DELAYED RESPONSE IN TRACER EXPERIMENTS AND FRAGMENT-CARRIER APPROACH TO TRANSIT TIME DISTRIBUTIONS IN NONLINEAR CHEMICAL KINETICS

2002 ◽  
Vol 12 (11) ◽  
pp. 2599-2618 ◽  
Author(s):  
MARCEL O. VLAD ◽  
JOHN ROSS ◽  
FEDERICO MORAN ◽  
YOEL RODRIGUEZ
Keyword(s):  
Time Dependence ◽  
Transit Time ◽  
Evolution Equations ◽  
Kinetic Equations ◽  
Mass Action ◽  
Rate Coefficients ◽  
Delayed Response ◽  
Linear Superposition ◽  
Highly Nonlinear ◽  
Kinetics Of

A delayed response tracer experiment is suggested, based on the following constraints: (1) The kinetics of the process can be expressed by local evolution equations without delays, for example by the mass action law. (2) The kinetic isotope effect can be neglected, that is, the rate coefficients for labeled and unlabeled chemicals are the same. (3) The total fluxes of the various chemicals are generally time dependent, but are not modified by the presence of the labeled compounds. (4) The experiment consists in the measurement of the time dependence of the fractions βu, u = 1, 2,… of labeled chemicals in the output fluxes as functionals of the time dependence of the fractions αu, u = 1, 2,… of labeled chemicals in the input fluxes, which are controlled by the researcher. We show that the output fluxes are related to the input fluxes by a linear delayed superposition theorem: βu(t) = ∑u′ ∫ χuu′(t,t′)αu′(t′)dt′, where χuu′(t,t′), is a delayed susceptibility function, which is related to the probability density of the transit time, that is, the time necessary for a molecular fragment to cross the system. This linear superposition law is not the result of a linearization procedure and holds even if the underlying kinetic equations are highly nonlinear. We establish a relationship between the transit time probability densities and the lifetime distributions of the various species in the system. The law permits extracting information about the mechanism and kinetics of chemical processes from response experiments.

The Kinetics of Glucose Decomposition with Sulfate Reduction in the Anaerobic Fluidized Bed Reactor

1993 ◽  
Vol 28 (2) ◽  
pp. 135-144 ◽  
Author(s):  
S. Matsui ◽  
R. Ikemoto Yamamoto ◽  
Y. Tsuchiya ◽  
B. Inanc
Keyword(s):  
Sulfate Reduction ◽  
Fluidized Bed ◽  
Kinetic Equations ◽  
Fluidized Bed Reactor ◽  
Order Reaction ◽  
First Order Reaction ◽  
First Order ◽  
Glucose Decomposition ◽  
Reaction Equations ◽  
Kinetics Of

Using a fluidized bed reactor, experiments on glucose decomposition with and without sulfate reduction were conducted. Glucose in the reactor was mainly decomposed into lactate and ethanol. Lactate was mainly decomposed into propionate and acetate, while ethanol was decomposed into propionate, acetate, and hydrogen. Sulfate reduction was not involved in the decomposition of glucose, lactate, and ethanol, but was related to propionate and acetate decomposition. The stepwise reactions were modeled using either a Monod expression or first order reaction kinetics in respect to the reactions. The coefficients of the kinetic equations were determined experimentally. The modified Monod and first order reaction equations were effective at predicting concentrations of glucose, lactate, ethanol, propionate, acetate, and sulfate along the beight of the reactor. With sulfate reduction, propionate was decomposed into acetate, while without sulfate reduction, accumulation of propionate was observed in the reactor. Sulfate reduction accelerated propionate conversion into acetate by decreasing the hydrogen concentration.

Kinetics of the catalytic hydrodesulphurization reaction system; hydrogenolysis of thiophene

1980 ◽  
Vol 45 (10) ◽  
pp. 2728-2741 ◽  
Author(s):  
Pavel Fott ◽  
Petr Schneider
Keyword(s):  
Atmospheric Pressure ◽  
Active Sites ◽  
Flow Reactor ◽  
Kinetic Equations ◽  
Reaction System ◽  
Reaction Products ◽  
Molybdenum Catalyst ◽  
Cobalt Molybdenum Catalyst ◽  
Kinetics Of ◽  
Reaction Schemes

Kinetics have been studied of the reaction system taking place during the reaction of thiophene on the cobalt-molybdenum catalyst in a gradientless circulation flow reactor at 360 °C and atmospheric pressure. Butane has been found present in a small amount in the reaction products even at very low conversion. In view of this, consecutive and parallel-consecutive (triangular) reaction schemes have been proposed. In the former scheme the appearance of butane is accounted for by rate of desorption of butene being comparable with the rate of its hydrogenation. According to the latter scheme part of the butane originates from thiophene via a different route than through hydrogenation of butene. Analysis of the kinetic data has revealed that the reaction of thiophene should be considered to take place on other active sites than that of butene. Kinetic equations derived on this assumption for the consecutive and the triangular reaction schemes correlate experimental data with acceptable accuracy.

