Kinetics criteria

This method is exemplified by its application to quinoline, isoquinoline, cinnoline, and isoquinoline 2-oxide, which are nitrated as their conjugate acids. The rate profiles for these compounds and their N- or O-methyl perchlorates show closely parallel dependences upon acidity (fig. 2.4). Quaternisation had in each case only a small effect upon the rate, making the criterion a very reliable one. It has the additional advantage of being applicable at any temperature for which kinetic measurements can be made (table 8.1, sections B and D). 

Recently kinetic data have become available for the nitration in sulphuric acid of some of these hydroxy compounds (table 10.3). For 4-hydroxyquinoline and 4-methoxyquinoline the results verify the early conclusions regarding the nature of the substrate being nitrated in sulphuric acid. Plots of log Q against — (Lf + logioflHao) fo " these compounds and for i-methyl-4-quinolone have slopes of i-o, i-o and 0-97 at 25 C respectively, in accord with nitration via the majority species ( 8.2) which is in each case the corresponding cation of the type (iv). At a given acidity the similarity of the observed second-order rate constants for the nitrations of the quinolones and 4-methoxy-quinoline at 25 °C supports the view that similarly constructed cations are involved. Application of the encounter criterion eliminates the possibilities of a... 

We now turn specifically to the thermodynamics and kinetics of reactions (5. EE) and (5.FF). The criterion for spontaneity in thermodynamics is AG <0 with AG = AH - T AS for an isothermal process. Thus it is both the sign and magnitude of AH and AS and the magnitude of T that determine whether a reaction is thermodynamically favored or not. As usual in thermodynamics, the A s are taken as products minus reactants, so the conclusions apply to the reactions as written. If a reaction is reversed, products and reactants are interchanged and the sign of the AG is reversed also. 

It is necessary to estabUsh a criterion for microbial death when considering a sterilization process. With respect to the individual cell, the irreversible cessation of all vital functions such as growth, reproduction, and in the case of vimses, inabiUty to attach and infect, is a most suitable criterion. On a practical level, it is necessary to estabUsh test criteria that permit a conclusion without having to observe individual microbial cells. The failure to reproduce in a suitable medium after incubation at optimum conditions for some acceptable time period is traditionally accepted as satisfactory proof of microbial death and, consequentiy, stetihty. The appHcation of such a testing method is, for practical purposes, however, not considered possible. The cultured article caimot be retrieved for subsequent use and the size of many items totally precludes practical culturing techniques. In order to design acceptable test procedures, the kinetics and thermodynamics of the sterilization process must be understood. 

Following this procedure urea can be determined with a linear calibration graph from 0.143 p.g-ml To 1.43 p.g-ml and a detection limit of 0.04 p.g-ml based on 3o criterion. Results show precision, as well as a satisfactory analytical recovery. The selectivity of the kinetic method itself is improved due to the great specificity that urease has for urea. There were no significant interferences in urea determination among the various substances tested. Method was applied for the determination of urea in semm. 

As with all of die processes described, drese are first studied in detail in the laboratoty with an industrial application as dre objective. Those processes which pass the criterion of economic potential are used in a pilot plant smdy, and dretr, if successful, at the production level which must be optimized. The materials which are produced are mainly, in the present instance, for application in the elecU onics industry where relatively high costs are acceptable. It will be seen drat the simple kinetic theory of gases is adequate to account for dre rates of these processes, and to indicate the ways in which production may be optimized on dre industrial scale. 

In the case of exothermic reactions, underestimating the transfer coefficients makes the real gradients less than the estimated ones. As such, this makes our estimates conservative, in the sense that if a criterion calls gradients negligible then they surely are. The intent here is to do most of the kinetic study and catalyst testing at gradientless conditions and this book will make use of the Colburn-type correlations as developed by Hougen (1951) and his associates. 

Qian, R., Chen, Z., Ni, H., Fan, Z. and Cai, F., 1987. Crystallization kinetics of potassium chloride from brine and scale-up criterion. American Institution of Chemical Engineers Journal, 33, 1690-1697. 

The kinetic energy criterion can be applied for fragment masses between 4.5 and 0.1 kg. For smaller masses, the following equation can be used ... 

In these circumstances a decision must be made which of two (or more) kinet-ically equivalent rate terms should be included in the rate equation and the kinetic scheme (It will seldom be justified to include both terms, certainly not on kinetic grounds.) A useful procedure is to evaluate the rate constant using both of the kinetically equivalent forms. Now if one of these constants (for a second-order reaction) is greater than about 10 ° M s-, the corresponding rate term can be rejected. This criterion is based on the theoretical estimate of a diffusion-controlled reaction rate (this is described in Chapter 4). It is not physically reasonable that a chemical rate constant can be larger than the diffusion rate limit. 

The standard state chosen for the calculation of controls its magnitude and even its sign. The standard state is established when the concentration scale is selected. For most solution kinetic work the molar concentration scale is used, so A values reported by different workers are usually comparable. Nevertheless, an important chemical question is implied Because the sign of AS may depend upon the concentration scale used for the evaluation of the rate constant, which concentration scale should be used when A is to serve as a mechanistic criterion The same question appears in studies of equilibria. The answer (if there is a single answer) is not known, though some analyses of the problem have been made. Further discussion of this issue is given in Section 6.1. 

According to this very simple derivation and result, the position of the transition state along the reaction coordinate is determined solely by AG° (a thermodynamic quantity) and AG (a kinetic quantity). Of course, the potential energy profile of Fig. 5-15, upon which Eq. (5-60) is based, is very unrealistic, but, quite remarkably, it is found that the precise nature of the profile is not important to the result provided certain criteria are met, and Miller " obtained Eq. (5-60) using an arc length minimization criterion. Murdoch has analyzed Eq. (5-60) in detail. Equation (5-60) can be considered a quantitative formulation of the Hammond postulate. The transition state in Fig. 5-9 was located with the aid of Eq. (5-60). 

