scholarly journals Integrated rate equations for enzyme-catalysed first-order and second-order reactions

1984 ◽  
Vol 223 (1) ◽  
pp. 15-22 ◽  
Author(s):  
E A Boeker
Keyword(s):  
Initial Rate ◽  
Second Order ◽  
Rate Equations ◽  
First Order ◽  
Rate Kinetics

Generalized rate equations covering all mechanisms giving hyperbolic initial-rate kinetics with stoichiometry A in equilibrium P, A in equilibrium P + Q, A + B in equilibrium P and A + B in equilibrium P + Q were integrated. The results are regular and reasonably economical.

Mechanisms of Nucleophilic Attack at Carbon - Nitrogen Double Bonds: Reactions of Benzohydrazonoyl Halides with Secondary Amines in Benzene

1997 ◽  
Vol 50 (8) ◽  
pp. 849 ◽  
Author(s):  
Jeffrey E. Rowe ◽  
Kam Lee
Keyword(s):  
Second Order ◽  
Secondary Amines ◽  
Nucleophilic Attack ◽  
Rate Equations ◽  
Rate Data ◽  
Double Bonds ◽  
Effect Data ◽  
First Order ◽  
Amine Molecule

The reactions of a series of substituted benzohydrazonoyl halides with cyclic secondary amines in benzene as solvent are investigated. The rate equations for these reactions were complex and the derived rate data are reported. The element effect data showed that the fluoro compounds only reacted when a second amine molecule was available to assist the reaction, whereas the chloro and bromo compounds reacted by reactions which were both first order and second order in amine (k′′Br : k′′Cl = 9·5 : 1 and k′′′Br :k′′′Cl : k′′′F = 4·7 : 1 : 0·65). The mechanism of these reactions is discussed.

scholarly journals Initial rates. A new plot

1982 ◽  
Vol 203 (1) ◽  
pp. 117-123 ◽  
Author(s):  
E A Boeker
Keyword(s):  
Rate Equation ◽  
Initial Rate ◽  
Initial Conditions ◽  
Equilibrium Constants ◽  
Order Reaction ◽  
First Order Reaction ◽  
Rate Equations ◽  
First Order ◽  
Straight Line ◽  
Instantaneous Concentration

Excellent estimations of initial rates can be obtained from plots of delta P/t versus product formed (where P is the instantaneous concentration of the product). delta P/t is the chord from P0,t0 to P,t on an ordinary P-versus-t plot. When the chord is plotted as a function of product, the intercept at P0 of the resulting curve is necessarily dP/dt0. This curve approximates to a straight line extremely closely in all cases tested thus far. If delta P/t versus product is calculated from the integrated rate equation for a first-order reaction, and if a straight line is fitted through points representing the first 50% of the reaction, the discrepancy between the true initial rate and dP/dt0 estimated from the plot is 0.68%. For the most common form of the integrated rate equation for catalysed reactions the discrepancy varies between 0 and 0.90%. Because of the complexities of the integrated rate equations, catalysed second-order reactions have not been evaluated directly; uncatalysed reactions have been done instead. For a reaction with one reactant and two products, the discrepancy varies from 0.68 to 2.02%. For two reactants and one product, it varies from 0 to 0.68%; for two and two, 0 to 2.02%. The larger discrepancies occur only when unfavourable equilibrium constants are being overcome by the initial conditions.

scholarly journals Integrated rate equations for irreversible enzyme-catalysed first-order and second-order reactions

1985 ◽  
Vol 226 (1) ◽  
pp. 29-35 ◽  
Author(s):  
E A Boeker
Keyword(s):  
Second Order ◽  
Rate Equations ◽  
Detailed Mechanism ◽  
First Order ◽  
Mechanism Of The Reaction

Integrated rate equations are presented that describe irreversible enzyme-catalysed first-order and second-order reactions. The equations are independent of the detailed mechanism of the reaction, requiring only that it be hyperbolic and unbranched. The results should be directly applicable in the laboratory.

