Matrix Formulation of Chemical Kinetics H.A. Aziz(a*), H. Hendrawan(a)
(a) Department of Chemistry Education, Indonesia University of Education
Jalan Dr. Setiabudi No 229, Bandung
*ha.aziz[at]upi.edu
Abstract
Linear algebra is the branch of mathematics that study linear transformation of vector in a vector space. There are many applications of the subject, including to solve system of linear differential equations with constant coefficients. In this study, we are revisiting the application of matrix reformulation of chemical kinetics. All calculation is performed using Python 3.8.3 using Jupyter Notebook and PyCharm Integrated Development Environment (IDE). The calculation performed is the diagonalization of the constant coefficients^ matrix.
We show that, using a slight abuse of notation, that for reactions where at every step of the reaction it is that of first order, the concentration of chemical species is given by
\[ \frac{d}{dt} \overrightarrow{C} (t) = K \overrightarrow{C} (t) \Leftrightarrow e^K \overrightarrow{C} (0) \]
We also show how equilibrium reaction can be considered as 2 component cyclic reaction, as well as how consecutive reaction can be generalized to include as many steps as needed.
By this reformulation, many types of reaction rate equation can be reduced to single type of equation, and more easily understandable.
Keywords: linear algebra, chemical kinetics, matrix diagonalization, eigenvalues, eigenvectors
