Analytical solutions for the rate equations of some two-step kinetic schemes including a reversible first order later step

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2025-04-08 DOI:10.1007/s10910-025-01726-9

Rebeka Szabó, Gábor Lente

引用次数: 0

Abstract

Analytical solutions for the ordinary differential equations are reported for the kinetics of two-step processes for which the later step is a first order reversible process. The earlier step is always irreversible: zeroth order, first order, second order and third order reactions are considered. For the first and second order cases, a qualitative analysis of the kinetic curves was also carried out and the parametric conditions of finding extrema on all the kinetic curves are explored. It is found that the scheme consisting of a second order or mixed second order earlier reaction and a reversible first order later one may feature a reactant with two extrema on its concentration–time trace. In such cases, the first extremum is always a maximum, and the second one is a minimum.

查看原文本刊更多论文

含可逆一阶后步的两步动力学方程的解析解

本文报道了后一步为一阶可逆过程的两步动力学常微分方程的解析解。前面的步骤总是不可逆的：零阶、一阶、二阶和三阶反应都被考虑在内。对于一阶和二阶情况，还进行了动力学曲线的定性分析，并探讨了在所有动力学曲线上求极值的参数条件。发现由二阶或混合二阶早期反应和可逆的一阶后反应组成的方案在其浓度-时间轨迹上可能具有两个极值。在这种情况下，第一个极值总是最大值，第二个极值总是最小值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

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.