On the Numerical Integration of Rate Equations

1964 ◽  
Vol 86 (13) ◽  
pp. 2747-2748 ◽  
Author(s):  
Ian D. Gay
Keyword(s):  
Numerical Integration ◽  
Rate Equations

scholarly journals Combining simulation to nonlinear fitting for the determination of rate constants of elementary reactions by using Excel spreadsheets

2012 ◽  
Vol 8 (4) ◽  
Author(s):  
Ammar M. Tighezza ◽  
Daifallah M. Aldhayan ◽  
Nouir A. Aldawsari
Keyword(s):  
Experimental Data ◽  
Numerical Integration ◽  
Chemical Kinetics ◽  
Chemical Reactions ◽  
Rate Constants ◽  
Model Equation ◽  
Rate Equations ◽  
Unknown Parameters ◽  
Elementary Reactions ◽  
Nonlinear Fitting

A common problem in chemistry is to determine parameters (constants) in an equation used to represent experimental data. Examples are fitting a set of data to a model equation (straight line or curve) to obtain unknown parameters. In chemical kinetics, a set of data is usually a number of concentrations versus time, but the model equation is not well defined! Instead of a well defined model equation we have a set of coupled ODE’s (ordinary differential equations) which represent rate equations for reactants and products. The analytical integration of these ODE’s is rarely possible. The numerical integration is the alternative. In this work are combined the simulation of chemical reactions, by using numerical integration, and nonlinear regression (curve fitting) by using “Solver add-in” of Microsoft Excel to find rate constants of elementary reactions from experimental data. This method is illustrated on three complex mechanisms. The simulation of chemical reactions in Excel spreadsheets is illustrated with/without VBA programming. The automation (automatic obtaining of rate equations from mechanism: no need of chemical kinetics knowledge from the end user!) of mechanism simulation is demonstrated on many example.

scholarly journals Analysis of progress curves by simulations generated by numerical integration

1989 ◽  
Vol 258 (2) ◽  
pp. 381-387 ◽  
Author(s):  
C T Zimmerle ◽  
C Frieden
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Rate Constants ◽  
Weighted Least Squares ◽  
Rate Equations ◽  
Kinetic Rate ◽  
Fitting Procedure ◽  
Progress Curve ◽  
Kinetic Rate Constants ◽  
Simulated Test

A highly flexible computer program written in FORTRAN is presented which fits computer-generated simulations to experimental progress-curve data by an iterative non-linear weighted least-squares procedure. This fitting procedure allows kinetic rate constants to be determined from the experimental progress curves. Although the numerical integration of the rate equations by a previously described method [Barshop, Wrenn & Frieden (1983) Anal. Biochem. 130, 134-145] is used here to generate predicted curves, any routine capable of the integration of a set of differential equations can be used. The fitting program described is designed to be widely applicable, easy to learn and convenient to use. The use, behaviour and power of the program is explored by using simulated test data.

Rate of Reaction of OH with HCN Between 298 and 563 K

1979 ◽  
Vol 32 (12) ◽  
pp. 2571 ◽  
Author(s):  
LF Phillips
Keyword(s):  
Numerical Integration ◽  
Rate Constant ◽  
Flow System ◽  
Rate Equations ◽  
Side Reactions ◽  
Resonance Fluorescence ◽  
Discharge Flow ◽  
Temperature Range ◽  
Rate Of Reaction ◽  
Estimated Error

Hyroxyl resonance fluorescence was used to study the reaction of OH with HCN in a discharge-flow system. The effect of side reactions involving OH was assessed by numerical integration of the rate equations for the system. The rate constant for the reaction: OH + HCN → products as measured at pressures above 10 Torr and under conditions where side reactions were believed to be unimportant, is given by the expression: k = 1.60 ° 10-11 T-1exp(-1.86 × 103/T) cm3 molecule -1 s-1 with an estimated error of � 20% over the temperature range from 298 to 563 K.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Sign in / Sign up

Export Citation Format

Share Document