Determination of Rate Constant of Chemical Reactions by Simple Numerical Nonlinear Analysis

TL;DR

This paper introduces nonlinear analysis methods for determining chemical reaction rate constants without precise initial concentration data, challenging the traditional assumption of constant rate constants and highlighting their variability.

Contribution

It presents simple nonlinear analysis techniques for kinetic parameter estimation, validated through experiments, showing rate constants are not truly constant even in elementary reactions.

Findings

Rate constants vary during reactions, not remaining constant as traditionally assumed.

Nonlinear methods can effectively estimate kinetic parameters without exact initial concentrations.

Experimental results support the theoretical conclusion that rate constants are averaged over the reaction pathway.

Abstract

For some centuries, first order chemical rate constants were determined mainly by a linear logarithmic plot of reagent concentration terms against time where the initial concentration was required, which is experimentally often a challenging task to derive accurate estimates. By definition, the rate constant was deemed to be invariant and the kinetic equations were developed with this assumption. A reason for these developments was the ease in which linear graphs could be plotted. Here, different methods are discussed that does not require exact knowledge of initial concentrations and which require elementary nonlinear analysis and the ensuing results are compared with those derived from the standard methodology from an actual chemical reaction, with its experimental determination of the initial concentration with a degree of uncertain. We verify experimentally our previous theoretical conclusion based on simulation data [ J. Math . Chem {\bf 43} (2008) 976--1023, arXiv:physics/0608073] that the so called rate constant is never constant even for elementary reactions and that all the rate laws and experimental determinations to date are actually averaged quantities over the reaction pathway. We conclude that nonlinear methods in conjunction with experiments could in the future play a crucial role in extracting information of various kinetic parameters.