Solubility radius

Bikerman [179] has argued that the Kelvin equation should not apply to crystals, that is, in terms of increased vapor pressure or solubility of small crystals. The reasoning is that perfect crystals of whatever size will consist of plane facets whose radius of curvature is therefore infinite. On a molecular scale, it is argued that local condensation-evaporation equilibrium on a crystal plane should not be affected by the extent of the plane, that is, the crystal size, since molecular forces are short range. This conclusion is contrary to that in Section VII-2C. Discuss the situation. The derivation of the Kelvin equation in Ref. 180 is helpful. 

The aluminium ion, charge -I- 3. ionic radius 0.045 nm, found in aluminium trifluoride, undergoes a similar reaction when a soluble aluminium salt is placed in water at room temperature. Initially the aluminium ion is surrounded by six water molecules and the complex ion has the predicted octahedral symmetry (see Table 2.5 ) ... 

Some metals are soluble as atomic species in molten silicates, the most quantitative studies having been made with Ca0-Si02-Al203(37, 26, 27 mole per cent respectively). The results at 1800 K gave solubilities of 0.055, 0.16, 0.001 and 0.101 for the pure metals Cu, Ag, Au and Pb. When these metal solubilities were compared for metal alloys which produced 1 mm Hg pressure of each of these elements at this temperature, it was found drat the solubility decreases as the atomic radius increases, i.e. when die difference in vapour pressure of die pure metals is removed by alloy formation. If the solution was subjected to a temperature cycle of about 20 K around the control temperamre, the copper solution precipitated copper particles which grew with time. Thus the liquid metal drops, once precipitated, remained stable thereafter. 

Many of the ionic fiuorides of M, M and M dissolve to give highly conducting solutions due to ready dissociation. Some typical values of the solubility of fiuorides in HF are in Table 17.11 the data show the expected trend towards greater solubility with increase in ionic radius within the alkali metals and alkaline earth metals, and the expected decrease in solubility with increase in ionic charge so that MF > MF2 > MF3. This is dramatically illustrated by AgF which is 155 times more soluble than AgF2 and TIF which is over 7000 times more soluble than TIF3. 

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

Ionic bond, 287, 288 dipole of, 288 in alkali metal halides, 95 vs. covalent, 287 Ionic character, 287 Ionic crystal, 81, 311 Ionic radius, 355 Ionic solids, 79, 81, 311 electrical conductivity, 80 properties of, 312 solubility in water, 79 stability of, 311... 

The influence of division on solubility has been mentioned in 137. According to Hulett if A, Aw are the solubilities of the substance in lumps and in grains of radius r respectively,... 

The following assumptions were made (1) The gas bubbles are evenly distributed throughout the liquid phase and have constant radius and composition (2) the concentration of the gas-liquid interface is constant and equal to C (3) no gross variations occur in liquid composition throughout the vessel and (4) the gas is sparingly soluble, and, in the case of a chemical reaction, it is removed by a first-order irreversible reaction with respect to the dissolving gas. 

What justification is there for regarding the ammonium ion as an analog of a Group 1 metal cation Consider properties such as solubility, charge, and radius. The radius of NH4+ is 137 pm. 

In almost all theoretical studies of AGf , it is postulated or tacitly understood that when an ion is transferred across the 0/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of AGfr°. Although Abraham and Liszi [17], in considering the transfer between mutually saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB andl,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170mM H2O in NB). In such a medium, hydrophilic ions such as Li, Na, Ca, Ba, CH, and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl-Fischer method [35 5]. Rais et al. [35] and Iwachido and coworkers [36-39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal... 

Bartle et al. [286] described a simple model for diffusion-limited extractions from spherical particles (the so-called hot-ball model). The model was extended to cover polymer films and a nonuniform distribution of the extractant [287]. Also the effect of solubility on extraction was incorporated [288] and the effects of pressure and flow-rate on extraction have been rationalised [289]. In this idealised scheme the matrix is supposed to contain small quantities of extractable materials, such that the extraction is not solubility limited. The model is that of diffusion out of a homogeneous spherical particle into a medium in which the extracted species is infinitely dilute. The ratio of mass remaining (m ) in the particle of radius r at time t to the initial amount (mo) is given by ... 

Q = saturation solubility of drug (macroparticles) y = interfacial tension between drug particles and the solubilizing fluids M = Molecular weight of the drug r = radius of the microscopic drug particle R = ideal gas constant... 

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