β Grain Growth Kinetics of a New Metastable β Titanium Alloy

2013 ◽  
Vol 747-748 ◽  
pp. 844-849 ◽  
Author(s):  
Yue Fei ◽  
Xin Nan Wang ◽  
Zhi Shou Zhu ◽  
Jun Li ◽  
Guo Qiang Shang ◽  
...  
Keyword(s):  
Titanium Alloy ◽  
Grain Growth ◽  
Kinetic Equations ◽  
Type Equation ◽  
Growth Exponent ◽  
Solution Treated ◽  
Growth Activation ◽  
Grain Growth Kinetics ◽  
Kinetics Of ◽  
Strength And Ductility

Ti-Mo-Nb-Cr-Al-Fe-Si alloy is a new metastable β titanium alloy with excellent combination of strength and ductility. The β grain-growth exponent and the activation energies for β grain growth for the investigated alloy at specified temperature were computed by the kinetic equations and the Arrhenius-type equation. The rate of β grain growth decreases with elongating solution treated time and increases with the increasing solution-treated temperature. The β grain-growth exponents, n, are 0.461, 0.464 and 0.469 at 1113, 1133 and 1153K, respectively. The β grain growth activation energy is determined to be 274 KJ/mol.

scholarly journals Fluoride Leaching of Titanium from Ti-Bearing Electric Furnace Slag in [NH4+]-[F−] Solution

Metals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1176
Author(s):  
Fuqiang Zheng ◽  
Yufeng Guo ◽  
Feng Chen ◽  
Shuai Wang ◽  
Jinlai Zhang ◽  
...  
Keyword(s):  
Activation Energy ◽  
Electric Furnace ◽  
Kinetic Equations ◽  
Surface Chemical ◽  
Leaching Rate ◽  
Surface Chemical Reaction ◽  
Mechanism And Kinetics ◽  
Semi Empirical ◽  
Kinetics Of ◽  
Furnace Slag

The effects of F− concentration, leaching temperature, and time on the Ti leaching from Ti-bearing electric furnace slag (TEFS) by [NH4+]-[F−] solution leaching process was investigated to reveal the leaching mechanism and kinetics of titanium. The results indicated that the Ti leaching rate obviously increased with the increase of leaching temperature and F− concentration. The kinetic equation of Ti leaching was obtained, and the activation energy was 52.30 kJ/mol. The fitting results of kinetic equations and calculated values of activation energy both indicated that the leaching rate of TEFS was controlled by surface chemical reaction. The semi-empirical kinetics equation was consistent with the real experimental results, with a correlation coefficient (R2) of 0.996. The Ti leaching rate reached 92.83% after leaching at 90 °C for 20 min with F− concentration of 14 mol/L and [NH4+]/[F−] ratio of 0.4. The leaching rates of Si, Fe, V, Mn, and Cr were 94.03%, 7.24%, 5.36%, 4.54%, and 1.73%, respectively. The Ca, Mg, and Al elements were converted to (NH4)3AlF6 and CaMg2Al2F12 in the residue, which can transform into stable oxides and fluorides after pyro-hydrolyzing and calcinating.

Preliminary Study on Reaction Kinetics of Ammonia Nitrogen in Aqueous Samples Removed by Microbial Nano-Silica Ball

2014 ◽  
Vol 1010-1012 ◽  
pp. 528-531
Author(s):  
Chao Yin ◽  
Jia Lu ◽  
Xiao Hou Shao ◽  
Xin Yu Mao ◽  
Long Wang ◽  
...  
Keyword(s):  
Reaction Kinetics ◽  
Enrichment Culture ◽  
Kinetic Equations ◽  
Culture Liquid ◽  
Ammonia Nitrogen ◽  
Aqueous Samples ◽  
Nano Silica ◽  
N Removal ◽  
Preliminary Study ◽  
Kinetics Of

EM enrichment culture liquid was immobilized on nano-silica carrier to form microbial nano ball, so as to investigate the reaction kinetics of ammonia nitrogen (NH4+-N) by microbial nano ball. The results showed that first order reaction kinetics model could describe NH4+-N removal by different diameter microbial nano-silica balls well. And the microbe could keep higher biological activity between 0-72h. Reaction kinetic equations of NH4+-N were: (1) when diameter was 10mm, (0-48h), (48-72h); (2) when diameter was 20mm, (0-48h), (48-72h); (3) (0-48h), (48-72h).

