First-order kinetics deviations

Data for the time to the onset of diffusion control, as determined by infrared spectroscopy, are also included in Fig. 15. The time to dififiision control was selected as the point at which the extent of conversion vs. time data, plotted for first order kinetics, deviated from linearity. The onset of diffusion control corresponds with vitrification, as determined by TBA, for the system of Fig. 15... 

If (A i[X ]/A 2[Y ]) is not much smaller than unity, then as the substitution reaction proceeds, the increase in [X ] will increase the denominator of Eq. (8-65), slowing the reaction and causing deviation from simple first-order kinetics. This mass-law or common-ion effect is characteristic of an S l process, although, as already seen, it is not a necessary condition. The common-ion effect (also called external return) occurs only with the common ion and must be distinguished from a general kinetic salt effect, which will operate with any ion. An example is provided by the hydrolysis of triphenylmethyl chloride (trityl chloride) the addition of 0.01 M NaCl decreased the rate by fourfold. The solvolysis rate of diphenylmethyl chloride in 80% aqueous acetone was decreased by LiCl but increased by LiBr. ° The 5 2 mechanism will also yield first-order kinetics in a solvolysis reaction, but it should not be susceptible to a common-ion rate inhibition. 

As for the dependence of the polymerization rate V on the monomer concentration some authors have also found first-order kinetics (84, 90, 96, 99), but sometimes deviations from the first order were observed (38, 51, 88) that may be connected with a change in the number of propagation centers with monomer concentration. 

In mild alkaline conditions, highly methylated pectin was demethylated following a (pseudo)-first order kinetics with respect to the concentration of methoxylated galacturonate moieties. Investigation in this pH range, where the initial concentration of methylesters was higher than the initial concentration of OH ions, was complicated by the necessity to use a buffer. This led to deviations from the theoretical behavior as the concentration of OH ions still varied in proportions which could not be neglected in the equations of the kinetics. However these deviations could be accounted for be the pH variation, and the pH variation itself predicted from the amount of liberated methanol. The constant we found was similar to previously reported data (Scamparini Bobbio, 1982). 

Organic peroxides and hydroperoxides decompose in part by a self-induced radical chain mechanism whereby radicals released in spontaneous decomposition attack other molecules of the peroxide.The attacking radical combines with one part of the peroxide molecule and simultaneously releases another radical. The net result is the wastage of a molecule of peroxide since the number of primary radicals available for initiation is unchanged. The velocity constant ka we require refers to the spontaneous decomposition only and not to the total decomposition rate which includes the contribution of the chain, or induced, decomposition. Induced decomposition usually is indicated by deviation of the decomposition process from first-order kinetics and by a dependence of the rate on the solvent, especially when it consists of a polymerizable monomer. The constant kd may be separately evaluated through kinetic measurements carried out in the presence of inhibitors which destroy the radical chain carriers. The aliphatic azo-bis-nitriles offer a real advantage over benzoyl peroxide in that they are not susceptible to induced decomposition. 

Pseudo-first order kinetics was assumed to interpret the experimental data. Fig. 5.4-36 shows that the fit of the experimental data using first order-kinetics is acceptable. However, a systematic deviation is observed in the curve obtained at 110 C. This indicates inadequacy of the first-order kinetics, which is inappropriate from the view of theory. On the other hand, the kinetic equation seems to describe the... 

The first term covers the short initiation period until maximum heat release rate occurs, which can be measured separately but is here neglected in the approximation to the right of equation (4). Also neglected are the existant deviations from first order kinetics. 

In this way the observed deviation from external first-order kinetics finds a natural explanation. 

Figure 5.2. Grabowski s model of TICT formation in DMABN the locally excited (LE) state with near-planar conformation is a precursor for the TICT state with near perpendicular geometry. The reaction coordinate involves charge transfer from donor D to acceptor A. intramolecular twisting between these subunits, and solvent relaxation around the newly created strong dipole. Decay kinetics of LE and rise kinetics of the TICT state can be followed separately by observing the two bands of the dual fluorescence. For medium polar solvents, well-behaved first-order kinetics are observed, with the rise-time of the product equal to the decay time of the precursor, but for the more complex alcohol solvents, kinetics can strongly deviate from exponentiality, interpretable by time-dependent rate constants. 52 ...

The deviation from first-order kinetics for the uridylic acids is also reflected in quantum yields which vary with concentration and which therefore vary during the course of a particular photolysis.7 These deviations from first-order kinetics have been discussed in terms of a collision-induced transition of an excited-singlet pyrimidine to a long-lived state.7 We shall say more about the probability of long-lived states later. 

