Edwards scale

Edwards scale of nucleophilicity is based on a combination of the reduction potentials of nucleophiles and their basicity  

In expression (2.7.4) is the rate constant of the reaction of a nucleophile (N) with a certain compound, and kQ is the rate constant of the analogous reaction with water kJkQ can be replaced by the equilibrium constants of these reactions). 

The a and /S constants are substrate constants, while and H are the nucle-ophilicity constants. E° is the standard electrode potential, e.g.  

The polarizability scale of a nucleophile (P) is determined according to the equation  

In this expression n is the refraction index, and V, is the molar volume. 

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Since Gaussian statistics contain only L and /K in the combination [Pg.55]

In Eq. (10-17), parameters a and b measure the sensitivity of the reaction to these nucleophilic parameters. Since H measures proton basicity and En the electron-donation ability, this treatment models nucleophilicity as a combination of electron loss and electron pair donation. The Edwards equation is thus an oxibase scale of nucleophilic reactivity. Table 10-5 summarizes the nucleophilic parameters. 

Schilling CH, Covert MW, Famili I, Church GM, Edwards JS, Palsson BO. Genome-scale metabolic model of Helicobacter pylori 26695. J Bacteriol 2002 184 4582-93. 

Edwards, J.O. (1954) Correlation of relative rates and equilibria with a double basicity scale. J. Am. Soc., 76, 1540-1547. 

Figure 1. Histogram of measurements of molar U/Ca ratio in a number of samples of reef-building corals and one giant clam sample (after Edwards 1988). Also indicated is the U/Ca ratio of seawater. This illustrates the point that corals do not fractionate U from Ca by large amounts when they make their skeletons. U/Ca ratios of corals are similar to values from inorganically precipitated marine aragonite. Mollusks along with most other biogenic minerals exclude uranium. Note that the horizontal axis is on a log scale and that the U/Ca ratio of the clam is almost 5 orders of magnitude lower than that of the corals. This difference is the fundamental reason why there are difficulties with uranium-series dating of mollusks.

Figure 9. SEM photographs of polished, etched thin sections of modem Acropora palmata coral (after Edwards 1988). The scale bar in a is 100 microns. Visible in a are large macroscopic pores in the skeleton and well as the textnre of the very fine aragonite crystals, b is the same section as a bnt at higher magnification. The scale bar is 10 microns. Individnal aragonite crystal fibers are visible in b. ...

Given that the long residence time of uranium should place limits on how much the marine value could change over Late Quaternary time scales, several workers have used models to determine what these limits should be (see Henderson and Anderson 2003). Chen et al. (1986) and Edwards (1988) used a simple one-box model and assumed steady state conditions. They showed that ... 

Figure 15. Error in age vs. age, both on log scales (after Edwards et al. 1997). Each data point represents data from a particular sample analyzed by thermal ionization mass spectrometric techniques. Solid circles represent Pa ages. Contours of aniytical error in Pa/ U pertain to the Pa data points. Shaded squares represent °Th ages. See text for discussion.

Fig. 30. Temperature dependence of the entanglement distance for polyethylene. > = 1 o O = 0.5. The dotted lines give a best fit for the data. The solid line represents the prediction by the scaling model of Graessley and Edwards (see text). (Reprinted with permission from [60]. Copyright 1993 American Chemical Society, Washington)...

Avidan and Edwards (1986) successfully scaled up from bench scale to demonstration plant from 0.04 m to 0.6 m diameter while maintaining nearly 100% conversion for a fluid bed methanol to gasoline process. In this case, they ran at a superficial gas velocity which was high enough to be in the turbulent flow regime suppressing bubbles. By this technique they eliminated the losses associated with gas bypassing in bubbles. 

E. P. Hunter, 1996 NIST Proton Affinity Scale, in preparation. We thank Edward Hunter for sharing his numbers with us. 

Amy Berger helped me write Chapter 10 (Surface Complexation), and Chapter 31 (Acid Drainage) is derived in part from her work. Edward Warren and Richard Worden of British Petroleum s Sunbury lab contributed data for calculating scaling in North Sea oil fields, Richard Wendlandt first modeled the effects of alkali floods on clastic reservoirs, and Kenneth Sorbie helped write Chapter 30 (Petroleum Reservoirs). I borrowed from Elisabeth Rowan s study of the genesis of fluorite ores at the Albigeois district, Wendy Harrison s study of the Gippsland basin, and a number of other published studies, as referenced in the text. 

The full-scale sampling of North American soils was initiated in 2007 with completion of the Maritime Provinces of New Brunswick, Nova Scotia, and Prince Edward Island in Canada and the New England states and New York in the US. Sample coverage at the end of 2008 is shown in Fig. 1. It is anticipated that this project will take approximately ten years to complete. 

For OSBL inventory values based on Mond Index (ICI, 1985) were used. These were used also for ISBL by Edwards et al. (1993) but the experts criticized this, since the relevant inventory scale in ISBL is much smaller (Lawrence, 1996). Also due to a tighter layout the same inventory in ISBL is more dangerous than in OSBL. Therefore a new scale was developed by scaling the Mond values by using the expert recommendations in Lawrence s work (1996). See Table 15. 

J. A. Papin, N. D. Price, J. S. Edwards, and B. O. Palsson, The genome scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy. J. Theor. Biol. 215, 67 82 (2002). 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

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