THE TRANSMISSION OF POLAR EFFECTS: IV. THE KINETICS OF ESTERIFICATION WITH DIAZODIPHENYLMETHANE OF SUBSTITUTED HETEROCYCLIC CARBOXYLIC ACIDS

1966 ◽  
Vol 44 (13) ◽  
pp. 1493-1499 ◽  
Author(s):  
Keith Bowden ◽  
D. C. Parkin
Keyword(s):  
Carboxylic Acid ◽  
Carboxylic Acids ◽  
Rate Coefficients ◽  
Relative Ability ◽  
Indole Carboxylic Acid ◽  
Kinetics Of ◽  
Electron Effects

The rate coefficients for the reaction with diazodiphenylmethane, in ethanol at 30.0°, of a number of substituted indole-2-carboxylic acids, indole-3-carboxylic acids, coumarin-3-carboxylic acids, coumarilic acids, and N-phenylglycines have been determined. The effect of substitution is assessed by use of adapted Hammett and Dewar–Grisdale relations. The relations give good correlations for oxygen-ring heterocyclic systems, and the relative ability of the systems to transmit π-electron effects has been determined. An anomalous perturbing effect appears to operate in the indole-carboxylic acid systems.

The Characteristics and Kinetics of 4-CP with Pb2+ Biodegradation by Fusarium sp.

2013 ◽  
Vol 726-731 ◽  
pp. 2506-2509
Author(s):  
Xiao Xiao Wang ◽  
Xiao Qin Yu ◽  
Jun Ya Pan ◽  
Ji Wu Li
Keyword(s):  
Carbon Source ◽  
Kinetic Equations ◽  
Order Reaction ◽  
Zero Order ◽  
Biodegradation Rate ◽  
Reaction Equation ◽  
Zero Order Reaction ◽  
Kinetics Of ◽  
Additional Carbon Source

The effects of Pb2+concentration, pH and additional carbon source on biodegradation of 4-chlorophenol (4-CP) byFusariumsp. were investigated, and the characteristic and kinetic of 4-CP biodegradation were analyzed. It was concluded that 4-CP biodegradation rate byFusariumsp. decreased a little at concentration of Pb2+0.20 mg/L and 4-CP 50 mg/L. The suitable biodegradation pH was range from 6 to 7. Additional carbon source (phenol) might increase the rate of 4-CP biodegradation. The kinetic equations of 4-CP biodegradation were well accord with the zero order reaction equation at different concentration of Pb2+.

THE TRANSMISSION OF POLAR EFFECTS: PART II. THE KINETICS OF ESTERIFICATION WITH DIAZODIPHENYLMETHANE AND THE IONIZATION OF 3-SUBSTITUTED ACRYLIC ACIDS

1965 ◽  
Vol 43 (12) ◽  
pp. 3354-3363 ◽  
Author(s):  
Keith Bowden
Keyword(s):  
Butyl Alcohol ◽  
Polar Effect ◽  
Rate Coefficients ◽  
Strengthening Effect ◽  
Benzoic Acids ◽  
Linear Free Energy ◽  
Substituted Benzoic Acids ◽  
Energy Relations ◽  
Acrylic Acids ◽  
Kinetics Of

The rate coefficients for the reaction with diazodiphenylmethane in ethanol, t-butyl alcohol, and ethyl acetate at 30° and the pKa values in water at 25° of fourteen 3-substituted acrylic acids have been determined. The effect of substitution is assessed by use of linear free energy relations. A definite incremental acid-strengthening effect solely due to cis-substitution is confirmed. This is not a "bulk" steric effect and is due solely to the orientation of substitution. The polar effect of a substituent is found to be approximately the same from the cis- or trans-position. An attempt is made to test the suggested mechanisms for the transmission of the polar effect. In the reactions studied the transmission of the polar effect in 3-substituted acrylic acid and ortho-substituted benzoic acids is approximately twice that of the meta- or para-substituted benzoic acids. This appears to be reasonably accommodated by a significant field effect.

scholarly journals The extraction of total lipids from parsley: Petroselinum crispum (mill.) Nym. Ex. A.W. Hill) seeds

2004 ◽  
Vol 58 (12) ◽  
pp. 563-568 ◽  
Author(s):  
Mihajlo Stankovic ◽  
Nadica Stojanovic ◽  
Nada Nikolic ◽  
Vesna Novkovic
Keyword(s):  
Kinetic Equations ◽  
Optimal Operation ◽  
Petroselinum Crispum ◽  
Optimal Conditions ◽  
Total Lipids ◽  
Operation Conditions ◽  
Lipid Fractions ◽  
Polar Organic Solvents ◽  
Layer Chromatography ◽  
Kinetics Of

The kinetics of extraction of total lipids from ground parsley (Petroselinum crispum (Mill.) Nym. ex. A.W. Hill) seeds with a mixture of ethanol or methanol with non-polar organic solvents, chloroform, carbon tetrachloride, trichloroethylene and petroleum ether, at various temperatures were studied. The maceration technique with reflux was used. The kinetic parameters were determined in extraction kinetic equations, as well as the optimal operation conditions for total lipids extraction. The maximum total lipids yield under optimal conditions was 33.7 g per 100 g of dry parsley seeds. Nine lipid fractions of the total lipids were separated by thin layer chromatography among which were phospholipids, sterol, mono-, di- and triacylglycerol, free fatty acids and carbohydrates.

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