Solution concentration ratios

The mass transfer coefficient can be calculated from the slope of the line obtained by plotting the solute concentration ratio (In [AC/AC ]) from Eq. (7) vs time. This iCjn is related to Eqs. (5) and (6). However, the parameters in the above Eqs. (5)-(7) are quite complicated functions. Hence, the gas absorption equations developed by Yang and Cussler [181] in hollow fiber contactors have been extended for liquid-liquid systems. The overall mass transfer resistance in hollow fiber modules is given by [2,182] ... 

Aqueous/Plasma Solutes Concentration Ratios in the Rabbit Eye... 

A study of microwave effects on the formation of nanoparticles in the hydrolysis reaction of FeCl3 with NaH2P04 to get spindle-type colloidal hematite particles under microwave radiation, was reported by Han and coworkers [183]. They found that the reaction rate increased greatly, and the reaction conditions, for example, the acidity of the solution, concentration ratio of the components, and the micro-wave radiation time, had important effects on the nanoparticle formation and their morphology. They discussed the roles of microwaves and the concentration of H2P04 during the hydrolysis process. 

Find solute concentration ratio The solute concentration ratio, SCR, could be find from... 

Table V. Calculated solution concentration ratios for the range of exothermic adsorption enthalpies listed in Table...

The [Ca2+ + Mg2"1-] tenn was necessary because many early water analyses did not distinguish between the two ions. The left side of Eq. 8.21 was termed the ESR (exchangeable sodium ratio). The solution concentration ratio on the right side was termed the SAR (sodium adsorption ratio). The SAR is written as [Na+]/([Ca2+ + Mg2+]/2)1/2 when the concentration units are millimoles of charge per liter. The reduced ratio (r) of the double-layer exchange equation (8.19) is equal to the SAR divided by (1000)1/2. 

A solute distribution exists in the melt because the solidification is carried out at a finite rate. For example, if k0 < 1, then solute is rejected and accumulates at the surface which is solidifying, and this creates solute gradients in the melt which tend to be relaxed by molecular diffusion and any convection which may exist. The interfacial distribution coefficient, k, refers to the solid to liquid solute concentration ratio at the interface. It is k which is used in transport calculations when one is trying to understand the dynamic behavior of zone refining systems. It usually is found that equilibrium exists locally at the solid-liquid interface, in which case k ko. 

SAMs are created by exposure of an adsorbate precursor (liquid or vapor) to a suitable substrate. Usually, the substrate is immersed in a dilute solution (10 -10 M) for a predetermined time (seconds to days) after which the electrode is removed, rinsed copiously with neat solvent, and dried before use. Mixed monolayers can be formed by the simultaneous deposition of multiple precursors from the same solution. However, caution must be exercised since the solution concentration ratio usually does not reflect the resulting surface composition. 

The Staverman reflection coefficient, o, measures the extent to which the membrane rejects a given solute purely transported by convection. Solutes fully rejected by the membrane feature o = 1. Solutes freely permeating the membrane feature ct = 0. Membrane rejection toward a given solute is experimentally assessed in the course of pure filtration experiments in terms of its rejection coefficient R, or its sieving coefficient S, with S = —R being the permeate-to-retentate solute concentration ratio. In fact, R is related to a as follows (Spiegler and Kedem, 1996) ... 

The foregoing equation reveals that essentially the concentration distribution ratio for trace concentrations of an exchanging ion is independent of the respective solution of that ion and that the uptake of each trace ion by the resin is directly proportional to its solution concentration. However, the... 

Parts per million (ppm) and parts per billion (ppb) are mass ratios of grams of solute to one million or one billion grams of sample, respectively. For example, a steel that is 450 ppm in Mn contains 450 pg of Mn for every gram of steel. If we approximate the density of an aqueous solution as 1.00 g/mL, then solution concentrations can be expressed in parts per million or parts per billion using the following relationships. 

Following the separation outlined in Example 7.10, an analysis is to be carried out for the concentration of Cu in an industrial plating bath. The concentration ratio of Cu to Zn in the plating bath is 7 1. Analysis of standard solutions containing only Cu or Zn give the following standardization equations... 

The problem with a simple extraction is that the separation only occurs in one direction. In a liquid-liquid extraction, for example, we extract a solute from its initial phase into the extracting phase. Consider, again, the separation of an analyte and a matrix interferent with distribution ratios of 5 and 0.5, respectively. A single liquid-liquid extraction transfers 83% of the analyte and 33% of the interferent to the extracting phase (Figure 12.1). If the concentrations of A and I in the sample were identical, then their concentration ratio in the extracting phase after one extraction is... 

Thus, a single extraction improves the separation of the solutes by a factor of 2.5. As shown in Figure 12.1, a second extraction actually leads to a poorer separation. After combining the two portions of the extracting phase, the concentration ratio decreases to... 

T — T (4) the ratio of the solute concentration and the equiUbrium concentration, c A, which is known as relative saturation or (5) the ratio of the difference between the solute concentration and the equiUbrium concentration to the equiUbrium concentration, s — [c — c which is known as relative supersaturation. This term has often been represented by O s is used here because of the frequent use of O for iaterfacial energy or surface tension and for variance ia distribution functions. 

Sorenson and Arlt Liquid-Liquid Equilihiium Data Collection, DECHEMA, Frankfurt, Germany, 1979) report several sets of liquid-liquid equilibrium data for the system acetone-water-chloroform, but the lowest solute concentrations reported at 25 C were. 3 weight percent acetone in the water layer in equilibrium with 9 weight percent acetone in the chloroform layer. This gives a partition ratio K of, 3.0. 

Selectivity. The relative separation, or selectivity, Ot of a solvent is the ratio of two components in the extraction-solvent phase divided by the ratio of the same components in the feed-solvent phase. The separation power of a hquid-liquid system is governed by the deviation of Ot from unity, analogous to relative volatility in distillation. A relative separation Ot of 1.0 gives no separation of the components between the two liquid phases. Dilute solute concentrations generally give the highest relative separation factors. 

Component A = feed solvent, component B = solute, and component S = extraction solvent. K is the partition ratio in weight-fraction solute if/x for the tie line of lowest solute concentration reported. Ordinarily, K will approach unity as the solute concentration is increased. 

The solution to the Kremser equation is shown graphically in Fig. 15-14. When a system responds with a constant number of theoretic stages N, the solute concentration in the raffinate X can readily be evaluated as the result of changing the ratio of solvent to feed [Eqs. (15-17) and (15-18)]. 

The response of solute concentration in the raffinate to the sol-vent-to-feed ratio S /F can be calculated by Eqs. (15-26) and (15-27) for a constant number of transfer units based on the overall raffinate phase N r-... 

Practical experience has shown that the most convenient and best means of expressing R is in terms of the solute concentrations in the washed cake hquid the feed liquid (or unwashed cake liquid), and the cake wash hquid. Furthermore, the wash ratio N may also be expressed either as a volume or weight ratio. 

As the peak represents the concentration profile of the eluting solute, the fraction of the peak height at which the points of inflexion are located will be the same as the ratio of the solute concentration after (n - Vn ) plate volumes of mobile phase has passed through the column to the solute concentration after (n) plate volumes of mobile phase have passed through the column. 

Permeate concentration The solute concentration in the permeate may be approximated by the ratio of the solute to water fluxes, i.e.. 

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