Concentration factor calculations

The hypothesis has been advanced that changes in relative concentrations of lipid type compounds, when comparing aquatic biota and their habitat, can be explained in large part by an estimate of their tendency to partition into tissues which has been related to octanol/water partition coefficients - K s (, 22). Table Vll presents tabulated data for and water to biota bloaccumu-latlon concentration factors calculated from data in Tables III and IV. Representative data from Table Vll are plotted in Figure 6 in the manner of Mackay (21) and Chlou (22), who have reviewed data on bloaccumulatlon of neutral hydrophobic compounds in aquatic biota. The solid line Is the expected distribution of data based on Chlou s review (22) of predictability for equilibrium situations. Our data is different in an absolute sense than the data used by Mackay and Chlou, because they used concentrations in biota... 

Comparisons (49) of measured concentrations of SFg tracer released from a 36-m stack, and those estimated by the PTMPT model for 133 data pairs over PasquiU stabilities varying from B through F, had a linear correlation coefficient of 0.81. Here 89% of the estimated values were within a factor of 3 of the measured concentrations. The calculations were most sensitive to the selection of stability class. Changing the stability classification by one varies the concentration by a factor of 2 to 4. 

It has been shown that for acrylic, glass-filled nylon and methyl pentene there is reasonable correlation between the reciprocal of the stress concentration factor, K, and impact strength. However, for PVC good correlation could only be achieved if the finite dimensions of the sample were taken into account in the calculation of stress concentration factor. 

We calculate the calibration (regression) coefficients on a rank-by-rank basis using linear regression between the projections of the spectra on each individual spectral factor with the projections of the concentrations on each corresponding concentration factor of the same rank. 

Iteration. Matrix correction factors are dependent on the composition of the specimen, which is not known initially. Estimated concentrations are initially used in the correction factor calculations and, having applied the corrections thus obtained the calculations are repeated until convergence is obtained, i.e. when the concentrations do not change significantly between successive calculations. 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

To use this method, the sample is dissolved in a system containing two phases (e.g., water and octanol) such that the solution is at least about 5 x 10-4 M. The solution is acidified (or basified) and titrated with base (or acid) under controlled conditions. The shape of the ensuing titration curve is compared with the shape of a simulated curve, which is created in silico. The estimated p0Ka values (together with other variables used to construct the simulated curve such as substance concentration factor, CO2 content of the solution and acidity error) are allowed to vary systematically until the simulated curve fits as closely as possible to the experimental curve. The p0Ka values required to achieve the best fit are assumed to be the correct measured p0Ka values. This computerized calculation technique is called refinement , and is described elsewhere [14, 15]. 

Combined results on ochre-precipitates and water from which they precipitate indicate strong enrichment regarding several relevant metals (Fig. 3). The concentration factor was estimated using the formulation by Munk et al. (2002), which calculates the ratio between the concentration of the elements in the solid and the concentration in the water. 

A convenient method of expressing this phenomena is by calculating a concentration factor (C) expressed by ... 

The concentration factor of the brine, the ratio of the concentrate and feed concentrations, can also be calculated. It is given as ... 

Table 2.3 shows the calculated ion concentrations with a concentration factor of 3.33, and compares them with actual plant values. Note that there are significant differences between the calculated and actual ion concentrations for most species, however this is likely to be a result of the plant operating below the stated recovery rate of 70%. The differences in the concentration factors from the actual plant data (ranging from 0.79 for nitrate to 3.03 for sodium) are largely a result of the different precipitation points for each of the species in the water. 

Calculation. The 25 g soil was shaken with 50 ml calcium chloride extractant, and 25 ml of this extract was diluted to 50 ml. There is therefore a x4 dilution factor. Calculate the concentration of SO -S in the blank and samples by comparison with the standard curve. Subtract the blank value from the sample values and multiply by 4 to give the pg SO -S g (= mg SO -S kg- ) air-dry soil. Include any extra dilution factors, and, if required, convert to oven-dry soil using the appropriate factor, as in Method 5.2, Calculation (2). 

The use of dispersion-normalized data is equivalent to adjusting all ambient concentrations to the same dispersion conditions and assuming that the remaining variations in concentrations are due to variations in source emissions. Although this is a logical approach conceptually, it is not known at present what uncertainties are associated with the use of a dispersion factor calculated from a 7 A.M. determination of mixing height and wind-speed. 

