Solubility of small crystals

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. 

Although many biological fluids appear to be supersaturated with calcite, spontaneous mineralization does not occur. A number of explanations have been proposed, including the effects of crystal poisons and the high solubility of small crystal nuclei. An alternative approach to the problem is to suggest that there is an energy barrier which has to be overcome by the... 

The solubility of so-called insoluble materials is often ignored in surface charging studies, but it must be realized that a certain fraction of the adsorbent undergoes dissolution in the form of various species. In some experiments, this solubility is in fact immaterial, but in a few other experiments, solubility matters. Solubility may be responsible for irreproducibility of experiments and for scatter in the PZCs/IEPs reported in the literature. Solubility depends on temperature, pH, and ionic strength. Solubilities of thermodynamically stable forms are lower than those of less stable forms, and solubilities of small crystals are higher than those of large crystals. Moreover, dissolution is a slow process, and the concentration of dissolved species in solution in many experiments is well below saturation. Thus, thermodynamic (equilibrium) data on solubility are of limited relevance to surface charging experiments with short equilibration times. 

In principle, then, small crystals should show a higher solubility in a given solvent than should large ones. A corollary is that a mass of small crystals should eventually recrystallize to a single crystal (see Ostwald ripening. Section IX-4). 

For crystallization, the RNase Nj fraction eluted from the CM-cellulose column or Sephadex G-75 column was concentrated by lyophilization and then dialyzed against distilled water at 4°. During dialysis, fine needle-shaped crystals were formed. The specific activity of the crystals was about 2200. The solubility of the crystals is small around neutrality and increases below pH 4.0. Thus, the crystals are usually dissolved in dilute acetic acid. 

Comparison of Solid-Solubilities. The limit of solid miscibility has been related to the energy of distortion of the crystal lattice when atoms of a second component are introduced into the lattice Scott (6) and Lawson (11) have expressed the distortion energy as a function of the molal volumes of the two components. Both authors recognized that the solubility of small atoms in a lattice of large atoms is greater than the... 

At this point the mother liquor should be rich enough in the more soluble Z-diacetate (2) for its isolation. Concentrate the methanol mother liquor and washings from the third crop of 1 to a volume of 4-5 mL, stopper the flask, and let the solution stand undisturbed overnight. The Z-diacetate (2) sometimes separates spontaneously in large rectangular prisms of great beauty. If the solution remains supersaturated, addition of a seed crystal of 2 causes prompt separation of the Z-diacetate in a paste of small crystals (e.g., 215 mg, mp 118-119°C then 70 mg, mp 116-117°C). 

Some solids are only weakly soluble in water but dissolve readily in acidic solutions. Copper and nickel sulfides from ores, for example, can be brought into solution with strong acids, a fact that aids greatly in the separation and recovery of these valuable metals in their elemental forms. The effect of pH on solubility is shown dramatically in the damage done to buildings and monuments by acid precipitation (Fig. 16.8). Both marble and limestone are made up of small crystals of calcite (CaCOs), which dissolves to only a limited extent in natural rain (with a pH of about 5.6) but dissolves much more extensively as the rainwater becomes more acidic. The reaction... 

The vapour pressure of water in small drops is greater than that of water in mass, and the solubility of a solid is greater when in a state of fine subdivision than when in large pieces cf. Hulett, Z, physzkal. Ckem, 1901, 37, 385). The vapour pressure of small crystals is also greater than that of large ones (Pawloff, Z. physikaL Ckem, 8, 3x6). 

It is interesting to note that when small mismatches in size occur, the solubility of small molecules in a host lattice of larger ones is more probable than the solubility of a large molecule in a lattice of smaller ones (Hildebrand and Scott 1950). A striking example of this behavior is found in a comparison of impurity incorporation in L-glutanic acid crystals where incorporation decreases with increasing molecular volume of impurity (Harano and Yamamoto 1982). A similar result is found for the incorporation of cationic species in ionic crystals where the uptake is found directly related to the charge on the species and its molecular size (van der Sluis et al. 1986). 

Crystals can only form from a supersaturated solution or a supercooled melt [Mers-mann 2000]. The initial formation of a solid phase requires a sufficiently large degree of supersaturation or supercooling because of the increased solubility of very small crystals. When small and large crystals are introduced into a saturated solution, the large crystals grow while the small crystal dissolve. This phenomenon is described by the Gibbs-Thomson equation, which describes how the solubility of a crystal depends on its thickness i (Equation 2.3.5-1) ... 

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