Ionic solvation numbers

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. 

Absolute Values of Ionic Solvation Number (SN) vs. Concentration at 298 K... 

Ionic Solvation Numbers Obtained in Dilute Solution... 

Apart from neutron diffraction, what other method distinguishes between the static or equilibrium coordination number and the dynamic solvation number, the number of solvent molecules that travel with an ion when it moves One method is to obtain the sum of the solvation numbers for both cation and anion by using a compressibility approach, assuming that the compressibility of the primary solvation shell is small or negligible, then using the vibration potential approach of Debye to obtain the difference in mass of the two solvated ions. From these two measurements it is possible to get the individual ionic solvation numbers with some degree of reliability. 

Table 1 summarizes the different methods employed for the determination of ionic solvation numbers and what they measure. While each method has distinct advantages over others, it is often useful to use more than one method, e.g., the Jahn-Teller distorted structure of the hexa-hydrated copper(II) ion in water was revealed by XRD, but by neutron diffraction (ND) the elongated Cu—OH2 bonds at the axial position were not clearly visible. ... 

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... 

Equation (7.44) is known as the third approximation of the Debye-Hiickel theory. Numerous attempts have been made to interpret it theoretically, hi these attempts, either individual simplifying assumptions that had been made in deriving the equations are dropped or additional factors are included. The inclusion of ionic solvation proved to be the most important point. In concentrated solutions, solvation leads to binding of a significant fraction of the solvent molecules. Hence, certain parameters may change when solvation is taken into account since solvation diminishes the number of free solvent molecules (not bonded to the ions). The influence of these and some other factors was analyzed in 1948 by Robert A. Robinson and Robert H. Stokes. 

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

In the previous section, a possible explanation was advanced for the observation of an unsymmetrical curve joining the ionic nucleus chemical shifts in the pure solvents. A possible alternative, and physically plausible, explanation is that the solvation number is not constant. The general case of variable n is intractable, but it is possible to treat the simple case of a change in n from an even integral value in one solvent to half its value in the other pure solvent. This corresponds to monodentate for bidentate competition for a transition metal ion in solution (52). 

Because NH3(1) has a much lower dielectric constant than water, it is a better solvent for organic compounds but generally a poorer one for ionic inorganic compounds. Exceptions occur when complexing by NH3 is superior to that by water. Thus Agl is exceedingly insoluble in water but NH3(1) at 25°C dissolves 207 g/100 cm3. Primary solvation numbers of cations in NH3(1) appear similar to those in H20 (e.g., 5.0 0.2 and 6.0 0.5 for Mg2+ and Al3+, respectively), but there may be some exceptions. Thus Ag+ appears to be primarily linearly 2-coordinate in H20 but tetrahedrally coordinated as [Ag(NH3)4]+ in NH3(1). It has also been suggested that [Zn(NH3)4]2+ may be the principal species in NH3(1) as compared to [Zn(H20)6]2+ in H20. 

To obtain individual ionic values, one has to make an assumption. One takes a large ion (e.g., larger than T) and assumes its primary solvation number to be zero," so that if the total solvation number for a series of salts involving this big anion is known, the individual hydration numbers of the cations can be obtained. Of course, once the hydration number for the various cations is determined by this artifice, each cation can be paired with an anion (this time including smaller anions, which may have significant hydration numbers). The total solvation numbers are determined and then, since the cation s solvation number is known, that for the anion can be obtained. 

In the next section it will be shown how these total solvation numbers for salts can be turned into individual solvation numbers for the ions in the salt by the use of information on what are called ionic vibration potentials, an electrical potential... 

Ionic Vibration Potentials Their Use in Obtaining the Difference of the Solvation Numbers of Two Ions in a Salt... 

Now, the question is how to get information on the more subtle quantity, the hydration numbers. Some confusion arises here, for in some research papers the coordination number (the average number of ions in the first layer around the ion) is also called the hydration number However, in the physicochemical literature, this latter term is restricted to those water molecules that spend at least one jump time with the ion, so that when its dynamic properties are treated, the effective ionic radius scans to be that of the ion plus one or more waters. A startling difference between co-ordination number and solvation number occurs when the ionic radius exceeds about 0.2 nm (Fig. 2.23a). 

Obtaining the individual properties of ions with solvation numbers from measurements of ionic vibration potentials and partial molar volumes is not necessary in the study of gas phase solvation (Section 2.13), where the individual heats of certain hydrated entities can be obtained from mass spectroscopy measurements. One injects a spray of the solution under study into a mass spectrometer and investigates the time of flight, thus leading to a determination of the total mass of individual ions and adherent water molecules. 

In the 1970s Bockris and Saluj a developed models incorporating and extending ideas proposed by Eley and Evans, Frank and Wen, and Bockris and Reddy. Three basic models of ionic hydration that differ from each other in the structure in the first coordination shell were examined. The features of these models are given in Table 2.16. The notations chosen for the models were lA, IB, 1C 2A, 2B, 2C and 3A, 3B, 3C, where 1, 2, and 3 refer to three basic hydration models, and A, B, and C refer to the subdivision of the model for the structure-broken (SB) region. These models are all defined in Table 2.16. A model due to Bockris and Reddy (model 3 in Table 2.16 and Fig. 2.37) recognizes the distinction between coordination number (CN) and solvation number (SN). 

One of the challenges of solvation studies consists in separating effects among the ions of a salt (e.g., those due to the anion and those due to the cation) and this difficulty, that of determining the individual solvation heats (see Section 2.15), invades most methods devoted to the determination of individual ionic properties (Fig. 2.46). When it comes to the solvation number of an ion, an unambiguous determination is even more difficult because not all workers in the field understand the importance of distinguishing the coordination number (the nearest-neighbor first-layer number) from... 

In cluster calculations, an element essential in solution calculations is missing. Thus, intrinsically, gas-phase cluster calculations cannot allow for ionic movement. Such calculations can give rise to average coordination numbers and radial distribution functions, but cannot account for the effect of ions jumping from place to place. Since one important aspect of solvation phenomena is the solvation number (which is intrinsically dependent on ions moving), this is a serious weakness. 

The activity and osmotic coefficients of sodium thiocyanate in water have been determined (531). The solvation number of NCS has been reported as zero. (588), and the ion tends to be less structure-breaking than most anions (136). Its transport number and ionic conductance have been measured in formamide (581), and 1 1 solvates have been reported from dimethylformamide solutions of M—NCS (M = NH4, Na, K) (595). 

The separation of the measured effect into ionic contributions requires assumptions on reference ions depending on the nature of the solvent. For acetonitrile solutions, a pattern of consistent solvation numbers is obtained at negligible kinetic depolarization for Li" (4),fVo (4),Br (2),Bu4fV+(0),/"(0),C /07(0) in agreement with those from FTIR measurements for Li., Na and CIO. Reasonable solvation numbers are found for Na ions in FA and DMF both for = 0(6) or 0(4). Independent of the choice... 

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