Relative dissolution rate, calculation

Figure 9. The relative dissolution rate, R/Rf)J as a function of pH. Dashed lines were calculated by using the equilibrium and surface complex formation constants for pH 2S at 10r2 atm = /SO/ / = 10 1 M and--------------= /H2P047 =...

Figure 9. The relative dissolution rate, R/Rf>, as a function of pH. Dashed lines were calculated by using the equilibrium and surface complex formation con-...

Results of the field experiment are shown in Eig. 16.27a, which is based on combined discharge from five extraction weUs. After about 50 days, TCM concentrations decreased. In contrast, concentrations of TCE fluctuated but remain relatively high. PCE concentrations continued to increase over time, exhibiting a higher dissolution rate over the first 100 days of the experiment. These results were used to plot (Eig. 16.27b) the observed relationship between concentration ratio and source transformation by dissolution-induced depletion, together with the equivalent theoretical relationships. Source depletion was calculated from the cumulative mass removed, as determined from monitoring of effluent at specific times, divided by the initial source mass. 

Convective dissolution rate for quartz in an andesitic melt may be calculated similarly, but the error may be larger than the normal 20% relative because quartz dissolution increases Si02 content so much, leading to orders of magnitude increase in viscosity for the interface melt (viscosity is about 120 Pa s for the initial andesitic melt and 1.7 x lO" Pa s for the interface rhyolitic melt). Because... 

For example, Murphy et al. (2002) determined the relative intrinsic dissolution rates of carbamazapine anhydrate (form III) and dihydrate forms in water at 10, 25, and 37 °C. Figure 3 shows the Van t Hoff-type plot of the intrinsic dissolution rates of the forms. A transition temperature of 102 °C was calculated by extrapolation of the intrinsic dissolution rate lines to the point of intersection. The anhydrous form is more stable above the transition temperature whereas the dihydrate is more stable below the transition temperature. 

As discussed earlier in the secondary structure model, Templeton et al. have shown that the steric arrangement of the methylene links in the novolac resin can have a profound effect on its dissolution rate and on lithographic performance. Using molecular mechanics, these authors have calculated the equilibrium secondary structures of cresol-formaldehyde oligomers. They found that the secondary structure of these molecules determines the relative positions of the hydroxyl groups in the novolac matrix, and hence the possibility of intramolecular hydrogen bonding. ... 

Relative reaction rates of hydrolysis, condensation, reesterification, and dissolution must be understood and controlled to dictate structural evolution. However, accurate values for rate constants are difficult to obtain because of the enormous number of distinguishable reactions as next nearest neighbors are considered, and to the concurrency of these reactions. Assink and Kay [45] use a simplified statistical model assuming that the local silicon environment does not affect reaction rates, and the reactions for a particular silicon species are the product of a statistical factor and rate constant. These assumptions ignore steric and inductive effects. For example, this model predicts that the relative rate constants for the four sequential hydrolysis steps leading from TMOS to Si(OH)4 would be 4 3 2 1. This model was applied to acid-catalyzed TMOS sols with W values ranging from 0.5 to 2.0. Si NMR spectra on the temporal evolution of various silicon species show the model is in excellent agreement with experimental results. A lower limit for fen was calculated as 0.2 L/mol-min. Values for few and feA are 0.006 and 0.001 L/mol-min, respectively. 

Goldich (1938) examined the mineral assemblages present in soil (Appendix, Plate 5) under a variety of environmental conditions and established a stability series for sand and silt-sized particles that illustrates the relative stability of primary silicate minerals (Goldich s weathering series) (Fig. 1.8). For example, Ca-plagioclase, olivine (Appendix, Plate 6) and pyroxene (Appendix, Plate 7) tend to be most easily suffered chemical weathering and quartz and mica are most resistant to the weathering. This order is quite consistent with calculated solubility (Fig. 1.7) and experimentally determined dissolution rate of silicate minerals (Fig. 1.10). The solubility and dissolution rate of silicate minerals are related to the crystal structures, which is described below. 

Figure 9 compares the quasielectrostatic potential with the electrostatic potential in the dilute solution model. The plotted potentials are those at the dissolving surface relative to the values at the pit mouth. The concentrated solution model predicts a much larger potential drop in the pit, primarily because it depends on the experimentally measured conductivity, which is again is reduced in concentrated solutions relative to the conductivity according to the dilute solution model. By comparison with Fig. 7, it may be seen that significant relative errors in the dilute solution calculation appear at concentrations less than 1 M. Since pit solutions are usually even more concentrated, large relative errors in potential calculations would be expected. This may be a serious concern because the metal dissolution rate increases exponentially with potential. 

Figure 12. Extent of dissolution and re-precipitation between aqueous Fe(III) and hematite at 98°C calculated using Fe-enriched tracers. A. Percent Fe exchanged (F values) as calculated for the two enriched- Fe tracer experiments in parts B and C. Large diamonds reflect F values calculated from isotopic compositions of the solution. Small circles reflect F values calculated from isotopic compositions of hematite, which have larger errors due to the relatively small shifts in isotopic composition of the solid (see parts B and C). Curves show third-order rate laws that are fit to the data from the solutions. B. Tracer experiment using Fe-enriched hematite, and isotopically normal Fe(lll). C. Identical experiment as in part B, except that solution Fe(lll) is enriched in Te, and initial hematite had normal isotope compositions. Data from Skulan et al. (2002).

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