A program system for computer integration of multistep reaction rate equations using the gear integration method

1978 ◽  
Vol 10 (5) ◽  
pp. 461-469 ◽  
Author(s):  
Robert N. Stabler ◽  
John P. Chesick
Keyword(s):  
Reaction Rate ◽  
Integration Method ◽  
Rate Equations ◽  
Computer Integration ◽  
Program System ◽  
Multistep Reaction

Potentiodynamic examination of electrode kinetics for electroactive adsorbed species: applications to the reduction of noble metal surface oxides

1969 ◽  
Vol 310 (1503) ◽  
pp. 541-563 ◽  
Keyword(s):  
Noble Metals ◽  
Reaction Rate ◽  
Substrate Surface ◽  
Intrinsic Property ◽  
Surface Heterogeneity ◽  
Surface Oxide ◽  
Rate Equations ◽  
Quasi Equilibrium ◽  
Linear Potential ◽  
Reaction Velocity

The relation between reaction rate and potential (or time) for electrochemical surface processes occurring under potentiodynamic control (linear potential-time programme) has been investigated with particular reference to the behaviour of thin surface oxide films on noble metals. The kinetics of processes involving adsorbed electroactive species are treated for several model cases; the rate equations are developed for mechanisms involving various reaction orders or for processes involving adsorbed reactant interactions and surface heterogeneity effects. By examination of the dependence of the reaction rate (current) with time and the effect of potential scan rate, v , on the maximum reaction velocity and the potential at which it occurs, the models may be distinguished. In this manner, the inter­dependence of v and the reaction velocity constants k a and k c for the anodic oxidation and the cathodic reduction processes respectively, can be quantitatively established. The relation between quasi-equilibrium situations where the reverse reaction is significant and irreversible situations where it is not can be demonstrated. Heterogeneity terms introduced into the kinetic relations express deviations from Langmuir adsorption behaviour and may be an intrinsic property of the substrate surface or a property of the adsorbed reactant (induced heterogeneity). Applications of the treatment are made to reduction of surface oxide species at the noble metals and the significance of hysteresis and time effects in the processes of electrochemical formation and reduction of surface oxide at platinum, rhodium, iridium and palladium is investigated.

Kinetic Studies on the Synthesis of Hydroxyapatite Nanowires by Solvothermal Methods

2007 ◽  
Vol 60 (2) ◽  
pp. 99 ◽  
Author(s):  
Shiying Zhang ◽  
Chen Lai ◽  
Kun Wei ◽  
Yingjun Wang
Keyword(s):  
Activation Energy ◽  
Reaction Rate ◽  
Kinetic Studies ◽  
Axial Ratio ◽  
Reaction Rate Constant ◽  
Rate Equations ◽  
Solvothermal Reaction ◽  
Growth Order ◽  
Constant Diffusion ◽  
Solvothermal Methods

Hydroxyapatite nanowires with a high axial ratio have been synthesized in reverse micelle solutions that consist of cetyltrimethylammonium bromide (CTAB), n-pentanol, cyclohexane, and the reactant solution by solvothermal methods. This paper focusses on the kinetic studies of the solvothermal reaction and the linear growth of hydroxyapatite nanowires. When the reaction was carried out at low temperatures (65°C), the experimental results showed that the reaction rate was of zero order since the whole reaction was diffusion controlled with constant diffusion coefficients. In the middle to high temperature range (130–200°C), the kinetics were characterized by second order reaction kinetics. Since the controlling factor was activation energy and the apparent activation energy was large, the reaction rate was more sensitive to the temperature. Therefore, the exponent of the reaction rate constant increased by two when the temperature was increased from 130 to 200°C. By calculating the yields of products and the specific surface areas at different times, the linear and overall growth rate equations of the hydroxyapatite nanowires could be obtained. The experimental effective growth order of the crystals was 11. The larger growth order indicated that the crystal could grow more effectively in one direction because of the induction of the surfactant in the experiment system.

Modeling of Gas Turbine Combustors—A Convenient Reaction Rate Equation

1972 ◽  
Vol 94 (3) ◽  
pp. 173-180 ◽  
Author(s):  
D. Kretschmer ◽  
J. Odgers
Keyword(s):  
Rate Equation ◽  
Reaction Rate ◽  
Reaction Order ◽  
Bimolecular Reaction ◽  
Rate Equations ◽  
Combustion System ◽  
Wide Range ◽  
Simple Mass ◽  
Rich Mixtures ◽  
Reaction Rate Equation

In order to model a practical combustion system successfully, it is necessary to develop one or more reaction rate equations which will describe performance over a wide range of conditions. The equations should be kept as simple as possible and commensurate with the accuracy needed. In this paper a bimolecular reaction is assumed, based upon a simple mass balance. Temperatures derived from the latter are related to measured practical ones such that, if required, an evaluation of the partly burned product composition can be made. A convenient reaction rate equation is given which describes a wide range of blow-out data for spherical reactors at weak mixture conditions. NVP2φ={1.29×1010(m+1)[5(1−yε)]φ[φ−yε]φe−C/(Ti+εΔT)}/{0.082062φyε[5(m+1)+φ+yε]2φ[Ti+εΔT]2φ−0.5} Analysis of the components used in the above equation (especially the variation of activation energy) clearly shows its empirical nature but does not detract from its engineering value. Rich mixtures are considered also, but lack of data precludes a reliable analysis. One of the major results obtained is the variation of the reaction order (n) with equivalence ratio (φ): weak mixtures, n = 2φ; rich mixtures, n = 2/φ. Some support for this variation has been noticed in published literature of other workers.

