Equilibrium attributes

As in Section III-2A, it is convenient to suppose the two bulk phases, a and /3, to be uniform up to an arbitrary dividing plane S, as illustrated in Fig. Ill-10. We restrict ourselves to plane surfaces so that C and C2 are zero, and the condition of equilibrium does not impose any particular location for S. As before, one computes the various extensive quantities on this basis and compares them with the values for the system as a whole. Any excess or deficiency is then attributed to the surface region. 

Theoretical work by the groups directed by Sustmann and, very recently, Mattay attributes the preference for the formation of endo cycloadduct in solution to the polarity of the solvent Their calculations indicate that in the gas phase the exo transition state has a lower energy than the endo counterpart and it is only upon introduction of the solvent that this situation reverses, due to the difference in polarity of both transition states (Figure 1.2). Mattay" stresses the importance of the dienophile transoid-dsoid conformational equilibrium in determining the endo-exo selectivity. The transoid conformation is favoured in solution and is shown to lead to endo product, whereas the cisoid conformation, that is favoured in the gas phase, produces the exo adduct This view is in conflict with ab initio calculations by Houk, indicating an enhanced secondary orbital interaction in the cisoid endo transition state . 

The Raman spectrum of nitric acid shows two weak bands at 1050 and 1400 cm. By comparison with the spectra of isolated nitronium salts ( 2.3.1), these bonds were attributed to the nitrate and nitronium ion respectively. Solutions of dinitrogen pentoxide in nitric acid show these bands , but not those characteristic of the covalent anhydride , indicating that the self-dehydration of nitric acid does not lead to molecular dinitrogen pentoxide. Later work on the Raman spectrum indicates that at —15 °C the concentrations of nitrate and nitronium ion are 0-37 mol 1 and 0 34 mol 1 , respectively. The infra-red spectrum of nitric acid shows absorption bands characteristic of the nitronium ion. The equivalence of the concentrations of nitronium and nitrate ions argues against the importance of the following equilibrium ... 

The thiazolium is not acidic enough for observing directly solvation of the molecule (or an hydrolysis and subsequent cleavage of the ring) (24) without adding a base, as it is the case for benzoxazolium or benzothiazolium. With the same dilution (10 mole liter ), it is necessary to add sodium ethylate to the solution of 2-methyl-4.5-diphenylthiazolium to observe the equilibrium described above. A new band appears in the UV spectrum at 320 nm that is attributed to the ethoxy derivative by analogy to what has been observed with other benzothiazoliums (26),... 

Except as an index of respiration, carbon dioxide is seldom considered in fermentations but plays important roles. Its participation in carbonate equilibria affects pH removal of carbon dioxide by photosynthesis can force the pH above 10 in dense, well-illuminated algal cultures. Several biochemical reactions involve carbon dioxide, so their kinetics and equilibrium concentrations are dependent on gas concentrations, and metabolic rates of associated reactions may also change. Attempts to increase oxygen transfer rates by elevating pressure to get more driving force sometimes encounter poor process performance that might oe attributed to excessive dissolved carbon dioxide. 

The other C=N systems included in Scheme 8.2 are more stable to aqueous hydrolysis than are the imines. For many of these compounds, the equilibrium constants for formation are high, even in aqueous solution. The additional stability can be attributed to the participation of the atom adjacent to the nitrogen in delocalized bonding. This resonance interaction tends to increase electron density at the sp carbon and reduces its reactivity toward nucleophiles. 

The dissociation constant is small, only about 2 x 10" M at room temperature. The presence of the small amount of the radical at equilibrium was deduced from observation of reactions that could not be reasonably attributed to a normal hydrocarbon. 

The acid-catalyzed conversion of the l,2,3,4-tetrahydro-j8-carboline derivative 337 (R = CHg) into the strychnine-type ring system 338 has been attributed to an equilibrium involving the protonated Schiff s base 339 of tryptamine (i.e., the intermediate in the Pictet-Spengler type synthesis of tetrahydro-j8-carbolines, cf. Section III, A, 1, a), and the a- (337) and the j8-condensation products (340). 