Kinetics of the Reaction for Generation of Chlorine Dioxide from Sodium Chlorate and Hydrochloric Acid

2013 ◽  
Vol 634-638 ◽  
pp. 546-550
Author(s):  
Xin Jie Li ◽  
Dan Dan Jiang ◽  
Yue Jun Zhang
Keyword(s):  
Hydrochloric Acid ◽  
Chlorine Dioxide ◽  
Reaction Rate ◽  
Initial Rate ◽  
Reaction System ◽  
Sodium Chlorate ◽  
Second Order ◽  
First Order ◽  
Mixed Order ◽  
Kinetics Of

Based on the mechanism of ClO3-/Cl-reaction system, the kinetics for reaction of sodium chlorate and hydrochloric acid to generate ClO2was studied. The rate equation of this reaction system was deduced and simplified as a formula with mixed-order (combination of first-order and second-order) towards ClO3-. This rate formula indicates that the initial rate of the reaction is the first-order with respect to ClO3-, and the reaction rate is the second-order with respect to ClO3-when [ClO3-] becomes close to zero. The rate constants of the first-order were determined as 0.0168s-1(30°C), 0.0221s-1(40°C), and 0.0279s-1(50°C), respectively, and that of the second-order were obtained for 0.0019L·mol-1·s-1(30°C), 0.0028L·mol-1·s-1(40°C), and 0.0060L·mol-1·s-1(50°C), respectively. The results of statistic test prove that the rate formula obtained in this work is credible.

Nonlinear Analysis of Visual Evoked Potentials Elicited by Color Stimulation

1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama
Keyword(s):  
Visual System ◽  
Evoked Potentials ◽  
Visual Evoked Potentials ◽  
Normal Subjects ◽  
Second Order ◽  
First Order ◽  
The Relationship ◽  
Perceived Color ◽  
Second Order Nonlinearity ◽  
Visual Evoked

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.

Imaginings

2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark
Keyword(s):  
Religious Tradition ◽  
Second Order ◽  
Fine Tuning ◽  
Intellectual Humility ◽  
First Order ◽  
Natural Processes ◽  
Empirically Supported ◽  
Group Violence ◽  
The World ◽  
The Universe

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 

Photocatalytic Discolouration of Solutions of Reactive Dyes in the Presence of H2O2

1995 ◽  
Vol 30 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Deng Nansheng ◽  
Tian Shizhong ◽  
Xia Mei
Keyword(s):  
Photochemical Reaction ◽  
Uv Light ◽  
Reactive Dyes ◽  
Solar Light ◽  
Rate Equations ◽  
Oh Radical ◽  
Test Results ◽  
Dye Molecules ◽  
First Order ◽  
Dye Solutions

Abstract Tests for the photocatalytic degradation of solutions of three reactive dyes, Red M-5B, Procion Blue MX-R and Procion Black H-N, in the presence of H2O2 were carried out. When the solutions of the three reactive dyes were irradiated by UV or solar light, the colour of the solutions disappeared gradually. A statistical analysis of the test results indicated a linear relation between the concentration of dyes and the time of irradiation. The discolouration reaction of the solutions was of the first order. Rate equations for the discolouration reactions of dye solutions were developed. The dark reactions or the dye solutions containing H2O2 were very slow, illustrating that the photochemical reaction played a very important role. It was demonstrated that UV light and solar light (300 to 380 nm) photolyzes the HO and that the resulting OH radical reacts with the dye molecules and destroys the chromophore.

Evidence for general base catalysis by protic solvents in a kinetic study of alcoholyses and hydrolyses of 1-(phenoxycarbonyl)pyridinium ions under both solvolytic and non-solvolytic conditions

2009 ◽  
Vol 74 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Dennis N. Kevill ◽  
Byoung-Chun Park ◽  
Jin Burm Kyong
Keyword(s):  
Second Order ◽  
Base Catalysis ◽  
Substitution Reactions ◽  
Third Order ◽  
Methoxy Derivative ◽  
First Order ◽  
General Base ◽  
Protic Solvents ◽  
Kinetics Of ◽  
Pyridinium Ions

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.

Metaontology

2018 ◽  
Author(s):  
Uriah Kriegel
Keyword(s):  
Second Order ◽  
Order Property ◽  
First Order ◽  
First Approximation

Brentano’s theory of judgment serves as a springboard for his conception of reality, indeed for his ontology. It does so, indirectly, by inspiring a very specific metaontology. To a first approximation, ontology is concerned with what exists, metaontology with what it means to say that something exists. So understood, metaontology has been dominated by three views: (i) existence as a substantive first-order property that some things have and some do not, (ii) existence as a formal first-order property that everything has, and (iii) existence as a second-order property of existents’ distinctive properties. Brentano offers a fourth and completely different approach to existence talk, however, one which falls naturally out of his theory of judgment. The purpose of this chapter is to present and motivate Brentano’s approach.

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