First-order Reaction Sequence Research Articles

Conservatively Perturbed Equilibrium (CPE) in chemical kinetics

The phenomenon of “Conservatively Perturbed Equilibrium” (CPE) in chemical kinetics is distinguished using a sequence of first-order reactions (linear mechanism) and non-linear mechanisms as well. In this phenomenon, some, not all initial concentrations of the closed chemical system are replaced by the corresponding equilibrium concentrations at the same total amount of each chemical element.Properties of CPE-phenomenon are described:1.For the substance which initial concentration is taken as the equilibrium one, the concentration extremum in a way to the equilibrium is unavoidable.2.This extremum can be a momentary partial equilibrium for some steps of the chemical mechanism.3.Time of occurrence of this extremum is independent of the perturbation.Properties 1 and 2 are general properties. Property 3 is specific for the linear mechanism studied.

Reaction chain modeling of denitrification reactions during a push–pull test

Field quantitative estimation of reaction kinetics is required to enhance our understanding of biogeochemical reactions in aquifers. We extended the analytical solution developed by Haggerty et al. (1998) to model an entire 1st order reaction chain and estimate the kinetic parameters for each reaction step of the denitrification process. We then assessed the ability of this reaction chain to model biogeochemical reactions by comparing it with experimental results from a push-pull test in a fractured crystalline aquifer (Ploemeur, French Brittany). Nitrates were used as the reactive tracer, since denitrification involves the sequential reduction of nitrates to nitrogen gas through a chain reaction (NO3(-)→NO2(-)→NO→N2O→N2) under anaerobic conditions. The kinetics of nitrate consumption and by-product formation (NO2(-), N2O) during autotrophic denitrification were quantified by using a reactive tracer (NO3(-)) and a non-reactive tracer (Br(-)). The formation of reaction by-products (NO2(-), N2O, N2) has not been previously considered using a reaction chain approach. Comparison of Br(-) and NO3(-) breakthrough curves showed that 10% of the injected NO3(-) molar mass was transformed during the 12 h experiment (2% into NO2(-), 1% into N2O and the rest into N2 and NO). Similar results, but with slower kinetics, were obtained from laboratory experiments in reactors. The good agreement between the model and the field data shows that the complete denitrification process can be efficiently modeled as a sequence of first order reactions. The 1st order kinetics coefficients obtained through modeling were as follows: k1=0.023 h(-1), k2=0.59 h(-1), k3=16 h(-1), and k4=5.5 h(-1). A next step will be to assess the variability of field reactivity using the methodology developed for modeling push-pull tracer tests.

Efficient hydrolysis of chitosan in ionic liquids

Effective hydrolysis of chitosan, the N-deacetylated product of chitin, remains challenging. Here, we report acid-promoted hydrolysis of chitosan in imidazolium based ionic liquids with good total reducing sugars (TRS) yield under mild conditions. TRS yield reached over 60% in the presence of about 6.0 wt% concentrated hydrochloric acid at 100 °C within 7 h. Kinetic modeling of a typical experimental data set suggested that the hydrolysis most likely followed a consecutive first-order reaction sequence, where k 1 and k 2, the rate constants for TRS formation and degradation, were determined to be 0.01372 and 0.00015 min −1, respectively. Our method may be useful to explore new applications of natural chitin resources.

Acid in ionic liquid: An efficient system for hydrolysis of lignocellulose

Acid in ionic liquid was demonstrated as an efficient system for hydrolysis of lignocellulosic materials with improved total reducing sugars (TRS) yield under mild conditions. TRS yields were up to 66%, 74%, 81% and 68% for hydrolysis of corn stalk, rice straw, pine wood and bagasse, respectively, in C4mimCl in the presence of 7 wt% hydrogen chloride at 100 °C under atmospheric pressure within 60 min. Different combinations between ionic liquids, such as C6mimCl, C4mimBr, AmimCl, C4mimHSO4, and SbmimHSO4, and acids, including sulfuric acid, nitric acid, phosphoric acid, as well as maleic acid, afforded similar results albeit longer reaction time was generally required comparing with the combination of C4mimCl and hydrochloric acid. FT-IR spectra and elemental analysis of the recovered residues indicated that modification of lignin occurred during sulfuric acid catalyzed hydrolysis. In addition, kinetic modeling based on experimental data suggested that the hydrolysis likely followed a consecutive first-order reaction sequence, where k1 and k2, the rate constants for TRS formation and TRS degradation, were determined as 0.068 min−1 and 0.007 min−1, respectively. This novel system may be valuable to facilitate cost-efficient conversion of biomass into biofuels and biobased products.

