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.

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.

Energy transfer through a dissociated diatomic gas in Couette flow

1958 ◽  
Vol 4 (5) ◽  
pp. 441-465 ◽  
Author(s):  
John F. Clarke
Keyword(s):  
Energy Transfer ◽  
Gas Phase ◽  
Couette Flow ◽  
Chemical Reaction ◽  
Chemical Equilibrium ◽  
Reaction Rate ◽  
Surface Reaction ◽  
Rate Equations ◽  
Equilibrium Flow ◽  
Diatomic Gas

The transfer of energy through a dissociated diatomic gas in Couette flow is considered, taking oxygen as a numerical example. The two extremes of chemical equilibrium flow and chemically frozen flow are dealt with in detail, and it is shown that the surface reaction rate is of prime importance in the latter case. The chemical rate equations in the gas phase are used to estimate the probable chemical state of the gas mixture, this being deduced from the ratio of a characteristic chemical reaction time to a characteristic time for atom diffusion across the layer. The influence of the surface reaction appears to spread outwards through the flow from the wall as gas-phase chemical reaction times decrease. For practical values of the surface reaction rate on a metallic wall, the energy transfer rate may be significantly lower in chemically frozen flow than in chemical equilibrium flow under otherwise similar circumstances.Similar phenomena to those discussed will arise in the more complicated case of boundary layer flows, so that a treatment of the simpler type of shear layer represented by Couette flow may be of some value in assessing the relative importance of the various parameters.

Modeling the Electrical Double Layer to Understand the Reaction Environment in a CO2 Electrocatalytic System

2019 ◽  
Author(s):  
Divya Bohra ◽  
Jehanzeb Chaudhry ◽  
Thomas Burdyny ◽  
Evgeny Pidko ◽  
wilson smith
Keyword(s):  
Electric Field ◽  
Double Layer ◽  
Electrical Double Layer ◽  
Surface Reaction ◽  
Catalyst Surface ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Alkali Metal Cations ◽  
Applied Potential ◽  
Critical Aspect

<p>The environment of a CO<sub>2</sub> electroreduction (CO<sub>2</sub>ER) catalyst is intimately coupled with the surface reaction energetics and is therefore a critical aspect of the overall system performance. The immediate reaction environment of the electrocatalyst constitutes the electrical double layer (EDL) which extends a few nanometers into the electrolyte and screens the surface charge density. In this study, we resolve the species concentrations and potential profiles in the EDL of a CO<sub>2</sub>ER system by self-consistently solving the migration, diffusion and reaction phenomena using the generalized modified Poisson-Nernst-Planck (GMPNP) equations which include the effect of volume exclusion due to the solvated size of solution species. We demonstrate that the concentration of solvated cations builds at the outer Helmholtz plane (OHP) with increasing applied potential until the steric limit is reached. The formation of the EDL is expected to have important consequences for the transport of the CO<sub>2</sub> molecule to the catalyst surface. The electric field in the EDL diminishes the pH in the first 5 nm from the OHP, with an accumulation of protons and a concomitant depletion of hydroxide ions. This is a considerable departure from the results obtained using reaction-diffusion models where migration is ignored. Finally, we use the GMPNP model to compare the nature of the EDL for different alkali metal cations to show the effect of solvated size and polarization of water on the resultant electric field. Our results establish the significance of the EDL and electrostatic forces in defining the local reaction environment of CO<sub>2</sub> electrocatalysts.</p>

A polycentric growth model of gallium arsenide epitaxial layers from the gas phase with simultaneous diffusion, adsorption and chemical reaction

1988 ◽  
Vol 53 (12) ◽  
pp. 2995-3013
Author(s):  
Emerich Erdös ◽  
Jindřich Leitner ◽  
Petr Voňka ◽  
Josef Stejskal ◽  
Přemysl Klíma
Keyword(s):  
Growth Rate ◽  
Gallium Arsenide ◽  
Epitaxial Growth ◽  
Gas Phase ◽  
Surface Reaction ◽  
Quantitative Description ◽  
The Other ◽  
Rate Equations ◽  
Impact Interaction ◽  
Partial Pressures

For a quantitative description of the epitaxial growth rate of gallium arsenide, two models are proposed including two rate controlling steps, namely the diffusion of components in the gas phase and the surface reaction. In the models considered, the surface reaction involves a reaction triple - or quadruple centre. In both models three mechanisms are considered which differ one from the other by different adsorption - and impact interaction of reacting particles. In every of the six cases, the pertinent rate equations were derived, and the models have been confronted with the experimentally found dependences of the growth rate on partial pressures of components in the feed. The results are discussed with regard to the plausibility of individual mechanisms and of both models, and also with respect to their applicability and the direction of further investigations.

