Rate of reaction defined

The more precise meaning of the term rate of reaction, defined as how fast the [reactant] changes with time, can be illustrated on graphs of concentration versus time (see Figures 3.3(a), (b) and (c)). 

The rate constant for the initial TGMDA-DDS reaction may be calculated from the extrapolated DSC rate of reaction defined... 

This is not the same as the condition for a maximum rate of reaction defined by the consumption of the reactant. 

Required Information Note that Equation 4.5 represents a system of ordinary differential equations (ODEs) that relate the rate of change of concentrations inside the reactor with respect to time, to the instantaneous rate of reaction defined by the system kinetics. In order to solve an ODE, an initial condition and integration time must be specified. 

Thus, one rate of reaction (e.g., it can of course be Rb or Rc or Rq, but only one rate of reaction) defines automatically, together with the stoichiometric numbers, the other rates of reactions as long as it is a single reaction system. 

Let us return to the rate of reaction defined in (2.2). Using the expression for the equilibrium constant, the reaction rate can be written in a form such that a driving force for the reaction can be recognized. This driving force is called the chemical affinity. First, we write the reaction rate in a form which visualizes how far the system is from equilibrium... 

The selectivity relationship merely expresses the proportionality between intermolecular and intramolecular selectivities in electrophilic substitution, and it is not surprising that these quantities should be related. There are examples of related reactions in which connections between selectivity and reactivity have been demonstrated. For example, the ratio of the rates of reaction with the azide anion and water of the triphenylmethyl, diphenylmethyl and tert-butyl carbonium ions were 2-8x10 , 2-4x10 and 3-9 respectively the selectivities of the ions decrease as the reactivities increase. The existence, under very restricted and closely related conditions, of a relationship between reactivity and selectivity in the reactions mentioned above, does not permit the assumption that a similar relationship holds over the wide range of different electrophilic aromatic substitutions. In these substitution reactions a difficulty arises in defining the concept of reactivity it is not sufficient to assume that the reactivity of an electrophile is related... 

In a closed system the rate of reaction is properly defined by a total time derivative of the concentration, if concentration is based on the closed total volume of the system or on a volume liquid of constant density. 

Empirical measures of nucleophilicity may be obtained by comparing relative rates of reaction of a standard reactant with various nucleophiles. One measure of nucleophilicity is the nucleophilic constant ( ), defined originally by Swain and Scott. Taking methanolysis of methyl iodide as the standard reaction, n was defined as... 

To discuss reaction rate meaningfully, it must be defined precisely. The rate of reaction is a positive quantity that expresses how the concentration of a reactant or product changes with time. To illustrate what this means, consider the reaction... 

It was shown in laboratory studies that methanation activity increases with increasing nickel content of the catalyst but decreases with increasing catalyst particle size. Increasing the steam-to-gas ratio of the feed gas results in increased carbon monoxide shift conversion but does not affect the rate of methanation. Trace impurities in the process gas such as H2S and HCl poison the catalyst. The poisoning mechanism differs because the sulfur remains on the catalyst while the chloride does not. Hydrocarbons at low concentrations do not affect methanation activity significantly, and they reform into methane at higher levels, hydrocarbons inhibit methanation and can result in carbon deposition. A pore diffusion kinetic system was adopted which correlates the laboratory data and defines the rate of reaction. 

The enantioselectivity of biocatalytic reactions is normally expressed as the enantiomeric ratio or the E value [la], a biochemical constant intrinsic to each enzyme that, contrary to enantiomeric excess, is independent of the extent of conversion. In an enzymatic resolution of a racemic substrate, the E value can be considered equal to the ratio of the rates of reaction for the two enantiomers, when the conversion is close to zero. More precisely, the value is defined as the ratio between the specificity constants (k st/Ku) for tho two enantiomers and can be obtained by determination of the k<-at and Km of a given enzyme for the two individual enantiomers. 

End-point methods are often not based on kinetic-ally optimum conditions. However, an end-point method is often the only convenient one available. In this case, the method should have been validated by showing that the catalysis of the substrate follows well defined kinetics, rate of reaction is proportional to enzyme concentration, blanks and interfering substances are corrected for, and that appropriate standards are available. 

The size of the cataly.st particle influences the observed rate of reaction the smaller the particle, the less time required for the reactants to move to the active catalyst sites and for the products to diffuse out of the particle. Furthermore, with relatively fast reactions in large particles the reactants may never reach the interior of the particle, thus decreasing the catalyst utilization. Catalyst utilization is expressed as the internal effectiveness factor //,. This factor is defined as follows ... 

Reaction rate. The rate of reaction is defined as the number of moles of reactant disappearing (or the number of moles of product formed) due to reaction per unit time and per unit volume of reaction mixture (or per unit mass of catalyst). Let us denote rs as the rate of disappearance of reactant S for the simple reaction ... 

Thus in defining the rate of reaction, it is important to state the particular reaction species. 

It may be recalled that in homogeneous reactions all reacting materials are found within a single phase, be it gas, liquid or solid if the reaction is catalytic, then the catalyst must also be present within the phase. Thus, there are a number of means of defining the rate of a reaction the intensive measure based on unit volume of the reacting volume (V) is used practically exclusively for homogeneous systems. The rate of reaction of any component i is defined as... 

To define the rate of a reaction, one of the components must be selected and the rate defined in terms of that component. The rate of reaction is the number of moles formed with respect to time, per unit volume of reaction mixture ... 

In this introductory chapter, we first consider what chemical kinetics and chemical reaction engineering (CRE) are about, and how they are interrelated. We then introduce some important aspects of kinetics and CRE, including the involvement of chemical stoichiometry, thermodynamics and equilibrium, and various other rate processes. Since the rate of reaction is of primary importance, we must pay attention to how it is defined, measured, and represented, and to the parameters that affect it. We also introduce some of the main considerations in reactor design, and parameters affecting reactor performance. These considerations lead to a plan of treatment for the following chapters. 

We define the rate of reaction verbally for a species involved in a reacting system either as a reactant or as a product. The system may be single-phase or multiphase, may have fixed density or variable density as reaction proceeds, and may have uniform or varying properties (e.g., p, CA, T, P) with respect to position at any given time. The extensive rate of reaction with respect to a species A, RA, is the observed rate of formation of A ... 

The rate, RA or rA, as defined is negative if A is consumed, and is positive if A is produced. One may also define a species-independent rate of reaction for a single reaction or step in a mechanism, but this requires further consideration of stoichiometry... 

Attempts to define operationally the rate of reaction in terms of certain derivatives with respect to time (r) are generally unnecessarily restrictive, since they relate primarily to closed static systems, and some relate to reacting systems for which the stoichiometry must be explicitly known in the form of one chemical equation in each case. For example, a IUPAC Commission (Mils, 1988) recommends that a species-independent rate of reaction be defined by r = (l/v,V)(dn,/dO, where vt and nf are, respectively, the stoichiometric coefficient in the chemical equation corresponding to the reaction, and the number of moles of species i in volume V. However, for a flow system at steady-state, this definition is inappropriate, and a corresponding expression requires a particular application of the mass-balance equation (see Chapter 2). Similar points of view about rate have been expressed by Dixon (1970) and by Cassano (1980). 

Note that the rate of formation of A is rA, as defined in section 1.4 for a reactant, this is a negative quantity. The rate of disappearance of A is (-rA), a positive quantity. It is this quantity that is used subsequently in balance equations and rate laws for a reactant. For a product, the rate of formation, a positive quantity, is used. The symbol rA may be used generically in the text to stand for rate of reaction of A where the sign is irrelevant and correspondingly for any other substance, whether reactant or product. 

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