Reactant first-order

One-Reactant, First-Order Reaction in PFR/Separation/Recycle Systems... 

Assuming pure reactant feed za = 1, plug flow, constant physical properties and one-reactant first-order reaction, the following dimensionless model can be derived ... 

FIGURE 10.6. The ratio of the rate of heat release of a strained flame to that of an unstrained flame as a function of the reciprocal of the nondimensional strain rate for various values of the nonadiabaticity parameter H calculations were performed for a one-reactant, first-order reaction in an ideal gas with constant specific heat and Lewis number of unity, with thermal conductivity proportional to temperature and an adiabatic flame temperature four times the initial temperature [HO]. 

Reactions are classified according to number of reacting species whose concentration determines the rate at which the reaction occurs, i.e. the order of reaction. We will concentrate mainly on zero-order reactions, in which the breakdown rate is independent of the concentration of any of the reactants first-order reactions, in which the reaction rate is determined by one concentration term, and second-order reactions, in which the rate is determined by the concentrations of two reacting species. 

Reactant First-order rate constant for hydrocracking... 

The order of a reaction relates to the exponents of the concentration factors in the rate law for a chemical reaction. The order can be stated with respect to a particular reactant (first order in A, second order in B,...) or, more commonly, as the overall order. The overall order is the sum of the exponents. 

There is one special class of reaction systems in which a simplification occurs. If collisional energy redistribution of some reactant occurs by collisions with an excess of heat bath atoms or molecules that are considered kinetically structureless, and if fiirthennore the reaction is either unimolecular or occurs again with a reaction partner M having an excess concentration, dien one will have generalized first-order kinetics for populations Pj of the energy levels of the reactant, i.e. with... 

How does one monitor a chemical reaction tliat occurs on a time scale faster tlian milliseconds The two approaches introduced above, relaxation spectroscopy and flash photolysis, are typically used for fast kinetic studies. Relaxation metliods may be applied to reactions in which finite amounts of botli reactants and products are present at final equilibrium. The time course of relaxation is monitored after application of a rapid perturbation to tire equilibrium mixture. An important feature of relaxation approaches to kinetic studies is that tire changes are always observed as first order kinetics (as long as tire perturbation is relatively small). This linearization of tire observed kinetics means... 

Multichannel time-resolved spectral data are best analysed in a global fashion using nonlinear least squares algoritlims, e.g., a simplex search, to fit multiple first order processes to all wavelengtli data simultaneously. The goal in tliis case is to find tire time-dependent spectral contributions of all reactant, intennediate and final product species present. In matrix fonn tliis is A(X, t) = BC, where A is tire data matrix, rows indexed by wavelengtli and columns by time, B contains spectra as columns and C contains time-dependent concentrations of all species arranged in rows. 

The reaction of MeO /MeOH with 2-Cl-5(4)-X-thiazoles (122) follows a second-order kinetic law, first order with respect to each reactant (Scheme 62) (297, 301). A remark can be made about the reactivity of the dichloro derivatives it has been pointed out that for reactions with sodium methoxide, the sequence 5>2>4 was observed for monochlorothiazole compounds (302), For 2.5-dichlorothiazole, on the contrary, the experimental data show that the 2-methoxy dehalogenation is always favored. This fact has been related to the different activation due to a substituent effect, less important from position 2 to 5 than from... 

The rate of this reaction is observed to be directly proportional to the concentration of both methyl bromide and sodium hydroxide It is first order m each reactant or second order overall... 

Direct-Computation Rate Methods Rate methods for analyzing kinetic data are based on the differential form of the rate law. The rate of a reaction at time f, (rate)f, is determined from the slope of a curve showing the change in concentration for a reactant or product as a function of time (Figure 13.5). For a reaction that is first-order, or pseudo-first-order in analyte, the rate at time f is given as... 

In a curve-fitting method the concentration of a reactant or product is monitored continuously as a function of time, and a regression analysis is used to fit an appropriate differential or integral rate equation to the data. Eor example, the initial concentration of analyte for a pseudo-first-order reaction, in which the concentration of a product is followed as a function of time, can be determined by fitting a rearranged form of equation 13.12... 

