Solubility infinitely soluble

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. 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

Monomers. A wide variety of monomers can be used, and they are chosen on the basis of cost and abiUty to impart specific properties to the final product. Water solubiUties of iadustriaHy important monomers are shown ia Table 1 (38). The solubiUty of the monomer ia water affects the physical chemistry of the polymerization. Functional monomers like methacrylic and acryUc acid, infinitely soluble ia water, are also used. These monomers impart long-term shelf stabiUty to latices by acting as emulsifiers. The polymerization behavior of some monomers, such as methacrylic acid, as well as the final latex properties are iafiuenced by pH. For optimum results with these acids, polymerization is best performed at a pH of ca 2. After polymerization, the latex is neutralized to give adequate shelf stabiUty at tractable viscosities. 

Like //-butyUithium, j iZ-butyUithium is infinitely soluble in most hydrocarbons, such as pentane and hexane. Its solutions in hexane are flammable and pyrophoric and therefore should be handled like //-butyUithium (96,100). j iZ-ButyUithium also is very soluble in ethers, but the ether solutions must be kept cold because ether cleavage is more rapid than in the presence of //—butyUithium (122). j iZ-ButyUithium has a t 2 of 2 d at 25°C in di-//-butyl ether and of 1 d at 25°C in di-//-hexyl ether. 

Properties. o-Nitiotoluene [88-72-2] is a clear yeUow liquid. The solid is dimorphous and the melting points of the a- and P-forms ate —9.55 and —3.85 C, respectively. o-Nitrotoluene is infinitely soluble in benzene, diethyl ether, and ethanol. It is soluble in most organic solvents and only slightly soluble in water (0.065 g in 100 g of water at 30°C). The physical properties of o-nitrotoluene are hsted in Table 9. 

Styrene is a colorless Hquid with an aromatic odor. Important physical properties of styrene are shown in Table 1 (1). Styrene is infinitely soluble in acetone, carbon tetrachloride, benzene, ether, / -heptane, and ethanol. Nearly all of the commercial styrene is consumed in polymerization and copolymerization processes. Common methods in plastics technology such as mass, suspension, solution, and emulsion polymerization can be used to manufacture polystyrene and styrene copolymers with different physical characteristics, but processes relating to the first two methods account for most of the styrene polymers currendy (ca 1996) being manufactured (2—8). Polymerization generally takes place by free-radical reactions initiated thermally or catalyticaHy. Polymerization occurs slowly even at ambient temperatures. It can be retarded by inhibitors. 

Infinitely soluble in acetone, carbon tetrachloride, benzene, diethyl ether, / -heptane, and ethanol. ... 

Calculation of Liquid-to-Gas Ratio The minimum possible liquid rate is readily calculated from the composition of the entering gas and the solubility of the solute in the exit liquor, saturation being assumed. It may be necessaiy to estimate the temperature of the exit liquid based on the heat of solution of the solute gas. Values of latent and specific heats and values of heats of solution (at infinite dilution) are given in Sec. 2. 

The more volatile (i.e., less soluble) components will be only partially absorbed even though the effluent liquid becomes completely saturated with respecd to these lighter substances. When a condition of saturation exists, the value of will remain finite even for an infinite number of plates or transfer units. This can be seen in Fig. 14-9, in which the asymptotes become vertical for values of greater... 

Very soluble (>50g/100g) oo Infinitely soluble (soluble in all proportions)... 

Aromatic steroids are virtually insoluble in liquid ammonia and a cosolvent must be added to solubilize them or reduction will not occur. Ether, ethylene glycol dimethyl ether, dioxane and tetrahydrofuran have been used and, of these, tetrahydrofuran is the preferred solvent. Although dioxane is often a better solvent for steroids at room temperature, it freezes at 12° and its solvent effectiveness in ammonia is diminished. Tetrahydrofuran is infinitely miscible with liquid ammonia, but the addition of lithium to a 1 1 mixture causes the separation of two liquid phases, one blue and one colorless, together with the separation of a lithium-ammonia bronze phase. Thus tetrahydrofuran and lithium depress the solubilities of each other in ammonia. A tetrahydrofuran-ammonia mixture containing much over 50 % of tetrahydrofuran does not become blue when lithium is added. In general, a 1 1 ratio of ammonia to organic solvents represents a reasonable compromise between maximum solubility of steroid and dissolution of the metal with ionization. 

The preceding example implied that water solubility is related to polarity, and indeed the equating of hydrophilic character with polarity (and of hydrophobic character with nonpolarity) is often made. Thus, we may add water solubility to the list of pertinent physical (or chemical) properties related to polarity. If a substance is infinitely soluble in water, high polarity is usually inferred. 

