“MODELS GOVERNING CHEMICAL KINETICS”

NAME : SHASHI PAUL

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COURSE : MSc.MICROBIOLOGY

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ACKNOWLEGMENT

It has been a great challenge but a plenty of learning and opportunities to gain huge knowledge on the way preparing this term paper. I would not succeed without my teacher Dr.Avadh kumar , who seemed to be with me always; and prepared to give me feedback and guidelines whenever I needed it.

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CONTENTS

ABSTRACT CHEMICAL KINETICS FACTORS AFFECTING REACTION RATE REACTION MECHANISM CHEMICAL KINETICS – REACTION RATE INSTANTANEOUS RATES OF REACTION RATE LAWS & RATE CONSTANTS COLLISION THEORY MODEL OF CHEMICAL REACTIONS KINETICS MODELING CHEMICAL KINETICS WITH STELLA A KINETIC MODEL OF CHxCL4-x/CH4 COMBUSTION EXGAS THE LEADS METHANE OXIDATION MECHANISM

ABSTRACT

The differential equations governing the propagation in time of the sensitivity matrix for a mathematical model given by a system of ordinary differential equations are derived. These equations are used to perform a statistical sensitivity analysis of models for chemical reactors. The behavior of the sensitivities at equilibrium is analyzed. It is shown that the sensitivity equations for linear kinetics may be solved using an analytic representation. The numerical solution of these equations is discussed, and illustrative examples are presented. The lognormal distribution is presented as being representative of errors in rate constants.

CHEMICAL KINETICS INTRODUCTION

Reaction rate tends to increase with concentration - a phenomenon explained by collision theory.

Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction. In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.

Chemical kinetics deals with the experimental determination of reaction rates from which rate laws and rate constants are derived. Relatively simple rate laws exist for zero-order reactions (for which reaction rates are independent of concentration), first-order reactions, and second-order reactions, and can be derived for others. In consecutive reactions the rate-determining step often determines the kinetics. In consecutive first-order reactions, a steady state

approximation can simplify the rate law. The activation energy for a reaction is experimentally determined through the Arrhenius equation and the Eyring equation. The main factors that influence the reaction rate include: the physical state of the reactants, the concentrations of the reactants, the temperature at which the reaction occurs, and whether or not any catalysts are present in the reaction.

FACTORS AFFECTING REACTION RATE

NATURE OF THE REACTANTS

Depending upon what substances are reacting, the reaction rate varies. Acid reactions, the formation of salts, and ion exchange are fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be very slow. Nature and strength of bonds in reactant molecules greatly influences the rate of its transformation into products. The reactions which involve lesser bond rearrangement proceed faster than the reactions which involve larger bond rearrangement.

PHYSICAL STATE

The physical state (solid, liquid, or gas) of a reactant is also an important factor of the rate of change. When reactants are in the same phase, as in aqueous solution, thermal motion brings them into contact. However, when they are in different phases, the reaction is limited to the interface between the reactants. Reaction can only occur at their area of contact, in the case of a liquid and a gas, at the surface of the liquid. Vigorous shaking and stirring may be needed to bring the reaction to completion. This means that the more finely divided a solid or liquid reactant, the greater its surface area per unit volume, and the more contact it makes with the other reactant, thus the faster the reaction. To make an analogy, for example, when one starts a fire, one uses wood chips and small branches—one doesn't start with large logs right away. In organic chemistry, On water reactions are the exception to the rule that homogeneous reactions take place faster than heterogeneous reactions.

CONCENTRATION

Concentration plays a very important role in reactions, because according to the collision theory of chemical reactions, molecules must collide in order to react together. As the concentration of the reactants increases, the frequency of the molecules colliding increases, striking each other more frequently by being in closer contact at any given point in time. Think of two reactants being in a closed container. All the molecules contained within are colliding constantly. By increasing the amount of one or more of the reactants it causes these collisions to happen more often, increasing the reaction rate

TEMPERATURE

Temperature usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have more thermal energy. Although collision frequency is greater at higher temperatures, this alone contributes only a very small proportion to the increase in rate of reaction. Much more important is the fact that the proportion of reactant molecules with sufficient energy to react (energy greater than activation energy: E > Ea) is significantly higher and is explained in detail by the Maxwell–Boltzmann distribution of molecular energies.