The order of the rate law with respect to the three reactants can be determined by comparing the rates of two experiments in which the concentration of only one of the reactants is changed. For example, in experiment 2 the [H+] and the rate are approximately twice as large as in experiment 1, indicating that the reaction is first-order in [H+]. Working in the same manner, experiments 6 and 7 show that the reaction is also first-order with respect to [CaHeO], and experiments 6 and 8 show that the rate of the reaction is independent of the [I2]. Thus, the rate law is... 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

A fixed-bed reactor for this hydrolysis that uses feed-forward control has been described (11) the reaction, which is first order ia both reactants, has also been studied kiaeticaHy (12—14). Hydrogen peroxide interacts with acetyl chloride to yield both peroxyacetic acid [79-21-0] and acetyl peroxide... 

For weU-defined reaction zones and irreversible, first-order reactions, the relative reaction and transport rates are expressed as the Hatta number, Ha (16). Ha equals (k- / l ) where k- = reaction rate constant, = molecular diffusivity of reactant, and k- = mass-transfer coefficient. Reaction... 

Fig. 6. Reaction zones for a first-order, fast irreversible homogeneous reaction, in reactants A and B with Ha > 2 and (a)

The kinetics of hydrolysis reactions maybe first-order or second-order, depending on the reaction mechanism. However, second-order reactions may appear to be first-order, ie, pseudo-first-order, if one of the reactants is not consumed in the reaction, eg, OH , or if the concentration of active catalyst, eg, reduced transition metal, is a small fraction of the total catalyst concentration. 

Diels-Alder reactions with butadiene are generally thermally reversible and can proceed in both gas and Hquid phases. The reactions are exothermic and foUow second-order kinetics first-order with respect to each reactant. 

Reactants must diffuse through the network of pores of a catalyst particle to reach the internal area, and the products must diffuse back. The optimum porosity of a catalyst particle is deterrnined by tradeoffs making the pores smaller increases the surface area and thereby increases the activity of the catalyst, but this gain is offset by the increased resistance to transport in the smaller pores increasing the pore volume to create larger pores for faster transport is compensated by a loss of physical strength. A simple quantitative development (46—48) follows for a first-order, isothermal, irreversible catalytic reaction in a spherical, porous catalyst particle. 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

In all of these expressions the order appears to be related to the number of molecules involved in tire original collision which brings about the chemical chatrge. For instance, it is clear that the bitrrolecular reaction involves the collision between two reactant molecules, which leads to the formation of product species, but the interpretation of tire first and third-order reactions cannot be so simple, since the absence of the role of collisions in the first order, and the rare occunence of tlrree-body collisions are implied. 

An explanation which is advanced for these reactions is that some molecules collide, but do trot immediately separate, and form dimers of dre reactant species which have a long lifetime when compared with the period of vibration of molecules, which is about 10 seconds. In the first-order reaction, the rate of tire reaction is therefore determined by the rate of break-up of tirese dimers. In the thud-order reaction, the highly improbable event of a tluee-body collision which leads to the formation of tire products, is replaced by collisions between dimers of relatively long lifetime widr single reactant molecules which lead to tire formation of product molecules. 

When a unimolecular reaction occurs with an initial product partial pressure of the reactant A, to yield an amount of die product, jc, the first-order reaction rate equation reads... 

For simulation on the IBM 360/65 computer, the reaction was represented as first order to oxygen, the limiting reactant, and by the usual Arrhenius form dependency on temperature. Since the changes here were rapid, various transport processes had significant roles. The following set of differential equations was used to describe the transient system ... 

Experimentally, it would be observed that the reaction rate would be proportional to both [A] and [B]. The reaction will be first-order in both reactants. 

The concerted displacement mechanism implies both kinetic and stereochemical consequences. The reaction will exhibit second-order kinetics, first-order in both reactant... 

TWo types of rate expressions have been found to describe the kinetics of most aromatic nitration reactions. With relatively unreactive substrates, second-order kinetics, first-order in the nitrating reagent and first-order in the aromatic, are observed. This second-order relationship corresponds to rate-limiting attack of the electrophile on the aromatic reactant. With more reactive aromatics, this step can be faster than formation of the active electrq)hile. When formation of the active electrophile is the rate-determining step, the concentration of the aromatic reactant no longer appears in the observed rate expression. Under these conditions, different aromatic substrates undergo nitration at the same rate, corresponding to the rate of formation of the active electrophile. 

There are relatively few kinetic data on the Friedel-Crafts reaction. Alkylation of benzene or toluene with methyl bromide or ethyl bromide with gallium bromide as catalyst is first-order in each reactant and in catalyst. With aluminum bromide as catalyst, the rate of reaction changes with time, apparently because of heterogeneity of the reaction mixture. The initial rate data fit the kinetic expression ... 

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