Ionization constant function

Use of a Monte Carlo or a cluster (Hybrid) algorithm to calculate ionization constants of the titratable groups, net average charges, and electrostatic free energies as functions of pH. 

The ionization eonstant should be a function of the intrinsic heterolytic ability (e.g., intrinsic acidity if the solute is an acid HX) and the ionizing power of the solvents, whereas the dissoeiation constant should be primarily determined by the dissociating power of the solvent. Therefore, Ad is expeeted to be under the eontrol of e, the dieleetrie eonstant. As a consequenee, ion pairs are not deteetable in high-e solvents like water, which is why the terms ionization constant and dissociation constant are often used interchangeably. In low-e solvents, however, dissociation constants are very small and ion pairs (and higher aggregates) become important species. For example, in ethylene chloride (e = 10.23), the dissociation constants of substituted phenyltrimethylammonium perchlorate salts are of the order 10 . Overall dissociation constants, expressed as pArx = — log Arx, for some substanees in aeetie acid (e = 6.19) are perchloric acid, 4.87 sulfuric acid, 7.24 sodium acetate, 6.68 sodium perchlorate, 5.48. Aeid-base equilibria in aeetie acid have been earefully studied beeause of the analytical importance of this solvent in titrimetry. 

Assume that the reaction occurs between the two uncharged species, MNNG and Am, with a rate constant kN. Express ks as a function of tN, K m, Kan, and [H. Sketch the anticipated pH profile. Actually, this situation is further complicated because kN, although constant over some pH range, shows a further variation that can be attributed to an acidic intermediate. Derive an expression for kN as a function of [H + ] from the scheme shown, denoting the acid ionization constant of the steady-state intermediate as Knl. 

Hydroxyl radicals. The acid ionization constant of the short-lived HO transient is difficult to determine by conventional methods but an estimate can be made because HO, but not its conjugate base, O -, oxidizes ferrocyanide ions HO + Fe(CN) — OH- + Fe(CN)g . Use the following kinetic data26 for the apparent second-order rate constant as a function of pH to estimate Ka for the acid dissociation equilibrium HO + H20 =... 

Figure 3.3 The six apparent ionization constants of vancomycin plotted as a function of weight % methanol. Unfilled circles denote acid groups, and filled circles denote basic groups. Acids usually are indicated by positive slopes and bases, by negative slopes. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]...

The titration curve of penicillamine hydrochloride at 25 °C revealed the presence of three ionizable groups with pKa values of 1.8 (carboxyl group), 7.9 (oc-amino group), and 10.5 (/J-thiol group). Recently, the ionization constants for the acidic functions of (D)-penicillamine were verified by pH titration at 37 °C and 0.15 M ionic strength [2], A 1% solution in water has a pH of 4.5-5.5 [3],... 

Strong et al. [8] have determined the ionization constant of benzoic acid in H2O as a function of ternperamre by conductance methods. Their data are listed in Table 20.3, with the pK based on a hypothetical standard state of 1 mol dm. Temperature was controlled to +0.002°C. 

TABLE 20.3. Ionization Constants of Benzoic Acid as a Function of Temperature... 

A graphical depiction of log(kjp) plotted as a function of log( Xa/p), where is the rate constant for general acid catalysis, is the acid ionization constant, p is the number of equivalent protons on the acid, and q is the number of equivalent positions where a proton can be... 

Potentiometric titration studies were used to obtain values for the two ionization constants of dorzolamide hydrochloride. The first of these yielded pK, = 6.35, corresponding to the secondary amino functional group. The second ionization corresponded to sulfonamido group, for which pK 2 ... 

The rate coefficient (k2 enc) for the collision of two species is given by 8RT/3Z (where Z is the viscosity of the medium at the reaction temperature), the Smoluchowski equation. This is the maximum possible rate of reaction, which is controlled by the rate at which the two reacting species diffuse together. For nitration in >90% H2S04, where nitric acid is completely ionized, if exclusively the free base nitrates the rate coefficient (k2 fb) would equal k2 obs KJhx (where Ka is the ionization constant of the base, and hx the acidity function that it follows). Thus, if k2 fb> k2 enc free base nitration is precluded, but if... 

The papers in the second section deal primarily with the liquid phase itself rather than with its equilibrium vapor. They cover effects of electrolytes on mixed solvents with respect to solubilities, solvation and liquid structure, distribution coefficients, chemical potentials, activity coefficients, work functions, heat capacities, heats of solution, volumes of transfer, free energies of transfer, electrical potentials, conductances, ionization constants, electrostatic theory, osmotic coefficients, acidity functions, viscosities, and related properties and behavior. 

