Titration dissociation constants

It has been shown that for most acid-base titrations the inflection point, which corresponds to the greatest slope in the titration curve, very nearly coincides with the equivalence point. The inflection point actually precedes the equivalence point, with the error approaching 0.1% for weak acids or weak bases with dissociation constants smaller than 10 , or for very dilute solutions. Equivalence points determined in this fashion are indicated on the titration curves in figure 9.8. 

The principal limitation to using a titration curve to locate the equivalence point is that an inflection point must be present. Sometimes, however, an inflection point may be missing or difficult to detect, figure 9.9, for example, demonstrates the influence of the acid dissociation constant, iQ, on the titration curve for a weak acid with a strong base titrant. The inflection point is visible, even if barely so, for acid dissociation constants larger than 10 , but is missing when is 10 k... 

Another situation in which an inflection point may be missing or difficult to detect occurs when the analyte is a multiprotic weak acid or base whose successive dissociation constants are similar in magnitude. To see why this is true let s consider the titration of a diprotic weak acid, H2A, with NaOH. During the titration the following two reactions occur. 

Since citric acid is a triprotic weak acid, we must first decide to which equivalence point the titration has been carried. The three acid dissociation constants are... 

Equilibrium Constants Another application of acid-base titrimetry is the determination of equilibrium constants. Consider, for example, the titration of a weak acid, HA, with a strong base. The dissociation constant for the weak acid is... 

Partanen, J. I. Karki, M. H. Determination of the Thermodynamic Dissociation Constant of a Weak Acid by Potentiometric Acid-Base Titration, /. Chem. Educ. 1994,... 

Directions are provided in this experiment for determining the dissociation constant for a weak acid. Potentiometric titration data are analyzed by a modified Gran plot. The experiment is carried out at a variety of ionic strengths and the thermodynamic dissociation constant determined by extrapolating to zero ionic strength. 

Using its titration curve, determine the acid dissociation constant for the weak acid in problem 6. 

The free maleic acid content in maleic anhydride is determined by direct potentiometric titration (166). The procedure involves the use of a tertiary amine, A/-ethylpipetidine [766-09-6J, as a titrant. A tertiary amine is chosen as a titrant since it is nonreactive with anhydrides (166,167). The titration is conducted in an anhydrous solvent system. Only one of the carboxyhc acid groups is titrated by this procedure. The second hydrogen s dissociation constant is too weak to titrate (166). This test method is not only used to determine the latent acid content in refined maleic acid, but also as a measure of the sample exposure to moisture during shipping. 

The titration curve of phosphoric acid in the presence of sodium hydroxide is shown in Figure 1. Three steps, corresponding to consecutive replacement of the three acidic hydrogens, and two inflection points, near pH = 4.5 and 9.0, are evident. Dissociation constants are = 7.1 x 10 = 6.3 x 10 ... 

The protonation equilibria for nine hydroxamic acids in solutions have been studied pH-potentiometrically via a modified Irving and Rossotti technique. The dissociation constants (p/fa values) of hydroxamic acids and the thermodynamic functions (AG°, AH°, AS°, and 5) for the successive and overall protonation processes of hydroxamic acids have been derived at different temperatures in water and in three different mixtures of water and dioxane (the mole fractions of dioxane were 0.083, 0.174, and 0.33). Titrations were also carried out in water ionic strengths of (0.15, 0.20, and 0.25) mol dm NaNOg, and the resulting dissociation constants are reported. A detailed thermodynamic analysis of the effects of organic solvent (dioxane), temperature, and ionic strength on the protonation processes of hydroxamic acids is presented and discussed to determine the factors which control these processes. 

In the discussion of the relative acidity of carboxylic acids in Chapter 1, the thermodynamic acidity, expressed as the acid dissociation constant, was taken as the measure of acidity. It is straightforward to determine dissociation constants of such adds in aqueous solution by measurement of the titration curve with a pH-sensitive electrode (pH meter). Determination of the acidity of carbon acids is more difficult. Because most are very weak acids, very strong bases are required to cause deprotonation. Water and alcohols are far more acidic than most hydrocarbons and are unsuitable solvents for generation of hydrocarbon anions. Any strong base will deprotonate the solvent rather than the hydrocarbon. For synthetic purposes, aprotic solvents such as ether, tetrahydrofuran (THF), and dimethoxyethane (DME) are used, but for equilibrium measurements solvents that promote dissociation of ion pairs and ion clusters are preferred. Weakly acidic solvents such as DMSO and cyclohexylamine are used in the preparation of strongly basic carbanions. The high polarity and cation-solvating ability of DMSO facilitate dissociation... 

The shapes of the titration curves of weak electrolytes are identical, as Figure 2.13 reveals. Note, however, that the midpoints of the different curves vary in a way that characterizes the particular electrolytes. The pV, for acetic acid is 4.76, the pV, for imidazole is 6.99, and that for ammonium is 9.25. These pV, values are directly related to the dissociation constants of these substances, or, viewed the other way, to the relative affinities of the conjugate bases for protons. NH3 has a high affinity for protons compared to Ac NH4 is a poor acid compared to HAc. 