The 'rule of thumb' that the rate of chemical reactions doubles for every 10 °C temperature rise is a common misconception. This may have been generalized from the special case of biological systems, where the Q10 (temperature coefficient) is often between 1.5 and 2.5.

A reaction's kinetics can also be studied with a temperature jump approach. This involves using a sharp rise in temperature and observing the relaxation rate of an equilibrium process.

CATALYSTS

Generic potential energy diagram showing the effect of a catalyst in an hypothetical endothermic chemical reaction. The presence of the catalyst opens a different reaction pathway (shown in red) with a lower activation energy. The final result and the overall thermodynamics are the same.

A catalyst is a substance that accelerates the rate of a chemical reaction but remains chemically unchanged afterwards. The catalyst increases rate reaction by providing a different reaction mechanism to occur with a lower activation energy. In autocatalysis a reaction product is itself a catalyst for that reaction leading to positive feedback. Proteins that act as catalysts in biochemical reactions are called enzymes. Michaelis-Menten kinetics describe the rate of enzyme mediated reactions. A catalyst does not affect the position of the equilibria, as the catalyst speeds up the backward and forward reactions equally.

In certain organic molecules, specific substituents can have an influence on reaction rate in neighbouring group participation.

Agitating or mixing a solution will also accelerate the rate of a chemical reaction, as this gives the particles greater kinetic energy, increasing the number of collisions between reactants and therefore the possibility of successful collisions.

PRESSURE

Increasing the pressure in a gaseous reaction will increase the number of collisions between reactants, increasing the rate of reaction. This is because the activity of a gas is directly proportional to the partial pressure of the gas. This is similar to the effect of increasing the concentration of a solution.

EQUILIBRIUM

While chemical kinetics is concerned with the rate of a chemical reaction, thermodynamics determines the extent to which reactions occur. In a reversible reaction, chemical equilibrium is reached when the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products no longer change. This is demonstrated by, for example, the Haber–Bosch process for combining nitrogen and hydrogen to produce ammonia. Chemical clock reactions such as the Belousov–Zhabotinsky reaction demonstrate that component concentrations can oscillate for a long time before finally attaining the equilibrium.

FREE ENERGY

In general terms, the free energy change (ΔG) of a reaction determines whether a chemical change will take place, but kinetics describes how fast the reaction is. A reaction can be very exothermic and have a very positive entropy change but will not happen in practice if the reaction is too slow. If a reactant can produce two different products, the thermodynamically most stable one will generally form except in special circumstances when the reaction is said to be under kinetic reaction control. The Curtin–Hammett principle applies when determining the product ratio for two reactants interconverting rapidly, each going to a different product. It is possible to make predictions about reaction rate constants for a reaction from free-energy relationships.

The kinetic isotope effect is the difference in the rate of a chemical reaction when an atom in one of the reactants is replaced by one of its isotopes.

APPLICATIONS

The mathematical models that describe chemical reaction kinetics provide chemists and chemical engineers with tools to better understand and describe chemical processes such as food decomposition, microorganism growth, stratospheric ozone decomposition, and the complex chemistry of biological systems. These models can also be used in the design or modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful by-products. When performing catalytic cracking of heavy hydrocarbons into gasoline and light gas, for example, kinetic models can be used to find the temperature and pressure at which the highest yield of heavy hydrocarbons into gasoline will occur.

REACTION MECHANISM

The detailed explanation at the molecular level how a reaction proceeds is called reaction mechanism. The explanation is given in some elementary steps. Devising reaction mechanisms requires a broad understanding of properties of reactants and products, and this is a skill for matured chemists. However, first year chemistry students are often given a mechanism, and be asked to derive the rate law from the proposed mechanism. The steady-state approximations is a technique for deriving a rate law from the proposed mechanism.

CHEMICAL KINETICS – REACTION RATES

Chemical kinetics is the branch of chemistry which addresses the question: "how fast do reactions go?" Chemistry can be thought of, at the simplest level, as the science that concerns itself with making new substances from other substances. Or, one could say, chemistry is taking molecules apart and putting the atoms and fragments back together to form new molecules. (OK, so once in a while one uses atoms or gets atoms, but that doesn't change the argument.) All of this is to say that chemical reactions are the core of chemistry.

