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Rate equation

About: Rate equation is a(n) research topic. Over the lifetime, 4249 publication(s) have been published within this topic receiving 90524 citation(s). The topic is also known as: rate law.

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Journal ArticleDOI
Henry L. Friedman1Institutions (1)
Abstract: A technique was devised for obtaining rate laws and kinetic parameters which describe the thermal degradation of plastics from TGA data. The method is based on the inter-comparison of experiments which were performed at different linear rates of heating. By this method it is possible to determine the activation energy of certain professes without knowing the form of the kinetic equation. This technique was applied to fiberglass-reinforced CTL 91-LD phenolic resin, where the rate law - (1/we)(dw/dt) = 1018e−55,000/RT [(w - wf)/w0,]5, nr.−1, was found to apply to a major part of the degradation. The equation was successfully tested by several techniques, including a comparison with constant temperature data that were available in the literature. The activation energy was thought to be correct within 10 kcal.

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2,571 citations


Book
Reinhart Heinrich1, Stefan SchusterInstitutions (1)
31 Aug 1996-
TL;DR: The basic equations of metabolic control analysis are rewritten in terms of co-response coefficients and internal response coefficients to describe the interaction of optimization methods and the interrelation with evolution.

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Abstract: Introduction Fundamentals of biochemical modeling Balance equations Rate laws Generalized mass-action kinetics Various enzyme kinetic rate laws Thermodynamic flow-force relationships Power-law approximation Steady states of biochemical networks General considerations Stable and unstable steady states Multiple steady states Metabolic oscillations Background Mathematical conditions for oscillations Glycolytic oscillations Models of intracellular calcium oscillations A simple three-variable model with only monomolecular and bimolecular reactions Possible physiological significance of oscillations Stoichiometric analysis Conservation relations Linear dependencies between the rows of the stoichiometry matrix Non-negative flux vectors Elementary flux modes Thermodynamic aspects A generalized Wegscheider condition Strictly detailed balanced subnetworks Onsager's reciprocity reactions for coupled enyme reactions Time hierarchy in metabolism Time constants The quasi-steady-state approximation The Rapid equilibrium approximation Modal analysis Metabolic control analysis Basic definitions A systematic approach Theorems of metabolic control analysis Summation theorems Connectivity theorems Calculation of control coefficients using the theorems Geometrical interpretation Control analysis of various systems General remarks Elasticity coefficients for specific rate laws Control coefficients for simple hypothetical pathways Unbranched chains A branched system Control of erythrocyte energy metabolism The reaction system Basic model Interplay of ATP production and ATP consumption Glycolytic energy metabolism and osmotic states A simple model of oxidative phosphorylation A three-step model of serine biosynthesis Time-dependent control coefficients Are control coefficients always parameter independent? Posing the problem A system without conserved moieties A system with a conserved moiety A system including dynamic channeling Normalized versus non-normalized coefficients Analysis in terms of variables other than steady-state concentrations and fluxes General analysis Concentration ratios and free-energy-differences as state variables Entropy production as response variable Control of transient times Control of oscillations A second-order approach A quantitative approach to metabolic regulations Co-response coefficients Fluctuations of internal variables versus parameter perturbations Internal response coefficients Rephrasing the basic equations of metabolic control analysis in terms of co-response coefficients and internal response coefficients Control within and between subsystems Modular approach Overall elasticities Overall control coefficients Flux control insusceptibility Control exerted by elementary steps in enzyme catalysis Control analysis of metabolic channeling Comparison of metabolic control analysis and power-law formalism Computational aspects Application of optimization methods and the interrelation with evolution Optimization of the catalytic properties of single enzymes Basic assumptions Optimal values of elementary rate constants Optimal Michaelis constants Optimization of multienzyme systems Maximization of steady-state flux Influence of osmotic constraints and minimization of intermediate concentrations Minimization of transient times Optimal stoichiometries.