CFD Modeling of a Bubble Column Reactor Carrying out a Consecutive A → B → C Reaction

AbstractIn this paper, we develop a CFD model for describing a bubble column reactor for carrying out a consecutive first‐order reaction sequence A → B → C. Three reactor configurations, all operating in the homogeneous bubbly regime, were investigated: (I) column diameter DT = 0.1 m, column height HT = 1.1 m, (II) DT = 0.1 m, HT = 2 m, and (III) DT = 1 m, HT = 5 m. Eulerian simulations were carried out for superficial gas velocities UG in the range of 0.005–0.04 m/s, assuming cylindrical axisymmetry. Additionally, for configurations I and III fully three‐dimensional transient simulations were carried out for checking the assumption of cylindrical axisymmetry. For the 0.1 m diameter column (configuration I), 2‐D axisymmetric and 3‐D transient simulations yield nearly the same results for gas holdup ϵG, centerline liquid velocity VL(0), conversion of A, χA, and selectivity to B, SB. In sharp contrast, for the 1 m diameter column (configuration III), there are significant differences in the CFD predictions of ϵG, VL(0), χA, and SB using 2‐D and 3‐D simulations; the 2‐D strategies tend to exaggerate VL(0), and underpredict ϵG, χA, and SB. The transient 3‐D simulation results appear to be more realistic. The CFD simulation results for χA and SB are also compared with a simple analytic model, often employed in practice, in which the gas phase is assumed to be in plug flow and the liquid phase is well mixed. For the smaller diameter columns (configurations I and II) the CFD simulation results for χA are in excellent agreement with the analytic model, but for the larger diameter column the analytic model is somewhat optimistic. There are two reasons for this deviation. Firstly, the gas phase is not in perfect plug flow and secondly, the liquid phase is not perfectly mixed. The computational results obtained in this paper demonstrate the power of CFD for predicting the performance of bubble column reactors. Of particular use is the ability of CFD to describe scale effects.

Cardiac transient outward potassium current: a pulse chemistry model of frequency-dependent properties.

Recent voltage-clamp studies of isolated myocytes have demonstrated widespread occurrence of a transient outward current (I(to)) carried by potassium ions. In the canine ventricle, this current is well developed in epicardial cells but not in endocardial cells. The resultant spatial dispersion of refractoriness is potentially proarrhythmic and may be amplified by channel blockade. The inactivation and recovery time constants of this channel are in excess of several hundred milliseconds, and consequently channel availability is frequency dependent at physiological stimulation rates. When the time constants associated with transitions between different channel conformations are rapid relative to drug binding kinetics, the interactions between drugs and an ion channel can be approximated by a sequence of first-order reactions, in which binding occurs in pulses in response to pulse train stimulation (pulse chemistry). When channel conformation transition time constants do not meet this constraint, analytical characterizations of the drug-channel interaction must then be modified to reflect the channel time-dependent properties. Here we report that the rate and steady-state amount of frequency-dependent inactivation of I(to) are consistent with a generalization of the channel blockade model: channel availability is reduced in a pulsatile exponential pattern as the stimulation frequency is increased, and the rate of reduction is a linear function of the pulse train depolarizing and recovery intervals. I(to) was reduced in the presence of quinidine. After accounting for the use-dependent availability of I(to) channels, we found little evidence of an additional use-dependent component of block after exposure to quinidine, suggesting that quinidine reacts with both open and closed I(to) channels as though the binding site is continuously accessible. The model provides a useful tool for assessing drug-channel interactions when the reaction cannot be continuously monitored.

Selective, Prolonged Alteration of Complement-Mediated Immune Clearance after Acute Exposure of Mice to Ethanol

A selective and prolonged alteration in complement-mediated immune clearance was found in mice given a single intraperitoneal injection of ethanol. Rate constants for the separate components of complement- and IgG Fcγ-mediated clearance were determined using a branched series, first-order reaction sequence model and measurements of the disappearance of radiolabeled IgG-opsonized murine erythrocytes from the circulation of BALB/c mice. The rate constant governing immune clearance mediated by IgG Fcγ receptors ( k 3) decreased to 16% of control at 1 hr after ethanol injection but returned to normal in 72 hr. A >50% decrease in complement-mediated clearance occurred, with a nadir of complement-mediated sequestration ( k 1) and complement-dependent phagocytosis ( k 4) at 1 hr (P < 0.001). In this case, however, k 1 and k 4 rate constant values did not return to control levels until 6 weeks after the injection of ethanol. The rate constant governing C3b deactivation and release of deactivated, sensitized cells back to the circulation before they undergo phagocytosis ( k 2) was initially normal, but decreased in Week 6 and remained low to the end of the observation period at 22 weeks (P < 0.0001). These changes resulted in a major reduction in overall complement-mediated immune clearance up to 4 weeks after the ethanol injection. The change to normal rates for sequestration and phagocytosis coupled with decreased deactivation and release at 6 weeks postinjection resulted in a small increase in overall complement-mediated clearance that persisted through Week 22.

