Concentrations dilute solutions

Ultrafiltration is an improvement on the dialysis principle. Filters having pore sizes over the range of biomolecular dimensions are used to filter solutions to select for molecules in a particular size range. Because the pore sizes in these filters are microscopic, high pressures are often required to force the solution through the filter. This technique is useful for concentrating dilute solutions of macromolecules. The concentrated protein can then be diluted into the solution of choice. 

First, it is observed that variation between Ac and C0 5 is not linear at high concentrations for the strong electrolytes. At relatively low concentrations (dilute solutions), however, the... 

The use of polyamide is advantageous because it separates natural from synthetic coloring material, removes sugars, acids, and flavoring materials, and concentrates dilute solutions of colors (156,167). However, the use of polyamide is not applicable to chocolate brown FB, chocolate brown HT, or indigotine, because the two chocolate browns are not completely eluted from the column and indigotine decomposes during extraction (157). 

Affinity chromatography can be applied as a purification technique to any pair of biologically complementary substances, for example, enzymes and inhibitors, steroids and binding proteins, antigens and antibodies. Insolubilization of one member of the pair yields an affinity column specific for the second member of the pair. Affinity chromatography can also be used to concentrate dilute solutions of purified substances and removal of soluble substances which are present as contaminants in low concentration. 

The major advantage of RO for handing process effluents is its ability to concentrate dilute solutions for recovery of salts and chemicals with low-power requirements. No latent heat of vaporization or fusion is required for effecting separations the main energy requirement is for a high-pressure pump. It also requires relatively limited floor space for compact, high-capacity units, and it exhibits good recovery and rejection rates for a number of typical process solutions (15). 

Real solutions do not obey Raoult s law at all concentrations, but they do follow Raoult s law in the limit of low solute concentration (dilute solution). 

Solvent Extraction [5.9,5.15,5.36-5.44]. Generally, SX in hydrometallurgy serves to concentrate diluted solutions, to separate, and to purify. In tungsten hydrometallurgy, as already explained, separation is the main target and, to a certain extent, piuification from ions which do not condense with tungstate and from those which are not extracted by the solvent can be achieved. 

The measurement of the osmotic pressure at various fixed concentrations p, immediately gives the basic quantity II(p). We observed in Chapter 5 that the molecular mass and the higher virial coefficients are derived from the function II(p), determined in the range of weak concentrations (dilute solutions). We must write the development (5.1.107) of the osmotic pressure in the... 

Ultrafiltration and dialysis can be combined. An arrangement suggested by Berggard (1961) made use of both techniques. The filter used provided an excellent way to concentrate dilute solutions of proteins with molecular weights larger than 20,000, or to remove such solutes from considerably smaller ones. 

MVR technology can be used for concentrating dilute solutions prior to drying. This technique is characterized by high efficiency and is used as a mechauical evaporator in many branches of the industry, for example, the Carver-Greenfield process for wastewater utilization [46]. 

For analysis of lanthanide ions in complex matrices like rocks, it is generally necessary to remove non-lanthanide components of the dissolved sample before conducting the analysis. Preconcentration is often essential for lanthanide analysis by neutron activation, wherein the y-emission spectra of certain matrix elements overlap with those of the target lanthanides. In mass-spectrometric analysis of samples, some matrix elements can interfere with lanthanide quantitation (for example, barium with lanthanum). Application of a preseparation step gives the added benefit of concentrating dilute solutions of lanthanides to improve detection limits. 

It is convenient to partition polymer solutions into three different cases according to their concentration. Dilute solutions involve only a minimum of interaction (overlap) between different polymer molecules. The Flory-Huggins theory does not represent this situation at all well due to its mean-field assumption. The semi-dilute case involves overlapping polymer molecules but still with a considerable separation of the segments of different molecules. 

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