Primary hydration number

Figure A2.4.3. The localized structure of a hydrated metal cation in aqueous solution (the metal ion being assumed to have a primary hydration number of six). From [5].

The coordination chemistry of the large, electropositive Ln ions is complicated, especially in solution, by ill-defined stereochemistries and uncertain coordination numbers. This is well illustrated by the aquo ions themselves.These are known for all the lanthanides, providing the solutions are moderately acidic to prevent hydrolysis, with hydration numbers probably about 8 or 9 but with reported values depending on the methods used to measure them. It is likely that the primary hydration number decreases as the cationic radius falls across the series. However, confusion arises because the polarization of the H2O molecules attached directly to the cation facilitates hydrogen bonding to other H2O molecules. As this tendency will be the greater, the smaller the cation, it is quite reasonable that the secondary hydration number increases across the series. 

A primary hydration number of 6 for Fe + in aqueous (or D2O) solution has been indicated by neutron diffraction with isotopic substitution (NDIS), XRD, 16,1017 EXAFS, and for Fe " " by NDIS and EXAFS. Fe—O bond distances in aqueous solution have been determined, since 1984, for Fe(H20)/+ by EXAFS and neutron diffraction, for ternary Fe " "-aqua-anion species by XRD (in sulfate and in chloride media, and in bromide media ), for Fe(H20)g by neutron diffraction, and for ternary Fe -aqua-anion species. The NDIS studies hint at the second solvation shell in D2O solution high energy-resolution incoherent quasi-elastic neutron scattering (IQENS) can give some idea of the half-lives of water-protons in the secondary hydration shell of ions such as Fe aq. This is believed to be less than 5 X I0 s, whereas t>5x10 s for the binding time of protons in the primary hydration shell. X-Ray absorption spectroscopy (XAS—EXAFS and XANES) has been used... 

In recent years, X-ray diffraction studies of aqueous solutions have established primary hydration numbers for several fast-exchange cations 45,187-190 the timescale of X-ray diffraction is very much shorter than that of NMR spectroscopy. Octahedral hydration shells have been indicated for Tl3+,191 Cd2+, Ca2+, Na and K+, for example. For the lanthanides, [Ln(OH2)9]3+ is indicated for La, Pr and Nd, but [Ln(OH2)8]3 for the smaller Tb to Lu.192,193 Sometimes there are difficulties and uncertainties in extracting primary hydration numbers from X-ray data. Thus hydration numbers of eight and of six have been suggested for Na+ and for K+,194 and for Ca2+,195 and 8 and 9 for La3+, 196 In some cases rates of water exchange between primary and secondary hydration shells are so fast as to raise philosophical questions in relation to specific definitions of hydration numbers.197... 

The theory of Frank and Wen (54) for ion hydration involves the notion that some water molecules intimately contact the ion under consideration and subject to the strong centrosymmetric force field, are highly ordered. Beyond this area is a region of disorder, beyond which, in dilute solutions, unaffected water prevails. Typical literature values for primary hydration numbers range from 2-8 water molecules. For divalent ions, primary hydration numbers range from 10-20 water molecules while some authors have suggested hydration numbers for trivalent ions (based on compressibility data) between 20 and 30 water molecules per ion. Many attempts have been made to extend theories of this type to account better for the hydration of ions. Thus, Azzam (7, 8) and Horne and Birkett (80) have proposed a multilayer model of ion hydration. 

An electrostatic hydration model has been applied to the trivalent lanthanide and actinide ions in order to predict the standard free energy (AG°) and enthalpy (AHt) of hydration for these series. Assuming crystallographic and gas-phase radii for Bk(III) to be 0.096 and 0.1534 nm, respectively, and using 6.1 as the primary hydration number, AG298 was calculated to be -3357 kJ/mol, and A/Z298 was calculated to be -3503 kJ/mol (187). 

The primary hydration shell for Li+ in aqueous solution is tetrahedral.31 Only tetrahydrated salts are formed except when there is also hydration of the anions. X-ray scattering studies show that the primary hydration number of K+ is 4, and since Na+ forms the stable Na(NH3)4+ ion in liquid ammonia, it too presumably has a first coordination sphere of four water molecules. There is no direct evidence regarding Rb+ or Cs+, but a higher number, probably 6, seems likely. 

The NMR spectrum of an aqueous A1(C104)3 solution in [Dgjacetone shows nicely the two different signals of bulk water and hydration water in the AP inner shell, even at room temperature [245]. The addition of acetone slows down the proton exchange rate. A primary hydration number of six for Al has been obtained in this way [245]. 

Primary Hydration Numbers from ionic Mobility Measurements... 

On the other hand, the transport or mobility approach to determining the primary hydration number does give a value for what is wanted, the number of water molecules that have lost their own degrees of translational freedom and stay with the ion in its motion through the solution. This approach has the advantage of immediately providing the individual values of the solvation number of a given ion, and not the sum of the values of those of the electrolyte. 

Bergstrom and Lindgren s Determination of Primary Hydration Number from IR Measurements (Transition-MetaMons and Lanthanides)... 

Swift and Sayne used concepts similar to those of Bockris and Saluja if a molecule stays associated with an ion for more than the time needed for a diffusional jump, it counts as a primary hydration number. This approach yields approximately 4 solvation molecules for and Ca ", and 5 for Ba and Sr", whereas nonspectroscopic methods for these systems yield values that are two to three times larger. Does NMR measure only water arranged in a first, octahedral layer in the first shell near the ion and is it insensitive to the rest of the water structure near an ion ... 