ChemInform Abstract: KINETIC ANALYSIS OF AN EXTENDED SINGLE‐PATH SEQUENCE OF FIRST‐ORDER REACTIONS. THE REACTION OF MESITONITRILE IN SULFURIC ACID

Chemischer InformationsdienstVolume 14, Issue 48 Preparative Organic Chemistry ChemInform Abstract: KINETIC ANALYSIS OF AN EXTENDED SINGLE-PATH SEQUENCE OF FIRST-ORDER REACTIONS. THE REACTION OF MESITONITRILE IN SULFURIC ACID J. AL-KA'BI, J. AL-KA'BISearch for more papers by this authorP. H. GORE, P. H. GORESearch for more papers by this authorE. F. SAAD, E. F. SAADSearch for more papers by this authorD. N. WATERS, D. N. WATERSSearch for more papers by this authorG. F. MOXON, G. F. MOXONSearch for more papers by this author J. AL-KA'BI, J. AL-KA'BISearch for more papers by this authorP. H. GORE, P. H. GORESearch for more papers by this authorE. F. SAAD, E. F. SAADSearch for more papers by this authorD. N. WATERS, D. N. WATERSSearch for more papers by this authorG. F. MOXON, G. F. MOXONSearch for more papers by this author First published: November 29, 1983 https://doi.org/10.1002/chin.198348131Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume14, Issue48November 29, 1983 RelatedInformation

Kinetics of sulphodeacylation of dimesityl ketone: a dual-path sequence of first-order reactions

The kinetics of the conversion in 89.8%(w/w) sulphuric acid of 2,2′,4,4′,6,6′-hexamethylbenzophenone (A) into 2,4,6-trimethylbenzenesulphonic acid (D) were measured, and analysed in terms of the dual-path first-order reaction sequence (A)[graphic omitted], where (B) and (C) are, respectively, 2,4,6-trimethylbenzoic acid and 1,3,5-trimethylbenzene.

An exact solution to a consecutive reaction sequence

A novel, more useful form of the exact solution to the rate laws for a irreversible second-order, first-order reaction sequence from which the rate constants can be obtained in a straightforward fashion.

Purely convective models for tubular reactors with non-Newtonian flow

A model relating non-Newtonian laminar flow reactor performance to a velocity profile index is developed. Any of four commonly used tracer displacement techniques can be used to obtain an empirical profile index if rheological properties are not accurately known. First order conversion can ordinarily be calculated using only a few terms of the analytical solution presented. The distribution of products resulting from a sequence of first order reactions can also be readily calculated using the model.

Estimation of the number of precursors in a sequence of first order reactions

For a sequence of first order reactions, X 1 → X 2 → … → X p → X p + 1, in which all materials is initially in X 1, a method of determining the minimum number of precursors is presented. The method is based on the observable ratio Qn(Tn) = Tnxn(Tn)⋎An, where 2 ⩽ n ⩽ p, Tn is the time of the unique maximum of xn( t), xn( Tn) is the value of xn at the maximum, and An = ∫ 0 ∞ xn(t)dt . The main result is that Qn( Tn) ⩽ ( n − 1) n / ( n − 1)! exp[−( n − 1)]. Since the sequence ( m − 1) m /( m − 1)! exp(−( m − 1)) = Rm, m = 1, 2, …, is an increasing sequence of numbers, the result provides a method of determining the minimum number of precursors: the integer m is chosen such that the observed Qn( Tn) satisfies Rm − 1 < Qn( Tn) ⩽ Rm; then m is the minimum number of precursors. A method of determining the maximum number of precursors based on the time of the maximum of xn( t) is also presented. The results are extended to schemes of first order reactions in which the shortest path from X 1 to X p is of length p − 1.

Kinetics of a Sequence of First-Order Reactions

Solutions are obtained for the finite set of coupled rate equations ∂Ci / ∂t = αi,i−1Ci−1 + αi,iCi + αi,i+1Ci+1 (i = 0, ···, N), where αi,j are given in general as αi,i−1 = A, αi,i+1 = B, αi,i = − (A + B), except that α0,0 = − α1,0 = − a, αNN = − αN−1,N = − b, α0,−1 = αN,N+1 = 0. Asymptotic expressions are given for the approach to equilibrium as a function of the various rate parameters and the chain length N. For large N, we find that if A &amp;lt; B, the eigenvalue spectrum approaches a continuum, and the approach to equilibrium is described by a simple relaxation time λ1 ≃ (A1/2 − B1/2)2. However, if A(1 − a / A)2 &amp;gt; B, the system exhibits a peculiar eigenvalue spectrum, and the relaxation is characterized by two distinct and well-separated relaxation times, λ1 and λ2 = − a{1 − B[A(1 − a / A}2]−1).

Mass diffusion and isothermal catalytic selectivity

An elementary analysis provides a general expression for isothermal selectivity in the first-order reaction sequence A → B → C as catalysed by porous pellets consisting of micropores branched from macropores. Selectivity (yield of B) is concisely related to the intrinsic rate constants, the micro- and macropore effectiveness factors and the fluid phase transport coefficients for the pertinent species. Conditions corresponding to zero and negative selectivity are specified in terms of effective rate coefficient and intraparticle diffusivity ratios for a given intrinsic (surface) selectivity.