First-order decomposition

Table B2.5.5. The photochemical decomposition of methyl radicals (UV excitation at 216 nm). ris tire wavenumber linewidth of the methyl radical absorption and /ris the effective first-order decay constant [54].

The concentration of nitromethane, CH3NO2, can be determined from the kinetics of its decomposition in basic solution. In the presence of excess base the reaction is pseudo-first-order in nitromethane. For a standard solution of 0.0100 M nitromethane, the concentration of nitromethane after 2.00 s was found to be 4.24 X 10 M. When a sample containing an unknown amount of nitromethane was analyzed, the concentration remaining after 2.00 s was found to be 5.35 X 10 M. What is the initial concentration of nitromethane in the sample ... 

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... 

Figure 6.1 Volume of nitrogen evolved from the decomposition of AIBN at 77°C plotted according to the first-order rate law as discussed in Example 6.1. [Reprinted with permission from L. M. Arnett, /. Am. Chem. Soc. 14 2021 (1952), copyright 1952 by the American Chemical Society.]...

Azobisnittiles are efficient sources of free radicals for vinyl polymerizations and chain reactions, eg, chlorinations (see Initiators). These compounds decompose in a variety of solvents at nearly first-order rates to give free radicals with no evidence of induced chain decomposition. They can be used in bulk, solution, and suspension polymerizations, and because no oxygenated residues are produced, they are suitable for use in pigmented or dyed systems that may be susceptible to oxidative degradation. 

Because the decomposition is first order, the rate of free-radical formation can be controlled by regulating the temperature equations relating half-life to temperature are provided in Table 7. These decomposition rates ate essentially independent of the solvent (73). 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

A cis-elimination mechanism has been postulated for this decomposition which foUows first-order kinetics (120). The rate is accelerated by addition of lithium j iZ-butoxide [4111-46-0] and other bases, and by an increase in temperature (120). Pyrolysis of j iZ-butyUithium in the presence of added alkoxide is one-half order in alkyUithium and first order in alkoxide (120). Thermal decomposition of j iZ-butyUithium at 0.18% alkoxide at 25, 40, 50, and 60°C is 0.1%, 0.6%, 2.0%, and 6.8%/d, respectively (121). 

Dioxetanones decompose near or below room temperature to aldehydes or ketones (56). The decomposition reactions are weakly chemiluminescent Qc ca 10 ein/mol) because the products are poorly fluorescent. However, addition of 10 M mbrene provides 2iQc ca 10 ein/mol, and 2iQc on the order of was calculated at mbrene concentrations above 10 M after correcting for yield loss factors (57). The decomposition rates are first order ia... 

Decomposition of diphenoylperoxide [6109-04-2] (40) in the presence of a fluorescer such as perylene in methylene chloride at 24°C produces chemiluminescence matching the fluorescence spectmm of the fluorescer with perylene was reported to be 10 5% (135). The reaction follows pseudo-first-order kinetics with the observed rate constant increasing with fluorescer concentration according to = k [flr]. Thus the fluorescer acts as a catalyst for peroxide decomposition, with catalytic decomposition competing with spontaneous thermal decomposition. An electron-transfer mechanism has been proposed (135). 

Therefore, first-order, decomposition rates for alkyl hydroperoxides, ie, from oxygen—oxygen bond homolysis, are vaUd only if induced decomposition reactions... 

Although primary and secondary alkyl hydroperoxides are attacked by free radicals, as in equations 8 and 9, such reactions are not chain scission reactions since the alkylperoxy radicals terminate by disproportionation without forming the new radicals needed to continue the chain (53). Overall decomposition rates are faster than the tme first-order rates if radical-induced decompositions are not suppressed. 

Thermal decomposition of 00-acyl O-alkyl monoperoxycarbonates (22, R, = alkyl or aryl) yield first-order decomposition rates between those... 

The first-order decomposition rates of alkyl peroxycarbamates are strongly influenced by stmcture, eg, electron-donating substituents on nitrogen increase the rate of decomposition, and some substituents increase sensitivity to induced decomposition (20). Alkyl peroxycarbamates have been used to initiate vinyl monomer polymerizations and to cure mbbers (244). They Hberate iodine quantitatively from hydriodic acid solutions. Decomposition products include carbon dioxide, hydrazo and azo compounds, amines, imines, and O-alkyUiydroxylarnines. Many peroxycarbamates are stable at ca 20°C but decompose rapidly and sometimes violently above 80°C (20,44). 

Thermal stabihty of the foaming agent in the presence of high temperature steam is essential. Alkylaromatic sulfonates possess superior chemical stabihty at elevated temperatures (205,206). However, alpha-olefin sulfonates have sufficient chemical stabihty to justify their use at steam temperatures characteristic of most U.S. steamflood operations. Decomposition is a desulfonation process which is first order in both surfactant and acid concentrations (206). Because acid is generated in the decomposition, the process is autocatalytic. However, reservoir rock has a substantial buffering effect. 

Many researchers have correlated the overall decomposition as an nxh. order reaction, with most paraffins following the first order and most olefins following a higher order. In general, isoparaffin rate constants are lower than normal paraffin rate constants. The rate constants are somewhat dependent on conversion due to inhibition effects that is, the rate constant often decreases with increasing conversion, and the order of conversion is not affected. This has been explained by considering the formation of aHyl radicals (38). To predict the product distribution, yields are often correlated as a function of conversion or other severity parameters (39). 