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1,236 citations


Journal ArticleDOI
J.D. Rimstidt1, H.L. Barnes1Institutions (1)
Abstract: A differential rate equation for silica-water reactions from 0–300°C has been derived based on stoichiometry and activities of the reactants in the reaction SiO2(s) + 2H2O(l) = H4SiO4(aq) ( ∂a H 4 SiO 4 ∂t ) P.T.M. = ( A M )(γ H 4 SiO 4 )(k+a SiO 2 a 2 H 2 O − k_a H 4 SiO 4 ) where ( A M ) = (the relative interfacial area between the solid and aqueous phases/the relative mass of water in the system), and k+ and k− are the rate constants for, respectively, dissolution and precipitation. The rate constant for precipitation of all silica phases is log k − = − 0.707 − 2598 T (T, K) and Eact for this reaction is 49.8 kJ mol−1. Corresponding equilibrium constants for this reaction with quartz, cristobalite, or amorphous silica were expressed as log K = a + bT + c T . Using K = k + k − , k was expressed as log k + = a + bT + c T and a corresponding activation energy calculated: a b c Eact(kJ mol -1) Quarts 1.174 -2.028 x 103 -4158 67.4–76.6 α-Cristobalite -0.739 0 -3586 68.7 β-Cristobalite -0.936 0 -3392 65.0 Amorphous silica -0.369 -7.890 x 10-4 3438 60.9–64.9 Upon cooling a silica-saturated solution below the equilibrium temperature, the decreasing solubility of silica causes increasing super saturation, which tends to raise the precipitation rate, but the rate constants rapidly decrease, which tends to lower the precipitation rate. These competing effects cause a maximum rate of precipitation 25–50°C below the saturation temperature. At temperatures below that of the maximum rate, silica is often quenched into solution by very slow reaction rates. Consequently, the quartz geothermometer will give the most accurate results if samples are taken from the hottest, highest flow rate, thermal springs which occur above highly fractured areas.

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1,114 citations


Journal ArticleDOI
Robert I. Cukier1, C. M. Fortuin1, Kurt E. Shuler1, A. G. Petschek  +1 moreInstitutions (1)
Abstract: A method has been developed to investigate the sensitivity of the solutions of large sets of coupled nonlinear rate equations to uncertainties in the rate coefficients. This method is based on varying all the rate coefficients simultaneously through the introduction of a parameter in such a way that the output concentrations become periodic functions of this parameter at any given time t. The concentrations of the chemical species are then Fourier analyzed at time t. We show via an application of Weyl's ergodic theorem that a subset of the Fourier coefficients is related to 〈∂ci/∂kl〉, the rate of change of the concentration of species i with respect to the rate constant for reaction l averaged over the uncertainties of all the other rate coefficients. Thus a large Fourier coefficient corresponds to a large sensitivity, and a small Fourier coefficient corresponds to a small sensitivity. The amount of numerical integration required to calculate these Fourier coefficients is considerably less than that requi...

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877 citations


Book
01 Jan 1981-
TL;DR: Reactions and reaction rates reactions with a simple kinetic form reversible and concurrent reactions consecutive reactions - the steady state and other approximations consecutive mechanisms - intermediates and numerical solutions deduction of reaction mechanisms transition state theory and microscopic reversibility chain reactions and oscillating reactions reactions in solution extrakinetic probes of mechanism reactions at extreme rates.

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Abstract: Reactions and reaction rates reactions with a simple kinetic form reversible and concurrent reactions consecutive reactions - the steady state and other approximations consecutive mechanisms - intermediates and numerical solutions deduction of reaction mechanisms transition state theory and microscopic reversibility chain reactions and oscillating reactions reactions in solution extrakinetic probes of mechanism reactions at extreme rates.

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818 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20225
202152
202054
201961
201880
201799

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Topic's top 5 most impactful authors

Ofer Biham

19 papers, 1K citations

Shengzhi Zhao

10 papers, 135 citations

Raoul Kopelman

9 papers, 46 citations

Dragan Indjin

7 papers, 103 citations

Paul Harrison

7 papers, 103 citations