Acid dissociation constant accuracy

Sadlej-Sosnowska, N. Calculation of acidic dissociation constants in water Solvation free energy terms. Their accuracy and impact. Theor. Chem. Acc. 2007,118(2), 281-93. 

Recent applications have shown the potential of flow titration as a modem tool in analytical chemistry. As the required amount of titrand is associated with the analytical signal, important parameters, e.g., oxidis-ability in wastewaters [339], bromine number in foodstuffs [340], bitterness of beers and similar [341], total acidity in wines and vinegars [342] and total alkalinity in natural waters [343], are efficiently determined. In addition, the total concentration of several analytes belonging to the same family, e.g., amines [344], can be determined. The entire titration curve is generally available, allowing the determination of weak acids, complex stability constants and acid dissociation constants [345]. The determination of humidity by the Karl Fischer method [346] is another important application of flow titrations. For single analyte determinations, the analytical characteristics inherent to titrimetric procedures, such as enhanced accuracy and precision, should be emphasised. 

Tam KY andTakacs-Novac K, Multi-wavelengfii spectrophotometric determination of acid dissociation constants. Anal. Chim. Acta, 434, 157-167 (2001). NB A new spectrophotometric method was validated by comparison wifii file standard method of Albert and Serjeant, using 10 M solutions in 0.15M KCl. No details of pH meter calibration. In the novel method, operational pH values were converted to p[H] by a multi-parametric equation (ref. 12, Avdeef A). Sample concentrations of 10-100 uM were titrated in a Sirius GLpKa instrument and pH data were collected when drift was <0.02 pH/min. 15-25 wavelengfiis were used for each measurement. Note that errors are for reproducibility only, not accuracy. 

Interestingly, by the time one reaches somewhat more advanced levels of study, one is likely to encounter a pH meter that is calibrated to be accurate to hundreds, perhaps even thousands, of a pH unit, and certainly one can look up long lists of experimental acid dissociation constants, typically in the form of pK values, that have been measured to exquisite accuracy. 

At room temperature, a change in 1/10 of a log unit in a pK value implies a change of 0.14 kcal/mol in the corresponding acid dissociation constant. The phrase chemical accuracy has come, for theorists, to imply accuracy to within 1.0 kcal/mol. Thus, application of a model expected to offer chemical accuracy would imply an expected error in a pK of roughly 0.7 log units—one certainly would not want to experience such a variation in pH in one s personal bloodstream (although one would not be burdened with said experience for overly long). 

L. Michaelis and M. Mizutani, and later Mizutani alone, have measured with the hydrogen electrode the pH of solutions of weak acids with their salts in the presence of varying amounts of alcohol. They assumed in their calculations that the constant of the hydrogen electrode remained unchanged by the addition of alcohol. Probably, only a small error enters when solutions with higher alcohol concentrations are involved. Michaelis and Mizutani were unable to calculate the true dissociation constants of the particular acids from their measurements because the activity of the anions was not known with sufficient accuracy. The quantity which they determined was the acidity constant (cf. page 90). 

Valik19 made differential potentiometric titrations of aspartic acid, one series of results being given in curve (c) of Fig. 6. The volume of solution of alkali necessary to titrate tlie second acid dissociation for which the ionization constant is 2.5 X 10"10 should be exactly equal to that for the first unless there is a difference between the potentiometric and stoichiometric end points. Within the rather large limit of error, this was found to be true, but the end point could not be located with accuracy due to the flatness of the curve, as shown above. Differences between the stoichiometric and potentiometric end points are predicted for titrations of weak acids or weak bases. Such a difference increases the weaker the acid or base, but the difficulty of locating the end point also increases. It may be safely concluded that within the accuracy to which the potentiometric end point of a titration can be established it is identical with the stoichiometric end point. 

The Ka value of -cyanobenzoic acid is 3.14. It has already been mentioned (Section IILB) that Widequist " found this acid to be rapidly hydrolysed in water (initially to phthalamic acid). He seems to have taken great care to minimize the effects of this on the conductivity measurements which were used to determine the dissociation constant, but it must be supposed that the above value is not of the highest accuracy possible for pX determinations. The pKa value for the para acid is about 3.55. Thus the general pattern for the effect of moving an electron-attracting group from para- to r / -position is followed, but the increase in acidity is not so marked as in most of the cases mentioned above. To decide whether the increase in acidity is reasonable requires correlation analysis by the extended Hammett equation (Section II.B) in the form of equation 15 ... 

Ives and his collaborators have inferred temperature variations in ACp from extremely accurate conductometric measurements of the dissociation constants of carboxylic acids, but this demands high experimental accuracy, very pure materials, and a considerable degree of sophistication in the statistical treatment of the experimental results. Most investigations of dissociation constants yield at best an average value of ACp for the temperature range studied, and even this is often uncertain. The precision of thermodynamic parameters derived from dissociation constants will always decrease rapidly in the series AG°, AH, AS°, ACp. 

The activity of the hydrated protons is a quantitative measure of the acidity of the solution and it can be measured by electrochemical methods with a high degree of accuracy. Another advantage is the fact that ionization of a compound, neutralization and hydrolysis (or more general solvolysis) are all considered as protolytic reactions. When is the ionic product of water or of the protonic solvent used and Ka the dissociation constant of the acid,... 

Chapter 3 is dedicated to comprehensive presentation of mathematical procedures associated with dissociation of dtric acid in water and in electrolyte solutions. Available in the literamre dissociation constants are tabnlated and their accuracy examined. Based on temperature and pressnre dependence of dissociation constants, the thermodynamic functions linked with dissociation process are discussed in a detail. It also includes description of mar aspects cormected with compositions and applications of citrate buffers. Besides, it gives a very extensive number of references related to citric acid complexes. 

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