At about the same time, hydroxamic adds and oximes were found to react directly with organophosphorus compounds.85 2-PAM I was found to react In vitro with sarin with marked deviation from first-order kinetics that suggested that the reaction actually consists of (at least) two sequential reactions. Green showed that quatemlzed pyridine aldoximes react with an organophosphorus (OP) compound In three steps ... 

In solvent DMSO, the rate of reaction (17) (R = Me, X = Cl) was too fast to follow, but using the mixture DMSO-dioxan (1 9 v/v) at 24.7 °C, rate coefficients for the substitution of the gold(I) complex by several alkylmercuric salts were obtained. It was found that in this mixed solvent, reaction (17) followed first-order kinetics, first-order in the gold(I) complex and zero-order in the alkylmercuric salt. Furthermore, the first-order rate coefficient had the same value no matter what alkylmercuric salt was used (methylmercuric acetate, methylmercuric chloride, methylmercuric bromide, and ethylmercuric chloride were the salts used). At 24.7 °C, the first-order rate coefficient has the value 0.0083 sec-1, with a standard deviation of 0.0006 sec-1. 

First-Order Kinetics. When the rate of a process is dependent on a rate constant and a concentration gradient, a linear or first-order kinetic process will be operative. The reader should be aware that there are numerous deviations from the first-order process when chemical transport in vivo is analyzed, and this can be deemed an approximation since, in many barriers, penetration is slow and a long period of time is required to achieve steady state. 

Sparks and Jardine (1984) studied the kinetics of potassium adsorption on kaolinite, montmorillonite, and vermiculite (Fig. 2.1) and found that a single first-order reaction described the data well for kaolinite and smectite while two first-order reactions described adsorption on vermiculite. One will note deviations from first-order kinetics at longer time periods, particularly for montmorillonite and vermiculite, because a quasi-equilibrium state is reached. These deviations result because first-order equations are only applicable far from equilibrium (Skopp, 1986) back reactions could be occurring at longer reaction times. 

It has been shown that changes in the UV and IR absorbance of unplasticized Cellophane films subjected to accelerated aging in a dry oven at 140 °C follow the behavior predicted by a first-order kinetic model, except for deviations in the early aging period, and that these deviations are most likely caused by oxidation products in the films. It has also been shown that, for Cellophane films, the changes in UV and IR absorbance follow the same kinetics as color change, and that these kinetics are nearly identical with those for rayon and cotton cloths aged under similar conditions. 

The majority of catalyst systems yield polymerization kinetics which comply with the requirement of first-order kinetics with respect to monomer conversion . Some of the investigated Nd-alcoholates and Nd-phosphates exhibit a deviating pattern of monomer consumption and belong to the few exceptions. Also for some of the Nd-carboxylate-based catalyst systems deviations from the first-order dependence of monomer consumption are reported for the first stage of the polymerization ( induction periods ). Induction periods are usually observed when the active catalyst is prepared in-situ (Sect. 2.1.6). In these cases the formation of the active Nd-species is slow in relation to the rate of polymerization. 

The deviation in the enantiomeric excess (ee) was small, and 90% of all data were within 40 and 48% ee [325]. A kinetic analysis was made by fitting the experimental data to empirical models by parity diagrams (see Figure 4.55). A statistical model with first-order kinetics for hydrogen gave the best fit. 141 from 170 experiments were... 

The deacylation reaction shows an accelerative deviation from the first-order kinetics. This peculiar behavior is most apparent for the samples 20% or more acylated, and explained best by intramolecular imidazole catalysis. Jencks and C riudo reported that imidazole catalyzed the hydrolysis of acetyl imidazc (61). A similar mechanism was proposed for the deacylation of pofyvinylimidazcde and the accelerative deacylation behavior was attributed to the increaang local imidazole concentration along the polymer chain. 

A kinetic model based on homogeneous polymerization was developed to describe the polymerization in CO2 [51, 54]. A model based on the reaction scheme in Fig. 3 adequately described the polymerization rates and the poly-dispersity of the polymer. Monomer inhibition was incorporated into the model to account for the observed deviation from first-order kinetics. However, imperfect mixing of the higher viscosity medium is an alternative explanation. It was concluded that termination was by combination, for three reasons. First, there was no existing literature to support termination by disproportionation for PVDF. Second, the polydispersity was approximately 1.5 at low monomer concentrations. Third, NMR studies showed no evidence of unsaturation. 

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