Phase relationships hydrides

Because these stability measurements pertain to the gas phase, it is important to consider the effects that solvation might have on the structure-stability relationships. Hydride affinity values based on solution measurements can be derived from thermodynamic cycles that relate hydrocarbon p T, bond dissociation energy and electrochemical potentials. The hydride affinity, AG, for the reaction... 

Bearing this correlation in mind, one can immediately say that the hydrides of Np, Pu and Am are rare-earth-like with wide cubic solid solution ranges up to H/M = 2.7-2.S and somewhat smaller lattice parameters. The hexagonal phase appears with regularity, unlike the behavior encountered for Ce, Pr and Nd. P-C-T data are not available for the Cm system and beyond, but relatively normal behavior is expected. As pointed out above, the large and simple lattices of the early rare earth and late-actinide hydride systems preclude f-f overlap. Since the actinide contraction is delayed as compared to the rare-earth contraction, phase relationships such as those seen for Gd hydride and beyond are not expected for the actinides. 

Thermodynamics of complex formation of silver with several ligands such amines,368 hindered pyridine bases,369 nitrogen donor solvents,370 and azoles371 have been carried out. Other studies include the secondary-ion mass spectra of nonvolatile silver complexes,372 the relationship between Lewis acid-base behavior in the gas phase and the aqueous solution,373 or the rates of hydride abstraction from amines via reactions with ground-state Ag+.374... 

Multilinear Regression Analysis. As an entry to the problem we have selected simple gas phase reactions involving proton or hydride ion transfer which are influenced by only a few effects and for which reactivity data of high accuracy are available. In these situations where a larger set of numerial data are available multilinear regression analysis (MLRA) was applied. Thus, the simplest mathematical form, a linear equation is chosen to describe the relationship between reactivity data and physicochemical factor. The number of parameters (factors) simultaneously applied was always kept to a minimum, and a particular parameter was only included in a MLRA study if a definite indication of its relevance existed. 

One of the most useful features of metal-hydrogen systems are their pressure-composition-temperature data, P-C-T. Such relationships for palladium-hydrogen are shown in Figure 1. For compositions and temperatures within the envelope, two solid phases coexist, as required by the phase rule. The lower hydrogen-content a-phase represents solution of hydrogen into the metal, and the higher hydrogen-content jS-phase is the hydride. Both a and (3 are... 

There are other types of equilibria, in addition to the invariant type, which can be deduced from Eq. 2.5. For example, when three phases of a two-component system are in equilibrium, such as with a closed vessel containing hydrogen gas in equilibrium with a metal and the metal hydride, immersed in a water bath, it is possible to change the value of just one variable (temperature or pressure or composition) without changing the number of phases in equilibrium. This is called univariant equilibrium (/ = 1). If the composition is held constant, temperature and pressure will have a fixed relationship in a univariant system. Hence, if the pressure of hydrogen gas in the vessel is increased slightly, the temperature of its contents remains the same as heat escapes through the vessel walls to the water bath. 

If the composition of hydrogen in this system were to be fixed at a lower concentration, such that there is but a single condensed phase comprised of the two components in equilibrium with hydrogen gas (i.e., a solid solution of metal and absorbed hydrogen gas, but no metal hydride), there will be two degrees of freedom (/ = 2). There is no fixed relationship between pressure and temperature at constant composition in such a system. Both temperature and hydrogen pressure may be varied, changing the absorption or desorption... 

Brinck T, Murray JS, Politzer P (1993) Molecular surface electrostatic potentials and local ionization energies of groups V-VII hydrides and their anions. Relationships for aqueous and gas phase acidities. Int. J. Quantum Chem. 48 73-88... 

Fig. 11.3. EquiUbrium relationship between the hydrogen pressure and the H/Pd ratio (n) in the metal. Shown are the domains of existence of the a and p palladium hydride phases. Reproduced...

Several investigators examined this relationship under extreme temperatures (20-1000 K), and as a probe for tunneling [26-28]. This isotopic relationship was also used in experimental and theoretical studies to suggest coupled motion between primary and secondary hydrogens for hydride transfer reactions, such as elimination in the gas phase, and in organic solvents [29, 30]. The power of the Swain-Schaad relationship is that it appears independent of the details of the reaction s potential surface and thus can be used to relate unknown KIEs (see Section 12.3.2). 

The equilibrium pressures (0.5—760Torr) of hydrogen existing above mixtures of lithium with lithium hydride (0.5—99 mol% LiH) sealed in iron capsules have been measured from 983 to 1176 K. The isotherms confirm the phase diagram to consist of two immiscible liquid phases with boundaries 25.2 and 98.4 mol% LiH at 983 K and 45.4 and 85.8 mol% LiH at 1176 K. For dilute solutions of lithium hydride in liquid lithium, the relationship between the mole fraction in solution, Xi.iH, and the equilibrium pressure, (phj)S at T(K) is given by... 

The question arises of to what extent these solid-phase calculations are applicable to the liquid state. Can the liquid be replaced by a nearly harmonic lattice Is rotation important as an accepting mode in the liquid only for hydride rotations, or will it contribute for heavier atoms as well There are a number of questions to be answered through both theoretical and experimental studies on the relationship between relaxation in the soUd and liquid phases. 

Desorption isotherms for the hydrides of LaNi eAlo,] and LaNij sAlo.s are presented and values for the enthalpy and entropy changes of the hydriding reactions are calculated from the vant Hoff plots of log P vs, i/T. A crystallographic model of LaNij Al is shown and consideration of the nearest neighbor atom distribution leads to a rationalization of the observed linear relationship between the enthalpy change, aH, and the aluminum composition. Brief discussions of methods to predict dissociation pressures or interstitial site occupation are included. The cubic and hexagonal ABs phases are compared and, finally, the application of these alloys in chemical heat pump systems is noted. 

One of the most important and general trends in organic chemistry is the increase in carbocation stability with additional alkyl substitution. This stability relationship is fundamental to understanding many aspects of reactivity, especially of nucleophilic substitution. In recent years, it has become possible to put the stabilization effect on a quantitative basis. One approach has been gas phase measurements which determine the proton affinity of alkenes leading to carbocation formation. From these data, the hydride affinity of the carbocation can be obtained. 

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