Solute, effective volume

According to the concept of free volume as the effective volume over which the centers of gravity of the molecules are distributed, the entropy may be taken as that of a perfect gas composed of the same number of molecules confined to a volume equal to the free volume. Since the entropy of a perfect gas consisting of n molecules depends on its volume as nk InF, the increase in entropy owing to the greater free volume available to the solvent molecules in the solution will be... 

According to the interpretation given above, the intrinsic viscosity is considered to be proportional to the ratio of the effective volume of the molecule in solution divided by its molecular weight. In particular (see Eq. 23), this effective volume is represented as being proportional to the cube of a linear dimension of the randomly coiled polymer chain,... 

The rheological behaviour of polymeric solutions is strongly influenced by the conformation of the polymer. In principle one has to deal with three different conformations, namely (1) random coil polymers (2) semi-flexible rod-like macromolecules and (2) rigid rods. It is easily understood that the hydrody-namically effective volume increases in the sequence mentioned, i.e. molecules with an equal degree of polymerisation exhibit drastically larger viscosities in a rod-like conformation than as statistical coil molecules. An experimental parameter, easily determined, for the conformation of a polymer is the exponent a of the Mark-Houwink relationship [25,26]. In the case of coiled polymers a is between 0.5 and 0.9,semi-flexible rods exhibit values between 1 and 1.3, whereas for an ideal rod the intrinsic viscosity is found to be proportional to M2. 

A similar effect may exist for hydrophobic interaction between solute and stationary phase, as one solute may adsorb more strongly to the stationary phase than another. It has also been remarked that a flexible polymer confined to a pore should be at a lower entropy than one in bulk solution, leading to exclusion in excess of that expected for a simple geometric solid.23 Even in the absence of interactions, a high concentration of a small component can lead to an excluded volume effect, since the effective volume inside the pore is reduced. 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

The principle of depletion is illustrated in Figure 1. If a surface is in contact with a polymer solution of volume fraction , there is a depletion zone near the surface where the segment concentration is lower than in the bulk of the solution due to conformational entropy restrictions that are, for nonadsorbing polymers, not compensated by an adsorption energy. The effective thickness of the depletion layer is A. Below we will give a more precise definition for A. 

A particularly simple case is shown in Figure 18.1, in which the volume is a linear function of the mole number of glycolamide in a kilogram of water. In this case, the partial molar volume of solute is constant and is equal to the slope of the line. The partial molar volume represents the effective volume of the solute in solution, that is, the increase in volume per mole of solute added. From Equation (9.27), written for the volume function. 

A Proposed Theory. In earlier publications (1-3), a theory was proposed to correlate solubilization rate, interfacial tension and size of the surfactant aggregate (1) the interfacial tension lowering between the oil-surfactant solution interface is a function of the rate of solubilization of oil, and (2) the rate of solubilization (AS/At) is a function of the effective volume for solubilization ... 

The simplest case of compositional dependence is the zero-order reaction, in which the concentration gradient is not affected by concentration. Denoting the molar concentration of the ith element (or component) as c, (and neglecting surface area and volume of solution effects), we have... 

Volume from which a segment of a macromolecule in solution effectively excludes all other segments, i.e., those belonging to the same macromolecule as well as those belonging to other macromolecules. 

Volume from which a macromolecule in a dilute solution effectively excludes all other macromolecules. 

After the N2 solute molecules are placed, all remaining sites are filled with solvent molecules. Since our model is specifically interested in the solute-solute excluded-volume effect, we may say that there is only one way for the solvent molecules to be placed. Although this overlooks details about the solvent, we see presently that such details would eventually be subtracted, so we lose nothing by this simplification. Equation (53) therefore gives the expression for Qmix we sought as the first step of our derivation. 

Busch and Bailar1 obtained optically active solutions of one of the enantiomers of the ethylenediaminetetraacetato-cobaltate(III) ion by selective adsorption on optically active quartz and by fractional crystallization of the strychnine salt. More recently Dwyer, Gyarfas, and Mellor2 reported the complete resolution using d and Z-tris(ethylenediamine) cobalt(III) chloride. Precipitation of the diastereoisomers was effected by addition of ethanol to the aqueous solution. The volume of ethanol used was critical and often merely the potassium salt separated. 

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