{"title":"含可逆一阶后步的两步动力学方程的解析解","authors":"Rebeka Szabó, Gábor Lente","doi":"10.1007/s10910-025-01726-9","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 5","pages":"1323 - 1341"},"PeriodicalIF":1.7000,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-025-01726-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Analytical solutions for the rate equations of some two-step kinetic schemes including a reversible first order later step\",\"authors\":\"Rebeka Szabó, Gábor Lente\",\"doi\":\"10.1007/s10910-025-01726-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":648,\"journal\":{\"name\":\"Journal of Mathematical Chemistry\",\"volume\":\"63 5\",\"pages\":\"1323 - 1341\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10910-025-01726-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Chemistry\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10910-025-01726-9\",\"RegionNum\":3,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-025-01726-9","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Analytical solutions for the rate equations of some two-step kinetic schemes including a reversible first order later step
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.
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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