Reversed Stability, Rule

More general is the rule of reversed stability (Miedema model) the more stable an intermetallic compound, the less stable is the corresponding hydride, and the other tvay around [36]. This model is based on the fact that hydrogen can only participate on a bond with a neighboring metal atom if the bonds between the metal atoms are at least partially broken (Figures 5.25 and 5.26). 

The rule of reversed stability is illustrated by Equation 15. When the stability of the intermetallic compound ABn is great, the stability of the ternary hydride is low therefore, the hydrogen dissociation pressure of the hydride is high (8). The rule of reversed stability aids in calculating approximate values... 

Considerations of enthalpy, as illustrated by the rule of reversed stability, and of configurational entropy provided insight into the factors governing the stabilities of the AB5 hydrides. Theoretical understanding to predict dissociation pressures should be developed on heat pump application, for example. Although... 

Relation (4.19) is usually called Miedema s rule of reversed stability and states that the heat of formation of a ternary hydride is the difference between the sum of the heat of formation of the elemental hydride and the alloy enthalpy of formation. Because atom A is hydride forming, the first term of the right-hand side is negative and has a large absolute value while the second term is small (or even positive) and... 

A scheme for correlating hydride stabilities, the so called rule of reversed stability see e.g., 18,19), states that for a series of analogous alloys, the more stable the alloy, the less stable (i.e., higher dissociation pressure) the corresponding hydride. Using Miedema s formula (20), the calculated heat of formation for LaNis is — II.2 kj/mol and for LaAls is — 42.1 kj/mol. Since LaAls is more stable (more negative AH) than LaNis, the rule of reversed stability predicts the LaNis- rAh hydrides to be less stable than LaNisHe contrary to observation. Similarly, Shinar et... 

One may rationalize emulsion type in terms of interfacial tensions. Bancroft [20] and later Clowes [21] proposed that the interfacial film of emulsion-stabilizing surfactant be regarded as duplex in nature, so that an inner and an outer interfacial tension could be discussed. On this basis, the type of emulsion formed (W/O vs. O/W) should be such that the inner surface is the one of higher surface tension. Thus sodium and other alkali metal soaps tend to stabilize O/W emulsions, and the explanation would be that, being more water- than oil-soluble, the film-water interfacial tension should be lower than the film-oil one. Conversely, with the relatively more oil-soluble metal soaps, the reverse should be true, and they should stabilize W/O emulsions, as in fact they do. An alternative statement, known as Bancroft s rule, is that the external phase will be that in which the emulsifying agent is the more soluble [20]. A related approach is discussed in Section XIV-5. 

The relative stability of the anions derived from cyclopropene and cyclopentadiene by deprotonation is just the reverse of the situation for the cations. Cyclopentadiene is one of the most acidic hydrocarbons known, with a of 16.0. The plCs of triphenylcyclo-propene and trimethylcyclopropene have been estimated as 50 and 62, respectively, from electrochemical cycles. The unsubstituted compound would be expected to fall somewhere in between and thus must be about 40 powers of 10 less acidic than cyclopentadiene. MP2/6-31(d,p) and B3LYP calculations indicate a small destabilization, relative to the cyclopropyl anion. Thus, the six-7c-electron cyclopentadienide ion is enormously stabilized relative to the four-7c-electron cyclopropenide ion, in agreement with the Hixckel rule. 

Based on the reversibility of their phase transformation behavior, polymorphs can easily be classified as being either enantiotropic (interchange reversibly with temperature) or monotropic (irreversible phase transformation). Enantiotropic polymorphs are each characterized by phase stability over well-defined temperature ranges. In the monotropic system, one polymorph will be stable at all temperatures, and the other is only metastable. Ostwald formulated the rule of successive reactions, which states that the phase that will crystallize out of a melt will be the state that can be reached with the minimum loss of free... 

This is because of retro-cycloaddition. In retro-cycloadditions, the reverse reactions are more favoured and the same selection rules apply. This is also because that X is normally a small inorganic molecule and of high thermodynamic stability. 

Our hypothesis of steric factors dominating the stability of the emerging radical centers in the transition states readily explains the enantioselective epoxide opening of meso-epoxide 35 to 36 that is shown in Fig. 3 [59,60]. In the case of a reversible epoxide opening, a stability difference of at least 3 kcalmol 1 between the two radicals 37 and 38 is necessary to explain the observed selectivity. According to the calculations this seems highly unlikely. A thermodynamically controlled epoxide opening can therefore be ruled out. 

This criterion was originally established for the fragmentation of alkanes by Stevenson [18] and was later demonstrated to be generally valid. [19,20] The rule can be rationalized on the basis of some ion thermochemical considerations (Fig. 6.4). Assuming no reverse activation barrier, the difference in thermodynamic stability as expressed in terms of the difference of heats of formation of the respective products determines the preferred dissociation pathway ... 

Bond angle/bond length relationships do not readily account for the bond localization noted for starphenylene (116) and triphenylene (124). A cursory examination of the structures reveals that in these cases the annelated cycles can have an aromatic character of their own. In staiphenylene the cycle would contain four electrons and be antiaromatic, whereas in triphenylene the cycle would have six electrons and be aromatic. From the simple Huckel rule, the antiaromatic cycle should be disfavored. In such a case, structural stabilization can be accomplished by greater contribution from the resonance form that has single-bond character at the endo-honA. The reverse is expected for the aromatic cycle. This model is simple, predictive, and accurate ... 

The choice of the proper stationary and mobile phases for the foregoing purpose would depend on several factors, such as the nature (polarity, stability in mobile phase) of the NOC analyzed and the availability/compatibility of the detector used. For example, if only a TEA is available as a detector, the use of an ion-exchange or a reversed-phase system is ruled out, because both require aqueous mobile phase for proper operation. Moisture in the mobile phase causes freeze-up of the cold traps in the TEA and also results in noisy response due to interference during chemiluminescence detection. Similarly, if one is using, as the detector the newly developed Hi-catalyzed denitrosation-TEA (62) or the photolytic cleavage-TEA (58), a reversed-phase system using aqueous mobile phase would be the method of choice. These detectors, however, have not been demonstrated to work in the normal-phase system. The use of an electrochemical detector will also be incompatible with an organic solvent as the mobile phase. 

The phase stability of organic extractant phases and classical reverse microemulsions are thus governed by the same rule. This general conclusion would not have been valid for extractant systems in the case of an emulsification failure mechanism, namely rejection of the internal phase, but this was not observed in liquid/liquid extraction systems when salt is extracted. 

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