A Model for Chemical Kinetics

Studies of the reaction under these conditions should show first-order dependence on [H2], as well as second-order dependence on [NO], if the suggested mechanism is valid. 

The ideas we have developed above for a specific mechanism can be generalized as follows. 

Analyzing a Mechanism Using the Steady-State Approximation 

Construct a steady-state expression for each intermediate I by applying the criterion 

This condition is implemented by identifying each step that produces or consumes I and writing the appropriate rate law for each. The sum of the rate laws that produce I are then set equal to the sum of the rate laws that consume I. 

F + NO, NO,F Is this an acceptable mechanism That is, does it satisfy the two requirements Solution 

The first requirement for an acceptable mechanism is that the sum of the steps should give the balanced equation  

The second requirement is that the mechanism must agree with the experimentally determined rate law. Since the proposed mechanism states that the first step is rate-determining, the overall reaction rate must be that of the first step. The first step is bi-molecular, so the rate law is 

This has the same form as the experimentally determined rate law. The proposed mechanism is acceptable because it satisfies both requirements. (Note that we have not proved that it is the correct mechanism.) 

Although the mechanism given in Example 12.6 has the correct stoichiometry and fits the observed rate law, other mechanisms may also satisfy these requirements. For example, the mechanism might be 

To decide on the most probable mechanism for the reaction, the chemist doing the study would have to perform additional experiments. 

How do chemical reactions occur We already have given some indications. For example, we have seen that the rates of chemical reactions depend on the concentrations of the reacting species. The initial rate for the reaction 

A plot showing the exponential dependence of the rate constant on absolute temperature. The exact temperature dependence of k is different for each reaction. This plot represents the behavior of a rate constant that doubles for every increase in temperature of 10 K. 

We can answer this question qualitatively from our experience. We use refrigerators because food spoilage is retarded at low temperatures. The combustion of wood occurs at a measurable rate only at high temperatures. An egg cooks in boiling water much faster at sea level than in Leadville, Colorado (elevation 10,000 feet), where the boiling point of water is about 90°C. These observations and others lead us to conclude that chemical reactions speed up when the temperature is increased. Experiments have shown that virtually all rate constants show an exponential increase with absolute temperature, as represented in Fig. 15.10. 

In this section we will introduce a model that can be used to account for the observed characteristics of reaction rates. This model, the collision model, is built around the central idea that molecules must collide to react. We have already seen that this assnmption can explain the concentration dependence of reaction rates. Now we need to consider whether this model can also account for the observed temperatnre dependence of reaction rates. 

The kinetic molecular theory of gases predicts that an increase in temperature increases molecnlar velocities and so increases the frequency of in-termolecular collisions. This agrees with the observation that reaction rates are greater at higher temperatnres. Thns there is qnalitative agreement between the collision model and experimental observations. However, it is found that the rate of reaction is mnch smaller than the calcnlated collision frequency in a given collection of gas particles. This mnst mean that only a small fraction of the collisions produces a reaction. Why  

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Rate Laws An Introduction First-Order Rate Laws 12.6 A Model for Chemical Kinetics... 

IBLG See questions from A Model for Chemical Kinetics and Catalysis ... 

As the fundamental concepts of chemical kinetics developed, there was a strong interest in studying chemical reactions in the gas phase. At low pressures the reacting molecules in a gaseous solution are far from one another, and the theoretical description of equilibrium thermodynamic properties was well developed. Thus, the kinetic theory of gases and collision processes was applied first to construct a model for chemical reaction kinetics. This was followed by transition state theory and a more detailed understanding of elementary reactions on the basis of quantum mechanics. Eventually, these concepts were applied to reactions in liquid solutions with consideration of the role of the non-reacting medium, that is, the solvent. 

C.J. Zea, N.L. Pohl, Kinetic and substrate binding analysis of phosphorylase b via electrospray ionization mass spectrometry a model for chemical proteomics of... 

One aspect that teachers recognise as difficult for their students is the relationship between empirical data and mathematical models for chemical kinetics. The monitoring of changes in concentration of a reactant or a product with time may be done continuously in a computer environment since the correspondent changes in some concentration-dependent property may be registered, data may be depicted graphically and equations may be derived from them. Additionally, students may produce hypotheses of how a reaction occurs or of how factors as temperature, for instance, influence the rate of a reaction when the software make possible the control of input values (Andaloro, Donzelli Sperandeo-Mineo, 1991 Hartley, 1988 Sutherland, 1989). The important understanding of the relationships between kinetic data and mechanism of a reaction would then be supported. 

The iodine chemistry model INSPECT and the aerosols/chemistry code VICTORIA have been inserted recently. We expect that ESTER-VICTORIA, because it is tightly coupled to the thermalhydraulics, will be easier to run than the old stand-alone version and, in some laboratories at least, may become the standard version. At this stage once the necessary drivers have been developed and tested it should be possible to calculate an entire Phebus test, from bundle to containment and ESTER will be the only European code able to do so. The JRC may then insert models for chemical kinetics and for nucleation developed under SCA, and possibly a special-purpose model for the difficult zone just above the bundle in Phebus. 

A classical non-linear model of chemical kinetics is defined by the Michaelis-Menten equation for rate-limited reactions, which has already been mentioned in Section 39.1.1 ... 

Winters and Lee134 describe a physically based model for adsorption kinetics for hydrophobic organic chemicals to and from suspended sediment and soil particles. The model requires determination of a single effective dififusivity parameter, which is predictable from compound solution diffusivity, the octanol-water partition coefficient, and the adsorbent organic content, density, and porosity. 

In a model for catalytic reforming of gasoline, cited in problem P2.03.26, some 300 chemical species are identified, broken up in one case into 13 lumps characterized by carbon number and hydrocarbon class. The kinetic characteristics of such lumps are proprietary information. 

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

The NIST Chemical Kinetics Model Database web site (http //kinetics.nist. gov/CKMech/) is a good resource for chemical kinetic models, thermochemical property data, and elementary rate coefficients. The book Gas-Phase Combustion Chemistry edited by W. C. Gardiner, Ir. (Springer-Verlag, NY, 1999) also lists many detailed mechanisms for different fuels that are available in technical papers and from the Internet. 

CHEMK, A Computer Modeling Scheme for Chemical Kinetics (undated). G. Z. Whitten and J. P. Meyer. Systems Applications, Inc., 950 Northgate Drive, San Rafael, CA 94903. 

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