Reaction rate first-order reaction

EFFECT OF PORE DIFFUSION ON REACTION RATE First-Order Reaction... 

For a certain concentration at the surface of the unreacted core, Ca c, and rate constant related to the surface area (m s ), the chemical reaction rate (first-order reaction) is given by... 

Fig. 12.17 Kinetic comparison of TFA cleavage reactions of all 16 resin-bound compounds (18-33). The kinetics of cleavage reaction was analyzed as in Figures 12.15 and 12.16. The curves represent the best fit and are displayed for each reaction. The first order reaction rate constants (s ) determined for these reactions are resins (18) (1%), 1.2x10 (19) (5%), 4.8x10 (20) (0.5%), 6.5x10 (21) (1%),...

Research with pilot scale units has shown that the major resistances to mass transfer of reactant to catalyst are within the liquid film surrounding the wetted catalyst particles and also intraparticle diffusion. A description of these resistances is afforded by Fig. 14. Equating the rate of mass transfer across the liquid film to the reaction rate, first order in hydrogen concentration... 

Figure 10. Effectiveness factor ij as a function of the Weisz modulus ji. Combined influence of intraparticle and interphase mass transfer and interphase heat transfer on the effective reaction rate (first order, irreversible reaction in a sphere, Biot number Bim = 100, Arrhenius number y — 20, modified Prater number ( as a parameter).

In this expression = 6.37 x 10 L/mol s at 25 C. The reverse reaction rate (first-order) is given by /f = k (FeSO ). The equilibrium constant is = 205/mol, from which (because = kjk and assuming the principle of detailed balancing) we compute k = 31/s. Calculated rates and concentrations for this reaction as a function of time are given in Fig. 2.8. Note that the overall rate R in Fig. 2.8[b]) equals the difference ( + - / ). 

Reactions displaying first-order reaction kinetics are extremely common. Fortunately, the mathematics needed to describe first-order reactions are also quite straightforward. In a first-order reaction, the reaction rate is directly proportional to the concentration of one of the reactant concentrations. Thus, increasing the concentration of this reactant will speed up the rate of the reaction proportionally. This behavior reflects the fundamental kinetic principle that the speed of most... 

The distinction between molecularity and order is an important one. It is therefore important that the terms unimolecular reaction and first-order reaction, and bimolecular reaction and second-order reaction are not synonyms. The first term refers to a type of molecular change whilst the second one to the type of applicable rate equation governed by the observed dependence of reaction rates on concentration. 

A similar circumstance is detectable for nitrations in organic solvents, and has been established for sulpholan, nitromethane, 7-5 % aqueous sulpholan, and 15 % aqueous nitromethane. Nitrations in the two organic solvents are, in some instances, zeroth order in the concentration of the aromatic compound (table 3.2). In these circumstances comparisons with benzene can only be made by the competitive method. In the aqueous organic solvents the reactions are first order in the concentration of the aromatic ( 3.2.3) and comparisons could be made either competitively or by directly measuring the second-order rate constants. Data are given in table 3.6, and compared there with data for nitration in perchloric and sulphuric acids (see table 2.6). Nitration at the encounter rate has been demonstrated in carbon tetrachloride, but less fully explored. ... 

The effect of nitrous acid on the nitration of mesitylene in acetic acid was also investigated. In solutions containing 5-7 mol 1 of nitric acid and < c. 0-014 mol of nitrous acid, the rate was independent of the concentration of the aromatic. As the concentration of nitrous acid was increased, the catalysed reaction intervened, and superimposed a first-order reaction on the zeroth-order one. The catalysed reaction could not be made sufficiently dominant to impose a truly first-order rate. Because the kinetic order was intermediate the importance of the catalysed reaction was gauged by following initial rates, and it was shown that in a solution containing 5-7 mol 1 of nitric acid and 0-5 mol 1 of nitrous acid, the catalysed reaction was initially twice as important as the general nitronium ion mechanism. 

