Isobaric decomposition mode

The value of the molar enthalpy, A Hf/a, for the isobaric decomposition mode does not depend on partial pressure of the excess of gaseous product in the system, i.e., for any magnitude of... 

The ratio of the E parameters or molar enthalpies for the isobaric and equimolar decomposition modes satisfies the condition ... 

Different Decomposition Modes As follows from the above kinetic equations (Sect. 3.6), the presence of a gaseous product in the reactor should cause variations of the A and E parameters in full conformity with Eq. 12.1. This can be shown using the example of the decomposition of a binary substance into two products in the equimolar and isobaric modes, when one of the products (A) is a low-volatility one. 

These achievements can he considered as a reliable confirmation of the CDV mechanism underlying the studies described. New trends have been revealed in the course of these studies, such as deceleration of the decomposition upon melting of the reactant, increase in the enthalpy of the reaction with temperature (for decomposition reactions yielding a solid product), correlation of the decomposition temperature with the molar enthalpy and existence of two basic decomposition modes (equimolar and isobaric). 

In order to increase the possibility of collisional activation, the current trend is to develop this mode (on universally accessible conventional geometry instruments), utilizing the detection of decomposition produced in the first FFR by the B/E linked scan method. Nevertheless, although the resolution of fragment ions is better in this mode, that of precursor ion resolution remains mediocre and does not lead to as good a separation of isobaric ions as in the case of MIKE mode. ... 

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

The next step in the calculation of absolute decomposition rates with Eqs. 3.14 and 3.16 consists in determining the equilibrium pressures of the products, Pa and Pb, through the reaction equilibrium constant and the corresponding ther-mod3mamic functions (the entropy and the enthalpy). The mode, equimolar or isobaric, in which the reactant is decomposing, should also be taken into account. 

Equimolar and Isobaric Modes These key concepts were introduced into the kinetics of decomposition reactions more than 20 years ago [24]. Equimolar is the mode in which the actual pressure of the primary gaseous product in the reactor jg lo gj- than its equilibrium value (Peqp), i.e., P < Peqp. 

This assumes not only the initial absence of the product in the reactor, but also that the product cannot accumulate during the course of decomposition. In the isobaric mode, the actual pressure of a gaseous product in the reactor exceeds by far its equilibrium value, i.e., p = >> Pgqp, and, significantly, remains constant during the course of measurement (P = = const). 

Similar discontinuities in Arrhenius plots are observed in thermal analysis (TA) as well, in particular, in the dehydration of crystalline hydrates performed in humid air. For illustration. Fig. 3.2 reproduces an Arrhenius plot for the dehydration of calcium oxalate monohydrate in an air flow, carried out under non-isothermal conditions by Dollimore et al. [28]. The equilibrium pressure of water vapour Pgqp measured at temperatures of up to 400 K and comparatively moderate decomposition rates turns out to be lower than its partial pressure in air which implies that the decomposition occurs in the isobaric mode. Above 400 K, the equilibrium pressure of H2O becomes higher than p with the process becoming equimolar. The slope of the plot decreases to one half of its former value in full agreement with theory (see Sect. 3.7). 

The equations presented in Tables 3.1 and 3.2 permit the estimation of both the absolute values of parameters A and their ratio for the isobaric and equimolar modes of decomposition. This ratio has the same form irrespective of the actual decomposition conditions (vacuum or foreign gas environment) ... 

The decomposition rate in the isobaric mode, Jg, other factors being equal, is inversely related to the magnitude (Pg ) / , i.e.. 

The final values of the molar enthalpy (parameter E) for decomposition of CaCOs, SrCOs, and BaCOs in the equimolar and isobaric modes are summarized in Table 5.8. The mean value of the ratio is 1.98 0.03, which... 

Table 5.8 Experimental values of the E parameter for the decomposition of carbonates in the isobaric [9] and equimolar [17, 23] modes...

The T-S effect becomes apparent under extreme conditions of such kind. The temperature for experiments on the T-S effect is chosen to be much higher than temperatures typical for usual experiments on the decomposition kinetics in the absence of an excess of gaseous product. For crystalline hydrates this excess of temperature may reach 30-50 K, and for calcium carbonate, 100-150 K. This is because the decomposition in the isobaric mode is slower than in the equimolar mode. However, for initial points of the T-S curve corresponding to the absence of gaseous product or to a very low pressure of this gaseous product, this temperature is obviously much higher than the optimal value. That is why self-cooling appears to be well above the common value. 

Confirmation of the CDV Mechanism The most important result following from the analysis of the material presented in Parts I and II of this book is the confirmation of the CDV mechanism, which provides the basis for the thermochemical approach. The major arguments confirming this mechanism are listed in Table 13.1. Some of the arguments result from the effects discovered experimentally, and some are predicted from theory. Among the latter are the increase of the reaction enthalpy with temperature (for decompositions with formation of a solid product) the deceleration of the decomposition rate during reactant melting, and the peculiarities of the A and E parameters in the isobaric mode of decomposition. 

Experimental The kinetics and mechanism of the dehydration of kaolinite, muscovite, and talc was studied by L vov and Ugolkov within the framework of the CDV mechanism [70]. The main goal of that study was determination of the enthalpy of decomposition by the third-law method in a high vacuum (equimolar mode) and in the presence of water vapour (isobaric mode). In the isobaric mode, the measurements were performed in air, to eliminate or minimize the effect of self-cooling on the results (see Sect. 15.4). 

Table 16.32 Average values of the reaction enthalpy and the E parameter for the equimolar and isobaric modes of clay decompositions Reactant Primary Products of Decomposition...

Invariance of the E parameter under pressure of gaseous products in the isobaric mode of decomposition Quantitative 5.5... 

Determination of the molar enthalpies of decompositions for hydrates and carbonates in the isobaric mode in air or inert gas 15.5... 

A.6. Perform structural analysis based on a steady-state model and evaluate the possibilities for decomposition of the control problem. To simply this step, we assume that the pressure and temperature control loops are essentially decoupled from the plant holdups (integrating modes), the compositions, and the liquid flows. If this assumption is approximately valid, we can analyze a core plant model ( core model ) that comprises the reactor, flash unit, and recycle tank—all assumed to operate isothermally and isobarically (see Fig. H.5). Thus, the approximate plant model consists only of material balances but includes the key flows, levels, and compositions. This type of approach, in which temperatures and pressures are assumed to remain constant at their nominal values, was employed by Robinson et al. (2001) in their analysis of a similar plant. 

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