Solution-crystal equilibrium

Prigogine, 1. and Defay, R. (1954) Solution-crystal equilibrium eutectics, in Chemical Thermodynamics, Longmans, Green, London, pp. 357-367. 

Colourless crystals m.p. I25°C, soluble in water and alcohol. In aqueous solution forms equilibrium with its lactones. Gluconic acid is made by the oxidation of glucose by halogens, by electrolysis, by various moulds or by bacteria of the Acetobacter groups. 

By saccharic acid is usually meant D-gluco-saccharic acid, m.p. 125-126°C, obtained by the oxidation of glucose or starch. This exists in water solution in equilibrium with its two y lactones, both of which can be obtained crystalline, though the acid itself does not crystallize readily. 

The amino form 66a of 5-pyridylamino-l,2,4-triazole stabilized by two intramolecular hydrogen bonds is the only tautomer observed by the X-ray study of the crystal (90KGS1632). However in DMSO-dg, DMF-d7, and HMPA-di8 solutions, the equilibrium involves three tautomeric forms 66a-66c (Scheme 31) (90KGS1632). 

The points R have to be on a straight line terminating in the composition of the methanol hydroquinone clathrate (A) in equilibrium with a-hydroquinone at 25°C. The point B roughly corresponds to the composition of the clathrate obtained by Palin and Powell24 when crystallizing hydroquinone from methanol points between A and B form a continuous range of solid solutions in equilibrium with liquid phases whose compositions lie on the curve CE. It is found that the equilibrium clathrate has a composition corresponding to y — 0.474 at 25°C. 

The activity of a solvent can be determined in a solution from the change in the freezing temperature or the boiling temperature due to the addition of a solute. Consider a process in which a solution is cooled until solid (component 1) crystallizes from solution. An equilibrium is established so that... 

Crystallization involves formation of a solid product from a homogeneous liquid mixture. Often, crystallization is required as the product is in solid form. The reverse process of crystallization is dispersion of a solid in a solvent, termed dissolution. The dispersed solid that goes into solution is the solute. As dissolution proceeds, the concentration of the solute increases. Given enough time at fixed conditions, the solute will eventually dissolve up to a maximum solubility where the rate of dissolution equals the rate of crystallization. Under these conditions, the solution is saturated with solute and is incapable of dissolving further solute under equilibrium conditions. In fact, the distinction between the solute and solvent is arbitrary as either component can be considered to be the solute or... 

Two equiv. of 6,6-di(cyclopropyl)fulvene react at 60 °C over a period of a week with Ca[N(SiMe3)2]2-(THF)2 bis in THF to yield the metallocene 170. The heteroleptic amido complex 171 is detected as an intermediate with 111 and 13C 1H NMR spectroscopy. A 1 1 reaction of the calcium amide and 170 also produces 171 in solution, an equilibrium involving these three derivatives exists (Equation (30)). The calcocene 170 crystallizes at — 20 °C from THF as colorless cuboids. The metal center is surrounded by the four ligands in a distorted tetrahedral manner, and the cyclopentadienyl group and the propylidene fragment are coplanar with each other.393... 

If the equilibrium expressed in Equation (7) is attained only between the crystal surface and the aqueous solution, the equilibrium is described by ... 

In solid-state electrodes the membrane is a solid disc of a relatively insoluble, crystalline material which shows a high specificity for a particular ion. The membrane permits movement of ions within the lattice structure of the crystal and those ions which disrupt the lattice structure the least are the most mobile. These usually have the smallest charge and diameter. Hence, only those ions that are very similar to the internal mobile ions can gain access to the membrane from the outside, a feature that gives crystal membranes their high specificity. When the electrode is immersed in the sample solution, an equilibrium is established between the mobile ions in the crystal and similar ions in the solution and the resulting potential created across the membrane can be measured in the usual manner. 

Porschke and colleagues have observed a curious isomerization of the complex Pd(dippe) 2 / i- 7 / -HC2C2H in dg-thf solution at —80°C. Over a period of about a week both Pd(dippe) moieties become coordinated to the same C C bond. Warming a solution of this lower symmetry isomer to 0°C results in only partial reversal of the isomerization. The isomers are apparently in slow equilibrium, with various subtle and unspecified factors determining which one is preferred and while the Pd(dippe) 2 Ai- M- -HC2C2H (68) form is thermodynamically favored in solution, crystallization affords Pd(dippe) 2 /z-/7 >7 -HC2CsCH (69) (Scheme 19). ... 

Let us consider the distribution of a trace element A and a carrier B between a crystal and an ideal aqueous solution at equilibrium. Defining... 

Saturated Beyond a certain point, adding more solute to a solution doesn t result in a greater amount of solvation. At this point, the solution is in dynamic equilibrium the rate at which solute becomes solvated equals the rate at which dissolved solute crystallizes, or falls out of solution. A solution in this state is saturated. 

The common ion effect must also be considered, since it affects each one of the crystallization equilibrium, both in supercritical and subcritical water. Adding sodium acetate, for instance, to a solution containing sodium salts would favour sodium bicarbonate precipitation (formed from oxidation of acetate), thus avoiding the precipitation of more corrosive salts, such as the chloride or sulfate [28],... 

Some carbohydrates actively inhibit the crystallization of lactose, whereas others do not. Carbohydrates that are active possess either the /3-galactosyl or the 4-substituted-glucose group in common with lactose, so that adsorption can occur specifically at certain crystal faces (Van Krevald 1969). (3-Lactose, which is present in all lactose solutions [see Equilibrium in Solution (Mutarotation )], has been postulated to be principally responsible for the much slower crystallization of lactose compared with that of sucrose, which does not have an isomeric form to interfere with the crystallization process (Van Krevald 1969). Lactose solubility can be decreased substantially by the pres-... 

It is a straightforward but rather lengthy exercise to write down and evaluate the flux equations jA, jA, jB, jB under the assumption of local (vacancy) equilibrium (A v = 0). We find that five independent L-ti are needed to fully describe the transport in such a system. However, only four experimental parameters DA, DB, DA, and Db are available from flux measurements. Since DA = DB, jA jB in the solid solution crystal. Lattice site conservation requires that the sum of the fluxes /a + 7b + 7v = 0, that is,, /v = 0, despite X = 0. The external observer of the A-B interdiffusion process therefore sees the fluxes... 

But where there is an equilibrium among two or more conformations of the enzyme in solution, crystallization may select out only one of the conformations. a-Chymotrypsin has a substantial fraction of an inactive conformation present under the conditions of crystallization, but only the active form of the enzyme crystallizes. An allosteric effector molecule that changes the conformation of the protein in solution may have no effect on the crystalline protein, as, for example, with phosphorylase b.5A The enzyme is frozen in one conformation, with the crystal lattice forces preventing any conformational change. On the other hand, the addition of an effector to phosphorylase a causes the crystals first to crack and then to anneal, giving crystals of the enzyme in a second conformation. 

FIGURE 11.5 A super- saturated solution of sodium acetate in water. When a tiny seed crystal is added, larger crystals begin to grow and precipitate from the solution until equilibrium is reached. 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

In a saturated solution, an equilibrium exists between the rate of precipitation of solute particles and the rate of dissolution of solute particles. The rate of precipitation equals the rate of dissolution. The shape of a crystal of solute added to a saturated solution will change after a period of time at a constant temperature and pressure, but its mass will remain the same. The equilibrium between dissolving and precipitation is dynamic, a continuous process. 

The dissolution of crystals is a well-known phenomenon. It has sometimes been misunderstood that the reaction is the reverse of the deposition process, but this is only true for a saturated solution in equilibrium with crystals. 

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