Decomposition constants

A critical size for "spontaneous detonation thru self-heating may be a general phenomenon, even though widely varying for different explosives. The view of this as a possibility arises from the indication, in the Arrhenius equation, that there is some decomposition constantly taking place even at room temperatures. As the linear dimension d of the charge increases, the rate of heat evolution increases as d, whereas the rate of heat dissipation by conduction increases only as d. Theoretically, therefore, a size must be attainable at which the sample will eventually... 

Figure 6.7. Simplifed soil carbon cycling scheme. Major inputs (plant litter) to and outputs (respiration and erosion) from the soil carbon reservoir. The observed flux of C out of the soil can be modeled by assuming three pools of carbon an active pool with a turnover time on the order of years, an intermediate pool with a turnover time on the order of decades to centuries, and a passive pool with a turnover time on the order of millennia. The decomposition constant is k = 1/t. Subscripts a, i, and p refer to the active, intermediate, and passive C pools, respectively. Adapted with permission from Amundson, R. (2001). The carbon budget in soils. Annu. Rev. Earth Planet. Sci. 29, 535-562.

I. Natural Radiocarbon—For Samples Collected Prior to 1950, or Assumed to Contain No Bomb Radiocarbon. For samples not complicated by the presence of bomb 14C, the ratio of 14C/12C measured in a sample represents the rate of decomposition relative to the rate of radiodecay of 14C. This treatment is most useful for very old C found in soils. For a homogeneous carbon-containing reservoir, i, with input rate Iu first-order decomposition constant kh and carbon content C the change in stock over time (balance of inputs and outputs) is... 

Figure 6.10. Accumulation of C in non-steady-state soils of a mature black spruce/moss forest in central Manitoba, Canada. Data shown are (A) for sphagnum moss that has accumulated since the site last burned (-100 yr before sampling), and (B) for the humus and charred layer below the regrowing moss and including the A horizon. The soil is developed on the sediments of a lake that dried up -7000 years ago. The parameters 7 = plant input (kgCuf2yr ) and k = decomposition constant (yr-1). Reprinted from Trumbore and Harden (1997), with permission from the American Geophysical Union.

The decomposition rates in methanol in Table 10 also show the influence of the position of the electron-withdrawing substituent. The decomposition of ///-NCL-phenylpentazole is slower than the decomposition of the /w/z-substituted compound. Otherwise, substitution in ortho- or ///////-position increases the decomposition rate compared to the /wra-substituted compounds, in case of the ////////-substitution drastically. The dipentazole compound l,4-bis(/>-pentazolylphenyl)butane has a decomposition constant of 12.7(1) 10-4s-1 and a half-life of 9.1(1) min in CDCI3 solution at 0 °C. The resulting decomposition product with one pentazole ring and an azide group decomposes with a reaction constant of 5.40(1) 10-4s-1 and a half-life of 21.4 min to the diazide and dinitrogen. 

Table 10 Decomposition constants of substituted phenylpentazoles in methanol at 0°C <1958CB531 >...

Table 12 Carbon storage, radiocarbon content, and the estimated decomposition constant (k) for the O and A horizons under oak and pine vegetation.

Rguie4.19 Logarillim of llie nitrazepam decomposition constant, k, as a function of relative humidity at various temperatures. 

Another method of preparing a cyanohydrin is to treat one cyanohydrin (usually a ketone cyanohydrin) with a different carbonyl compound (usually an aldehyde) in the presence of a small amount of an alkaline catalyst 172 an equilibrium is set up in which the cyanohydrin with the smaller decomposition constant preponderates ... 

Table VI. Critical Decomposition Constants, Heat of Reaction, Compositions,...

It was further demonstrated that the above correlation is also valid for liquid mixtures [Le 73a]. The decomposition constants measured in the methanol-water and dioxane-water systems, for example, lay on a common curve if they were plotted as a function of the surface tension of the mixtures. 

According to Equation (20-53), a combination of the propagation rate constant with rate constants of other elementary reactions is always obtained instead of the rate constant of propagation, alone, from the polymerization kinetics at low conversions. The free radical yield and the initiator decomposition constant are obtained in separate experiments with added inhibitor. The inhibitor reacts with the initiator free radicals, so that the product fk can be calculated from its consumption ... 

Equation (20-68) can also serve to determine the decomposition constant d. By combining Equations (20-67) and (20-68), we obtain... 

Because of the activation energy of about 125 kJ/mol which is necessary for such reactions, these times depend considerably on the temperature. The rate constant also depends somewhat on the solvent, as with BPO (Table 20-2), but not so much as the rate constants of ionic reactions. Therefore the mean decomposition constant of initiator mixtures can be compiled additively from the individual constants. 

Most emulsion polymerisations are free radical processes (318). There are several steps in the free radical polymerisation mechanism initiation (324), propagation and termination (324, 377, 399). In the first step, an initiator compound generates free radicals by thermal decomposition. The initiator decomposition rate is described by an Arrhenius-type equation containing a decomposition constant ( j) that is the reciprocal of the initiator half-life (Ph). The free radicals initiate polymerisation by reaction with a proximate monomer molecule. This event is the start of a new polymer chain. Because initiator molecules constantly decompose to form radicals, new polymer chains are also constantly formed. The initiated monomeric molecules contain an active free radical end group. 

The degradation (decomposition) constant relates to the degradation curve determined in the lab, while the degradation constant kic characterizes the degradation curve in the drainage ditch under natural conditions. The model uses = 0.1 (1/day) throughout. 

The method was introduced by Landler and Lebel who determined the decomposition constants of ozonized polyethylene, pol5winylchloride, and polystyrene, without distinction between peroxides and hydroperoxides. Zeppenfeld demonstrated that only hydroperoxides in acidic medium can oxidize ferrous ions according to the following reactions ... 

The first microscopic process, the formation of primary radicals by the decomposition of initiator governs the rate of initiation and starts the growth of the macromolecule. The rate of initiation is known to be a function of the initiator efficiency (f), the initiator decomposition constant (k ) and the initiator concentration ([I]) and can be expressed by the following equation... 

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