Solubility cross-sectional area

The conditions for surfactants to be useful to form Hquid crystals exist when the cross-sectional areas of the polar group and the hydrocarbon chain are similar. This means that double-chain surfactants are eminently suited, and lecithin (qv) is a natural choice. Combiaations of a monochain ionic surfactant with a long-chain carboxyHc acid or alcohol yield lamellar Hquid crystals at low concentrations, but suffer the disadvantage of the alcohol being too soluble ia the oil phase. A combination of long-chain carboxyHc acid plus an amine of equal chain length suffers less from this problem because of extensive ionisa tion of both amphiphiles. 

The adsorption of hafnium species on glass was found to increase with the solution pH and hafnium concentration. The effects on the adsorption of the solution preparation and age were studied and the equilibration time for the adsorption process was determined. The surface area of the glass sample was determined by the B.E.T. method using water vapor. The results are discussed in terms of the hydrolyzed hafnium(IV) species. At equilibrium, nearly monolayer coverage was obtained at pH > 4.5. Under these conditions hafnium is in the solution in its entirety in the form of neutral, soluble Hf(OHspecies. In the close packed adsorption layer the cross-sectional area of this species is 24 A which is nearly the same as for water on silica surfaces. 

Orifice size. To achieve an optimal zero-order delivery profile, the cross-sectional area of the orifice must be smaller than a maximum size S lnax to minimize drug delivery by diffusion through the orifice. Furthermore, the area must be sufficiently large, above a minimum size S mm, to minimize hydrostatic pressure buildup in the system. Otherwise, the hydrostatic pressure can deform the membrane and affect the zero-order delivery rate. Therefore, the cross-sectional area of the orifice S0 should be maintained between the minimum and maximum values. Typically, a diameter of about 0.2 mm through a membrane of 0.2-mm thickness is needed to maintain a delivery rate on the order of 10 mg/h for water-soluble compounds.11 The minimum cross-sectional area can be estimated from the following equation ... 

Here, II,L is the hydrogen solubility, which is assumed to remain essentially constant along the entire length of the reactor. The quantity r.V is the open volume of the reactor, A is the transverse cross-sectional area for the hydrogen transfer (as shown in Fig. 7-32), k, is the liquid-film mass-transfer coefficient at the gas -liquid interface, and a is the gas-liquid interfacial area per unit volume of the open space in the reactor. In a physical sense, Eq. (7-39) equates the mass transfer from the gas into the liquid phase with the mass transfer at the surface of the catalyst tube. The constant C, in Eq. (7-39) is obtained, by using the condition (7-40), as... 

In comparison with saturated chains containing the same number of carbon atoms, organic compounds possessing unsaturated chains exhibit a lower melting point, higher solubility, CMC, chemical activity, and larger chain cross-sectional area. This is shown in Table 5.13. Four factors that affect the solubility products of reagents with unsaturated chains are ... 

A tower packed with metal Montz B1-300 structured packing is to be designed to absorb S02 from air by scrubbing with water. The entering gas, at an S02-free flow rate of 37.44 mol/m2-s of bed cross-sectional area, contains 20 mol% of S02. Pure water enters at a flow rate of 1976 mol/m2-s of bed cross-sectional area. The exiting gas is to contain only 0.5 mol% S02. Assume that neither air nor water will transfer between the phases and that the tower operates isothermally at 2 atm and 303 K. Equilibrium data for solubility of S02 in water at 303 K and 1 atm have been fitted by least squares to the equation (Seader and Henley, 1998) ... 

Harkins calculated from the solubility of styrene in water (0.00368 mol dm at 50 °C [50]) that there are 4 x 10 molecules dm . In a 3% solution of potassium dodecanoate there are about 1 x 10 micelles dm , but with 61 molecules per micelle with an unswollen radius of 2.1 nm the cross-sectional area of the monomer-swollen micelles exceeds that of the styrene molecules by a factor of at least 12. Hence the micelles are more likely to capture initiator radicals produced in the aqueous phase. Polymerization within the micelles must be much faster than in the water because the concentration of styrene will be much the same as in bulk (8.5 mol dm ). The molar mass of the polystyrene produced is much larger than the molar mass of all the styrene molecules solubilized in a micelle thus, the monomer must be able to diffuse through the aqueous phase from other micelles and monomer droplets to allow the polymer radical to continue to grow until it is finally terminated by the entry of another initiator radical from the aqueous phase. Under the standard conditions of the mutual recipe (Table 4.1) there is 180 g water to 100 g styrene taking the emulsion droplets to have a radius of 1 pm, the ratio of the total cross-sectional areas of droplets to micelles to monomer molecules is about 1 30 2.5. The ratio of total surface areas would be even more heavily biased in favour of micelles. Hence it is probable that many more radicals will be captured from the aqueous phase by the micelles than by the emulsion droplets or than react with the monomer molecules in aqueous solution. 

The cross-sectional area of the hydrophobic chain or of the hydrophilic head group, whichever is greater, determines the molecular occupied area. Since the adsorbing species forming the Gibbs mono-layer has a sufficiently large solubility in the solvent, when the area of the saturated surface is more expanded, the surface-active molecules dissolved in the solution will fill in the created area. 

Permeability equations for diffusion in solids. In many cases the experimental data for diffusion of gases in solids are not given as diffusivities and solubilities but. as permeabilities, Pm, in m of solute gas A at STP (0°C and 1 atm press) diffusing per second per m cross-sectional area through a solid 1 m thick under a pressure difference of 1 atm pressure. This can be related to Pick s equation (6.5-2) as follows. 

The reciprocal value of the Henry coefficient is also denoted as gas solubility. For a given diffusion coefficient in the membrane material, the molar flux per unit cross-sectional area is ... 

Throughout this discussion, unless otherwise specified, x and y will refer to solute concentrations expressed as mole fractions in the raffinate and extract, respectively, and rates of flow of raffinate R and of extract E will be expressed as mol/(cross-sectional area)(time). Except in special cases, the transfer of solute usually results in changes of mutual solubility of the contacted liquids, so that in general all components of the systems transfer from one phase to the other. The F-type mass-transfer coefficients are capable of handling this problem, but in... 

The permeability of a system represents the amount of gas passing through a material specimen with cross-sectional area A and thickness d in a specific unit of time t. The process involves two basic mechanisms, namely, thermodynamic solubility of the permeant in the surface of the films and kinetic diffusion of the permeating molecules across the film to the other surface (Shields, 2008 Gonzo et al., 2006 Robeson, 2003 Kamal and Jinnah, 1984). Thus, permeability can be expressed as a product of solubility constant S and diffusion coefficient D, P = S x D. 

The instability of the fluorocarboxylic acid film on water may have been caused by the significant, albeit very low, solubility of the acid in water. The fact that the fluorocarbon chain has a larger cross-sectional area than the carboxyl group may also have contributed to film instability. 

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