Transient rates of gas sorption. II. Rate equations for transport and adsorption in porous adsorbents

1953 ◽  
Vol 6 (3) ◽  
pp. 234 ◽  
Author(s):  
KL Sutherland ◽  
ME Winfield
Keyword(s):  
Rate Constant ◽  
Rate Constants ◽  
Reaction Rate ◽  
Reaction Rate Constant ◽  
Rate Equations ◽  
Limiting Factor ◽  
Gas Sorption ◽  
Gas Uptake ◽  
Knudsen Flow ◽  
Factor Ii

Equations are derived to describe the rate at which gas passes into a bed of adsorbent under conditions of constant volume and diminishing pressure. Of the processes which may be responsible for the observed rate of gas uptake, the following three are considered : (i) Knudsen flow within the bed, or within the granules of which it is composed, with simultaneous adsorption that is too fast to be a limiting factor ; (ii) chemisorption which is controlled by the rate of Knudsen flow ; (iii) unrestricted chemisorption.It is shown how the rate constants used in the equations are related to the overall reaction rate constant in a catalyst pore.

scholarly journals Analytical application of acidic victoria blue 4R mixture with KBrO3 for the kinetic determination of traces of antimony(III) by spectrophotometry

2012 ◽  
Vol 31 (1) ◽  
pp. 29
Author(s):  
Violeta Mitić ◽  
Snežana Nikolić-Mandić ◽  
Vesna Stankov-Jovanović
Keyword(s):  
Reaction Rate ◽  
Kinetic Method ◽  
Operating Conditions ◽  
Rate Equations ◽  
Optimum Operating ◽  
Acid Media ◽  
Kinetic Determination ◽  
Hydrochloric Acid Media ◽  
Optimized Conditions

The present paper describes a simple, selective and sensitive kinetic method for the determination of trace amounts of Sb(III) in the presence of Sb(V) based on its inhibition effect on the redox reaction between bromate and Victoria blue 4R (V.B. 4-R) in hydrochloric acid media. The reaction was followed spectrophotometrically by measuring the decrease in the absorbance of V.B. 4-R at 596.3 nm. Optimum operating conditions regarding reagent concentrations were established. The optimized conditions yielded a theoretical detection limit of 1.30·10‒8 g cm–3 Sb(III) based on the 3S0 criterion. The method allows the determination of Sb(III) in the range of 5·10‒8 ‒ 1.1·10‒6 g cm–3. The effects of certain foreign ions the reaction rate were determined for an assessment of the selectivity of the method. The kinetic parameters of the reaction were reported, and the rate equations were suggested. The results were validated statistically and through recovery studies. The proposed method has been successfully applied to the determination of Sb(III) in various model and real samples.

scholarly journals Modified Rate Law for Bimolecular Reactions: Applicable to Surface as well as Non-surface Reactions

2021 ◽  
Vol 37 (6) ◽  
pp. 1429-1433
Author(s):  
Gami Girishkumar Bhagavanbhai ◽  
Rawesh Kumar
Keyword(s):  
Reaction Rate ◽  
Surface Reaction ◽  
Catalyst Surface ◽  
Chemical Species ◽  
Bimolecular Reaction ◽  
Rate Equations ◽  
Bimolecular Reactions ◽  
Rate Law ◽  
Langmuir Adsorption ◽  
Adsorption Desorption

The rate equations in kinematics are expressed through basic laws under surface reaction as well as non-surface reaction. Rate law is center theme of non-surface reaction whereas Langmuir adsorption isotherms are basis of surface reaction rate expressions. A modified rate equation for bimolecular reaction is presented which considers both catalyst surface affairs as well as fraction of successful collision of different reactant for cracking and forming bonds. The modified rate law for bimolecular reaction for surface as well as non-surface reaction is stated as “Rate of a reaction is directly proportional to concentration as well as catalyst surface affair of each reactant” as r = k ΩA[A] ΩB[B] where catalyst surface affair of ith species is defined as Ωi = Ki/(1+Ki[i] + Kj[j] + …). Here, Ki is the equilibrium constant of “i” species for adsorption-desorption processes over catalyst. i, j,… indicates the different adsorbed chemical species at uniform catalyst sites and the same [i], [j], … indicates the concentration of different adsorbed chemical species at uniform catalyst sites.

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