Hydration equation

Table 46 Reaction of 1,3,4-oxadiazole-2-(3H)-thiones with hydrazine hydrate (Equation 69)... 

Divalent or higher-valent cations and, in particular, transition metal cations, are likely to be covalently solvated by solvents that are strong electron pair donors (have large solvatochromic P values). This solvation often persists in crystals, so that the salt that is in equilibrium with the saturated solution in such solvents may not be the anhydrous salt (nor the salt hydrate). Equation (2.56) omits any consideration of the solvent of crystallization and pertains to the solventless (anhydrous) salt. For a salt hydrated by n water molecules in the crystal, the activity of water raised to the nth power must multiply the right-hand side of Eq. (2.56) for it to remain valid. A similar consideration applies for salts crystallizing with other kinds of solvent molecules, the activity of the solvent in the saturated solution replacing that of water. Such situations must be... 

Similarly 258 gives 259 when treated with hydrazine hydrate (Equation 31). 

An interesting application of this synthetic methodology is the conversion of 265 into 266 upon reflux with hydrazine hydrate (Equation 35) <2004ZNB1132>. 

Quite similar is the reported conversion of 379 into 380 upon reflux in EtOH with hydrazine hydrate (Equation 56) <2003PS199>. 

Water adds to the carbonyl group of aldehydes and ketones to yield hydrates (Equation 8.4). For ketones and aryl aldehydes, equilibrium constants of the... 

Functional groups in the vicinity of the C—C double bond can also have a substantial effect on the re-giochemistry of hydration (equations 208 and 209).315-317... 

CH3. OH. CH2HgI, might serve as that intermediate but that would be difficult to reconcile with relative reactivities. The rate-determining step for allylmercuric iodide cleavage could be written as shown in equation (58) if the carbonium ion were the intermediate. This is analogous to the rate-determining step for propene hydration (equation... 

Another rationalization for a lack of buildup of iminium ion is that both reactions which destroy it, namely hydration (equation 16) and deprotonation (reverse of equations... 

Selenoxides derived from unsymmetrical selenides are chiral and stable toward pyramidal inversion at room or even higher temperatures. They are produced enantioselectively by the use of chiral oxidants such as the Sharpless reagent or camphor-derived oxaziridines or diastereoselectively with achiral oxidants when one of the selenide substituents is itself chiral (see Section 9). Racemic selenoxides have been resolved by chromatography over chiral adsorbents. Chiral selenoxides racemize readily in water, particularly under acid-catalyzed conditions, presumably via the intermediacy of achiral selenoxide hydrates (equation 2). 

Methyl and methylene groups adjacent to carbonyl groups are easily oxidized to carbonyls to yield a-keto aldehydes or a-diketones. The reagent of choice is selenium dioxide or selenious acid. The reaction is catalyzed by acids and by acetate ion and proceeds through transition states involving enols of the carbonyl compounds [518]. The oxidation is carried out by refluxing the ketone with about 1.1 mol of selenium dioxide in water, dilute acetic acid, dioxane, or aqueous dioxane [517]. The byproduct, black selenium, is filtered off, but small amounts of red selenium sometimes remain in a colloidal form and cannot be removed even by distillation of the product. Shaking the product with mercury [523] or Raney nickel [524] takes care of the residual selenium. The a-dicarbonyl compounds are yellow oils that avidly react with water to form white crystalline hydrates (equations 407 and 408). 

The additions of iodine azide (equations 99, 100) and the mercury catalysed hydration (equation 101) were rationalized on the basis of Ad reactions with cyclic intermediates having relatively little car-bonium ion character. Orientation is then dependent on the inductive effects of the methyl and bromo substituents with little orientational effect of the phenyl group. In contrast, the orientation of the acid... 

The Bronsted equation is a Class I free energy relationship and this may be shown by considering as an example the acid-catalysed dehydration of acetaldehyde hydrate (Equation 30). This reaction also provides a good example of an acid-catalysed reaction following a Bronsted equation (Figure 7). 

The formation of pyridazines from three components was reviewed in CHEC-I and the most common examples are of reaction of an a-diketo compound, a hydrazine, and an ester or nitrile containing an adjacent activated methylene group, to give compounds like 4-cyano-3(2//)-pyr-idazinone or 3-amino-4-cyanopyridazines. A different type of example is illustrated by the condensation of a nitrostyrene with two equivalents each of methyl acetoacetate and hydrazine hydrate (Equation (36)) to give the pyridazine (126) in good yield <87JHC23>. 

The 7-imino[l,2,4]triazolo[3,2-Z)][l,3]triazine compounds (71) when deprotonated, were found to form a ring-chain equilibrium with (72) (Equation (1)) <88KGS992>. Opening of the thiadiazole ring of (73) and formation of (74) was observed in the reaction with hydrazine hydrate (Equation (2))... 

Keywords Gas hydrate, equation of state, methane, natural gas, monoethylene glycol, experimental data... 

In these treatments, the hydration index h was treated as a constant. It is, however, reasonable to expect h to decrease as the ionic strength increases. Indeed, Bates (1986) found support for a linear decrease with I from its limiting value (h ) at zero ionic strength (63). His modification of the hydration equation for mean activity coefficients is as follows ... 

The three parameters h, and q were derived from mean activity coefficients by nonlinear least-squares procedures. The hydration indexes were found to decrease from 12 for Mg2+ and 11 for Ca2+ to 5.2, 3.8, and 2.5 for Li, Na", and id", respectively. Pan (64) has preferred to fix the ion-size parameter in the hydration equation at the sum of the crystallographic radii of the ions. If this is done, he has found that much larger values of h (about 21, 13, and 7 for the lithium, sodium, and potassium halides, respectively) are obtained from mean activity coefficients. 

When the parameters of the Stokes-Robinson modification of the hydration equation for simple electrolytes were examined. Bates, Staples, and Robinson (66) noted that values of h for the alkali chlorides varied in nearly linear fashion with the reciprocal of the radii of the cations. The intercept for very large cations was near h=0. On the strength of this observation, together with the assumption that h values for cation and anion are additive, the convention that h=0 for chloride ion was advanced. From this point of departure, together with the Gibbs-Duhem equation, the following reasonable separation of Y+ for a 1 1 electrolyte MX into its ionic contributions was derived ... 

TABLE 4.9 Hydration Numbers of Ions At infinite Dilution Obtained from Electrostriction, Equation 4.36 [84], Compressibility, Equation 4.37 [52], Entropy of Hydration, Equation 4.41 [52], and Empirically, = 0.360 ... 

The dependences of rates of dissociation and racemization of iron(n), iron(ra), and nickel(ii) complexes of 2,2 -bipyridyl or 1,10-phenanthroline on water activity in strong hydrochloric or sulphuric acids are attributed to equilibrium formation of covalent hydrates [equation (5).]... 

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