Eigenanalysis of the Coupled First-Order Isomerization Reactions of the Bis[(S)-alaninato]dinitrocobaltate(III) Ion

1989 ◽  
Vol 42 (10) ◽  
pp. 1647
Author(s):  
JK Beattie ◽  
MB Celap ◽  
MT Kelso ◽  
SM Nesic
Keyword(s):  
Differential Equations ◽  
Aqueous Solutions ◽  
Rate Constants ◽  
Chromatographic Separation ◽  
Reaction Scheme ◽  
Isomerization Reaction ◽  
Geometric Isomers ◽  
First Order ◽  
Kinetics Of ◽  
First Order Differential Equations

Three of the five possible geometric isomers of the bis[(S)-alaninato] dinitrocobaltate (III) ion isomerize to the stable fourth isomer by a series of first-order reactions. The fifth isomer is not observed. The kinetics of the isomerizations in neutral, aqueous solutions between 65 and 95 C have been studied by chromatographic separation of the isomers. The data were fitted by eigenanalysis of the coupled first-order differential equations. The results are consistent with a reaction scheme requiring five rate constants, kxy, where xy represents isomerization from isomer x to isomer y. lsomer A is the Λ-(-)589-cis-NO2/cis-N/cis-O complex; isomer B the trans-NO2/cis-N/cis-O complex; isomer C the trans-NO2/trans-N/trans-O complex; and isomer D is the mixture of both diastereomers of the cis-NO2/trans-N/cis-O complex that is formed from B and C. The rate constants required are kAB, kbc , kBD , kCB and kCD . The same reaction scheme had been found previously for the analogous glycinato complexes, but the activation energies differ. For the valine and leucine analogues, the rate constants and activation enthalpies for the first isomerization reaction, represented by kAB, are similar to that of the alanine complex.

The Decomposition of Sodium Nitrite Solutions in Aqueous Sulphuric and Perchloric Acids

1963 ◽  
Vol 16 (6) ◽  
pp. 927 ◽  
Author(s):  
NS Bayliss ◽  
DW Watts
Keyword(s):  
Aqueous Solutions ◽  
Acid Composition ◽  
Sodium Nitrite ◽  
Decomposition Rate ◽  
Rate Constants ◽  
First Order ◽  
Order Dependence ◽  
Gaseous Products ◽  
Kinetics Of

The kinetics of the decomposition of aqueous solutions of sulphuric and perchloric acids containing sodium nitrite have been investigated at a number of temperatures. The technique involved flushing the decomposing solutions with dry nitrogen to remove the gaseous products. A first-order dependence of decomposition rate on "analytical nitrite" was found, the rate constants being dependent on the solvent acid composition.

Submerged upflow biotower operation and computer simulation

1994 ◽  
Vol 30 (11) ◽  
pp. 143-146
Author(s):  
Ronald D. Neufeld ◽  
Christopher A. Badali ◽  
Dennis Powers ◽  
Christopher Carson
Keyword(s):  
Computer Simulation ◽  
Benzoic Acid ◽  
Computer Model ◽  
Rate Constants ◽  
Batch Mode ◽  
Operational Conditions ◽  
First Order ◽  
Low Concentrations ◽  
Biological Transformation ◽  
Kinetics Of

A two step operation is proposed for the biodegradation of low concentrations (< 10 mg/L) of BETX substances in an up flow submerged biotower configuration. Step 1 involves growth of a lush biofilm using benzoic acid in a batch mode. Step 2 involves a longer term biological transformation of BETX. Kinetics of biotransformations are modeled using first order assumptions, with rate constants being a function of benzoic acid dosages used in Step 1. A calibrated computer model is developed and presented to predict the degree of transformation and biomass level throughout the tower under a variety of inlet and design operational conditions.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals Kinetics of thiamin cleavage by sulphite

1969 ◽  
Vol 113 (4) ◽  
pp. 611-615 ◽  
Author(s):  
J. Leichter ◽  
M. A. Joslyn
Keyword(s):  
Aqueous Solutions ◽  
Rate Constant ◽  
Sulphur Dioxide ◽  
First Order ◽  
Ph Values ◽  
Rate Of Reaction ◽  
Kinetics Of

Results are presented on the rate of thiamin cleavage by sulphite in aqueous solutions as affected by temperature (20–70°), pH(2·5–7·0), and variation of the concentration of either thiamin (1–20μm) or sulphite (10–5000μm as sulphur dioxide). Plots of the logarithm of percentage of residual thiamin against time were found to be linear and cleavage thus was first-order with respect to thiamin. At pH5 the rate was also found to be proportional to the sulphite concentration. In the pH region 2·5–7·0 at 25° the rate constant was 50m−1hr.−1 at pH5·5–6·0, and decreased at higher or lower pH values. The rate of reaction increased between 20° and 70°, indicating a heat of activation of 13·6kcal./mole.

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