Dissociation constants, correlation

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

Various Langmiiir-Hinshelwood mechanisms were assumed. GO and GO2 were assumed to adsorb on one kind of active site, si, and H2 and H2O on another kind, s2. The H2 adsorbed with dissociation and all participants were assumed to be in adsorptive equilibrium. Some 48 possible controlling mechanisms were examined, each with 7 empirical constants. Variance analysis of the experimental data reduced the number to three possibilities. The rate equations of the three reactions are stated for the mechanisms finally adopted, with the constants correlated by the Arrhenius equation. 

Analogous plots for many other reactions of aromatic compounds show a similar linear correlation with the acid dissociation constants of the corresponding benzoic acids. 

The numerical values of the terms a and p are defined by specifying the ionization of benzoic acids as the standard reaction to which the reaction constant p = 1 is assigned. The substituent constant, a, can then be determined for a series of substituent groups by measurement of the acid dissociation constant of the substituted benzoic acids. The a values so defined are used in the correlation of other reaction series, and the p values of the reactions are thus determined. The relationship between Eqs. (4.12) and (4.14) is evident when the Hammett equation is expressed in terms of fiee energy. For the standard reaction, o%K/Kq = ap. Thus,... 

It was pointed out above that, if we choose any two acids at random from Table 9, we are not likely to find any correlation between the position of the maximum of K and the value of K itself. But this would not be true, if we compare two acids, paying due regard to the probable value of J non. Three dissociation constants in Table 9 have values smaller than 10 7 and in all three cases the value of 0 falls above 40°. This is doubtless because, in aqueous solution, such a low degree of... 

In deciphering the role of the different NTs, or more precisely their antagonists, in the antischizophrenic action of neuroleptic drugs it must be remembered that published binding data and calculated dissociation constants vary considerably, which, of course, affects correlation coefficients made with clinical activity. Factors to bear in mind are ... 

Acid dissociation constant Regression correlation coefficient Regression coefficient of determination Water solubility... 

Grunwald, E. Berkowitz, B. J., The measurement and correlation of acid dissociation constants for carboxylic acids in the system ethanol-water. Activity coefficients and empirical activity functions, j. Am. Chem. Soc. 73, 4939 -944 (1951). 

By correlating the observed spectral changes with the concentrations of added cycloamylose, dissociation constants of the cycloamylose-substrate adducts may be calculated (Rossotti and Rossotti, 1961). Values of the dissociation constants determined in this manner for a variety of complexes are presented in Table II. In most cases, stoichiometries of the complexes have been shown to be 1 1 from the presence of distinct isosbestic points in the spectrophotometric titrations. In a few cases, additional spectral perturbations are observed as the cycloamylose concentration is increased, indicating more complex modes of association. Methyl orange, for example,... 

Values of /c2, the maximal rate constant for disappearance of penicillin at pH 10.24 and 31.5°, and Ka, the cycloheptaamylose-penicillin dissociation constant are presented in Table VII. Two features of these data are noteworthy. In the first place, there is no correlation between the magnitude of the cycloheptaamylose induced rate accelerations and the strength of binding specificity is again manifested in a rate process rather than in the stability of the inclusion complex. Second, the selectivity of cycloheptaamylose toward the various penicillins is somewhat less than the selectivity of the cycloamyloses toward phenyl esters—rate accelerations differ by no more than fivefold throughout the series. As noted by Tutt and Schwartz (1971), selectivity can be correlated with the distance of the reactive center from the nonpolar side chain. Whereas the carbonyl carbon of phenyl acetates is only two atoms removed from the phenyl ring, the reactive center... 

The proton dissociation constants, of two series of 3,7-bis(arylazo)-2,6-diphenyl-1 //-irnidazo[l,2-7]pyrazoles, in the ground state and the excited state were determined by the spectrophotometric method and utilizing the Forster energy cycle, respectively. These constants were correlated by the Hammett equation and the results of such correlations with spectral data indicated that both series of compounds exist in solution almost exclusively in the l//-bis-(arylazo) tautomeric form A <2002T2875> (Scheme 3). 

Co-catalysts other than water. Trichloro- and monochloro-acetic acids, when used as cocatalysts, induced instantaneous polymerisation at -140°. With the following co-catalysts the rate of polymerisation at -78° decreased in the order acetic acid > nitroethane > nitromethane > phenol > water [75a]. Since this is also the sequence of the acid dissociation constants of these substances in water, it appears that the catalytic activity , as shown by the rate of polymerisation, is correlated with the acidity of the cocatalyst in aqueous solution. Flowever, there are two reasons for questioning the validity of this correlation. 

For linear, primary alcohols (n-alkanols) the strength of complexation with CDs, expressed by pKs = —logKs, where Ks is the dissociation constant of the complex, correlates strongly with their coefficients for partition (Pe) between diethyl ether and water (Matsui and Mochida, 1979 Matsui et al., 1985), with slopes close to 1 (la and lb). It has also been... 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

The study of solute-solvent and solvent-solvent interactions in mixed solvents has been gaining significance in recent years61-64, because of the increasing application of these solvents. Casassas and collaborators67 have used the Kamlet-Taft multiparametric equation for the correlation of dissociation constants of acids in 1, 4-dioxane-water mixtures. They found that when the main solvent is retained the property does not involve significant changes in the cavity volumes and, in those cases, the pK in binary solvents can be described by equation 8 ... 

The agreement between the observed and predicted k values of aromatic acids was within 10%. The correlation coefficient was 0.954 (n = 32). An error of greater than 10% for 3-hydroxy-2-naphthoic acid and 2-hydroxybenzoic acid was attributed mainly to an error in their K.A values.25 The partition coefficient, logP, and dissociation constant, pKA, of analytes can be obtained by simple calculations and by computational chemical calculations, and thus the retention time can be predicted in reversed-phase liquid chromatography. 

The earliest LFER, advanced by Bronsted, correlates the acid dissociation constant and base strength (1/A h) of species with its effectiveness as a catalyst in general acid (At h) and base (Atgl-catalyzed reactions respectively. The relationships take the form... 

Hydrogen bond formation between dissimilar molecules is an example of adduct formation, since the hydrogen atom that is bonded to an electronegative atom, such as oxygen or nitrogen, is a typical acceptor atom. The ability of molecules to donate a hydrogen bond is measured by their Taft-Kamlet solvatochromic parameter, a, (or a . for the monomer of self-associating solutes) (see Table 2.3). This is also a measure of their acidity (in the Lewis sense, see later, or the Brpnsted sense, if pro tic). Acetic acid, for instance, has a = 1.12, compared with 0.61 for phenol. However, this parameter is not necessarily correlated with the acid dissociation constant in aqueous solutions. 

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. 

Using this screening approach, a fourfold amplification of the designed library member A-P was observed. Interestingly, a fivefold amplification of the peptidic dimer P-P was also observed. Amplification factors correlated well with dissociation constants (K ) subsequently measured by surface plasmon resonance (SPR) A-P was found to have a of 30 [tM, while the more strongly amplified P-P was found to have a of 22.5 [tM. 

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