphilicity in Oxygen Atom Transfer Reactions of Oxobis(iminoxolene)osmium Complexes

Amphiphilicity in Oxygen Atom Transfer Reactions of Oxobis(iminoxolene)osmium Complexes

Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Photophysics and kinetics of naphthopyran derivatives, part 2: Analysis of diarylnaphthopyran kinetics. Degeneracy of the kinetic solution

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