Researchers Kaveh Ostad-Ali-Askari and Shayan Shamohammadi have proposed a new mathematical framework for chemical kinetics that shifts the foundational basis from mass-time relationships to mass-mass relationships. Published in the journal Discover Chemical Engineering, the study introduces a model based on the law of conservation of dynamic mass. This approach aims to address limitations in traditional kinetic models, which the authors argue are unable to fully explain the entire kinetic curves of chemical reactions. The new model utilizes a dynamic mass equation that allows for the derivation of both mass-mass and mass-time kinetic models, offering a unified perspective on reaction rates and product capacities.
The core of the proposed method relies on the concept of dynamic mass, defined as the process of converting one or more substances into others. In this framework, the law of conservation of mass is expressed as the ratio of mass to mass, denoted as ∂M/∂M, which always equals one. This stands in contrast to the conventional law of conservation of mass, which is typically based on mass-time, or ∂M/∂T. The authors suggest that by avoiding the time parameter in the initial modeling phase, the model can reduce errors associated with the non-compliance of experimental time intervals with the actual speed of chemical processes. This theoretical shift is grounded in the idea that time may be a function of the mass process rather than an independent variable.
The study distinguishes between two primary conditions for initial concentration: constant and variable. In the constant concentration scenario, the supply source of the initial concentration is considered fixed, a condition typically found in laboratory settings. The model is designed to accommodate both of these states, providing a more flexible tool for analyzing chemical systems under different operational constraints. This dual applicability is highlighted as a significant advantage over conventional kinetic models, which the authors note do not exhibit these features.
For equilibrium reactions, the model assumes that an irreversible reaction occurs before the equilibrium state is established. This premise is supported by previous studies cited in the article, including work by Krishnan and Anirudhan, as well as Shamohammadi et al. The authors argue that in equilibrium conditions, while microscopic chemical interactions continue, they do not significantly affect mass transfer. Instead, macroscopic interactions that cause mass transfer become the primary focus. By integrating these assumptions into the dynamic mass equation, the researchers derived specific mathematical models for the concentrations of products and reactants. These models allow for the calculation of the maximum production capacity of a product, a feature that the authors claim is not available in traditional kinetic approaches.
The mathematical derivation leads to a specific equation for the product concentration, expressed as xp = xpmax * C / (xep + C), where xpmax represents the maximum production capacity and xep is the equilibrium product concentration. The authors further show that by substituting the time variable T for the concentration variable C, the model can be transformed into a mass-time kinetic model. This transformation is facilitated by the assumed linear relationship between time and dynamic mass. The resulting kinetic models, such as xp = xpmax * T / (xep + T), provide a means to calculate product values over time, bridging the gap between the mass-mass and mass-time perspectives.
In addition to calculating product concentrations, the model enables the determination of instantaneous reaction rates. By differentiating the kinetic models with respect to time, the authors derived equations for the rate of product production and the rate of reactant consumption. These rate equations show that the rate of product production decreases as time increases, eventually tending toward zero. The authors note that in the state of chemical equilibrium, the rate of product production is equal to the rate of reactant consumption, a finding that is consistent with conventional kinetic models. However, the new model provides the entire instantaneous velocity curve, rather than just the linear rate, offering a more comprehensive view of the reaction dynamics.
The study also examines the threshold of dynamic equilibrium, defined as the border between one-way products and equilibrium products. At this threshold, the equilibrium concentrations are equal to zero. The authors introduce a parameter, Ksh, which is determined by the difference between the maximum production capacity and the product concentration at the threshold. This parameter is crucial for calculating the specific amounts of product resulting from one-way reactions versus equilibrium reactions. By separating these two components, the model allows for a detailed analysis of the reaction pathway, distinguishing between the initial irreversible phase and the subsequent equilibrium phase.
The authors compare their findings with conventional kinetic models, highlighting several key differences. They argue that traditional models, which are based on the classical law of conservation of mass, only calculate the linear rate of the reaction and do not provide information about the overall trend or production capacity. In contrast, the dynamic mass model can predict the amount of product material for any given amount of reactant elements. This predictive capability is particularly important for understanding the potential of chemical processes. The authors also note that the dynamic mass equation is applicable to both reversible and irreversible reactions, whereas Le Chatelier’s principle is only valid for equilibrium states. This broader applicability makes the new model more versatile for various chemical systems.
The discussion section of the article explores the philosophical implications of the model, particularly regarding the role of time in chemical kinetics. The authors reference the theories of Rovelli and Einstein, suggesting that time lacks originality and essence. They argue that in chemical kinetic experiments, time changes are often considered small initially but become larger as the reaction rate decreases. This observation supports the idea that time is a function of the mass process. The authors use the analogy of refrigerated meat to illustrate this point, noting that the freshness of the meat is determined by the mass process rather than the passage of time. This perspective aligns with the dynamic mass approach, which treats time as a shadow of the dynamic mass variable.
The results of the study are summarized in several key points. First, the model is based on the law of conservation of mass for a mass flow, allowing for the easy access of both mass-mass and mass-time models. Second, the model is applicable to both fixed and variable concentrations, a feature not observed in conventional kinetic models. Third, the chemical models obtained from the dynamic mass equation are valid for both equilibrium and non-equilibrium reactions. Fourth, the use of these mathematical models makes the production capacity calculable, enabling the prediction of product amounts for various reactant quantities. Finally, the study claims to be the first to obtain an equilibrium reaction rate model for the entire process, providing a new tool for chemical engineering and kinetics research.
The authors acknowledge that the model is based on certain assumptions, such as the linear relationship between time and dynamic mass. They note that while time may be a reality, it has no effect on the model method, as it can be considered logical to the mass process. The study provides a theoretical framework that could potentially be applied to other areas of science, such as the kinetics of absorption or penetration of water into soil. The authors suggest that the dynamic mass equation offers a more robust and flexible approach to modeling chemical processes, addressing the limitations of existing models. This work contributes to the ongoing development of mathematical tools in chemical engineering, offering new insights into the dynamics of chemical reactions.
Subject of Research: Mathematical modeling of chemical kinetics using dynamic mass conservation
Article Title: Presenting a mathematical model of chemical kinetics based on dynamic mass
Article References: Ostad-Ali-Askari, K., & Shamohammadi, S. (2026). Presenting a mathematical model of chemical kinetics based on dynamic mass. Discover Chemical Engineering, 6(1), Article 28. https://doi.org/10.1007/s43938-025-00092-x
Image Credits: AI Generated
DOI: 10.1007/s43938-025-00092-x
Keywords: chemical kinetics, dynamic mass, mathematical modeling, reaction rates, equilibrium, conservation of mass, chemical engineering, product capacity, Presenting, mathematical, model, chemical
News Source: Denise Maddox. (November 10, 2026). New Dynamic Mass Model Recasts Chemical Kinetics. Scienmag.
