Hydrogen entropy

For those who are familiar with the statistical mechanical interpretation of entropy, which asserts that at 0 K substances are nonnally restricted to a single quantum state, and hence have zero entropy, it should be pointed out that the conventional thennodynamic zero of entropy is not quite that, since most elements and compounds are mixtures of isotopic species that in principle should separate at 0 K, but of course do not. The thennodynamic entropies reported in tables ignore the entropy of isotopic mixing, and m some cases ignore other complications as well, e.g. ortho- and para-hydrogen. 

As is suggested frequently , this term might well result from the restriction of the hydrogen bonding possibilities experienced by the water molecules in the first hydration shell. For each individual water molecule this is probably a relatively small effect, but due to the small size of the water molecules, a large number of them are entangled in the first hydration shell, so that the overall effect is appreciable. This theory is in perfect agreement with the observation that the entropy of hydration of a nonpolar molecule depends linearly on the number of water molecules in the first hydration shell ". ... 

If one would ask a chemist not burdened with any knowledge about the peculiar thermodynamics that characterise hydrophobic hydration, what would happen upon transfer of a nonpolar molecule from the gas phase to water, he or she would probably predict that this process is entropy driven and enthalpically highly unfavourable. This opinion, he or she wo ild support with the suggestion that in order to create room for the nonpolar solute in the aqueous solution, hydrogen bonds between water molecules would have to be sacrificed. 

Solubility in Water A familiar physical property of alkanes is contained m the adage oil and water don t mix Alkanes—indeed all hydrocarbons—are virtually insoluble m water In order for a hydrocarbon to dissolve m water the framework of hydrogen bonds between water molecules would become more ordered m the region around each mole cule of the dissolved hydrocarbon This increase m order which corresponds to a decrease m entropy signals a process that can be favorable only if it is reasonably... 

Polyamides. The next two compounds are the amide counterparts of the esters listed under item (4). Although the values of AH j are less for the amides than for the esters, the values of T j, are considerably higher. This is a consequence of the very much lower values of AS j for the amides. These, in turn, are attributed to the low entropies of the amide in the liquid state owing to the effects of hydrogen bonding and chain stiffness arising from the contribution of the resonance form... 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

This situation does not improve greatly with increasing temperature, because the entropy change is small. At 2000 K (1727°C) and 101.3 kPa (1 atm), the hydrogen mole fraction at equihbrium is 0.036 at 3000 K (2727°C) the hydrogen mole fraction is about 0.2 (154). 

The entropy value of gaseous HCl is a sum of contributions from the various transitions summarized in Table 4. Independent calculations based on the spectroscopic data of H Cl and H Cl separately, show the entropy of HCl at 298 K to be 186.686 and 187.372 J/(mol K) (44.619 and 44.783 cal/(mol K), respectively. The low temperature (rhombic) phase is ferroelectric (6). SoHd hydrogen chloride consists of hydrogen-bonded molecular crystals consisting of zigzag chains having an angle of 93.5° (6). Proton nmr studies at low temperatures have also shown the existence of a dimer (HC1)2 (7). 

Bond dissociation energies (BDEs) for the oxygen—oxygen and oxygen— hydrogen bonds are 167—184 kj/mol (40.0—44.0 kcal/mol) and 375 kj/mol (89.6 kcal/mol), respectively (10,45). Heats of formation, entropies, andheat capacities of hydroperoxides have been summarized (9). Hydroperoxides exist as hydrogen-bonded dimers in nonpolar solvents and readily form hydrogen-bonded associations with ethers, alcohols, amines, ketones, sulfoxides, and carboxyhc acids (46). Other physical properties of hydroperoxides have been reported (46). 

Various equations of state have been developed to treat association ia supercritical fluids. Two of the most often used are the statistical association fluid theory (SAET) (60,61) and the lattice fluid hydrogen bonding model (LEHB) (62). These models iaclude parameters that describe the enthalpy and entropy of association. The most detailed description of association ia supercritical water has been obtained usiag molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

Thermodynamic data on H2, the mixed hydrogen—deuterium molecule [13983-20-5] HD, and D2, including values for entropy, enthalpy, free energy, and specific heat have been tabulated (16). Extensive PVT data are also presented in Reference 16 as are data on the equihbrium—temperature... 

Values extracted and sometimes rounded off from tte tables of McCarty, Hord, and Roder, NBS Monogr. 168, 1981. This source contains an exhaustive tabulation of property values for botb tbe normal and tbe para forms of hydrogen, v = specific volume, mVkg h = specific enthalpy kj/kg s = specific entropy, kJ/(kg-K). 

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