Here are some examples. Consider the reaction, 2 H2(g) + O2(g) → 2 H2O(l).We can calculate ΔrGo for this reaction from tables of free energies of formation (actually this one is just twice the free energy of formation of liquid water). We find that ΔrGo for this reaction is very large and negative, which means that the reaction wants to go very strongly. A more scientific way to say this would be to say that the equilibrium constant for this reaction is very very large.

However, we can mix hydrogen gas and oxygen gas together in a bulb or other container, even in their correct stoichiometric proportions, and they will stay there for centuries, perhaps even forever, without reacting. (If we drop in a catalyst - say a tiny piece of platinum - or introduce a spark, or even illuminate the mixture with sufficiently high frequency uv light, or compress and heat the mixture, the mixture will explode.) The problem is not that the reactants do not want to form the products, they do, but they cannot find a "pathway" to get from reactants to products.

REACTION RATES

Consider the reaction,

2 NO(g) + O2(g) → 2 NO2(g).

We can specify the rate of this reaction by telling the rate of change of the partial pressures of one the gases. However, it is convenient to convert these pressures into concentrations, so we will write our rates and rate equations in terms of concentrations, where square brackets, [ ], mean concentration in mol/L.

We might try to write the rate variously as,

or as

but these are not the same because each molecule of O2 gives two molecules of NO2. To arrive at an unambiguous definition of reaction rate we define the "reaction velocity," v, as

                (1)This is unambiguous. The negative sign tells us that that species is being consumed and the fractions take care of the stoichiometry.  Any one of the three derivatives can be used to define the rate of the reaction.

For a general reaction,

aA + bB → cC + dD,                (2)

the reaction velocity can be written in a number of different but equivalent ways,

                (3)As in our previous example, the negative signs account for material that is being consumed in the reaction and the positive signs account for material that is being formed in the reaction. The stoichiometry is preserved by dividing the rate of change of concentration of each substance by its stoichiometric coefficient.  

Instantaneous Rates of Reaction and the Rate Law for a Reaction

The rate of the reaction between phenolphthalein and the OH- ion isn't constant; it changes with time. Like most reactions, the rate of this reaction gradually decreases as the reactants are consumed. This means that the rate of reaction changes while it is being measured.

To minimize the error this introduces into our measurements, it seems advisable to measure the rate of reaction over periods of time that are short compared with the time it takes for the reaction to occur. We might try, for example, to measure the infinitesimally small change in concentration d(X) that occurs over an infinitesimally short period of time dt. The ratio of these quantities is known as the instantaneous rate of reaction.

The instantaneous rate of reaction at any moment in time can be calculated from a graph of the concentration of the reactant (or product) versus time. The graph below shows how the rate of reaction for the decomposition of phenolphthalein can be calculated from a graph of concentration versus time. The rate of reaction at any moment in time is equal to the slope of a tangent drawn to this curve at that moment.

The instantaneous rate of reaction can be measured at any time between the moment at which the reactants are mixed and the reaction reaches equilibrium. Extrapolating these data back to the instant at which the reagents are mixed gives the initial instantaneous rate of reaction.

Rate Laws and Rate Constants

An interesting result is obtained when the instantaneous rate of reaction is calculated at various points along the curve in the graph in the previous section. The rate of reaction at every point on this curve is directly proportional to the concentration of phenolphthalein at that moment in time.

Rate = k(phenolphthalein)

Because this equation is an experimental law that describes the rate of the reaction, it is called the rate law for the reaction. The proportionality constant, k, is known as the rate constant.

 

Different Ways of Expressing the Rate of Reaction

There is usually more than one way to measure the rate of a reaction. We can study the decomposition of hydrogen iodide, for example, by measuring the rate at which either H2 or I2 is formed in the following reaction or the rate at which HI is consumed.

2 HI(g) H2(g) + I2(g)

Experimentally we find that the rate at which I2 is formed is proportional to the square of the HI concentration at any moment in time.

What would happen if we studied the rate at which H2 is formed? The balanced equation suggests that H2 and I2 must be formed at exactly the same rate.

What would happen, however, if we studied the rate at which HI is consumed in this reaction? Because HI is consumed, the change in its concentration must be a negative number. By convention, the rate of a reaction is always reported as a positive number. We therefore have to change the sign before reporting the rate of reaction for a reactant that is consumed in the reaction.

The negative sign does two things. Mathematically, it converts a negative change in the concentration of HI into a positive rate. Physically, it reminds us that the concentration of the reactant decreases with time.