Pure NI3 has not been isolated, but the structure of its well-known extremely shock-sensitive adduct with NH3 has been elucidated — a feat of considerable technical virtuosity.Unlike the volatile, soluble, molecular solid NCI3, the involatile, insoluble compound [Nl3.NH3] has a polymeric structure in which tetrahedral NI4 units are comer-linked into infinite chains of -N-I-N-I- (215 and 230 pm) which in turn are linked into sheets by I-I interactions (336 pm) in the c-direction in addition, one I of each NI4 unit is also loosely attached to an NH3 (253 pm) that projects into the space between the sheets of tetra-hedra. The stmcture resembles that of the linked Si04 units in chain metasilicates (p. 349). A further interesting feature is the presence of linear or almost linear N-I-N groupings which suggest the presence of 3-centre, 4-electron bonds (pp. 63, 64) characteristic of polyhalides and xenon halides (pp. 835-8, 897). 

The critical hydrogen content for the ductility loss increased with increasing hydrogen solubility in the alloy. The fracture surfaces were not characteristic of those found under conditions of SCC. In terms of hydrogen and deuterium solubility in a similar series of bcc alloys, the equilibrium constants were determined at infinite dilution as a function of temperature The free energy function was expressed in terms of the bound-proton model. 

Of the relatively few organic compounds that dissolve readily in water, many contain —OH groups. Three familiar examples are methyl alcohol, ethyl alcohol, and ethylene glycol, all of which are infinitely soluble in water. 

If the solubility of either component in the other is unlimited ( free miscibility, as with alcohol and water), there may be an infinite number of solutions, lying between the two pure substances as limiting cases. The solubility may be limited in one or both directions. Thus, water and salt form a series of solutions extending indefinitely towards pure water as one limit, but bounded by saturated salt solution as the other limit water and ether form a continuous series of solutions bounded on one side by a saturated solution of ether in water, and on the other side by a saturated solution of water in ether. In the region of continuous miscibility all the properties of the solution vary... 

Show by substitution that when a gas of solubility C 1 is absorbed into a stagnant liquid of infinite depth, the concentration at time r and depth x is ... 

In a continuous steady state reactor, a slightly soluble gas is absorbed into a liquid in which it dissolves and reacts, the reaction being second order with respect to the dissolved gas. Calculate the reaction rate constant on the assumption that the liquid is semi-infinite in extent and that mass transfer resistance in the gas phase is negligible. The diffusivity of the gas in the liquid is 10" 8 m2/s, the gas concentration in the liquid falls to one half of its value in the liquid over a distance of 1 mm, and the rate of absorption at the interface is 4 x 10"6 kmol/m2 s. 

A soluble gas is absorbed into a liquid with which it undergoes a second-order irreversible reaction. The process reaches a steady-state with the surface concentration of reacting material remaining constant at (.2ij and the depth of penetration of the reactant being small compared with the depth of liquid which can be regarded as infinite in extent. Derive the basic differential equation for the process and from this derive an expression for the concentration and mass transfer rate (moles per unit area and unit time) as a function of depth below the surface. Assume that mass transfer is by molecular diffusion. 

If hydrogen bonding is possible between solute and solvent, this greatly increases solubility and often results in large or even infinite solubility where none would otherwise be expected. 

The molecular distributions for polymers formed by condensations involving polyfunctional units of the type R—A/ resemble those for the branched polymers mentioned above, except for the important modification introduced by the incidence of gelation. The generation of an infinite network commences abruptly at the gel point, and the a-mount of this gel component increases progressively with further condensation. Meanwhile, the larger, more complex, species of the sol are selectively combined with the gel fraction, with the result that the sol fraction decreases in average molecular complexity as well as in amount. It is important to observe that the distinction between soluble finite species on the one hand and infinite network on the other invariably is sharp and by no means arbitrary. 

It is not only the solid state of a drug that suffers from ambiguities, but also the aqueous state. The state relevant for the intrinsic solubility is the state of the saturated solution of the neutral species. Since most aqueous drug solubilities are small, direct interactions of the drug molecules are usually rare. Hence, this state is usually very similar to the state of the drug at infinite dilution in water. Most computational methods disregard saturation effects. Usually this is a good approximation, but one should keep in mind that this approximation may result in some moderate, but systematic errors at the upper end of the solubility scale. 

Salts such as silver chloride or lead sulfate which are ordinarily called insoluble do have a definite value of solubility in water. This value can be determined from conductance measurements of their saturated solutions. Since a very small amount of solute is present it must be completely dissociated into ions even in a saturated solution so that the equivalent conductivity, KV, is equal to the equivalent conductivity at infinite dilution which according to Kohlrausch s law is the sum of ionic conductances or ionic mobilities (ionic conductances are often referred to as ionic mobilities on account of the dependence of ionic conductances on the velocities at which ions migrate under the influence of an applied emf) ... 

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 ... 

Polymer-bound antioxidants must be molecularly dispersed (i.e. infinitely soluble) and cannot be physically lost from the substrate. High-MW phenolic AOs are preferred for applications requiring FDA approval, minimal discoloration, and long service life at high temperatures. Antioxidants are used for protection of polymers, plastics, elastomers, foods, fuels and lubricants. 

The solubility of ethyl alcohol in water is said to be infinite. What does that mean ... 

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