Absolute Rates of Decomposition

Decomposition in Vacuum Substitution of the quantities P and Pg into Eqs. 3.14 and 3.16 yields the final expressions for calculation of the absolute rates of decomposition. Thus, for the decomposition of reactant R into volatile gaseous products A and B in accordance with reaction (3.10)  

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  

Relation Between the Quantities k and J To compare the Arrhenius equation with the Langmuir vaporization equations, consider first how the rate constant k is related to the absolute decomposition rate J. For the steady-state 

Equation 3.31 was proposed by Roginsky and Schultz [29] to describe the kinetics of a reaction at the stage where its rate slows down as a result of the decreasing crystal surface area. Using the relations connecting the mass (m), radius 

There is an essential difference between the decomposition rates expressed by the quantities J and k. Unlike J, which does not depend on the particle size, k is inversely proportional to the initial dimensions of the particle. For pro = 1 (e.g., for p = 2,000 kg m and rg = 0.5 mm = 5 x 10 m), the rates J and k are numerically equal. The difference between these rates increases proportionately with increasing size and density of the particles. Equation 3.32 permits conversion from relative values of the rate constants k expressed in per second to the absolute rates J in units of kg m s. This opens up an attractive possibility for the interpretation of data obtained by traditional measurement of the a—t kinetic curves in terms of the Langmuir vaporization equations. 

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The method of absolute rate of decomposition has appeared [51[. Substantiation of the equimolar and isobaric modes of evaporation [52]. 

As follows from the consideration of the third-law method (Chapter4), its use for determining the reaction enthalpy requires estimation of the equivalent pressure Peqp of the gaseous product under the conditions of free-surface vaporization of the reactant. This, in turn, involves determination of the absolute rate of decomposition J (kg m and, hence, of the effective surface area of the decomposing sample. This problem, as applied to crystals, powders, and melts, is discussed below. 

Crystals For crystals, or pressed materials with a very low porosity, the effective surface area can be readily determined from the known sample geometry. It is convenient to use for this purpose an optical microscope with a scale and magnification of 20-30. The absolute rate of decomposition is evaluated by dividing the change in sample mass per unit time. Am/At, measured under isothermal conditions, by the area of the external surface of the crystal at the instant of the measurement Sn... 

An experimental check of these conclusions showed that the apparent absolute rate of decomposition of powders (Jp ), related to the external surface area of a powder pellet, is always higher than that of crystals (Jc). It was also found that the difference between the decomposition rates is independent of temperature, residual air pressure in the reactor, sample mass and powder particle size. The mean value of Jp /Jc was 2.8 0.4. This value somewhat exceeds the theoretical estimate, which may be due to the rough external surface of the powder. Evidently, the area of a pimpled surface formed by spherical particles should be at least twice that of the flat surface. 

In this monograph, the kinetics of carbonate decompositions have been considered in several sections concerning the formation of oversaturated vapour and nucleation (Sect. 2.4), the structure of the solid product (Sect. 2.6), the influence of the reaction mode and stoichiometry on the molar enthalpy (Sect. 5.4), the experimental estimation of the self-cooling (Sect. 6.3), the T-S effect (Sect. 7.3), the variation of the enthalpy of decomposition with temperature (Sect. 8.2), the compensation effect (Chapter 12), and the determination of the absolute rates of decomposition of single crystals and powders in a vacuum and in air (Sects. 15.1 and 15.5). 

Relationship between the rate constant k and the absolute rate of decomposition J Quantitative 3.7... 

This success would be impossible without a new methodology of thermochemical studies, based on the third-law method, and without certain additional techniques (such as measurements of the absolute rates of decomposition for powders and melts, and determinations of the molar enthalpies of decompositions in the excess of gaseous product) that have greatly improved the precision and accuracy of measurements and simplified and extended the current thermal methods used to study decomposition kinetics (Table 17.2). 

Measurement of the absolute rates of decomposition for powders and melts 15.1... 

Dinitrogen pentoxide is readily soluble in absolute nitric acid and chlorinated solvents. The polarity of the solvent has a significant effect on the rate of decomposition in solution. The rate is fastest in nonpolar solvents like chloroform and slower in polar solvents like nitromethane. ° The decomposition rate for solutions of dinitrogen pentoxide in nitric acid is very slow and these solutions are moderately stable at subambient temperatures. ... 

The absolute and relative rates of decomposition of tcrt-butyl phenylperacetates were measured in CDCI3 at 60, 70, 80, 90, 100 and 110°C and Hammett correlations were obtained (Table 3). An Eyring plot gave the activation parameters (Table 4). 

Relative rates of decomposition at 35°. (Absolute rates calculated by the method of initial Blopes.)... 

Examples have not infrequently been found of reactions which involve the intervention of some impurity in the system, not at first imagined to be playing any part in the chemical change. For example, the rate of decomposition of hydrogen peroxide in aqueous solution is very variable, and Rice and Kilpatrick traced the cause of this behaviour to the fact that the decomposition is mainly determined by the catalytic action of dust particles. As a result, the view has sometimes been held that pure substances are in general very unreactive, and that velocity measurements have no absolute significance, because the reaction mechanism is quite different from what it appears to be, and involves the participation of accidental impurities. Among such impurities water occupies the most prominent position. 