The main purpose of this section is to give the basis of how measurements of the dielectric constants of ionic solutions can give information on solvation, particularly primary hydration numbers. However, dielectric measurements as a function of frequency also give information on the dynamic behavior of water by allowing us to determine the relaxation time of water in ionic solutions and expressing the changes in terms of the number of water molecules bound to the ion. 

Now, an interesting thing can be done with the AH values obtained as indicated earlier. One takes the best estimate available for the primary hydration number in solution (see, e.g.. Tables 2.7 and 2.11). One then calculates the corresponding heat of hydration in the gas phase for this number and compares it with the corresponding individual heat of hydration of the ion in solution. The difference should give the residual amount of interaction heat outside the first layer (because in the gas phase there is no outside the fu-st laya ). 

Thus, a major misunderstanding is committed by those who confuse solvation numbers with the number of solvent molecules in contact with an ion, the coordination number. It has already been implied and indeed spelled out that the term solvation number implies a dynamic concept. Solvation numbers reflect the dynamic situation of the ion as it moves around in the solution. Thus, two hydration numbers may be described, but only one of these is open to numerical determination. This is the so-called primary hydration number, that is, the number of water molecules that have lost their own freedom of translational motion and move along with the ion in its random movements in the solution. A secondary hydration number rtitts to the water molecules in the area around the ion that are affected by the ion s presence. Clearly, this second quantity depends entirely on the degree of the effect on the solvent molecules outside the first and second layers and hence on the sensitivity of the method being used. It includes waters in the structurally broken-down region out from the first layer of waters attached to the anion. 

A Reconsideration of the Methods for Determining the Primary Hydration Numbers Presented in Section 2.15... 

Summary of Primary Hydration Numbers for Aikaii Metai and Halide Ions... 

If the total primary hydration number of NaCl in a 1 M solution is 6, make a rough calculation of the dielectric constant of the solution by assuming that the dielectric constant of pure water is 80 and that of the water molecule in the primary hydration sheath is 6. 

Concentrated salt solutions are a class of solvent whose properties have hardly begun to be appreciated. The ratio of water to salt in these media is so low that the primary hydration number (the number of water molecules about each ion) must be far lower than in dilute solutions. A saturated D2O solution of KF, for example, which is 12.4M with a density of 1.563, has only 3.4 moles of D2O per mole of KF while perhaps eight moles of water per mole of KF (4) are required for the primary hydration sphere in a dilute solution. The enhanced complex formation which necessarily results may lead to a chemistry different from aqueous chemistry. Asprey and Penneman (3) have reported that Am " is both stable and soluble in saturated NH4F, RbF, and KF. 

Ionic mobility measuremoits, and primary hydration numbers, 72... 

Physical chemistry, related to electrochemistry. Primary hydration numbers, their values, sum-... 

An electrostatic hydration model, previously developed for ions of the noble gas structure, has been applied to the tervalent lanthanide and actinide ions. For lanthanides the application of a single primary hydration number resulted in a satisfactory fit of the model to the experimentally determined free energy and enthalpy data. The atomization enthalpies of lanthanide trihalide molecules have been calculated in terms of a covalent model of a polarized ion. Comparison with values obtained from a hard sphere modeP showed that a satisfactory description of the bonding in these molecules must ultimately be formulated from the covalent perspective. 

Semiempirical calculations of free energies and enthalpies of hydration derived from an electrostatic model of ions with a noble gas structure have been applied to the ter-valent actinide ions. A primary hydration number for the actinides was determined by correlating the experimental enthalpy data for plutonium(iii) with the model. The thermodynamic data for actinide metals and their oxides from thorium to curium has been assessed. The thermodynamic data for the substoicheiometric dioxides at high temperatures has been used to consider the relative stabilities of valence states lower than four and subsequently examine the stability requirements for the sesquioxides and monoxides. Sequential thermodynamic trends in the gaseous metals, monoxides, and dioxides were examined and compared with those of the lanthanides. A study of the rates of actinide oxidation-reduction reactions showed that, contrary to previous reports, the Marcus equation ... 

In addition to n and n, which are the primary hydration numbers of cation and anion, respectively, and , the average number of water molecules bound in the ydrative associations of States 3 and 4-, are also computed using the model for the association-dissociation equilibrium between bound and unbound cations described previously. 

Ions and charged surfaces can break down the ice slurry structure of water. The electric charges are stronger than dipole forces and tend to pull water molecules away from their groups by attracting the positive or negative ends of the water dipoles. Solutes and water molecules are constantly in motion, but they remain in the vicinity of each other for some period of time. If water molecules remain near an ion longer than the time required for the water molecules to dissociate from the water structure, the ion will have a sphere of water molecules (a solvation sphere or sheath) around itself. The number of water molecules in the closest solvation sphere is called the primary hydration number. 

The value of the primary hydration number is in dispute. Different methods of measurement yield quite different values because they respond to different strengths and times of ion-water interaction. Careful measurements of the hydration number of Na+, for example, yielded values of 1, 2, 2.5, 4.5, 6 to 7, 16.9, 44.5, and 71, depending on the method used. Table 3.1 shows hydration numbers for common ions determined by several methods that tend to agree. The last column shows Bockris and Reddy s estimates of primary hydration numbers for the univalent ions. 

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