Hydration radius

Again, ions of higher charge and smaller hydrated radius bind more strongly than ions with a lower charge and a larger hydrated radius. 

Ion Ionic radius, pm CoUoidal hydrous manganese dioxide, mol/mol Hydrated radius, pm 5-Mn02, )J.mol/g... 

Mg2+ has properties that make it quite unique among biological cations. Inspection of Table 10.1 reveals that of the four common biological cations, the ionic radius of Mg2+ is much smaller than the others, whereas its hydrated radius is the largest of all four. This means that the volume of the hydrated Mg2+ cation is 400 times larger than its ionic volume (since the radius enters into the equation to the power three), compared to values around 25 times for Na+ and Ca2+, and a mere 5 times for K+. 

Cation Ionic radius (A) Hydrated radius (A) Ionic volume (A3) Hydrated volume (A3) Exchange rate (s ) Transport number... 

From the above equations, it could be easily understood that the key properties of the analytes are the hydration radius, the p A, the diffusion coefficient, and the mass fraction. They will play a role in the separation. Another important factor is the /tjff of the ion and the fidi of the EOF in accordance with Equation (8). For /tapp.AT Oj they need to have the same sign or the /teff of the ion must be smaller than the effective mobility of the EOF. 

The effect of the hydration radius of these cations is very important, and mobilities are sometimes very close or the same as for potassium and ammonium. For this reason, a complexing agent is added to the buffer. Several complexing agents such as a-hydroxyiso-butyric acid (HIBA), 18-crown-6, phthalic, malonic, tartaric, lactic, citric, oxalic, or glycolic acid may be used. 

Using a simple electrostatic interaction-based model factored into reaction rate theory, the energy barrier for ion hopping was related to the cation hydration radius. The conductance versus water content behavior was suggested to involve (1) a change in the rate constant for the elementary ion transfer event and (2) a change in the membrane microstructure that affects conduction pathways. 

The lanthanide ions, Ln are known to contract with increasing atomic number (Z), from La with a hydrated radius of 103 pm to Lu of 86 pm (lanthanide contraction). Thus one expects that the neutral LnAj complex becomes smaller with increasing atomic number, and consequently that P3 should increase and K c decrease with increasing Z. Figure 4.15d shows that measured... 

Tabled shows the results for the regression analysis of dodecylsul-fate surfactants with different alkali counterions. The degree of surfactant ion/counterion association in the adsorption layer is evidently high (from 89.9% to 92.6% counterion coverage). There is also a correlation between the hydrated radius (volume) of the counterions and Coo. The decrease in the hydrated volume of the coimterions results in the higher value of Coo, and increases the attractive force between the molecules. A pictorial presentation...

Fig. 6 Compression of the Stern layer due to the decrease in the hydration radius of the counterions...

The equilibrium constant is called the selectivity coefficient, because it describes the relative selectivity of the resin for Li+ and Na+. Selectivities of polystyrene resins in Table 26-3 tend to increase with the extent of cross-linking, because the pore size of the resin shrinks as cross-linking increases. Ions such as Li+, with a large hydrated radius (Chapter 8 opener), do not have as much access to the resin as smaller ions, such as Cs+, do. 

Remember that Na+ has a smaller hydrated radius than Li. ... 

In general, ion exchangers favor the binding of ions of higher charge, decreased hydrated radius, and increased polarizability. A fairly general order of selectivity for cations is... 

Here rh is the hydrated radius or Stokes radius of the protein. On this assumption s will be expected to increase with the relative molecular mass approximately as Mr2/3. A plot of log s against log Mr should be a straight line. Figure 3-8 shows such a plot for a number of proteins. The plots for nucleic acids, which can often be approximated as rods rather than spheres, fall on a different line from those of proteins. Furthermore, the sedimentation constant falls off more rapidly with increasing molecular mass than it should for spheres. 

The much higher capacity of the active carbon for HC104 than for HC1 has been observed by others for ion exchange resins (5). The observation is in keeping with the smaller hydrated radius of the C104" ion as noted above. Chu et al. (5) have claimed that an additional effect derives from the inability of the C104" ion to orient surrounding water molecules in bulk solution as effectively as does the Cl" ion. The water... 

Dissolution of alkali metal cations such as Cs+ results in short-range liquid order in water as a primary solvation shell of about eight water molecules is established about the metal cation. Lithium, however, exerts a much greater polarising power and is capable of organising a first- and second-coordination sphere of about 12 water molecules about itself, resulting in a much larger hydrated radius for the ion and hence decreased ionic mobility. 

For some electrolytes, the characteristic distance d, required to fit the experimental data on surface tension with Eq. (17) is smaller than the hydrated radius of the ions and might even become negative (e.g. HC1, HN03, HC104 [29]). This means that at least one component of the electrolyte is preferentially adsorbed on the interface. Therefore, dB can be regarded only as a parameter in an extremely simplified theory. 

It is obvious, that the cation and anion radius are mostly different, for example the hydrated radius of r(Na+) = 102 + 116, r(Cs+) = 170 + 49, r(Cl ) = 181 +43, r(I ) = 220 + 26 [pm]. As can be seen, the radii of the hydrated anions are usually larger than that of the hydrated cations. This relation is valid for the ion devoid of the hydration shield. From this reason the assumption of the separate IHP planes for adsorbing cations and anions is rational. 

A. Generally, for two cations with the same valence (e.g. Na+ vs. K+), the cation with the smaller hydrated radius, or least negative heat of hydration (Tables 4.1 and 4.4), is preferred (e.g., K+). 

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