Linearized model for error-compensated kinetic determinations without prior knowledge of reaction order or rate constant

Abstract

This paper describes a new algorithm for calculation of reaction orders, rate constants, and initial and final values of detector signal from several signal vs time data points. The algorithm utilizes a linearized version of the rate equation and is intended primarily to provide initial estimates of these kinetic parameters for other curve-fitting methods. However, under some circumstances, the linearized model can provide sufficiently reliable results that subsequent processing by other methods is not needed. Simulated data with different levels of superimposed noise, data densities, reaction orders, rate constants, and signal change are used to evaluate the algorithm both for its primary purpose of providing initial estimates for other curve-fitting methods and as an independent method. Results are compared with those obtained with a nonlinear least-squares method and two initial-rate methods. The new algorithm provides less reliable results than those obtained by the nonlinear curve-fitting method for some situations (e.g. reaction orders greater than two, low data densities) but has the advantage that it is applicable to reaction orders at and near unity where the nonlinear method to which it is compared fails.

Chemometric investigation of complex equilibria in the solution phase. 3. Chemical models for the complexation of nickel(II) with adipic acid dihydrazide and 2-furoic acid hydrazide in water-N,N'-dimethylformamide and water-dioxane media. Correlation with solvent parameters

“…Similar equations can be written for Tlc; and Thc;• Necessity of Approximate Stability Constants. Although wild constants which are far away from true values should converge in principle, recent studies by Sylva et al (12) and Larsson and Pardue (13) advocate the necessity of fairly good initial estimates especially in complex systems (more than two overlapping equilibria). Otherwise the species that really exist may be rejected or the model leads to an ill-conditioned matrix.…”

“…AG' = µ4 (12) If the electrostatic interactions alone operate, AG* is proportional to the reciprocal of the dielectric constant (Dm) of the medium by eq 13, where Dw is the dielectric constant AG'=c 1/Dm-1/Dw (13) of water. In order to understand the relative importance of electrostatic and nonelectrostatic forces, a detailed analysis of the variation of the logarithm of the equilibrium constant with 1/Dm and nx is carried out.…”

Analytical Applications of Monte Carlo Techniques

“…Noisy signals generated by Monte Carlo simulations can be used to study correlations among different sources and to solve complex systems such as multicomponent "matrix correction" equations (13). In other examples, simulated data with different levels of superimposed noise have been used to evaluate curve-fitting algorithms (14,15) and to study error propagation in analytical procedures (16).…”

Analytical applications of Monte Carlo techniques

“…Noisy signals generated by Monte Carlo simulations can be used to study correlations among different sources and to solve complex systems such as multicomponent "matrix correction" equations (J3). In other examples, simulated data with different levels of superimposed noise have been used to evaluate curve-fitting algorithms (14,15) and to study error propagation in analytical procedures (16).…”