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... 

Description of Method. Creatine is an organic acid found in muscle tissue that supplies energy for muscle contractions. One of its metabolic products is creatinine, which is excreted in urine. Because the concentration of creatinine in urine and serum is an important indication of renal function, rapid methods for its analysis are clinically important. In this method the rate of reaction between creatinine and picrate in an alkaline medium is used to determine the concentration of creatinine in urine. Under the conditions of the analysis, the reaction is first-order in picrate, creatinine, and hydroxide. 

First-Order Reactions The simplest case is a first-order reaction in which the rate depends on the concentration of only one species. The best example of a first-order reaction is an irreversible thermal decomposition, which we can represent as... 

The simplest way to demonstrate that a reaction is first-order in A, is to double the concentration of A and note the effect on the reaction s rate. If the observed rate doubles, then the reaction must be first-order in A. Alternatively, we can derive a relationship between the [A] and time by rearranging equation A5.6... 

Proceeding in the same manner as for a first-order reaction, the integrated form of the rate law is derived as follows... 

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... 

In the normal process ( ), step (J) occurs very rapidly and step (/) is the rate-determining step, whereas in the inhibition process (B), step (3) occurs very slowly, generally over a matter of days, so that it is rate determining. Thus it has been demonstrated with AChE that insecticides, eg, tetraethyl pyrophosphate and mevinphos, engage in first-order reactions with the enzyme the inhibited enzyme is a relatively stable phosphorylated compound containing one mole of phosphoms per mole of enzyme and as a result of the reaction, an equimolar quantity of alcohoHc or acidic product HX is hberated. 

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. 15. Temperature vs heat generation or removal in estabHshing stationary states. The heavy line (—) shows the effect of reaction temperature on heat-generation rates for an exothermic first-order reaction. Curve A represents a high rate of heat removal resulting in the reactor operating at a low temperature with low conversion, ie, stationary state at a B represents a low rate of heat removal and consequently both a high temperature and high conversion at its stationary state, b and at intermediate heat removal rates, ie, C, multiple stationary states are attainable, c and The stationary state at c ...

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. 

The influence of temperature, acidity and substituents on hydrolysis rate was investigated with simple alkyldiaziridines (62CB1759). The reaction follows first order kinetics. Rate constants and activation parameters are included in Table 2. 

The second type of coalescence arises from the rupture of films between adjacent bubbles [Vrij and Overbeek, y. Am. Chem. Soc., 90, 3074 (1968)]. Its rate appears to follow first-order reaction kinetics with respect to the number of bubbles [New, Proc. 4th Int. Congr. Suif. Active Substances, Brussels, 1964, 2, 1167 (1967)] and to decrease with film thickness [Steiner, Hunkeler, and Hartland, Trans. In.st. Chem. Fng., 55, 153 (1977)]. Many factors are involved [Biker-man, Foams, Springer-Verlag, New York, 1973 and Akers (ed.). Foams, Academic, New York, 1976]. 

FIG. 23-17 Multiple steady states of CSTRs, stable and unstable, adiabatic except the last item, (a) First-order reaction, A and C stable, B unstable, A is no good for a reactor, the dashed line is of a reversible reaction, (h) One, two, or three steady states depending on the combination Cj, Ty). (c) The reactions A B C, with five steady states, points 1, 3, and 5 stable, (d) Isothermal operation with the rate equation = 0 /(1 -I- C y = (C o Cy/t. 

The numerical solution of these equations is shown in Fig. 23-28. This is a plot of the enhancement fac tor E against the Hatta number, with several other parameters. The factor E represents an enhancement of the rate of transfer of A caused by the reaction compared with physical absorption with zero concentration of A in the liquid. The uppermost line on the upper right represents the pseudo-first-order reaction, for which E = P coth p. 

For a first-order reaction, m = I, the catalyst effectiveness T] is independent of A so that after elimination of A and A, the exphcit solution for the rate is... 

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. 

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