Apparent hydrated radii

Classical measurements such as ion mobilities, apparent hydrated radii, enthalpies and entropies of solution, etc. fail to provide an explicit distinction between water molecules in zones A and B. Methods which can probe the primary hydration sphere of a cation include optical spectroscopy, nuclear magnetic resonance, electron spin resonance, extended X-ray absorption fine structure (EXAFS), X-ray diffraction and... 

Apparent hydration numbers have been derived from experimental measurements assuming the formation of a hydration complex studied as a chemical reaction. xhe change of volume for the reaction is calculated from an equation of state which includes variation of the dielectric constant based on the solvent isothermal compressibility, while the bare ion and the complex are assumed spherical with crystallographic and Stokes-Einstein radii respectively. The latter radius is obtained from conductance measurements. Due to these assumptions, the apparent hydration numbers increase when temperature increases and diverge near the critical point due to the divergence of the solvent compressibility. Furthermore, negative values are obtained when the Stokes-Einstein radius for the complex is smaller than the crystallographic radius. 

Within the first-order estimations made here, it is apparent that no change in d-d repulsion energy accompanies the hydration process. Second-order adjustments would, of course, take account of the change in mean i/-orbital radius on complex formation. Let us agree to stop at the simple level of correction here. Overall, therefore, the significant Coulombic change on hydration concerns the loss of exchange stabilization. 

In almost all theoretical studies of AGf , it is postulated or tacitly understood that when an ion is transferred across the 0/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of AGfr°. Although Abraham and Liszi [17], in considering the transfer between mutually saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB andl,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170mM H2O in NB). In such a medium, hydrophilic ions such as Li, Na, Ca, Ba, CH, and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl-Fischer method [35 5]. Rais et al. [35] and Iwachido and coworkers [36-39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal... 

The values for the enthalpies of hydration of ions may be forced to conform to the expectations of the Born equation (2.43) by estimating a suitable value for each ionic radius or by estimating an apparent ionic charge. 

From the plots shown in Fig. 1, it is evident that Eq. 3 is valid for the hydrophilic solutes examined in the present study. The dependence of Dm on cross sectional radius is evident from the linearity of the plots. The water contents of p-HEMA and p-HEMA crosslinked with 1 mole % EGDMA are 42° (w) and 37% (w) respectively. This effect of membrane hydration is contained in the slope of the plots given in Fig. 1. It is apparent that as the membrane hydration is increased, Dm is less sensitive to changes in the size of the permeating solute. 

The Stokes radius will also depend on the solvation of the macromolecule. Even for a perfectly spherical molecule, the solvent molecules in the immediate vicinity will tend to stick to the macromolecule surface, creating a solvation or hydration shell that will travel with the molecule. Consequently, will often appear larger than the apparent... 

It is naive to correlate Kq directly with molecular weight because it is apparent that the relationship actually exists between the retention volume of a molecule and its hydrodynamic size rather than its molecular weight. The radius of a molecule in solution, relative to its molecular weight, is influenced by its degree of hydration, its molecular asymmetry, and, occasionally, its ionic and/or hydrophobic character. 

The polar nature of proteins causes them to bind multiple molecules of water, the number of which depends on solution pH and ionic strength. For proteins, the degree of hydration commonly varies from 0.3 to more than 1.0. Cantor and Schinunel [7] calculated that a monolayer of water bound to the surface of a 30,000-Da spherical protein would cause a 13.6% increase in the hydrated molecular radius. It is apparent that the relative degree of hydration will cause... 

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