Solvation numbers

In order to determine the solvation numbers and the exchange constants it is assumed that one (Lys HBr)n residue consists of two parts, namely, the ionic group (numbered 2) and the less polar remainder of the molecule (numbered 1). Plotting... 

Various methods are available for determining the solvation number hj and (or) the radius of the primary solvation sheath (1) by comparing the values of the true and apparent ionic transport numbers, (2) by determining the Stokes radii of the ions, or (3) by measuring the compressibility of the solution [the compressibility decreases... 

The values of hj for different ions are between 0 and 15 (see Table 7.2). As a rule it is found that the solvation number will be larger the smaller the true (crystal) radius of the ion. Hence, the overall (effective) sizes of different hydrated ions tend to become similar. This is why different ions in solution have similar values of mobilities or diffusion coefficients. The solvation numbers of cations (which are relatively small) are usually higher than those of anions. Yet for large cations, of the type of N(C4H9)4, the hydration number is zero. 

Three types of methods are used to study solvation in molecular solvents. These are primarily the methods commonly used in studying the structures of molecules. However, optical spectroscopy (IR and Raman) yields results that are difficult to interpret from the point of view of solvation and are thus not often used to measure solvation numbers. NMR is more successful, as the chemical shifts are chiefly affected by solvation. Measurement of solvation-dependent kinetic quantities is often used (<electrolytic mobility, diffusion coefficients, etc). These methods supply data on the region in the immediate vicinity of the ion, i.e. the primary solvation sphere, closely connected to the ion and moving together with it. By means of the third type of methods some static quantities entropy and compressibility as well as some non-thermodynamic quantities such as the dielectric constant) are measured. These methods also pertain to the secondary solvation-sphere, in which the solvent structure is affected by the presence of ions, but the... 

The H2S+ ion is generally termed a lyonium ion and the S" ion is termed a lyate ion. The symbol H2S+ (for example H30+, CH3COOH2+, etc.) refers only to a proton solvated by a suitable solvent and does not express either the degree of solvation (solvation number) or the structure. For example, two water molecules form the lyonium ion H30+, termed the oxonium (formerly hydronium or hydroxonium) ion, and the lyate ion OH", termed the hydroxide ion. 

At the beginning of this decade, Zewail and coworkers reported a fundamental work of solvation effect on a proton transfer reaction [195]. a-naphthol and n-ammonia molecules were studied in real-time for the reaction dynamics on the number of solvent molecules involved in the proton transfer reaction from alcohol towards the ammonia base. Nanosecond dynamics was observed for n=l and 2, while no evidence for proton transfer was found. For n=3 and 4, proton transfer reaction was measured at pisosecond time scale. The nanosecond dynamics appears to be related to the global cluster behavior. The idea of a critical solvation number required to onset proton transfer... 

The existence of critical solvation numbers for a given process to happen is an important concept. Quantum chemical calculations using ancillary solvent molecules usually produce drastic changes on the electronic nature of saddle points of index one (SPi-1) when comparisons are made with those that have been determined in absence of such solvent molecules. Such results can not be used to show the lack of invariance of a given quantum transition structure without further ado. Solvent cluster calculations must be carefully matched with experimental information on such species, they cannot be used to represent solvation effects in condensed phases. 

Gas-phase solvation has so far given only very indirect evidence concerning the structure and details of molecular interactions in solvation complexes. Complex geometries and force constants, which are frequently subjects of theoretical calculations, must therefore be compared with solution properties, however, the relevant results are obscured by influences arising from changes in the bulk liquid or by the dynamic nature of the solvation shells. With few exceptions, structural information from solutions cannot be adequately resolved to yield more than a semiquantitative picture of individual molecular interactions. The concepts used to convert the complex experimental results to information for structural models are often those of solvation numbers 33>, and of structure-making or structure-... 

Before we consider substitution processes in detail, the nature of the metal ion in solution will be briefly reviewed.A metal ion has a primary, highly structured, solvation sheath which comprises solvent molecules near to the metal ion. These have lost their translational degrees of freedom and move as one entity with the metal ion in solution. There is a secondary solvation shell around the metal ion, but the solvent molecules here have essentially bulk dielectric properties. The (primary) solvation number n in M(S)"+ of many of the labile and inert metal ions has been determined, directly by x-ray or neutron diffraction of concentrated solutions, from spectral and other considerations and by examining the exchange process... 

