三个耦合不可逆基本反应的动力学:两个平行混合二阶反应,然后是一个一阶反应

IF 1.7 3区 化学 Q3 CHEMISTRY, MULTIDISCIPLINARY Journal of Mathematical Chemistry Pub Date : 2024-02-14 DOI:10.1007/s10910-024-01580-1
E. Ventura, Rodolpho L. R. Alves, Silmar A. do Monte
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引用次数: 0

摘要

在两个平行的二阶混合反应之后是一个一阶反应的情况下,得出了中间体浓度随时间变化的半解析解。该解仅限于反应物初始浓度相等的情况,并与指数积分相关联。根据解法,并通过适当选择无量纲时间(u)和中间体浓度(y),可以得到中间体最大浓度(ymax)和与该浓度相关的时间(umax)之间的简单关系。这一关系受一个参数 (β)的制约,该参数取决于三个速率常数和初始浓度。β 越小,umax 和 ymax 就越大,y 的衰减也就越慢。我们还得到了连接 umax 和 β 的近似表达式,它得出的 umax 和 ymax 的最大误差分别为 ~8% 和 ~15%。从实验角度来看,得到的表达式非常有用,因为只需将其时间分辨率与 tmax(即转换为时间单位的 umax)进行比较,就能预先选择最适合的实验技术来检测中间体。本文还讨论了一个示例计算。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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The kinetics of three coupled irreversible elementary reactions: two parallel mixed second order reactions followed by a first order reaction

A semi-analytical solution for the time dependence of the concentration of the intermediate is derived, in the case of two parallel mixed second order reactions followed by a first order reaction. The solution is restricted to equal initial concentrations for the reactants, and it is connected to the exponential integral. From the solution and through a proper choice of the dimensionless time (u) and concentration of the intermediate (y) one obtains a very simple relation between the maximum concentration of the intermediate (ymax) and the time associated with this concentration (umax). This relation is governed by a parameter (β) which depends on the three rate constants and on the initial concentration. The smaller is β the larger are umax and ymax, and the slower is the decay of y. An approximate expression connecting umax and β, has also been obtained, and it yields maximum errors of ~ 8% and ~ 15% for umax and ymax, respectively. The obtained expression can be very useful from the experimental point of view, as it allows an a priori selection of the most suitable experimental technique to detect the intermediate, simply comparing its time resolution with tmax (that is, umax transformed to a time unit). An illustrative calculation is also discussed.

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来源期刊
Journal of Mathematical Chemistry
Journal of Mathematical Chemistry 化学-化学综合
CiteScore
3.70
自引率
17.60%
发文量
105
审稿时长
6 months
期刊介绍: The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.
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