The Uncertainties in Thermochemical Data

The random uncertainties in thermochemical measurements have been discussed by several authors, notably Rossini and Deming [26], Rossini [27], and Olofsson [28], The accepted thermochemical convention [29], summarized next, follows the procedure suggested in the first two of these publications. 

Assuming that only random errors affect the laboratory determinations of a given reaction enthalpy, the overall uncertainty interval associated with the mean value (ATH) of a set of n experiments is usually taken as twice the standard deviation of the mean (erm)  

Equation 2.26 must be used to derive the overall uncertainty of the enthalpy of any reaction, calculated from the standard enthalpies of formation of reactants and products. 

Equation 2.26 is also used to evaluate the uncertainty of a standard enthalpy of formation, calculated from a reaction enthalpy. Consider, for instance, a selected value for the standard enthalpy of combustion of ferrocene, A CH° [Fe(r 5-C5H5)2, cr] = —5891.5 4.2 kJ mol-1 [31], 

Assigning uncertainties to experimental (or even theoretical [33]) results is a very important issue and deserves careful consideration. As already pointed out, this is not observed in many recent publications, hindering (to some extent) a reliable assessment of the data given there. If the accepted rules are followed, we may draw useful conclusions from the error bars. For instance, when the difference between two literature values for the enthalpy of the same reaction is larger than the sum of the respective uncertainties, it is likely that at least one of the results is affected by systematic errors. This is the case, for example, of two literature values for Ac//0[Fc(q5-C51 (5)2, cr], —5891.5 4.2 kj mol-1 and —5877.7 5.0 kJ mol-1 [31 ]. On the other hand, if the difference between a pair of values is smaller than the sum of the uncertainties, as in Af77°(LiOC2H5, cr), —477.1 4.0 kJ mol-1 and —473.1 2.5 kj mol-1 [25], we may conclude that systematic errors are probably absent in both results. 

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Nevertheless, I believe that this property of experimental temperature brackets of providing very tight "windows for free energies of reaction will play a major role in reducing the uncertainties in thermochemical data. This will be discussed further in the next section. 

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