Uncertainty thermochemical data

It is somewhat disappointing to realize that the thermochemistry of germanium, tin and lead organometallic compounds is still at the level achieved ten years ago, in contrast to the considerable recent efforts to probe the energetics of the silicon analogues. The data analysis in the previous sections shows that many key values are either missing or require experimental confirmation. To a certain extent, an overall discussion of the thermochemical data for Ge, Sn and Pb is therefore hindered by the probable inaccuracies and the uncertainties that affect those values. 

A significant contribution to the uncertainty interval assigned to the O-H bond dissociation enthalpy in benzoic acid comes from the estimate of the activation enthalpy for the radical recombination. The experimental determination of this quantity is not easy because diffusion-controlled recombination rate constants are very high (109 mol-1 dm3 s 1 or larger) [180]. Therefore, most thermochemical data derived from kinetic experiments in solution rely on some similar assumptions. 

Eventually, a polymeric substance of the form -(As GaCH2)w- may be formed. Adduct formation is thought to be responsible for the observed lower decomposition temperature of Ga(CH3)3 in the presence of AsH3 relative to Ga(CH3)3 in a carrier gas (120, 121). Furthermore, with AsH3 and D2, the primary reaction product appears to be CH4 rather than CH3D, as expected on the basis of the free-radical mechanism (equations 16a-f). However, the formation of CH4 may be due to reactions of Ga(CH3)t and CH3 with adsorbed AsH v species (122). Estimates indicate that the adduct is too unstable to play a major role in the growth chemistry (129), but this conclusion is subject to uncertainties in the thermochemical data base. 

Gaussian-2 (G2) theory Ideally, a sucessful method for computation of thermochemical data has several features (1) it should be applicable to any molecular system in an unambiguous manner, (2) it must be computationally efficient so that it can be widely applied, (3) it should be able to reproduce known experimental data to a prescribed accuracy, and (4) it should give similar accuracy for species for which the data are not available or for which experimental uncertainties are large. The Gaussian-n methods were developed with these objectives in mind. Gaussian-1 (Gl) theory was the first in this series.27 28 We will not cover Gl theory in this chapter because it was replaced by G2 theory, which eliminated several deficiencies in Gl, and because G2 is currently the most widely used method of this series. 

Often there are cases where the submodels are poorly known or misunderstood, such as for chemical rate equations, thermochemical data, or transport coefficients. A typical example is shown in Figure 1 which was provided by David Garvin at the U. S. National Bureau of Standards. The figure shows the rate constant at 300°K for the reaction HO + O3 - HO2 + Oj as a function of the year of the measurement. We note with amusement and chagrin that if we were modelling a kinetics scheme which incorporated this reaction before 1970, the rate would be uncertain by five orders of magnitude As shown most clearly by the pair of rate constant values which have an equal upper bound and lower bound, a sensitivity analysis using such poorly defined rate constants would be useless. Yet this case is not atypical of the uncertainty in rate constants for many major reactions in combustion processes. 

Curves plotted for AH° conv. hyd. and ionic radii given in Tables 5 and 6, and in col. 2 of Table 1 are shown in Fig. 4 for both alkali cations and halide anions. The uncertainty in the thermochemical data is taken as 0.5 kcal and the uncertainty in ionic radii is based on deviations from additivity of r0 values. From these curves A(AH° conv. hyd.) can be estimated and in Fig. 5 these values halved are plotted against (R- -a) 3. This curve becomes linear for large (i a)-3 values and this supports the use of the model based on charge-quadrupole interactions and assumptions concerning differences in kinetic contributions to the internal energy (39). 

In alkaline media it is reported that the reaction of e-q with Zn(II) is reversible and that the Zn(I) is hydrolyzed (142). Unfortunately, because of uncertainty regarding the degree of hydrolysis in both oxidation states, no thermochemical data could be derived. Ershov and Sukhov used periodicity arguments to estimate p/fa = 7-9forZn+ (117). 

