Radius of hydration

The type of catalyst influences the rate and reaction mechanism. Reactions catalyzed with both monovalent and divalent metal hydroxides, KOH, NaOH, LiOH and Ba(OH)2, Ca(OH)2, and Mg(OH)2, showed that both valence and ionic radius of hydrated cations affect the formation rate and final concentrations of various reaction intermediates and products.61 For the same valence, a linear relationship was observed between the formaldehyde disappearance rate and ionic radius of hydrated cations where larger cation radii gave rise to higher rate constants. In addition, irrespective of the ionic radii, divalent cations lead to faster formaldehyde disappearance rates titan monovalent cations. For the proposed mechanism where an intermediate chelate participates in the reaction (Fig. 7.30), an increase in positive charge density in smaller cations was suggested to improve the stability of the chelate complex and, therefore, decrease the rate of the reaction. The radii and valence also affect the formation and disappearance of various hydrox-ymethylated phenolic compounds which dictate the composition of final products. 

Fig. 5.13 Hydraulic radius of hydrated Ca3Si05 calculated from the adsorption side of water vapour isotherms (Skalny). 

Figure 2.18 Effect of radius of hydration on distance between counterion and fixed charge of ion-exchange stationary phase. Cesium, with smaller radius of hydration, is shown with one water molecule (small circle) between it and fixed charge of the bead. Lithium is shown with three water molecules.

The reason for this anomaly is that the ions are hydrated in solutions. Since Li+ is very small, it is heavily hydrated. This makes the radius of hydrated ion large, and hence it moves very slowly. Cs+ is least hydrated and radius of hydrated Cs+ ion is smaller. 

Between the diffuse layer and the interface lies the Stern layer, i.e., layer of ions, which are not subjected to Brownian motion. Two levels are identified within it the internal with unhydrated ions and external with hydrated ions. Most of ions in the Stern layer are hydrated, so they caimot approach too closely the mineral surface. Because of this Helmholtz plane is drawn through the centers of immobile hydrated ions, and the thickness of Stern layer 8 is assumed equal to half of the median radius of hydrated ions (about 2 A). Electrostatic field in such layer is defined by the charge of mineral s surface, on the one hand, and by the charge of Helmholtz plane, on the other. It characterizes the density of electric permittance, which, according to equation (2.98), is equal to... 

Polymeric betaines are usually insoluble in pure water and have gel characteristics but are soluble in salt-containing solutions. The loss of water solubihty and gel-like structure that adopts polybetaines are probably due to the formation of intra- and interchain ion contacts which result in the appearance of cross-linked networks. The intrinsic viscosity [t]], second virial coefficient A2, exponent a in the MKH equation, the radius of hydration Rg and the hydrodynamic radius % increase with the increase in salt concentration [132] (Table 16). 

Rate Constants and Ionic Radius of Hydrated Cations Applied for Synthesis of Resoles by Using a Ratio of Methanal/Phenol = 1.5 at 60°CandapH Valueof 8 (data from ref [73])... 

From regular solution theory it is found that the extent of ion pairing in a system will increase as the polarizability and valence of the counterion increase. Conversely, a larger radius of hydration will result in greater ion separation. It has been found that, for a given hydrophobic tail and anionic head group, the cmc decreases in the order Li+ > Na > > Cs >... 

The effectiveness of a given ion at altering the miceUization process can be qualitatively related to the radius of hydration of the added ions, and the contribution of the cations and anions will be approximately additive. In general, the smaller the radius of hydration of the ion, the greater is its effect on the cmc. The approximate order of effectiveness of anions at decreasing the cmc is the following ... 

With the knowledge now of the magnitude of the mobility, we can use equation A2.4.38 to calculate the radii of the ions thus for lithium, using the value of 0.000 89 kg s for the viscosity of pure water (since we are using the conductivity at infinite dilution), the radius is calculated to be 2.38 x 10 m (=2.38 A). This can be contrasted with the crystalline ionic radius of Li, which has the value 0.78 A. The difference between these values reflects the presence of the hydration sheath of water molecules as we showed above, the... 

The surface behavior of Na is similar to that of Cs, except that inner sphere complexes are not observed. Although Na has the same charge as Cs, it has a smaller ionic radius and thus a larger hydration energy. Conseguently, Na retains its shell of hydration waters. For illite (Figure 6), outer sphere complexes resonate between -7.7 and -1.1 ppm and NaCl... 

A. Hydration energy profile, using the Bom formalism (Eqn. 1), shows the drop of ion self energy as a function of the radius of a hydration sphere. Note that even with a hydration shell of 10 A radius not all of the hydration energy is obtained. 

The radii av a2 and coordination numbers zv z2 follow from x-ray analysis (cf. Section I.B), and aQ/2 — 1.25 A corresponds to Pauling s van der Waals radius of 1.40 A for a covalently bound oxygen atom.25 The value of eQlk — 166.9°K was chosen to obtain agreement between calculated and experimental values of the equilibrium vapor pressure of argon hydrate at 0°C. 

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