Decomposition rate coefficient

It is also necessary to select the initiator according to the particular monomer(s) and the substrate. Factors to consider in this context, aside from initiator half-lives and decomposition rates, are the partition coefficient ot the initiator between the monomer and polyolefin phases and the reactivity of the monomer vs the polyolefin towards the initiator-derived radicals. 

Nitrocellulose powders (U.S.A.) Heat of explosive decomposition (water liquid) kcal/kg Gas volume (water vapour) l./kg Linear coefficient for rate of burning from one surface in./sec/in2... 

The high decomposition rate of pollutants is dependent on the high value of the molar extinction coefficient at 254 nm, the quantum yield of M, and the concentration of oxidation by-products. 

Kusakabe et al. (1990) reported that the destruction rate coefficients increase as temperature increases. UV light intensity of 8.7 W/m2 yielded a slightly more than tenfold increase in the decomposition rate. The decomposition rate of ozone increases with UV intensity. These results imply that, under UV irradiation, radical chain reactions are predominant over molecular ozone reactions. When light intensity is greater than 3 W/m2, the degradation rate of TOC by UV/03 can be expressed as follows ... 

The first-order rate coefficient, k, of this pseudo-elementary process is assumed to vary with temperature according to an Arrhenius law. Model parameters are the stoichiometric coefficients v/ and the Arrhenius parameters of the rate coefficient, k. The estimation of the decomposition rate coefficient, k, requires a knowledge of the feed conversion, which is not directly measurable due to the complexity of analyzing both reactants and reaction products. Thus, a supplementary empirical relationship is needed to relate the feed conversion (conversion of A) to some experimentally accessible variable (Ross and Shu have chosen the yield of C3 and lighter hydrocarbons). It is observed that the rate coefficient, k, is not constant and decreases with increasing conversion. Furthermore, the zero-conversion rate coefficient depends on feed specifications (such as average carbon number, hydrogen content, isoparaffin/normal-paraffin ratio). Stoichiometric coefficients are also correlated with conversion. Of course, it is necessary to write supplementary empirical relationships to account for these effects. 

A more general discussion of the dependence of the decomposition rate on internal energy was developed by Marcus and Rice [4] and further refined and applied by Marcus [5] (RRKM). Their method is to obtain the reaction rate by summing over each of the accessible quantum states of the transition complex. The first-order rate coefficient for decomposition of an energised molecule is shown to be proportional to the ratio of the total internal quantum states of the transition complex divided by the density of states (states per unit energy) of the excited molecule. It is a great advance over previous theory because it can be applied to real molecules, counting the states from the known vibrational frequencies. 

Finally, the diffusion coefficients can also be estimated using alternative techniques, such as the analysis of Hall effect, electrode reaction kinetics, or solids decomposition rate. 

Figure 38 Path diagram describing the structure of the relationship between decomposition rate constants (k) and climate (AET) and litter quality (lignin/N ratio) for first-year decomposition from 44 locations. Numbers in bold type are the Pearson correlation coefficients among variables and the numbers in parentheses partition the coefficients into direct and indirect effects of the predictor variables (AET and lignin/N) (source Aerts, 1997).

Five internal rotations are restricted in the 8-center transition state however, three bonds (instead of two as in the former cases) are broken. Although this process produces the wrong products, this is not necessarily a serious problem (see below). Transition state estimates of the 4-factors favor the 6-center displacement process although 4-center transition states had formerly been proposed It has been noted that the decomposition rate coefficient reported for acetic anhydride, the product of the methylene diacetate reaction, was an order of magnitude larger than that for methylene diacetate. This seemed to suggest errors in one or both sets of rate data. The problem has been resolved however, from an examination of the thermodynamics of the acetic anhydride decomposition ... 

Kinetic results are given in Table 9. The toluene carrier technique often yields low values of the activation energies and 4-factors. Results for the benzyl esters, however, appear to be reasonably good. Note that the estimated reaction enthalpies compare favorably with the observed activation energies and that -factors are reasonable (AS 5 cal.deg mole ). Since only absolute decomposition rate coefficients were reported for the allyl esters, we have estimated the Arrhenius parameters on the assumption that the -factors were all 10 sec The activation energies so obtained are reasonable, since they compare quite favorably to those estimated by group additivities and the accepted heats of formation of the product radicals (Column 3, Table 9). 