What is the relationship between the rate of reaction obtained by monitoring the formation of H2 or I2 and the rate obtained by watching HI disappear? The stoichiometry of the reaction says that two HI molecules are consumed for every molecule of H2 or I2 produced. This means that the rate of decomposition of HI is twice as fast as the rate at which H2 and I2 are formed. We can translate this relationship into a mathematical equation as follows.

As a result, the rate constant obtained from studying the rate at which H2 and I2 are formed in this reaction (k) is not the same as the rate constant obtained by monitoring the rate at which HI is consumed (k')

The Rate Law Versus the Stoichiometry of a Reaction

In the 1930s, Sir Christopher Ingold and coworkers at the University of London studied the kinetics of substitution reactions such as the following.

CH3Br(aq) + OH-(aq) CH3OH(aq) + Br-(aq)

They found that the rate of this reaction is proportional to the concentrations of both reactants.

Rate = k(CH3Br)(OH-)

When they ran a similar reaction on a slightly different starting material, they got similar products.

(CH3)3CBr(aq) + OH-(aq) (CH3)3COH(aq) + Br-(aq)

But now the rate of reaction was proportional to the concentration of only one of the reactants.

Rate = k((CH3)3CBr)

These results illustrate an important point: The rate law for a reaction cannot be predicted from the stoichiometry of the reaction; it must be determined experimentally. Sometimes, the rate law is consistent with what we expect from the stoichiometry of the reaction.

2 HI(g) H2(g) + I2(g) Rate = k(HI)2

Often, however, it is not.

2 N2O5(g) 4 NO2(g) + O2(g) Rate = k(N2O5)

Collision Theory Model of Chemical Reactions

The collision theory model of chemical reactions can be used to explain the observed rate laws for both one-step and multi-step reactions. This model assumes that the rate of any step in a reaction depends on the frequency of collisions between the particles involved in that step.

The figure below provides a basis for understanding the implications of the collision theory model for simple, one-step reactions, such as the following.

ClNO2(g) + NO(g) NO2(g) + ClNO(g)

The kinetic molecular theory assumes that the number of collisions per second in a gas depends on the number of particles per liter. The rate at which NO2 and ClNO are formed in this reaction should therefore be directly proportional to the concentrations of both ClNO2 and NO.

Rate = k(ClNO2)(NO)

The collision theory model suggests that the rate of any step in a reaction is proportional to the concentrations of the reagents consumed in that step. The rate law for a one-step reaction should therefore agree with the stoichiometry of the reaction.

The following reaction, for example, occurs in a single step.

CH3Br(aq) + OH-(aq) CH3OH(aq) + Br-(aq)

When these molecules collide in the proper orientation, a pair of nonbonding electrons on the OH- ion can be donated to the carbon atom at the center of the CH3Br molecule, as shown in the figure below.

When this happens, a carbon-oxygen bond forms at the same time that the carbon-bromine bond is broken. The net result of this reaction is the substitution of an OH-

ion for a Br - ion. Because the reaction occurs in a single step, which involves collisions between the two reactants, the rate of this reaction is proportional to the concentration of both reactants.

Rate = k(CH3Br)(OH-)

Not all reactions occur in a single step. The following reaction occurs in three steps, as shown in the figure below.

(CH3)3CBr(aq) + OH-(aq) (CH3)3COH(aq) + Br-(aq)

In the first step, the (CH3)3CBr molecule dissociates into a pair of ions.

First step

The positively charged (CH3)3C+ ion then reacts with water in a second step.

Second step

The product of this reaction then loses a proton to either the OH- ion or water in the final step.

Third step

The second and third steps in this reaction are very much faster than first.

(CH3)3CBr (CH3)3C+ + Br- Slow step

(CH3)3C+ + H2O (CH3)3COH2+ Fast step

(CH3)3COH2+ + OH- (CH3)3COH + H3O Fast step

The overall rate of reaction is therefore more or less equal to the rate of the first step. The first step is therefore called the rate-limiting step in this reaction because it literally limits the rate at which the products of the reaction can be formed. Because only one reagent is involved in the rate-limiting step, the overall rate of reaction is proportional to the concentration of only this reagent.

