Extract calculations

Extract calculations may also be limited in their use if (1) the liquid line of descent is actually a mix of several lines (2) solid solution changes the composition of the crystallizing phases during fractionation (3) the phenocrysts present in magma are not representative of the fractionating phases. 

Some common reasons for scattered trends on varation diagrams for igneous rocks are  

Bivariate plot of CaO vs MgO for basalts and related rods from Hawaii. The diange in slope at about MgO 7 % suggests a change in the fractionating phases at this point (after Peterson and Moore, 1987 courtesy of the US Geological Survey). 

The samples are not from a single magma. This can be true even for lavas from a single volcano. 

Uncertainty in the analytical measurements. This may be due to the fact that analyses were made using different techniques or in different laboratories — both practices to be avoided if the data are to be plotted on the same diagram. 

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Aqueous solutions buffered to a pH of 5.2 and containing known total concentrations of Zn + are prepared. A solution containing ammonium pyrrolidinecarbodithioate (APCD) is added along with methyl isobutyl ketone (MIBK). The mixture is shaken briefly and then placed on a rotary shaker table for 30 min. At the end of the extraction period the aqueous and organic phases are separated and the concentration of zinc in the aqueous layer determined by atomic absorption. The concentration of zinc in the organic phase is determined by difference and the equilibrium constant for the extraction calculated. 

Figure 8.5 illustrates the sort of separation this approach predicts. Curve A in Fig. 8.5 shows the weight fraction of various n-mers plotted as a function of n. Comparison with Fig. 6.7 shows that the distribution is typical of those obtained in random polymerization. Curve B shows the distribution of molecular weights in the more dilute phase-the coacervate extract-calculated for the volumes of the two phases in the proportion 100 1. The distribution in the concentrated phase is shown as curve C it is given by the difference between curves A and B. 

The sample equivalent Cex corresponds to the amount (in grams) of sample material in 1 mL of extract. Calculate Cex in g mL using the following equation ... 

Table II. Selective Solvent Extraction, Calculated Mc PDMAAm, and Differential Scanning Calorimetry Data...

Equations which predict the volume or equivalent spherical diameter of a formed drop are not sufficient for extraction calculations, in the light of the very high rate of mass transfer during drop formation. It is desirable that the equation also lend itself to mathematical manipulation for the calculation of instantaneous interfacial area. To do this, the shape of the drop throughout the formation period must be defined. 

Extraction calculations involving more than three components cannot be done graphically but must be done by numerical solution of equations representing the phase equilibria and material balances over all the stages. Since extraction processes usually are adiabatic and nearly isothermal, enthalpy balances need not be made. The solution of the resulting set of equations and of the prior determination of the parameters of activity coefficient correlations requires computer implementation. Once such programs have been developed, they also may be advantageous for ternary extractions,... 

Chou, G. E, and Prausnitz, J. M., Supercritical fluid extraction calculations for high-boiling petroleum fractions using propane. Application of continuous thermodynamics. Ber. Bunsenges. Phys. CWm. 88,796(1984). 

Sample Preparation of Foam and Water Samples and Humic Substances Isolation. All foam and water samples were filtered through 0.45- Lim silver filter using stainless-steel filtration units. Silver filtration of Como Creek and Suwannee River foam samples resulted in build up of a brown extract on the filter paper, which was readily solubilized in 0.1 N sodium hydroxide. This extract was refiltered through silver filters as a sodium hydroxide solution. This fraction was believed to be colloidal in nature and was treated as a separate humic fraction, called the "foam-extract" fraction. A part of the filtered foam was freeze dried directly and considered "raw" foam. Fulvic and humic acids were isolated from foam and stream-water samples via the XAD-8 adsorption technique developed by Thurman and Malcolm (77), freeze dried, and weighed. To obtain a sufficient mass of humic substances, each entire sample was used for one extraction. As multiple samples were not extracted, calculation of the error associated with humic substances isolation cannot be made, and the contributions of humic substances to the DOC content must be regarded as estimates. 

If an apphcation proves to be technically feasible, the choice of solvent-to-feed ratio is determined by identifying the most cost-effective ratio between the minimum and maximum limits. For most applications, the maximum solvent-to-feed ratio will be much larger than the ratio chosen for the commercial process however, the maximum ratio can be a real constraint when dealing with applications exhibiting high mutual solubility, especially for systems that involve high solute concentrations. Additional discussion is given by Seader and Henley [Chap. 8 in Separations Process Principles (Wiley, 1998)]. Solvent ratios are further constrained for a fractional extraction scheme, as discussed in Fractional Extraction Calculations. ... 

Of course, this theoretical maximum can never be attained in practice. Equation (15-94) follows from Eq. (15-93), noting that 0/0, = 1/0, for iV —> as discussed by Brian [Staged Cascades in Chemical Processing (Prentice-Hall, 1972), p. 50]. As noted earlier, the ability to purify a desired solute is greatly enhanced by using fractional extraction (see Fractional Extraction Calculations ). 

Another point that should be observed in extraction calculations is the non-ideal nature of the system, which is responsible for the occurrence of two liquid phases in equilibrium. The liquid-liquid equilibrium distribution coefficients, or A -values, are highly composition-dependent and must be calculated by appropriate methods, namely those based on liquid activity coefficients. The NRTL and UNIQUAC liquid activity equations (Chapter 1) are among the more accurate ones for predicting liquid-liquid equilibria. The A -Value is defined as the ratio of the mole fraction of a component in one liquid phase to its mole fraction in the other, and is calculated as... 

Extraction calculations - it is necessary to calculate volumes of solvents and number of extractions when attempting to maximize the economics of an industrial-scale extraction process. 

Eq. (10.7-3). The causes for this abnormality are not wholly dear, but sol id-structure nonuniformity is probably a major factor. Because of this abnomatl behavior it is difficult to cany om valid unsteedy-state extraction calculations for oilseeds. 

Difference point in extraction calculations Differential contactors Diffuse wave Diffusion... 

If the number of ideal stages is specified, the fraction of solute extracted and the final compositions are determined by trial and error. The fraction extracted or the final extract composition is assumed, and the curved operating line is constructed. If too many stages are required, a smaller fraction extracted is assumed and the calculations are repeated. Computer programs for extraction calculations are available. ... 

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