Reaction Schemes That Are Easily Confused with a Reversible First-Order Reaction

Abstract

A detailed kinetic analysis of two schemes, one involving coupled consecutive processes and another featuring parallel reactions and decay of ???, is presented here using Taylor series expansion. It is shown that both of these schemes are easily confused with the reversible second order reaction in a routine kinetic study. The kinetic traces predicted by both schemes are sufficiently close to pseudo-first order curves so that it is practically impossible to identify the deviations based on data with the usual experimental errors, which was also demonstrated by fitting simulated theoretical curves to exponential functions. The dependence of the pseudo-first order rate constants on the concentration of the excess reagent features the same trend as in the case of a reversible reaction: a straight line with an intercept is observed. This analysis emphasizes that the reversible nature of reactions should be demonstrated by direct equilibrium studies, kinetic observations alone might be misleading.

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

“…We further analyze how the following modifications-the absolute Newton step and the Armijo second-order line search-influence frequency of convergence. To estimate the influence, provided by the absolute Newton step, we calculate a quantity of absolute = [total percent of points converged to global solution given the absolute Newton step modification (options 5-8, 10) is used] -[total percent of points converged to global solution given the modification is not used (options [1][2][3][4]9)]. For example, the influence provided by the absolute Newton step for the A → B → C reaction is A→B→C = [50 + 50 + 63 + 63 + 38]% -[38 + 38 + 50 + 50 + 25]% = 264% -201% = 63%.…”

“…Second, multiple solutions may exist due to nonuniqueness of the kinetic model itself: Different chemical networks can account for the same experimental data, a well‐known external factor . Santosa and Weitz state the problem: “The mathematical model of the kinetic system leads to a system of ordinary differential equations…It is possible for a system involving multiple species with different reaction rates to lead to exactly the same set of differential equations.” Balogh et al have conducted a detailed study on this topic and state that kinetic schemes involving consecutive (first‐order) reactions can be easily confused with those involving reversible second‐order or pseudo–first‐order reactions. They note that if there exist several kinetic schemes describing experimental data equally well, then it is not possible to choose the right model without additional chemical information, for example, knowledge of the stoichiometry, the number of absorbing species, etc.…”

“…It is possible for a system involving multiple species with different reaction rates to lead to exactly the same set of differential equations." Balogh et al [3,4] have conducted a detailed study on this topic and state that kinetic schemes involving consecutive (first-order) reactions can be easily confused with those involving reversible second-order or pseudo-first-order reactions. They note that if there exist several kinetic schemes describing experimental data equally well, then it is not possible to choose the right model without additional chemical information, for example, knowledge of the stoichiometry, the number of absorbing species, etc.…”

Double Exponential Evaluation under Non-Pseudo-First-Order Conditions: A Mixed Second-Order Process Followed by a First-Order Reaction

“…Furthermore, it is also clear that the methods used for monitoring processes have limited precision, and the error in the observations may make the detected kinetic trace undistinguishable from one described by a simpler function. An excellent example of this phenomenon was given recently by Balogh et al, who showed two irreversible two‐step models, in which the experimental observations were kinetically indistinguishable from the reversible first‐order reaction . These two models were based on experimental examples, and it was extrakinetic information that primarily led to the rejection of the simple single‐step reversible model in these cases .…”

“…It is well known that relatively simple mathematical formulas can sometimes be used to describe the kinetic curves in mechanisms that are in fact more complex than implied by the simple function in the fitting process [3,4,6,[10][11][12][13][14]. There are a large number of reasons why this phenomenon might arise.…”