Rate = k((CH3)3CBr)

The rate law for this reaction therefore differs from what we would predict from the stoichiometry of the reaction. Although the reaction consumes both (CH3)3CBr and OH-, the rate of the reaction is only proportional to the concentration of (CH3)3CBr.

The rate laws for chemical reactions can be explained by the following general rules.

The rate of any step in a reaction is directly proportional to the concentrations of the reagents consumed in that step.

The overall rate law for a reaction is determined by the sequence of steps, or the mechanism, by which the reactants are converted into the products of the reaction.

The overall rate law for a reaction is dominated by the rate law for the slowest step in the reaction.

Kinetics

Kinetics is the area of chemistry concerned with reaction rates. The rate can be expressed as:

rate = change in substance/time for change to occur (usually in M/s)

There are several factors that determine the rate of a specific reaction and those are expressed in the "collision theory" that states that for molecules to react, they must:

1. collide 2. have the right energy

3. have the right geometry

To increase the rate, you must make the above more likely to occur. This is possible by changing other factors such as:

increasing the surface area (of solids)-this allows for more collisions and gives more molecules the right geometry

increasing the temperature-this gives more molecules the right energy (also called the activation energy, Ea)

increasing the concentration (of gases and solutions)-this allows for more collisions and more correct geometry

using a catalyst-helps molecules achieve the correct geometry by providing a different way to react

A catalyst is a substance added to a reaction that comes out of the reaction unchanged. As mentioned earlier, catalysts help lower the activation energy as shown in the following graph. They do this by changing the reaction mechanism.

Modeling Chemical Kinetics with Stella

The models below were contributed by Shawn Sendlinger, Associate Professor of Chemistry at North Carolina Central University. The basics of each of the models is described below. The Stella models are in a zip file that can be downloaded by clicking on the link below. You will need Winzip for Windows or Stuffit Expander for the Macintosh to unpack the file.

Chemical Kinetics using STELLA

A simple chemical equation can be described as:

A→B

The rate at which this reactions proceeds depends on a number of things. These factors include k (the rate constant), and Ao (the initial amount of compound A). In differential form, the rate equations are:

These equations can also be written as integrated rate equations:

The STELLA software program can readily be used to build a model of this reaction. The stock icon is used to represent the chemical species “A” and “B”. A flow icon represents the conversion of stock A into stock B. A converter icon is used to hold a value for the rate constant k. Finally, the connector icon is used to show the mathematical dependence shown in the above equations.

The STELLA model (SimpleAtoB.STM) would look like:

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Notice that the flow out of stock “A” represents a decrease in the stock, so the negative sign from the above equation is taken into account. Similarly, the flow into stock “B” is automatically considered an increase (a positive sign in the above equation). To give good results that reflect those determined experimentally, the best integration method available (Runge-Kutta 4) should be used in conjunction with a small “dt” value (0.01 or smaller). Try setting the initial amount of “A” to 1000, “B” to zero, and a small value for the rate constant k (1 x 10-3). A graph of A will show the expected exponential decrease, while the graph of B will show the expected exponential increase.

The above model can be easily modified in a number of ways. These are enumerated below.

Modification #1: Equilibrium(A ↔ B)

In addition to the forward reaction where “A” turns into “B”, now the reverse is also true: “B” can turn back into “A”. Now we have forward (kf) and reverse (kr) rate constants. The differential form

In addition to the forward reaction where “A” turns into “B”, now the reverse is also true: “B” can turn back into “A”. Now we have forward (kf) and reverse (kr) rate constants. The differential form of the rate equations look like:

The above STELLA model now includes a second flow in the opposite direction, as well as a second converter for the additional rate constant. This model is shown below (AequilB):

To check if this model is working properly, the sum of “A” and “B” at any time should be a constant.

Modification #2: Consecutive Reactions (A → B → C)

It is quite easy to modify the first model to include an additional reaction step by adding another stock and another flow. A second converter for the new rate constant is also required. The equations for the consecutive reaction model look like (A to B to C):

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The model is shown here:

Again, note that the direction of the flows automatically takes care of the signs from the differential equations shown above.

If needed, each of the reactions steps in this model could be made reversible. Additional chemical species could also be added (“D”, “E”, “F”, etc.).

