Hydrogen isotope effects, thermodynamics

The Titanium-Molybdenum-Hydrogen System Isotope Effects, Thermodynamics, and Phase Changes... 

A physical implication of this assumption is that the occurrence of isotopic substitution in one of the positions of XLm has no effect on the exchange equilibrium of any of the other positions, i.e. the exchange behaviour of the molecule XLm is equivalent to m molecules of a hypothetical solute X L containing one hydrogen nucleus per molecule (Block and Gold, 1959). In other words, thermodynamic secondary hydrogen isotope effects are assumed to be absent. 

Table 10.2. These results can be interpreted either as the kinetic effects measured for a single-step proton transfer or as the inverse thermodynamic isotope effects in fast preequilibria [5]. Unfortunately, in contrast to the isotope effects measured for classical hydrogen bonds [24], the effects of denterinm on the thermodynamics of dihydrogen bonding are still nnknown.

The natural cycles of the bioelements carbon, oxygen, hydrogen, nitrogen and sulphur) are subjected to various discrimination effects, such as thermodynamic isotope effects during water evaporation and condensation or isotope equilibration between water and CO2. On the other hand, the processes of photosynthesis and secondary plant metabolism are characterised by kinetic isotope effects, caused by defined enzyme-catalysed reactions [46]. 

Pressure-composition-temperature and thermodynamic relationships of of the titanium-molybdenum-hydrogen (deuterium) system are reported. 0-TiMo exhibits Sieverts Law behavior only in the very dilute region, with deviations toward decreased solubility thereafter. Data indicate that the presence of Mo in the 0-Ti lattice inhibits hydrogen solubility. This trend may stem from two factors for Mo contents >50 atom %, an electronic factor dominates whereas at lower Mo contents, behavior is controlled by the decrease in lattice parameter with increasing Mo content. Evidence suggests that Mo atoms block adjacent interstitial sites for hydrogen occupation. Thermodynamic data for deuterium absorption indicate that for temperatures below 297°C an inverse isotope effect is exhibited, in that the deuteride is more stable than the hydride. There is evidence for similar behavior in the tritide. 

The numerical factors in these equations are statistical they correspond to differences in the number of the relevant hydrogen nuclei. The factor consisting of a power of l represents a thermodynamic secondary isotope effect. 

Many of the thermodynamic and transport properties of liquid water can be qualitatively understood if attention is focused on the statistical properties of the hydrogen bond network [9]. As an example, let us observe the temperature dependence of density and entropy. As temperature decreases, the number of intact bonds increases and the coordination number is closer to the ideal value 4. Because of the large free volume available the temperature decrease is associated with an increase of the local molecular volume. This effect superimposes of course to the classical anharmonic effects which dominate at high temperature, when the number of intact bonds is smaller. The consequence of both effects is a maximum on the temperature dependence of the liquid density. This maximum is actually at 4°C for normal water and 11 °C for heavy water. Such a large isotopic effect can also be understood because the larger mass of the deuterium makes the hydrogen bonds more stable. 

Part V is devoted to the study of H transfers in organic and organometallic reactions and systems. In Ch. 18 Koch describes kinetic studies of proton abstraction from CH groups by methoxide anion, of the reverse proton transfer from methanol to hydrogen bonded carbanion intermediates, and of proton transfer associated with methoxide promoted dehydrohalogenation reactions. Substitutent effects, kinetic isotope effects and ah initio calculations are treated. Of great importance is the extent of charge delocalization in the carbanions formed which determine the kinetic and thermodynamic acidities. 

Chandra, D., et al.. Vanadium Hydrides at Low and High Pressure, Final Report to Tritium Science and Engineering Group, 2006, Los Alamos National Laboratory. Luo, W.R, Clewley, J.D. and Flanagan, T.B., Thermodynamics and isotope effects of the vanadium-hydrogen system using differential heat conduction calorimetry. Journal of Chemical Physics, 1990, 93(9) p. 6710-6722. 

Since these first reports, Iwahara and other investigators have studied the conductivities (both ionic and electronic), conduction mechanism, deuterium isotope effect, and thermodynamic stability of these materials. The motivation for most of this work derives from the desire to utilize these materials for high temperature, hydrogen-fiieled solid oxide fuel cells. In a reverse operation mode, if metal or metal oxide electrodes are deposited onto a dense pellet of this material and heated to temperature T, the application of an electric potential to the electrodes will cause a hydrogen partial pressure difference across the pellet according to the Nemst equation ... 

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