Apparent Exceptions to the Third Law

Several cases exist in which calculations of the entropy change of a reaction from values of the entropy obtained from thermal data and the third law disagree with values calculated directly from measurements of AH and determinations of AG from experimental equilibrium constants. For example, for the reaction 

a large discrepancy exists between the two entropy values. 

A satisfactory explanation for this discrepancy was not available until the development of statistical thermodynamics with its methods of calculating entropies from spectroscopic data and the discovery of the existence of ortho- and parahydrogen. It then was found that the major portion of the deviation observed between Equations (11.24) and (11.25) is from the failure to obtain a tme equilibrium between these two forms of H2 molecules (which differ in their nuclear spins) during thermal measurements at very low temperatures (Fig. 11.4). If true equilibrium were established at all times, more parahydrogen would be formed as the temperature is lowered, and at 0 K, all the hydrogen molecules would be in the 

When the corrections for ortho/parahydrogen are applied to Equation (11.24), the value obtained is —163.2 JmoP which is in agreement with the equilibrium value. Most recent critical tables list 6m 29S corrected for the effects discussed here. 

With the development of statistical thermodynamics and the calculations of the entropies of many substances from spectroscopic data, several other substances in addition to hydrogen have been found to have values of molar entropies that disagree with those calculated from thermal data alone [13] (Table 11.1). The discrepancies can be accounted for on the assumption that even near absolute zero not all molecules are in the same state and that tme equilibrium has not been attained. For CO, COCI2, N2O, NO, and CIO3F, the close similarity in the sizes of the atoms makes different 

---