Analysis of chemical effects on reflected-shock flow fields in combustible gas

1985 ◽  
Vol 160 ◽  
pp. 29-45 ◽  
Author(s):  
Yasunari Takano ◽  
Teruaki Akamatsu
Keyword(s):  
Heat Release ◽  
Chemical Reactions ◽  
Induction Time ◽  
Combustion Process ◽  
Chemical Species ◽  
Flow Fields ◽  
Rate Equations ◽  
Reflected Shock ◽  
Combustible Gas ◽  
Analytical Results

This paper analyses effects of chemical reactions on reflected-shock flow fields in shock tubes. The method of linearized characteristics is applied to analyse gasdynamic disturbances due to chemical reactions. The analysis treats cases where combustible gas is highly diluted in inert gas, and assumes that flows are one-dimensional and that upstream flows in front of the reflected-shock waves are in the frozen state. The perturbed gasdynamic properties in the reflected-shock flow fields are shown to be expressible mainly in terms of a heat-release function for combustion process. In particular, simple relations are obtained between the heat-release function and the physical properties at the end wall of a shock tube. As numerical examples of the analysis, the present formulation is applied to calculate gasdynamic properties in the reflected-shock region in a H2–O2–Ar mixture. Procedures are demonstrated for calculation of the heat-release function by numerically integrating rate equations for chemical species. The analytical results are compared with rigorous solutions obtained numerically by use of a finite-difference method. It is shown that the formulation can afford exact solutions in cases where chemical behaviours are not essentially affected by gasdynamic behaviours. When the induction time of the combustion process is reduced to some extent owing to gasdynamic disturbances, some discrepancies appear between analytical results and rigorous solutions. An estimate is made of the induction-time reduction, and a condition is written down for applicability of the analysis.

scholarly journals Differential Diffusivity Effects in Reactive Convective Dissolution

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 83 ◽  
Author(s):  
V. Loodts ◽  
H. Saghou ◽  
B. Knaepen ◽  
L. Rongy ◽  
A. De Wit
Keyword(s):  
Diffusion Coefficients ◽  
Reaction Rate ◽  
Chemical Species ◽  
Mixing Zone ◽  
Simultaneous Presence ◽  
Dynamic Effects ◽  
Density Profiles ◽  
Differential Diffusion ◽  
Different Types ◽  
Double Diffusive

When a solute A dissolves into a host fluid containing a reactant B, an A + B → C reaction can influence the convection developing because of unstable density gradients in the gravity field. When A increases density and all three chemical species A, B and C diffuse at the same rate, the reactive case can lead to two different types of density profiles, i.e., a monotonically decreasing one from the interface to the bulk and a non-monotonic profile with a minimum. We study numerically here the nonlinear reactive convective dissolution dynamics in the more general case where the three solutes can diffuse at different rates. We show that differential diffusion can add new dynamic effects like the simultaneous presence of two different convection zones in the host phase when a non-monotonic profile with both a minimum and a maximum develops. Double diffusive instabilities can moreover affect the morphology of the convective fingers. Analysis of the mixing zone, the reaction rate, the total amount of stored A and the dissolution flux further shows that varying the diffusion coefficients of the various species has a quantitative effect on convection.

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.

scholarly journals Study of UiO-66 and UiO-66 Modulated with Acetic Acid as the Adsorbent for Eriochrome Black T Dye

2021 ◽  
Vol 8 (3) ◽  
pp. 183-193
Author(s):  
M. Anugrah Rizky Pambudi ◽  
Nanda Prayogo ◽  
Muhammad Nadjib ◽  
Ratna Ediati
Keyword(s):  
Acetic Acid ◽  
Reaction Rate ◽  
Metal Organic Framework ◽  
X Ray Diffraction ◽  
Adsorption Selectivity ◽  
X Ray ◽  
Langmuir Adsorption ◽  
Eriochrome Black T ◽  
Metal Organic ◽  
Pseudo Second Order

