The Self-cooling Effect

The mean value of the E parameter at low dehydration temperatures (<300K), applicable to eight of the reactants, was 49 10 kJ moP. This magnitude exceeds the enthalpy of evaporation of free water at 298K(Afl298 = 44.0kJ mol ). However, for three reactants the E parameter turned out to be lower than 44 kJ moP. This indicates an obvious measurement error, associated, most likely, with the self-cooling effect. If it is assumed that this systematic error affects both parameters, E and E equally then their ratio is close to the true value. 

If the only cause of overestimation of the experimental values Eexpt, calculated by the third-law method, is the self-cooling effect, then its magnitude can be easily determined. If it is also assumed that the E magnitude at the lower temperature is free of this effect (i.e., that the sample temperature, Tg, is equal to the furnace temperature, Tf) and corresponds to the true value of the E parameter, Etrue, then it becomes possible to determine the actual value of sample temperature for any higher decomposition temperature. This temperature is equal to ... 

Fig. 7.6). At higher magnitudes of e the maximum disappears and only a small distortion of the J = /(PcOs) curve is observed. The self-cooling effect appears to be insignificant and, thus, some increase of CaCOs temperature... 

Historically the underestimation of the role and magnitude of the self-cooling effect in kinetic studies of thermal decomposition has turned out to be one of the most important reasons which hindered interpretation of the T-S effect and, to some extent, the compensation effect, and promoted some misconceptions [19, 26-28], based on the confidence in infallibility of the second-law method in determination of thermochemical parameters (the enthalpy and entropy for decomposition reactions). 

Table 16.17 presents also the A H /i/ values determined in the papers cited by the second-law method. These values are less reliable than those determined by the third-law method and are lower in seven cases out of ten. The difference in the A H /v values for BN reaches 60%. This systematic underestimation may be attributing to the self-cooling effect, which is particularly pronounced... 

Inclusion of the self-heating effect yields an additional temperature dependence of the thermal time constant. Differences in the time constants for heating and cooling are evident, and the real thermal time constant can be observed only in the cooling cycle with 4eat = 0. 

Somorjai and Lester [40] detail some of the problems likely to be encountered in vaporization measurements. These include (i) the effects of variations of with crystal surface, which are particularly important in the use of polycrystalline samples (ii) the self-cooling resulting from the endothermic vaporization, which may cause temperature gradients in the sample, especially at high fluxes and (iii) the complications caused by vapour-vapour collisions when measurements are made in a significant partial pressure of vapour. 

Underestimated because of the possible catalytic effect of H2O impurity Overestimated because of the strong self-cooling effect in vacuum The E values in a and b cases are excluded from calculation... 

Interpretation of Unusual Effects Modelling of the temperature distribution has allowed, for the first time, some unusual effects observed for powder decomposition to be explained quantitatively. One of these is associated with an independence of the overall decomposition rate on the powder mass, which seems to be inexplicable at first thought. However, when the self-cooling of the sample is taken into account, this effect seems obvious. Irrespective of the total number of layers, i.e., of the powder mass, the effective number of layers Ue, involved in the decomposition process should remain practically constant (the height of powder filling is assumed to be much less than its diameter). 

The above assumption, that self-cooling is the only cause of overestimation of the experimental values Texpt, is valid only for reactants decomposing to gaseous products. For decompositions with formation of a solid product, there is an additional reason for overestimation related to the condensation effect (Sect. 8.2). Therefore, it is more appropriate to call this combined effect the apparent self-cooling effect. 

The model suggested by Bertrand et al. [11-13] assumed the existence of a spatial gradient of temperature in the reaction zone. In this model the abnormal rise of the dehydration rate with was attributed to the increase of heat transfer from the furnace to the self-cooled reactant. Model calculations and experiments on the evaporation and condensation of ethanol and water vapours provided a convincing proof of this mechanism. In the experiments [13], the temperature of the evaporating liquids turned out to be much lower than that of the heater. For instance, for ethanol the difference from the thermostat temperature (300 K) was as much as 45 K or 15%. However, this model remained unclaimed during the following 20 years of studies on the T-S effect. Such a considerable difference in temperatures between the crystalline hydrate and the furnace seemed improbable to the majority of researchers. 

Unresolved Problems Against the background of above listed achievements, there are still some unanswered questions that appear in the course of the research. These include, in particular, the mechanism of condensation energy transfer from a low-volatility product to a reactant, and the influence of the symmetry of the reactant crystal structure on the composition of the gaseous decomposition products. It would be worthwhile to perform a more thorough analysis of the dependence of the t coefficient and the sizes of the condensate particles on the vapour oversaturation of the low-volatility product, as well as of the relative contributions of the condensation and self-cooling effects to the underestimation of enthalpies determined by the second-law and Arrhenius plot methods. 

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). 

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