Modification #3: Parallel Reactions from One Reactant

Sometimes, a given reactant might form two different products, as shown below:

A → BandA → C

In differential form, the rate equations are:

The STELLA model will now have two flows originating from the “A” stock, and each flow will have its respective rate constant

The STELLA model will now have two flows originating from the “A” stock, and each flow will have its respective rate constant:

Modification #4: Parallel Reactions to Form One Product

This situation is opposite to that of Modification #3 shown above. In this case, reactants “A” and “B” combine together to form one product “C”:

A → C ← B

The rate equations are:

The STELLA model is shown below: The STELLA model is shown below:

Be careful to notice the directions of the flows in the above model.

Summary:

STELLA is a convenient and easily understood tool for constructing and studying chemical kinetics. All of the simple models here can have “real” chemical names substituted for “A”, “B”, etc., and experimentally determined rate constants can be entered. The resulting models accurately predict the concentration of the various chemical species at any time of interest. In their “general” form, the models can be experimented with to gain an understanding of the important factors that govern kinetics.

A KINETIC MODEL OF CHxCl4-x/CH4 COMBUSTION

Laminar Flame Speeds and Oxidation Kinetics of Tetrachloromethane

ABSTRACT

The laminar flame speeds of tetrachloromethane (CCl4) with methane in air at room temperature and atmospheric pressure were experimentally determined using the counterflow twin-flame technique, varying both the amount of CCl4 in the fuel and the equivalence ratio of the unburned mixture. Comparison between the experimental results and the previous data of CH3Cl-, CH2Cl2-, and CHCl3-CH4-air flames demonstrates the dominant influence of the atomic Cl-to-H ratio on the propagation rate of laminar flames with chlorinated methane addition. A detailed kinetic model previously employed for CH3Cl, CH2Cl2, and CHCl3 combustion was expanded to include additional pathways pertinent to tetrachloromethane combustion. Numerical simulation shows that the model predicts the laminar flame speeds reasonably well. Carbon flux and sensitivity analyses indicate that the oxidation kinetics of CH4 flames doped with CCl4 are essentially the same as those doped with other chloromethanes.

1.

EXGAS : Automatic generation of detailed and reduced mechanism

The development of validated and reliable kinetic models to represent the oxidation and the combustion of organic compounds is of particular interest. For instance, in the case of spark ignited engines, this type of model could help the research works aiming at formulating gasolines which present optimal octane number properties and which lead to minimal pollutants formation. In the purpose of modelling the combustion of an organic compound or, what is the actual case in most practical applications, of a mixture of organic compounds, in the large temperature field which can be observed in an engine, it is necessary to consider several thousands of reactions. Since automatic procedure would be a convenient and rigorous way to write such huge mechanisms, EXGAS was designed for a computer aided construction of mechanisms.

CO-C2 Reactions DataBase

Detailed Primary Mechanism

Lumped Primary Mechanism

Lumped Secondary Mechanism

Corresponding kinetic data are calculated by

KINGAS or estimated by correlations

Global of scheme EXGAS Description

THE LEEDS METHANE OXIDATION MECHANISM

The common feature of all published mechanisms is that although they are up-to-date at the time of compilation, they might become out-of-date at the time of

publication and they surely become more-and-more out-of-date as the time passes. Here we are trying to maintain a methane oxidation mechanism that is always up-to-date. We are inviting everyone to criticise this mechanism (we prefer private e-mails to public criticism). This mechanism will be continously updated according to the suggestions from the chemical kinetic/combustion community and whenever new information about reactions becomes available.

In order to help checking the information in the mechanism, each reaction is annotated with a classification of the rate data (which spans from A (well know data) to U (entirely uncertain data)), an estimate of the uncertainty, the temperature interval of recommendation, and a reference to the origin of data.

A manuscript has been published in Int.J.Chem.Kinet. that contains a description of the mechanism and its testing and a comparison of selected parameters with the GRI, Warnatz, and Konnov mechanisms.

The methane mechanism has since been extended to include nitrogen and sulphur containing species.

The most recent version of the Leeds Methane Oxidation Mechanism is version 1.5Earlier versions can be found in the Archive.

REFERENCE

Preparing for the Chemistry AP Exam. Upper Saddle River, New Jersey: Pearson Education, 2004. 131–134. ISBN 0-536-73157-8

K.J. Laidler, Chemical Kinetics (3rd Ed.), Benjamin Cummings, San Francisco, 1987.

Model Files to Download: kinetics

http://en.wikipedia.org/wiki/Chemical_kinetics "

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