UiO-66, as one of the metal-organic framework (MOF) compounds, has been used to treat some anionic and cationic dye waste. In order to determine the adsorption selectivity decisively, the synthesis of UiO-66 and UiO-66 modulated with acetic acid had been carried out, along with their adsorption tests for Eriochrome Black T (EBT) dye solution. The synthesis was performed by utilizing a solvothermal method with the reaction mixtures of zirconium (IV) chloride (ZrCl4) and terephthalic acid (H2BDC) as a ligand heated at 120 oC for 24 hours. Both UiO-66 (without acetic acid) and acetic acid modulated UiO-66 were obtained as a white powder. Acetic acid as a modulator was added and being investigated for the adsorption capability compared to the normal UiO-66. This study showed that normal UiO-66 exhibited better adsorption than acetic acid modulated UiO-66 with a mmol ratio of acetic acid:ligand varied from 50:1, 100:1, and 150:1. Acetic acid modulated UiO-66 with a mmol ratio of 50 exhibited the best crystallinity as observed by using x-ray diffraction. It can be concluded that the adsorption of EBT using normal and acetic acid modulated UiO-66 obeyed the pseudo-second-order reaction rate law as well as the Langmuir adsorption isotherm pattern.

scholarly journals PENGEMBANGAN BAHAN AJAR KIMIA RINTISAN SMA BERTARAF INTERNASIONAL KELAS XI MATERI LAJU REAKSI

2012 ◽  
Vol 13 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Inova Putri Carera ◽  
I Wayan Dasna
Keyword(s):  
High School ◽  
High School Students ◽  
Reaction Mechanism ◽  
Reaction Rate ◽  
Reaction Order ◽  
Average Score ◽  
School Students ◽  
Factors Affecting ◽  
Rate Law

This study was aimed to develop teaching materials about chemical reaction rate which covered materials adapted to A-Level High School students of grade XI in Pioneer International Standard High School (RSMA-BI). The developmental research was adopting the instructional development model 4D which include four stages of development, namely define, design, develop, and disseminate. Instructional materials were written in English consist of seven topics titled: Reaction Rate Concept, The Exchange's Expressions, Rate Law and Reaction Order, Experimental Determination of a Rate Law, Reaction Mechanism, Theories of Reaction Rate, Factors Affecting Reaction Rate. Results of content validation from content experts obtained the average score of 3. 56 of 14 range of scores which means valid / good / decent. Test limited to high school students of RSBI obtained an average score of 3.35 (valid / good / decent). The results of the use of teaching materials obtained a score of 77.8 which is above the minimal passing grade (75). Therefore it can be concluded that the materials were feasible to be used in the classroom.Penelitian ini bertujuan untuk mengembangkan bahan ajar laju reaksi dengan cakupan materi yang disesuaikan dengan A-Level untuk siswa kelas XI Rintisan Sekolah Menengah Atas Bertaraf Internasional (RSMA-BI. Rancangan penelitian pengembangan mengadaptasi model pengembangan bahan ajar Model 4D yang meliputi empat tahap pengembangan, yaitu define, design, develop dan disseminate. Produk pengembangan adalah bahan ajar kimia RSMA-BI kelas XI materi laju reaksi yang ditulis dalam bahasa Inggris menggunakan pendekatan kontekstual. Bahan ajar terdiri atas empat bagian utama yaitu pendahuluan, materi, evaluasi dan penutup. Materi tersusun atas tujuh sub materi yaitu Reaction Rate Concept, The Rates Expressions, Rate Law and Reaction Order, Experimental Determination of a Rate Law, Reaction Mechanism, Theories of Reaction Rate, Factors Affecting Reaction Rate. Hasil validasi isi dari ahli materi diperoleh nilai rata-rata 3,56 dari rentang skor 1-4 dengan kriteria valid/baik/layak. Hasil uji terbatas pada siswa SMA RSBI diperoleh nilai rata-rata 3,35 dari rentang skor 1-4 dengan kriteria valid/baik/layak. Hasil uji penggunaan bahan ajar diperoleh skor sebesar 77,8. Skor ini diatas SKM (Skor Kelulusan Minimal) yaitu 75 sehingga dapat disimpulkan bahwa bahan ajar telah layak dan dapat digunakan dalam pembelajaran di kelas.

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