Hydration of cations and anions

This treatment illustrates the inherent difficulty of the problem. Any cycle of this type will allow the calculation of sums of enthalpies of hydration of cations and anions, but it will not allow the estimation of the separate quantities. There are two ways of dealing with the matter. One is to use the conventional reference zero that the enthalpy of hydration of the proton is zero, i.e. Ahyti// (H+, g) = 0. The second approach is to estimate an absolute value for A Z/tH h, g) that may be used to estimate the absolute values for enthalpies of hydration of any other ions. Both are exemplified in the text, but only the second is of general use in the study of the hydration of ions and the discussion of the factors that determine the values of enthalpies of hydration of individual ions. 

It should be emphasized that none of the methods in categories (ii) and (iii) that have been used to obtain the absolute enthalpies of hydration of ions is theoretically rigorous. For example, Conway and Salomon (54) have made a detailed critique of the Halliwell—Nyburg type of treatment. If the water dipole orientation is not exactly opposite at cations and anions, as seems to be indicated by various previous calculations (55, 56), then the assumption that the difference between heats of hydration of cations and anions of the same radius originates from the ion-quadrupole interaction could be inaccurate. However, the results given in Table 7 are probably reliable to within a few kcal mole-1, despite the fact that it is impossible to assess their accuracy specifically. They indicate that an anion has a more negative absolute heat of hydration than a cation of the same crystal radius. 

Dipoles tend to orient in an electric field, directed along the field gradient. Thus, dipoles are attracted to ions, and ion-dipole forces are in large part (if not solely) responsible for the tendency of cations and anions to hydrate in water, a compound with a large dipole moment. Hydration of cations and anions is depicted in Figure 1.2. The energy of an ion-dipole interaction is given by... 

How does each of the following affect the solubility of an ionic compound (a) lattice energy, (b) solvent (polar versus nonpolar), (c) enthalpies of hydration of cation and anion... 

Thus, the heat of solution for ionic compounds in water combines the lattice energy (always positive) and the combined heats of hydration of cation and anion (always negative),... 

Figure 2.4 Hydration of cations and anions. Dipoles H O form with ions aqua complexes and prevent their interaction.

The cycle allows the overall enthalpy of formation of the aqueous solution of cations and anions to be sub-divided into stages whose enthalpy changes are known except for the two enthalpies of hydration, allowing their sum to be estimated. The equation to be solved is ... 

From the values for the conventional enthalpies of hydration of the Group 1 cations (Table 2.4) and those of the halide ions (Table 2.5), it is clear that they differ enormously. This leads to the quest for absolute values, which can be compared on a more equal basis. Equations (2.17) and (2.22) connect the conventional and absolute values of cations and anions respectively, and an approximate value for Ahyd//TH +, g) may be obtained by comparing the conventional values of the enthalpies of hydration of the Group I cations and the Group 17 halide anions by using equation (2.16) modified for singly charged cations ... 

In this section the standard molar entropies of a small selection of cations and anions are tabulated and the manner of their derivation discussed. The values themselves are required in the calculation of entropies of hydration of ions, discussed in Section 2.7.2. 

The Born equation for the solvation of ions provides a means of determining the hydration energy of a charge in an aqueous medium. When two ions in an aqueous medium react (as in the case of cations and anions in an acid-base reaction), the reaction may be considered as occurring between the dissociated ions whose energy is modified due to this hydration. 

Defined as the reciprocal of resistance (siemens, ft-1) conductance is a measure of ionic mobility in solution when the ions are subjected to a potential gradient. The equivalent conductance A of an ion is defined as the conductance of a solution of unspecified volume containing one gram-equivalent and measured between electrodes I cm apart. Due to interionic effects, A is concentration dependent, and the value, A0, at infinite dilution is used for comparison purposes. The magnitude of A0 is determined by the charge, size and degree of hydration of the ion values for a number of cations and anions at 298.15K are given in table 6.6. It should be noted that HjO and... 

Chantooni and Kolthoff " derived equations which permit the calculation of hydration constants of cations and anions from the solubility products of slightly soluble salts in solutions of acetonitrile with various concentrations of water. The ionic solubility of a salt was determined by measuring the conductance. The water concentration of the acetonitrile solution was always less than 1 M. The total ionic solubility product was expanded in powers of the water concentration. The coefficients are related to the individual ionic hydration constants and were evaluated by... 

In an ionic crystal the structure adopted represents the most efficient packing of ions of opposite charge subject to the additional influence of thermal energy. Electrostatic forces are non-directional and the structure adopted is determined by three main controls (i) the relative numbers of cations and anions, (ii) the relative sizes of positive and negative ions and (iii) ionic shapes. Additional species, including hydrated or otherwise coordinated ions together with molecules of water... 

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. 

For an ionic solid whose electronic band gap is so great that no mobile electrons and holes are available, the corrosion occurs through the transfer of cations and anions from the ionic bonding state into the state of hydrated ions in aqueous solution. Let us suppose an ionic solid, MO, consisting of cation M2+ and anion O2. The ionic transfer occurs across the solid-aqua-solution interface ... 

Hydrogen-bond interactions between the water molecules of neighbouring hydration shells of cations and anions are much stronger than hydrogen-bond interactions in pure water. 

Thus, cation water clusters favour internal structures in contrast to the surface strucmres favoured by anionic water clusters. This critical difference in the structural preferences of hydrated cation and anion clusters provides important cues for the design of cation- and anion-specific ionophores and receptors. Indeed, we note that most cation receptors have spherical structures, while almost all anion receptors do not have compact spherical structures but have a vacant space around the anion binding site without full coordination (which might be exceptional for the F ion with strong electronegativity for which the excess electron is strongly bound to F due to its small ion radius). However, as the temperature increases, the hydration structure tends to be more spherical due to entropy effects. 

In this chapter, studies on the modification of ion exchange membranes to change the permselectivity between cations and that between anions are separately explained because ionic size and, especially, the hydration behavior of cations and anions are different (Table 5.1).11,12... 

---