Tliis conclusion is supported by the data on the azide-tetrazole equilibrium for s-triazolo[2,3-d]tetrazoles (128) [79JCS(P1)2886]. Methylation of neutral azide resulted in the 1-methyl derivatives of 3-azidotriazole 128A only, whereas on methylation of the anion 128A, the tetrazoles 129 and 130 were also trapped in 25 and 10% yields, respeetively. Tire predominanee of 128T over 128T" was attributed to these two bieyelie anions but no ealeu-lations on relative energies have been performed. Tire azide-tetrazole equilibrium eonstants were measured for 128A7T in DMSO-dg 0.45 at 27°C (R = H), and 0.78 at 23°C and 1.80 at 80°C (R = Ph). 

Tautomeric equilibrium in the symmetrical phenoxy-substituted derivative 136 (R = Ph, r = R = OPh) is fast at ambient temperature on the NMR time scale however, at —84°C the proton exchange becomes frozen and both annular tautomers 136a and 136b can be observed (Scheme 40). The similar exchange was also found for P-aryl-substituted 136 (R = Me, Ft, Ph R = R = Ph). In these cases, the equilibrium is very slow, even at ambient temperature, which was attributed to increased steric demands of four phenyl substituents. Unsymmetrically substituted azaphosphorinanes (R R ) provide even more interesting examples. These compounds (R = Ph R = Me, -Pr R = MeO, -PrO) were found to... 

The observation of the departure from cubic symmetry above Tm co-incident with the appearance of the central peak scattering serves to resolve the conflict between dynamic and lattice strain models. The departure from cubic symmetry may be attributed to a shift in the atomic equilibrium position associated with the soft-mode anharmonicity. In such a picture, the central peak then becomes the precusor to a Bragg reflection for the new structure. 

The oxidation rates in carbon monoxide (Fig. 5.12) are less than those for carbon dioxide. They increase steadily with temperature up to 800°C but then decrease markedly by a factor of 100 up to 1 000°C. The decrease in rate can be attributed to the beneficial factors operating at the higher temperatures with carbon dioxide and to the unfavourable thermodynamics for reaction 5.2 resulting in low equilibrium partial pressures of carbon dioxide. 

Attempts to determine the equilibrium constant for Equation (60), applying the method proposed by Fialkov [313] for an AB2 = A+2B type interaction, provided values that defy physical logic. This means that the equilibrium in Equation (60) shifts almost completely to the left, and that it is also disturbed by A + B = AB type interactions [313], which, in this case, correspond to the interaction F" + TaFs = TaF6". Due to the improbability of the presence of TaF5 in the melts, it makes more sense to attribute the TaFg ions to the equilibrium described in Equation (61), which provides an analogical effect on the additive values of the property. 

The rubidium-containing system Rb2TaF7 - RbF displays similar behavior, but the band attributed to the TaF6 ion vibration disappears at a RbF concentration of 0.6 mol fraction and higher (Fig. 76, c). This means that in the case of rubidium-containing melts, the equilibrium in Equation (89) is more significantly shifted to the left. 

Our sun is, of course, a star. It is a relatively cool star and, as such, contains a number of diatomic molecules (see Figure 25-3). There are many stars, however, with still lower surface temperatures and these contain chemical species whose presence can be understood in terms of the temperatures and the usual chemical equilibrium principles. For example, as the star temperature drops, the spectral lines attributed to CN and CH become more prominent. At lower temperatures, TiO becomes an important species along with the hydrides MgH, SiH, and A1H, and oxides ZrO, ScO, YO, CrO, AlO, and BO. 

Since nitration produces acetic acid, the concentration of this as well as of acetyl nitrate can be shown to depend upon the nitric acid concentration giving kinetics third-order in nitric acid (3.16 actually observed). It follows that in the presence of acetic acid the order in nitric acid should fall to 2 (2.31 observed). Likewise, in the presence of added sulphuric acid, from equilibrium (31) it follows that the order in nitric acid should fall, the observed order in this being 1.4 and 1.7 in added sulphuric acid. The retardation by added nitrate was attributed to competition by this ion for protonated acetyl nitrate, viz. 

In the above work the velocity of bromination was found to increase along with the concentration of phosphate buffer, whereas when the acid component of the buffer is varied, no such rate change occurred. The rate change was, therefore, attributed to the equilibrium... 

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