Frey s variant of the silvered vessel test has been in use in the Germany. In its variant, different amounts of heat are supplied to the electric heating elements mounted inside the Dewar flask, and the temperature differences between the interior of the Dewar vessel and the furnace are measured by thermocouples. A calibration curve is plotted from the values thus obtained, and the heat of decomposition of the propellant is read off the curve. In this way, the decomposition temperature at a constant storage temperature can be determined as a function of the storage time, and the heat of decomposition of the propellants can thus be compared with each other. If the measurements are performed at different storage temperatures, the temperature coefficient of the decomposition rate can be calculated. (-< also Differential Thermal Analysis.)... 

The rates of initiation depend on the type of activation ch.osen. In photochemical initiation, Vs = 2 0/, where I is the absorbed light intensity and 0 = the efficiency coefficient. With an average intensity, rates of initiation of approximately 10"7 mole l 1 s 1 are attained. In thermal activation, autoinitiation by interaction between oxygen and aldehyde gives low values of approximately 10 9 mole l-1 s"1 under standard laboratory conditions. When azonitrile is used, since the thermal decomposition rate of this product is approximately first order [62], Vi is given by... 

Figure 6.8 shows the first-order loss rate of PAN as a function of altitude by thermal decomposition and photodissociation. The thermal decomposition rate coefficient for PAN can be obtained from the forward rate coefficient for reaction 3, 3, and the equilibrium constant for reactions 3 and 4, 3,4 (Sander et al. 2003),... 

The study of the influence of lower temperatmre in both the aerobic and anaerobic environment showed that the decomposition rate of planktonic OM even at a low temperature of 8°C (estimated by the dry weight, organic C, N and P, carbohydrates and protein) decreased with time (Bikbulatov et al., 1978). The main difference in the decomposition at 8°C and 20°C was observed in the initial stages, where mainly the labile OM was subjected to d adation. At the same time a drop in temperature of 10° C decreased the rate of the process by 2.5 times, according to the Van t Hoff rule. For lipids this coefficient rose to 7.6. With the gradual increase of the resistant fraction of OM in particles, the rate of the process became slower and slower. 

Estimates of the thermal-decomposition rate coefficients of C2H5O radicals have been made by Batt and Milne (1977b) based on thermochemical data and comparisons with similar reactions. Their results are listed in Table 10. 

C3H7O. Only very limited data exist on the abstraction of H atoms by i-C3H70 radicals. Batt and Milne (1977a), in their study of the thermal decomposition of 1-C3H7O radicals, found that at 160 C, 1-C4H10 at 10 M could remove —25% of the radicals. If we take our recommended value for the decomposition rate coefficient of 10 °exp —17.5// 7 sec , then the abstraction rate coefficient is 2.0 x lO Af -sec at 160°C. 

The values for the exudation rate F, interaction coefficient (A), buffer power of exudate in soil b and the decomposition rate constant for the exudate k were adopted from Kirk (1999). The value of the forward rate constant was estimated from Scheckel and Sparks (2001), who evaluated kinetic adsorption data of Ni to different minerals where ranged from 2.5 x 10 to 9.78 X 10 s For the simulation, an average value of 5.00 x 10 was used. This value also coincides with the values that Kirk and Staunton (1989) suggested for the kinetic adsorption of Q to soil, where the values ranged from lO" to 10 2 s f This same value was assumed for the rate constant for the two-stage sorption model, a2- The fraction of type 1 sites (F ) was assumed to be 0.3. Table 7 summarizes all input parameter values. 

Decomposition in a Foreign Gas Similarly, equations can be derived for the calculation of absolute decomposition rates in an atmosphere of foreign gases. Disregarding the differences in the diffusion coefficients of different gaseous products (A and B), one arrives eventually at the following final relations. For one-dimensional diffusion of both gaseous products from a plane surface ... 

Misconception and its Interpretation The low magnitudes of the vaporization coefficients for many substances (effusion method, which is used for estimations of the maximum decomposition rate or of the equilibrium pressure of the product. The ratio of the equilibrium pressure inside the cell, P q, to the effusion pressure, P g, is governed by [3] ... 

A theoretical simulation of the powder decomposition rate was attempted by L vov et al. [2, 3] in 1998 (Chapter 6). Later L vov and Ugolkov [4] continued these theoretical and experimental studies with dolomite crystals and powders of various particle sizes. Calculations performed for powders with varied numbers of layers n = 10 and 100), emittance coefficients (from 0.01 to 1), and residual air pressures in the reactor (10 and 10 bar) showed that the differences in the particle size and powder mass do not noticeably affect the temperature distribution and the effective number of powder layers Ue (see Sect. 6.3) decomposing at the same rate as does the surface layer. Furthermore, it was found that the decomposition rates of crystals and powders with the same external surface area and coefficients ranging from 0.01 to 0.3 should differ by a factor of no more than 2. 

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