From the ratio of the areas of nmr peaks due to coordinated and free solvent, or from simple isotopic analyses, the value of n can be determined. It may be necessary to slow the exchange process (4.4) by lowering the temperature of the solution. A variety of solvation numbers n is observed, with four and six being the most prevalent. As we have noted already, there is a wide range of labilities associated with the solvent exchanges of metal ions (Fig. 4.1). 

The ion Cr(H20)g is one of the few aqua species that is sufficiently inert that the solvent exchange rate and solvation number may be determined by conventional sampling or nmr analytical methods. Improved techniques enable lower concentrations of Cr(IlI) and H+ to be used than in the early studies of the 50 s. This allows the determination of an extended rate law for HjO exchange with Cr(III)... 

When the solvent is a good solvater, the determination of the solvation number b is difficult, unless the dependence of the extractant concentration on the solvent can be obtained. Solvation numbers can be obtained in mixtures of a solvating extractant and an inert diluent like hexane. Further, in these systems the extraction of the metal commonly requires high concentrations of salt or acid in the aqneons phase, so the activity coefficients of the solutes must be taken into acconnt. 

Increasing the solvation causes the C,—Li contact to be gradually given up whereas the electrostatic contact of the lithium to the a-carbon is maintained. However, the estimation of the solvation number in the solid state shows the presence of two THF molecules per lithium. This study suggests that specific solvation increases the ability of the sulfur group to localize the negative charge on the a-carbon atom (a-heteroatom stabilization). 

Again, solvation numbers in methanol can be calculated by altering the constants to account for halving the number of O-H oscillators per solvent molecule, giving Eqs. (4) and (5) ... 

X-ray and neutron diffraction methods and EXAFS spectroscopy are very useful in getting structural information of solvated ions. These methods, combined with molecular dynamics and Monte Carlo simulations, have been used extensively to study the structures of hydrated ions in water. Detailed results can be found in the review by Ohtaki and Radnai [17]. The structural study of solvated ions in lion-aqueous solvents has not been as extensive, partly because the low solubility of electrolytes in 11011-aqueous solvents limits the use of X-ray and neutron diffraction methods that need electrolyte of -1 M. However, this situation has been improved by EXAFS (applicable at -0.1 M), at least for ions of the elements with large atomic numbers, and the amount of data on ion-coordinating atom distances and solvation numbers for ions in non-aqueous solvents are growing [15 a, 18]. For example, according to the X-ray diffraction method, the lithium ion in for-mamide (FA) has, on average, 5.4 FA molecules as nearest neighbors with an... 

Li+-0 distance of 224 pm, while the chloride ion is coordinated by 4.5 FA molecules and the CT- -N distance is 327 pm the amino group of FA interacts with the chloride ion in a bifurcated manner through the two hydrogen atoms [18]. The solvation numbers obtained by these methods correspond to the number of solvent molecules in the first solvation shell immediately neighboring the ion here, the solvent molecules may or may not interact strongly with the ion.6a ... 

Here, Vs is the molar volume of the solvent and NA is the Avogadro constant. Some of the ionic solvation numbers obtained by this method are listed in Table 7.3. 

Tab. 7.3 Solvation numbers of ions calculated from the effective ionic radii...

As mentioned in Section 7.1, if we determine the molar conductivity of an electrolyte as a function of its concentration and analyze the data, we can get the value of limiting molar conductivity A°° and quantitative information about ion association and triple-ion formation. If we determine the limiting molar conductivity of an ion (7 °) by one of the methods described in Section 7.2, we can determine the radius of the solvated ion and calculate the solvation number. It is also possible to judge the applicability of Walden s rule to the ion under study. These are the most basic applications of conductimetry in non-aqueous systems and many studies have been carried out on these problems [1-7]. 

A method of prediction of the salt effect of vapor-liquid equilibrium relationships in the methanol-ethyl acetate-calcium chloride system at atmospheric pressure is described. From the determined solubilities it is assumed that methanol forms a preferential solvate of CaCl296CH OH. The preferential solvation number was calculated from the observed values of the salt effect in 14 systems, as a result of which the solvation number showed a linear relationship with respect to the concentration of solvent. With the use of the linear relation the salt effect can be determined from the solvation number of pure solvent and the vapor-liquid equilibrium relations obtained without adding a salt. 

Prediction of Salt Effect from Preferential Solvation Number... 

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