Another example of a reaction nearly independent of pressure in this way is the catalytic decomposition of hydrogen iodide on the surface of a heated gold wire. X The initial pressure of the gas can be varied from 100 mm. to 400 mm. with a resulting change in the absolute rate of reaction which amounts to about 45% only instead of 400%. 

According to the absolute rate theory, the rate of the overall reaction corresponding to eqn. (126) is equal to the rate of decomposition of the activated complex corresponding to the highest activation barrier. 

Martin et al. (1989) studied the oxidation of HMSA by Fenton s reagent and investigated the decomposition of both hydrogen peroxide and HMSA. They determined an estimate of the absolute rate of reaction between HMSA and hydroxyl radicals. The decomposition of hydrogen peroxide follows the first-order kinetics and can be described as follows ... 

The rate of decomposition of hydrogen peroxide by colloidal platinum has been made use of in determining the absolute and relative influences of different protective colloids upon the colloidal metal,2 the times required for the decomposition of a definite percentage of the peroxide under varying conditions being noted. 

When an explosive slowly decomposes, the products may not follow the previously described hierarchy or be at the maximum oxidation states. The nitro, nitrate, nitramines, acids, etc., in an explosive molecule can break down slowly. This is due to low-temperature kinetics as well as the influence of light, infrared, and ultraviolet radiation, and any other mechanism that feeds energy into the molecule. Upon decomposition, products such as NO, NO2, H2O, N2, acids, aldehydes, ketones, etc., are formed. Large radicals of the parent explosive molecule are left, and these react with their neighbors. As long as the explosive is at a temperature above absolute zero, decomposition occurs. At lower temperatures the rate of decomposition is infinitesimally small. As the temperature increases, the decomposition rate increases. Although we do not always, and in fact seldom do, know the exact chemical mechanism, we do know that most explosives, in the use range of temperatures, decompose with a zero-order reaction rate. This means that the rate of decomposition is usually independent of... 

The photolysis of aryl azides in low-temperature matrices yields triplet (ground) state nitrenes which have been identified by and absorption spectroscopy. Dinitrenes and trinitrenes have also been reported in the solid-state photolysis of di- and triazides. Quantum yields of photolysis of some aromatic azides are listed in Table 21 and it appears that nitrenes are produced in solution, at room temperature, as well. The lifetimes of some aromatic nitrenes and the absolute rates of some of their reactions have been measured . Some interesting features of photolytic azide decompositions will now be briefly described. 

In so far as the rate of formation of radicals reflects their stability or reactivity the findings of Hart and Wyman are instructive. In carbon tetrachloride the rate of decomposition of benzoyl peroxide was twice as fast as that of biscyclopropanoyl peroxide. Ingold and coworkers have found that in the photodecomposition of benzoyl and biscyclopropanoyl peroxides, in carbon tetrachloride at 298 K, the phenyl radicals produced reacted faster (7.8 x 10 M s ) than the cyclopropyl radicals (1.5 X 10 M s ). These results are consistent with C-H bond dissociation energies for benzene (llOkcalmol) and cyclopropane (106kcal mol ) which implies that the cyclopropyl radical should be less reactive than the phenyl radical. In subsequent work they also showed that at ambient temperatures radical reactivities decreased along the series /c = Ph > (Me)2 C=CH > cyclopropyl > Me. Table 4 records the absolute rate constants for the reaction of these radicals with tri-n-butylgermane. 

In relating transition state structure and behaviour to reactivity, transition state theory relies on two key assumptions. These are that the absolute rate of reaction depends upon the rate of decomposition of the transition state, and that any transition state is in quasiequilibrium with its corresponding reactants. Hence, if we consider the most rudimentary of reaction schemes (Figure 8.53, Scheme 8.17), then a simple rate equation may be devised in which rate of formation of product P obeys... 

Third, these equations permit the calculation of the absolute rates of a process, a possibility that had been believed unrealizable before their first application in 1981 to the kinetics of solid decomposition [25], The interest in theories of the transition state and of the activated complex was primarily stimulated by the possibility of calculating absolute reaction rates, although the attempts to use them in studies of heterogeneous processes met with only limited success [1, 2]. In contrast, the first comparison of theoretical with experimental values of the A parameters performed within the framework of Langmuir vaporization equations was much more successful [25]. 

Table 15.1 Absolute rate of CaCOs decomposition in air at 995 K (crystal mass 20 mg...

The approach presented here does not pay attention to which degree of freedom of an activated complex leads to its decomposition in either direction. In particular, not only oscillatory, but also translational, rotary and electronic degrees of a freedom are responsible for the decomposition of an activated complex. That is why one of the tasks of the absolute rates of reactions theory is determination of the degree of freedom for the motion of the... 

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

Hydroxyurea [127-07-1] M 76.1, m 70-72 (unstable form), m 133-136°, 141 (stable form), pK 10.6. Recrystallise from absolute EtOH (lOg in 150mL). Note that the rate of solution in boiling EtOH is slow (15-30 min). It should be stored in a cool dry place but some decomposition could occur after several weeks. lOrg Synth Coll Vol V 645 1973.] It is very soluble in H2O and can be crystd from Et20. [Acta Chem Scand 10 256 1956.]... 

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