Hydration numbers, cations/anions

Table 12.2 Apparent dynamic hydration numbers Cation Hydration number Anion...

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. 

The ionic mobility and diffusion coefficient are also affected by the ion hydration. The particle dimensions calculated from these values by using Stokes law (Eq. 2.6.2) do not correspond to the ionic dimensions found, for example, from the crystal structure, and hydration numbers can be calculated from them. In the absence of further assumptions, diffusion measurements again yield only the sum of the hydration numbers of the cation and the anion. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

In the case of a few relevant anions we found a good linear correlation between the hydration enthalpies in the gas phase and the hydration numbers when these anions are associated with quaternary cations under PTC conditions (19). The hydration numbers measured for OH (11.0+1) and F (8.5+1) are in good agreement with those previously extrapolated, i.e. OH (10.0) and F (9.4) (20,21). 

We can now discuss the solvation number. In systems such as the metha-nol-water-CaCl2 system shown in Figure 5, the hydration number is the greatest, that is, 11 at x3 = 0.020. If the hydration number of ions is calculated from the hydration entropy, Ca2+ is seven and Cl is two (3). If it is assumed that CaC is completely dissociated and both the cation and anion forms hydrate, the hydration number becomes 7 + 2X2 = 11, which agrees with the value obtained from the salt effect. 

Adducts prepared in aqueous media generally possess one or more molecules of water of hydration per molecule, the number being a function of cation, anion, and the combining ratio of carbohydrate to salt. Available data on complexes of simple carbohydrates indicate that three molecules of water per molecule may be the maximum for adducts of alkali metal salts as many as seven have been reported for those of the alkaline-earth metal salts. Most complexes, however, possess only one or two molecules per molecule. Generally, the higher the combining ratio, the smaller is the number of water molecules that can be accommodated by a molecule of the adduct. 

The hydrated ion may be pictured as having a small number — possibly four or six — of water molecules firmly held in contact with the ion and constituting an inner shell, and a larger, less well defined, number more loosely held in an outer shell. Round a cation the inner shell water molecules are probably bonded by the strong ion-dipole force which operates when the water molecule is held in some such position as is indicated in formula (8). Anions are usually less hydrated than cations. The inner shell water molecules may not fit so well. Probably they are hydrogen bonded as shown in (9). In all cases, the outer shell water molecules are supposed to be hydrogen bonded to those of the inner shell. 

Rutgers and Hendrikx (126) have reviewed existing hydration numbers and have provided some new values for the hydration of several cations and anions based on measurements with a membrane transference cell. Their results are hydration numbers higher than those normally assumed. Thus, apparent hydration numbers for lithium, sodium, and potassium were respectively 22, 13, and 7 while for magnesium, calcium, and zinc, values of 36, 20, and 44 were obtained. 

Both are ionic substances with lattice sites occupied by cations and anions. In perchloric acid monohydrate, the cation is H30+ and there are no water molecules of hydration. The cations in the two crystals, H30+ and NH ", should occupy nearly equal amounts of space because they are isoelectronic (having the same number of electrons). 

Group VI. O-Donor ligands. 1H N.m.r. shifts have been measured for aqueous AgN03 and AgBF4 between 15 and 100°C.200 The very small influence of the salts on the chemical shift of H20 is attributed to almost exact cancellation of upheld anionic and downfield cationic contributions. The cationic hydration number appears to be less than 1 owing to the lability of the complex. 

Anions have a much weaker tendency to coordinate water molecules than cations and precise values for hydration numbers are difficult to obtain from X-ray data. Although a hydration sphere around an anion is often included in the least-squares analysis of an intensity curve for a metal salt solution, meaningful values are usually obtained only for the bond lengths. Coordination numbers and rms variations are often kept constant at assumed values. For the halide ions the bond lengths found show no significant deviations from values in crystal structures. 

Water will also flow. Thus, the cations and anions bring their hydration waters with them and since the hydration number (Vol. 1, Section 2.7) of a cation generally exceeds that of an anion, the net water transport will be toward the cathode. Apart from this effect as the origin of flow, there is a drag effect of the ion on its secondary solvation waters, the motion of which moves water outside the primary solvation sheath. 

The final section of Fig. 19, E, shows the EIS response anticipated if the accumulation of hydrated deposits were to partially reseal the pores. These deposits tend to act like a capacitor, CH. Such an EIS response would be anticipated in complex environments (e.g., ones containing a number of anions) or in pores with complex chemistry (e.g., containing large gradients in pH and/or metal cation complexants). It is clear from the Bode plots in Fig. 19 that distinguishing between possible behaviors is not simple. 

The structures and dynamics of hydrates have been studied by both ab initio calculations24 and by a variety of experimental techniques. Hydration numbers for the most common cations and anions are known.25... 

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 this complex, Zn2(H20)3(0H)4, each zinc ion is surrounded by four oxygen atoms (of OH"" or H O), exactly as in the hydrated zinc cation or the zincate anion the loss of water without decrease in coordination number is achieved by tire dual role played by on hydroxide oxygen atom, which serves as part of the coordination tetrahedron for both zinc ions. By continuing this process ail of the tetrahedra can be linked together into an infinite framework, in c hich each tetrahedron shares its corners with four other tetrahedra. This is the structure of the Zn(OH)o precipitate. 

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. 

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