Acidity constant estimation correlation

Estimation of Acidity Constants The Hammett Correlation Illustrative Example 8.2 Estimating Acidity Constants of Aromatic Acids and Bases Using the Hammett Equation... 

On CNDO/2 calculations with pK (as base) = 2.30 for triazole, the basicities of H and AH tautomers are estimated to be equal, and maximum separation of protonated nitrogens i.e. N-1 and N-4 rather than N-1 and N-2) is predicted to afford the most stable cation (68TL3727). Acidity constants of 1,2,4-triazoles correlate with total and rr-electron densities but not with the lone pair character of the pyridine-type N in MO calculations (70JCS(B)i692, 70BCJ3344). 

It has been shown (Schindler and Stumm, 1987) that equilibrium constants characterizing the amphoteric behavior of metal oxides (the surface acidity) are linearly correlated with the equilibrium constants for the amphoteric behavior of the same metal ions in solution (acidity in solution). This finding supported the model in which the metal oxide surface is described with the same acid-base equations as the metal ions in solution, and allows the equilibrium constants for the oxide surfaces to be estimated from those determined in solution. 

Tyn-Calus This correlation requires data in the form of molar volumes and parachors = ViCp (a property which, over moderate temperature ranges, is nearly constant), measured at the same temperature (not necessarily the temperature of interest). The parachors for the components may also be evaluated at different temperatures from each other. Quale has compiled values of fj for many chemicals. Group contribution methods are available for estimation purposes (Reid et al.). The following suggestions were made by Reid et al. The correlation is constrained to cases in which fig < 30 cP. If the solute is water or if the solute is an organic acid and the solvent is not water or a short-chain alcohol, dimerization of the solute A should be assumed for purposes of estimating its volume and parachor. For example, the appropriate values for water as solute at 25°C are = 37.4 cmVmol and yn = 105.2 cm g Vs mol. Finally, if the solute is nonpolar, the solvent volume and parachor should be multiplied by 8 Ig. 

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

The situation just discussed probably applies also to the attack of water on other kinds of stabilized carbocations. For example, some of the many transient carbocations studied in recent years by McClelland and Steenken, and their coworkers (e.g. Steenken et al., 1986 McClelland and Steenken, 1988), have relatively constant kOH/kw ratios. For alkyldialkoxy cations [41], oh w = 103 to 104 m-1 and so pKt = 10 to 11 for the trialkoxy analogues [42], kon/kw == 104 to 106m i and p/Cf = 8 to 10 (Table A6.3), suggesting a more acidic transition state for [42], due to the extra oxygen atom. Within each series there is a systematic variation of p/C, since logfc0H correlates with logfcw, with a slope of approximately 0.6 (McClelland and Steenken, 1988), rather than 1. Estimates of the Leffler indices for the two series of... 

PhC properties most investigated by scientists to date are their water solubility (s, mg/mL), volatility (correlated to the Henry constant H) (pg m atr/pg m wastewater), biodegradability (correlated to pseudo-first-order degradation constant bioi L gSS d ), acid dissociation constant K, distribution and sorption (through the sludge-water distribution coefficient K, expressed in L gSS or the octanol-water partition coefficient Kg ). The main focus has been to find any correlations between these parameters and to determine PhC removal rates during the different treatment steps. Thus, different properties have been quantified for many compounds, and software, such as EPl Suite 4.00 [54], consenting their estimation, is available. 

Values of electrical effect substituent constants for oxime and hydroxylamino groups have been reported ° their values are set forth in Tables la-c. No value for the acid group, CO(NHOH), was available. We have estimated values for it they are given in Tables la-c. Also in Tables la-c are values for some other types of substituents either for purposes of comparison or because they were used in correlations in this work. 

The Bronsted correlation given by Eq. (15) is so extensive that it can be used to predict a pKa value once the rate constant or relative rate constant for N-methylation under the conditions employed to construct this plot is known. This approach is especially valuable for weakly basic heterocyclic compounds, which are protonated only in strongly acidic media. Even for such, it is comparatively easy to determine a rate or relative rate constant for N-methylation. The pKa values of several molecules so estimated are given in Table V. They are expected to be... 

The effect of group (a) (non-polar solvents) was examined in the esterification of benzoic acid with 1-butanol over a Dowex-W X2 catalyst [454]. The solvent affected both the Helfferich distribution coefficients and the esterification rates. Dielectric constants, corresponding to the composition of the pore liquid, were estimated and the kinetic data related to the polar properties of the medium within the catalyst. In Fig. 18 are plotted specific rate coefficients versus the reciprocal value of dielectric constant of the pore liquid. The slope of the correlation is positive as for... 

When several temperature-dependent rate constants have been determined or at least estimated, the adherence of the decay in the system to Arrhenius behavior can be easily determined. If a plot of these rate constants vs. reciprocal temperature (1/7) produces a linear correlation, the system is adhering to the well-studied Arrhenius kinetic model and some prediction of the rate of decay at any temperature can be made. As detailed in Figure 17, Carstensen s adaptation of data, originally described by Tardif (99), demonstrates the pseudo-first-order decay behavior of the decomposition of ascorbic acid in solid dosage forms at temperatures of 50° C, 60°C, and 70°C (100). Further analysis of the data confirmed that the system adhered closely to Arrhenius behavior as the plot of the rate constants with respect to reciprocal temperature (1/7) showed linearity (Fig. 18). Carsten-sen suggests that it is not always necessary to determine the mechanism of decay if some relevant property of the degradation can be explained as a function of time, and therefore logically quantified and rationally predicted. 

The free ion, Cu2+, appears to be the major species of Cu taken up by plants (Graham, 1981 Jones and Jarvis, 1981). Hence Cu complexation will decrease uptake (DeKock and Mitchell, 1957) unless the complex can dissociate and/or diffuse quickly enough to maintain a constant supply of Cu2+ at the root surface. In the case of Zn, the presence of humic acid (Chen and Aviad, 1990) and carboxylic acids (EDTA, diethylenetriamine pentaacetic acid (DTPA), nitrilotriacetic acid (NTA) DeKock and Mitchell, 1957) has been found to decrease absorption but it is not known whether Zn uptake is correlated with Zn2+ in solution because Zn speciation was not estimated. Other work has shown that Zn initially complexed with citrate is taken up by barley from nutrient solutions (Chairidchai and Ritchie, 1993) and the presence of chelates (EDTA, citrate) can speed up the diffusion of Zn to a root surface in soils (Hodgson et al., 1967 Elgawhary et al., 1970). Speciation in solution is particularly important in the uptake of iron because of its extremely low solubility in the absence of complexing anions... 

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