Acid-ionization constants approximation method

Write the acid ionization constant (A J in terms of the equilibrium concentrations. First solve for x by the approximate method. If the aprroximation is not valid, use the quadratic equation or the method of successive approximation to solve for x. 

Find the percentage ionization of acetic acid in molal solution. Take the value of the ionization constant as 0.000018 and solve the quadratic equation by the method of approximation. 

In practice the potentials of a series of cells of type (1) are measured in which the molalities of the acid, its salt, and of sodium chloride are known. In the more dilute solutions however there is an appreciable change of the molalities from the stoichiometric values due to the reaction represented by equation (3) but a correction can be made for this effect using a preliminary value of the ionization constant in evaluating the third term on the left-hand side of equation (8) and in computing the ionic strength, 0), which is used as described below. The method may thus involve a series of approximations, but a single approximation is usually sufficient. 

Where it has been possible to compare these different expressions for Kt with values obtained by an independent method, such as that based on spectrometry, the one using both XmgN and K ex has proved superior to the more approximate forms using only one of these constants . This method of studying tautomerism was first used with amino acids and applied to heterocyclic compounds by Tucker and Irvin Table 5.12 records values for Kt obtained from ionization constants, and Table 5.10 includes values of the... 

Our approach was developed from a plot of logarithms of rate constants for methyl tosylate versus Y values. This method can be illustrated by the plot (Figure 1) versus YOTs, a scale of solvent ionizing power based on solvolyses of 2-adamantyl tosylate (II, X = OTs) (3). The normal alcohols, water, and alcohol-water mixtures form a line of similar slope to a line joining the data points for acetic and formic acids (Figure 1). The slope of these lines is approximately 0 3, which was assumed (3, 46) to be the sensitivity of solvolyses of methyl tosylate to solvent ionizing power (m value, equation 1). 

Less commonly used measurement techniques include the pH dependence of partition coefficients [74], fluorescence spectra [75], nuclear magnetic resonance chemical shifts or coupling constants, HPLC or CE retention volumes [76,77], and the dependence of reaction rates for ionizable substrates on pH (also called kinetic methods). Kinetic methods were amongst the earliest methods to be used for pKg determination. In some cases, they may be the only feasible method, for example, extremely weak acids (pKa > 12) without suitable absorption spectra. The difficulty with kinetic methods is that they may not actually measure the pKg value for the substrate, but that of the reaction transition state. If the electronic configuration of the transition state is similar to that of the reactant (early transition state), then the kinetic may be quite close to the equilibrium value. However, if the transition state more nearly approximates the reaction products (late transition state), then the kinetic value may bear little resemblance to that for the reactant. This explanation might account for the lack of agreement between the first apparent kinetic pK = 4.0) and equilibrium (pK = 8.6) pKg values for hydrochlorothiazide at 60 °C [78]. Similar restrictions may be placed on the use of pKa values from the pH dependence of fluorescence spectra, as these reflect the properties of the first excited state of the molecule rather than its ground state [75]. 

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