The Law of mass action: Mathematical modelling and python implementation for chemical kinetics

This article explores the mathematical framework and computational implementation of the “Law of Mass Action” to model the kinetics of chemical reaction. The study begins with a detailed explanation of the governing equations, emphasizing the role of stoichiometry and reaction orders in dynamic systems. Using Python, a generalized computational framework was developed to solve systems of ordinary differential equations (ODEs) that describe concentration changes over time. The function solve_ivp has been used from the SciPy module to perform the task of solving ODEs. The solver is capable of handling complex reaction networks by incorporating a stoichiometric matrix, reaction rate constants, and reaction orders as inputs. The results are plotted and tabulated with the help of Matplotlib.pylab and Pandas modules. Two representative examples, including real-world chemical reactions, were solved to demonstrate the versatility and accuracy of the approach. Results show that this generalized methodology provides an efficient and adaptable tool for chemical reaction modelling. This work highlights the power of combining mathematics with modern programming to solve practical chemical engineering problems.