The enthalpy change on formation of Portland cement clinker cannot be calculated with high precision, mainly because of uncertainties associated with the clay minerals in the raw material. Table 3.1 gives data for the main thermochemical components of the reaction, almost all of which have been calculated from a self-consistent set of standard enthalpies of formation, and which are therefore likely to be more reliable than other values in the literature. The conversion of the clay minerals into oxides is an imaginary reaction, but valid as a component in a Hess s law calculation. Few reliable thermochemical data exist for clay minerals those for pyrophyllite and kaolinite can probably be used with sufficient accuracy, on a weight basis. 

Gaydon gives 3 5 ih0 2 eV from thermochemical data. There is some uncertainty about the heat of sublimation of solid Lil... 

The major difference between this mechanism and the one given in (5) is that HOx radicals are not consumed in (15). The major weakness of this scheme is that the best available thermochemical data on sulfur species [8] indicates that Reaction (13) is endothermic by approximately 6 kcal mol . This is an uncomfortably large figure but the uncertainty in the heat of formation of HOSO2 is probably large enough that one is not convinced that (15) is incorrect. 

There are no thermochemical data for the bromophenols. For the iodophenols, there are enthalpy data only for the solid phases. Our estimation procedure, using the enthalpy of formation of iodobenzene and the OH/H exchange increment, predicts —86 kJ moG. How the iodophenols could be stabilized by ca 10 kJ moG is not clear, except that the experimental uncertainty is somewhat large and we know very little about the solid phase. 

One of the objectives of the NBA Thermochemical Data Base (TDB) project is to provide an idea of the uncertainties associated with the data selected in this review. As a rule, the uncertainties define the range within which the corresponding data can be reproduced with a probability of 95% at any place and by any appropriate method. In many cases, statistical treatment is limited or impossible due to the availability of only one or few data points. A particular problem has to be solved when significant discrepancies occur between different source data. This appendix outlines the statistical procedures which were used for fundamentally different problems and explains the philosophy used in this review when statistics were inapplicable. These rules are followed consistently throughout the series of reviews within the TDB Project. Four fundamentally different cases are considered ... 

The saturation index module would be the location for additional enhancements to the system to make it applicable to waters from formations of more complex mineralogy, to include uncertainty in the thermochemical data used, and perhaps to consider mineral reaction rates and water residence times. The direction of such enhancements are sketched below. 

The present saturation index module considers only minerals common in carbonate aquifers and assumes that water residence times are sufficient to assure mineral-water equilibria. The next step might consider geothermal systems of simple mineralogy. For this step the expert system might include various chemical geothermometers as indicators of analytical reliability. While high temperatures would promote the attainment of mineral-water equilibria, they would also add to the uncertainty in the thermochemical data used for modeling those equilibria. 

In principle, such an expert system could also consider the extent to which a wide variety of minerals would influence ground-water chemistry at various temperatures and reaction times, as well as the natural variability and experimental uncertainties associated with the thermochemical data used to model geochemical equilibrium. To develop a consensus in the geochemical community about the categories of information required to evaluate mineral reactivity and the properties appropriate for each of many minerals, would be a time consuming task. Thus, in the near future at least, such enhancements will probably be limited to consideration of tightly defined problems of simple mineralogy. 

From the inspection of reactions (3a), (4), (7) and (8), it follows immediately that the uncertainties on the standard enthalpies of formation of gaseous ions are determined by those affecting the thermochemical data for the relevant neutral species (molecules or free radicals) and the specific method used for ion generation. The uncertainty assigned to the standard enthalpy of formation of a gaseous ion is the root-sum-of-squares combination of the individual uncertainties of the various contributions." ... 

This paper gives thermochemical data for zirconium orthophosphate, its monohydrate and tetrahydrate and zirconium pyrophosphate and its dihydrate. The experimental and auxiliary data used to determine the enthalpy of formation of the various compounds was not presented by the authors. The data obtained in the study are given in Table A-18 and are compared, where possible, with the same data selected in the present review no uncertainties were given by [75FIL/CHE]. 

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