The above results are part of the general rule that the plot of the equilibrium constant K or the rate constant k for the process X — Y as a function of pH follows the ionization constants of X. Let us now apply this rule to scheffte 5.14, bearing in mind that the substrate may also have ionizing groups ... 

J. Kendall and co-workers also computed values of a from the cryoscopic data. Phosphoric acid is a comparatively weak acid which ionizes in three stages H3P04 u H -f H2P0 4 2H-fHP04", at moderate dilutions, and even at extreme dilutions it is but partially resolved HgPO -SH -fPO/". The first hydrogen ion has the strongest acidic function, the third the weakest. 6. A. Abbott and W. C. Bray have also measured the ionization constants of orthophosphoric acid and find at 18° ... 

The parent acid, H3B03, functions as a weak acid in aqueous solution, possessing an ionization constant of about 6 x 10-, at 25°C in dilute solution. As its concentration increases, the ionization constant increases markedly. Kolthoff (220) investigated this effect by electrical conductivity and emf measurements, obtaining values of 4.6 x 1010 and 408 x 10 1 for boric acid concentrations of 0.1 M and 0.75 M respectively at 18°C. These results were attributed to the formation of tetraboric acid. 

Following on from the substituent constant methods, a number of other approaches have been applied to the prediction of pKa. The main prediction methods for pKa are summarized in Table 3.4. Of the methods to calculate pKa some are derived from atom and fragment values, others are derived from molecule orbital properties. Because of the problems of modeling ionization constants for molecules with multiple ionizable functional groups, the accuracy and predictivity of these methods remains questionable. 

Here, the symbol A represents an electron affinity and I an ionization energy with their subscripts indicating the relevant electron number. Equations (30a, b) show that n Jf) is a piecewise-constant function of Jf, multivalued at Jf an integer. The ground-state energy ES0 is known but not proven to be convex in N0 in the sense that its second difference is positive [8],... 

Thermodynamic functions (entropy, heat capacity, enthalpy and free energy functions) have not been reported for 1,2,4-thiadiazoles. The ionization constants of a number of 1,2,4-thiadiazoIes have been determined potentiometrically or by Hammett s method (65AHC(5)ll9). Polarographic measurements of a series of methylated 5-amino-l,2,4-thiadiazoles show that thiadiazoles are not reducible in methanolic lithium chloride solution, while thiadiazolines are uniformly reduced at E0.s = -1.6 0.02 V. This technique has been used to assign structures to compounds which may exist theoretically as either thiadiazoles or thiadiazolines (65AHC(5)119). 

The derivation of these different retention equations is important in several respects. First, they allow for calculation of micelle-solute binding constants, parameters which are important in many areas of micellar kinetics or chemistry. There have been several reports in the literature demonstrating this chromatographic approach for determination of micelle - solute binding constants (1,8,104,105). More importantly, they allow for prediction of retention behavior as a function of surfactant concentration (or of pH at constant micelle concentration), provided that the micelle - solute binding constant (or solute ionization constant) is known (which can be determined spectroscopically or from kinetic studies) (1,96,102). Consequently, the theory allows the chromatographer to determine the optimum conditions required for a desired separation. 

Our primary objective was to develop a computational technique which would correlate the ionization constant of a weak electrolyte (e.g., weak acid, ionic complexes) in water and the ionization constant of the same electrolyte in a mixed-aqueous solvent. Consideration of Equations 8, 22, and 28 suggested that plots of experimental pKa vs. some linear combination of the reciprocals of bulk dielectric constants of the two solvents might yield the desirable functions. However, an acceptable plot should have the following properties it should be continuous without any maximum or minimum the plot should include the pKa values of an acid for as many systems as possible and the plot should be preferably linear. The empirical equation that fits this plot would be the function sought. Furthermore, the function should be analogous to some theoretical model so that a physical interpretation of the ionization process is still possible. 

Figure 5. Ionization constants of acids in various solvents vs. the dielectric constant function at 25°C. A,B,C ethanol-water (O), methanol-water (A), dioxane-water ( ). B,C acetone-water ( ), glycerol-water (W). B 2-methoxyethanol-water (V), dimethyl-sulfoxide-water (M).

Equation (2-80) expresses the retention of an ionizable basic analyte as a function of pH and three different constants ionization constant adsorption constant of ionic form of the analyte (7 bh+) and adsorption constant of the neutral form of the analyte (T b)- These three constants describe three different equilibrium processes, and they have their own relationships with the system temperature and Gibbs free energy with respect to the particular analyte form. 

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