A criterion for the position of the extent of the mesomerism of type 9 is given by the bond order of the CO bond, a first approximation to W hich can be obtained from the infrared spectrum (v C=0). Unfortunately, relatively little is known of the infrared spectra of amide anions. How-ever, it can be assumed that the mesomeric relationships in the anions 9 can also be deduced from the infrared spectra of the free amides (4), although, of course, the absolute participation of the canonical forms a and b in structures 4 and 9 is different. If Table I is considered from this point of view, the intimate relationship betw-een the position of the amide band 1 (v C=0) and the orientation (0 or N) of methylation of lactams by diazomethane is unmistakeable. Thus the behavior of a lactam tow ard diazomethane can be deduced from the acidity (velocity of reaction) and the C=0 stretching frequency (orientation of methylation). Three major regions can be differentiated (1) 1620-1680 cm h 0-methylation (2) 1680-1720 cm i, O- and A -methylation, w ith kinetic dependence and (3) 1730-1800 em , A -methylation, The factual material in Table I is... 

Kinetic observations of the homogeneous part of the reaction in water12,13 do not provide any substantially new element to the knowledge of this system. The obvious observations that the rate of resinification increases with increasing temperature and decreasing pH of the mixture only provide technically useful correlation parameters and the zero-order of reactions carried out to small conversion of 2-furfuryl alcohol13 does not indicate anything except an elementary kinetic approximation (the use of colour build-up as a criterion for the extent of alcohol consumed is also questionable since no firm relationship has ever been established between these two quantities). 

Hence, Flory s theory offers an objective criterion for chain flexibility and makes possible to divide all the variety of macromolecules into flexible-chain (f > 0.63) and rigid-chain (f < 0.63) ones. In the absence of kinetic hindrance, all rigid-chain polymers must form a thermodynamically stable organized nematic phase at some polymer concentration in solution which increases with f. At f > 0.63, the macromolecules cannot spontaneously adopt a state of parallel order under any conditions. 

No single criterion has been recognized as constituting a satisfactory basis for the systematic classification of the kinetics of solid-phase reactions (Chapt. 1, Sect. 3). A classification based on the anion is preferred here since it is this constituent which undergoes breakdown in most reactions of interest and proposed reaction mechanisms for substances containing a common anion often include similar features. 

The chemical properties of oxide surfaces have been studied by several methods, including oxygen exchange. This method has been used to investigate the mechanisms of heterogeneous reactions for which oxides are active catalysts [36]. The dimerization step does not necessarily precede desorption and Malinin and Tolmachev [634], in one of the few reviews of decomposition kinetics of solid metal oxides, use this criterion to distinguish two alternative reaction mechanisms, examples being... 

The kinetics of decomposition of these solids may be classified according to the process which has been identified as rate-limiting. This criterion allows a more concise presentation but is not completely satisfactory since some reactions show a sensitivity of behaviour to the conditions prevailing [1270]. Furthermore, certain of the reactions discussed are reversible. Reference to the extensive literature devoted to the thermodynamic properties of these solids and phase stabilities and interactions will only be made where kinetic observations or arguments have been used. 

The recipe (5.58) is even more sensitive to the high-frequency dependence of kjj than similar criterion (5.53), which was used before averaging over kinetic energy of collisions E. It is a much better test for validity of microscopic rate constant calculation than the line width s j-dependence, which was checked in Fig. 5.6. Comparison of experimental and theoretical data on ZR for the Ar-N2 system presented in [191] is shown in Fig. 5.7. The maximum value Zr = 22 corresponding to point 3 at 300 K is determined from the rate constants obtained in [220],... 

For the determination of stabilizations of carbonium ions the equilibrium constants of carbonylation-decarbonylation have been used in previous Sections. For the ions discussed in this Seetion, however, the rate constants of decarbonylation are not known and, therefore, the rate constants of carbonylation will be used as a criterion for such stabilizations. This kinetic criterion is a useful indicator if there are no significant steric factors in the carbonylation step and if this step is indeed rate-determining in the overall process (Hogeveen and Gaasbeek, 1970). The following rate constants in Table 2 are of particular importance. 

Secondly, the stabilization of alkylcarbonium ions can be conveniently determined by measuring the equilibrium constants of the carbonylation-decarbonylation reactions. For some cases the rates of carbonylation are used as a kinetic criterion for stabilization. 

Law C.K. and Egolfopoulos F.N., A kinetic criterion of flammability limits The C-H-O-inert system, Proc. Combust. Inst., 23 413 21,1990. 

The positive values obtained in practically all cases indicate that all these models may be plausible representations of the data and indeed, the correlation coefBcients, R, are greater than 0.9. Thus, statistical compliance is not a sufficient basis for model discrimination. Specifically, the thermodynamic consistency of the estimates, as proposed by Boudart et al. [3], is appropriate further scrutinizing criterion during kinetic modelling and has been gainfully employed in other reactions [4-6]. 

In a practical sense, stability of a dispersion ofttimes is accompanied by a retarded separation of the phases. Unfortunately, a quantitative definition cannot be based on this rate of separation because of the overwhelming influence of density, viscosity, and thermal effects. In short, a kinetic criterion, such as sedimentation rate, is not as likely to portray stability as one based on thermodynamic considerations. In this latter category are sediment volumes, turbidity, consistency, and electrical behavior. 

---