First order decomposition was established for dimethyldiazirine (215) and ethylmethyl-diazirine (216). The activation energy is 139 kJ moF for (215) the half life at 100 °C is 97 h. On decomposition of (216) the products formed and their respective yields are as indicated. The products correspond qualitatively and quantitatively with the results of thermal decomposition of 2-diazobutane formed in situ in aprotic solvents. Analogous comparisons of decomposition products of diethyldiazirine, isopropylmethyldiazirine, n-butyl- and t-butyl-diazirine agree equally well 66TL1733). 

Kinetic investigations of alkylchlorodiazirine thermolysis were carried out in the gas phase 70JCS(A)1916). Chloromethyldiazirine (232) decomposition follows first order kinetics giving nitrogen and vinyl chloride, easily interpretable as isomerization of a carbene. 

Decomposition of more complex diaziriries follows first order kinetics also. Chlorophenyl-carbene adds to cyclohexene to give a norcarane derivative. Substituent effects of m-Cl, m-NOa or m-Me groups, as well as solvent effects, are small. Chlorotrichloromethyldiazirine yields tetrachloroethylene chlorocyclooctyldiazirine also leads to an alkene 74CJC246). 

Decompositions may be exothermic or endothermic. Solids that decompose without melting upon heating are mostly such that can give rise to gaseous products. When a gas is made, the rate can be affected by the diffusional resistance of the product zone. Particle size is a factor. Aging of a solid can result in crystallization of the surface that has been found to affect the rate of reaction. Annealing reduces strains and slows any decomposition rates. The decompositions of some fine powders follow a first-order law. In other cases, the decomposed fraction x is in accordance with the Avrami-Erofeyev equation (cited by Galwey, Chemistry of Solids, Chapman Hall, 1967)... 

Organic Solids A few organic compounds decompose before melting, mostly nitrogen compounds azides, diazo compounds, and nitramines. The processes are exothermic, classed as explosions, and may follow an autocatalytic law. Temperature ranges of decomposition are mostly 100 to 200°C (212 to 392°F). Only spotty results have been obtained, with no coherent pattern. The decomposition of malonic acid has been measured for both the solid and the supercooled liquid. The first-order specific rates at 126.3°C (259.3°F) were 0.00025/min for solid and 0.00207 for liquid, a ratio of 8 at II0.8°C (23I.4°F), the values were 0.000021 and 0.00047, a ratio of 39. The decomposition of oxalic acid (m.p. I89°C) obeyed a zero-order law at 130 to I70°C (266 to 338°F). 

Ammonium nitrate decomposes into nitrous oxide and water. In the solid phase, decomposition begins at about I50°C (302°F) but becomes extensive only above the melting point (I70°C) (338°F). The reaction is first-order, with activation energy about 40 kcal/g mol (72,000 Btii/lb mol). Traces of moisture and Cr lower the decomposition temperature thoroughly dried material has been kept at 300°C (572°F). All oxides of nitrogen, as well as oxygen and nitrogen, have been detected in decompositions of nitrates. 

Figure 13.6 shows the influence of temperature on specific volume (reciprocal specific gravity). The exaet form of the eurve is somewhat dependent on the crystallinity and the rate of temperature change. A small transition is observed at about 19°C and a first order transition (melting) at about 327°C. Above this temperature the material does not exhibit true flow but is rubbery. A melt viseosity of 10 -10 poises has been measured at about 350°C. A slow rate of decomposition may be detected at the melting point and this increases with a further inerease in temperature. Processing temperatures, exeept possibly in the case of extrusion, are, however, rarely above 380°C. 

The thermal decompositions described above are unimolecular reactions that should exhibit first-order kinetics. Under many conditions, peroxides decompose at rates faster than expected for unimolecular thermal decomposition and with more complicated kinetics. This behavior is known as induced decomposition and occurs when part of the peroxide decomposition is the result of bimolecular reactions with radicals present in solution, as illustrated below specifically for diethyl peroxide. 

The following mechanism has been postulated for the decomposition of ethane into ethylene and hydrogen. The overall rate expression is first order in ethane. 

Acetyiated castor oil is hydrolyzed for the manufacture of drying oils in kettles operated batchwise. Grummit and Eieming (1945) correlated the decomposition data on the basis of a first order reaction as ... 

The Cs structure and dimensions (Fig. 17.26b) were established by microwave spectroscopy which also yielded a value for the molecular dipole moment p. 1.72D. Other physical properties of this colourless gas are mp -115° (or -123°), bp -6°, A//f(g,298K) —34 10kJmol [or — 273kJmol when corrected for A//f(HF, g) ]. FCIO2 is thermally stable at room temperature in dry passivated metal containers and quartz. Thermal decomposition of the gas (first-order kinetics) only becomes measurable above 300° in quartz and above 200° in Monel metal ... 

Perchloryl fluoride is thermally stable up to about 400°. Above 465° it undergoes decomposition with first-order kinetics and an... 

The reverse reaction (formation of metal alkyls by addition of alkenes to M-H) is the basis of several important catalytic reactions such as alkene hydrogenation, hydroformylation, hydroboration, and isomerization. A good example of decomposition by y3-elimination is the first-order intramolecular reaction ... 

For the decomposition of N205 and other first order reactions of the type... 

It follows that the rate constant is 0.35/min the integrated first-order equation for the decomposition of N205 is... 

For the first-order decomposition of N2Os at 67°C, where k = 0.35/min, calculate... 

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