Note that reactions 2.14, 2.15, and 2.23 involve fractional stoichiometric coefficients on the left-hand sides. This is because we wanted to define conventional enthalpies of formation (etc.) of one mole of each of the respective products. However, if we are not concerned about the conventional thermodynamic quantities of formation, we can get rid of fractional coefficients by multiplying throughout by the appropriate factor. For example, reaction 2.14 could be doubled, whereupon AG° becomes 2AG, AH° = 2AH , and AS° = 2ASf, and the right-hand sides of Eqs. 2.21 and 2.22 must be squared so that the new equilibrium constant K = K2 = 1.23 x 1083 bar-3. Thus, whenever we give a numerical value for an equilibrium constant or an associated thermodynamic quantity, we must make clear how we chose to define the equilibrium. The concentrations we calculate from an equilibrium constant will, of course, be the same, no matter how it was defined. Sometimes, as in Eq. 2.22, the units given for K will imply the definition, but in certain cases such as reaction 2.23 K is dimensionless. 

Consider the same unidirectional lamina with the stresses now applied perpendicular to the fiber axis as shown in Fig. 12. The local stress at the fiber matrix interface can be calculated and compared to the nominally applied stress on the whole lamina to give K, the stress concentration factor. The plot of the results of this analysis shows that the interfacial stresses at the point of maximum principal stress can range up to 2.6 times the applied stress depending on the moduli of the constituents and the volume fraction of the reinforcement. For a typical graphite-epoxy composite, with a modulus ratio of 70 and a volume fraction of 70 % the stress concentration factor at the interface is about 2.4. That is, the local stresses at the interface are a factor of 2.4 times greater than the applied stress. 

The effectiveness factors calculated for the parallel, equilibrium-restrained reaction systems are not able to predict the catalyst internal-surface utilization accurately. Therefore, the intraparticle distributions of the temperature, the concentrations of species and so on should be taken into account. 

Scale is caused by precipitation of dissolved metal salts in the feed water on the membrane surface. As salt-free water is removed in the permeate, the concentration of ions in the feed increases until at some point the solubility limit is exceeded. The salt then precipitates on the membrane surface as scale. The proclivity of a particular feed water to produce scale can be determined by performing an analysis of the feed water and calculating the expected concentration factor in the brine. The ratio of the product water flow rate to feed water flow rate is called the recovery rate, which is equivalent to the term stage-cut used in gas separation. 

PCDD/PCDF in soil are the contaminants of concern for this project. The required information is the concentrations of PCDD/PCDF in soil, expressed in the units of 2,3,7,8-tetrachlorodibenzodioxin (2,3,7,8-TCDD) toxicity equivalents (TEQ). The TEQ is a calculated value, which contains all of the PCDD/PCDF homologue concentrations factored in according to their toxicity. YOCs are the contaminants of concern for this project. The required information is the VOC concentrations in the effluent water stream. To support decisions related to the treatment system operation, YOC concentrations in influent samples are also required. 

The single-chain structure factors calculated in the previous sections correspond to the infinite dilution limit. This limit also corresponds to zero scattering intensity and is not useful so that concentration effects have to be included in the modeling of polymer solutions. First, Zimm s single-contact approximation [5] is reviewed for dilute polymer solutions then, a slight extension of that formula which applies to semidilute solutions, is discussed. 

The method of separation results in the Am being diverted to the aqueous waste stream of the second plutonium solvent extraction cycle (2 AW). The calculated predicted volume of this stream for the full campaign was 2.2 x 10 L. Physical limitations of equipment required that the solution be evaporated in two steps instead of one. The first step could result in a concentration factor of 25 to 50. The second step included nitric acid stripping and evaporation to the final volume. 

Calculate the response factors of the standards by dividing their concentrations by their peak areas. Calculate the concentration of each component in the sample by multiplying the individual peak areas corresponding to each component by the appropriate response factor calculated for its standard, giving the concentration in w/w percent. A comparison of sorbitol and dextrose peak areas shows that at least 95% of the sum of these peak areas is sorbitol. A similar comparison of maltitol and maltose peak areas shows that at least 95% is maltitol. Neither sorbitol nor maltitol fractions comprise more than 50% of the sample. 

Plots of selectivity factor (calculated using Equation 2 and the data from Table I) for mephenytoin and hexobarbital enantiomers versus CD concentration are shown in Figure 3 a,b (22) The profiles of relation oC vs [(3-CD] for these two compounds are different because two different factors determine resolution of their enantiomers difference in K- values for hexobarbital and difference in kl t ftnn values for mephenytoin. The latter case represents 5nuinteresting example the resolution of its enantiomers arises from the great differentiation in the adsorption of diastereoisomeric (3-CD complexes. The calculated selectivity factor for these complexes is ca 3 (see Table I). In this particular case selectivities of the two processes adsorption and com-plexation in the bulk mobile phase solution are opposite to each other enantioselectivity arising from selective adsorption dominating over differentiation in the solution. Unfortunately the stabilities of diastereoisomeric -CD mephenytoin complexes are relatively small and solubility of -CD in the mobile phase solution is rather limited. Therefore one cannot shift the comple-xation equilibrium... 

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