It was found already by Cattelain that the 3-thioxo derivatives behave as monobasic acids that can be titrated on phenolphthalein and he considered them as more acid than the analogous 3,5-dioxo-triazines. This assumption was recently confirmed by determining the dissociation constants. Just as with 6-azauracil, it was possible to demonstrate, by comparing the dissociation constants of the V-methyl derivatives of all the thioxo analogs, that with the 3-thioxo compounds too, dissociation proceeds first at the NH group in position 3 122... 

Potentiometric titration curves The procedure involves the addition of a salt of a weak acid to the resin and the determination of the pH of the equilibrated solution. Table 9 shows the pK values of the OH groups and dissociation constants of the studied resin. The first ionization occurs at a pH slightly higher than that of sul-... 

The formation of a single complex species rather than the stepwise production of such species will clearly simplify complexometric titrations and facilitate the detection of end points. Schwarzenbach2 realised that the acetate ion is able to form acetato complexes of low stability with nearly all polyvalent cations, and that if this property could be reinforced by the chelate effect, then much stronger complexes would be formed by most metal cations. He found that the aminopolycarboxylic acids are excellent complexing agents the most important of these is 1,2-diaminoethanetetra-aceticacid (ethylenediaminetetra-acetic acid). The formula (I) is preferred to (II), since it has been shown from measurements of the dissociation constants that two hydrogen atoms are probably held in the form of zwitterions. The values of pK are respectively pK, = 2.0, pK2 = 2.7,... 

With a knowledge of the pH at the stoichiometric point and also of the course of the neutralisation curve, it should be an easy matter to select the appropriate indicator for the titration of any diprotic acid for which K1/K2 is at least 104. For many diprotic acids, however, the two dissociation constants are too close together and it is not possible to differentiate between the two stages. If K 2 is not less than about 10 7, all the replaceable hydrogen may be titrated, e.g. sulphuric acid (primary stage — a strong acid), oxalic acid, malonic, succinic, and tartaric acids. 

Boric acid behaves as a weak monoprotic acid with a dissociation constant of 6.4 x 10-10. The pH at the equivalence point in the titration of 0.2M sodium tetraborate with 0.2 M hydrochloric acid is that due to 0.1 M boric acid, i.e. 5.6. Further addition of hydrochloric acid will cause a sharp decrease of pH and any indicator covering the pH range 3.7-5.1 (and slightly beyond this) may be used suitable indicators are bromocresol green, methyl orange, bromophenol blue, and methyl red. 

The theory of titrations between weak acids and strong bases is dealt with in Section 10.13, and is usually applicable to both monoprotic and polyprotic acids (Section 10.16). But for determinations carried out in aqueous solutions it is not normally possible to differentiate easily between the end points for the individual carboxylic acid groups in diprotic acids, such as succinic acid, as the dissociation constants are too close together. In these cases the end points for titrations with sodium hydroxide correspond to neutralisation of all the acidic groups. As some organic acids can be obtained in very high states of purity, sufficiently sharp end points can be obtained to justify their use as standards, e.g. benzoic acid and succinic acid (Section 10.28). The titration procedure described in this section can be used to determine the relative molecular mass (R.M.M.) of a pure carboxylic acid (if the number of acidic groups is known) or the purity of an acid of known R.M.M. 

Weak acid with a strong base. In the titration of a weak acid with a strong base, the shape of the curve will depend upon the concentration and the dissociation constant Ka of the acid. Thus in the neutralisation of acetic acid (Ka— 1.8 x 10-5) with sodium hydroxide solution, the salt (sodium acetate) which is formed during the first part of the titration tends to repress the ionisation of the acetic acid still present so that its conductance decreases. The rising salt concentration will, however, tend to produce an increase in conductance. In consequence of these opposing influences the titration curves may have minima, the position of which will depend upon the concentration and upon the strength of the weak acid. As the titration proceeds, a somewhat indefinite break will occur at the end point, and the graph will become linear after all the acid has been neutralised. Some curves for acetic acid-sodium hydroxide titrations are shown in Fig. 13.2(h) clearly it is not possible to fix an accurate end point. 

This potential reflects itself in the titration curves of weak polyacids such as poly(acrylic acid) and poly(methacrylic acid) [32]. Apparent dissociation constants of such polyacids change with the dissociation degree of the polyacid because the work to remove a proton from the acid site into the bulk water phase depends on the surface potential of the polyelectrolyte. 

It is worth mentioning that an attempt was made by Tsao and Willmarth to determine the acid dissociation constant of HO2. The reaction between hydrogen peroxide and peroxydisulphate was used for the generation of the HO2 radical. However, these experiments, like others where the HO2 radical is studied under steady-state conditions, could yield only a value of acidity constant multiplied by a coefficient consisting of a ratio of kinetic parameters. Unfortunately, in this case there are no independent data for the kinetic coefficient, and the value of cannot be evaluated. Considering the kinetic analogue of the titration curve it can be stated only that ionization of HO2 becomes important in the pH range from 4.5-6.5. The value of acidity constant of HO2 obtained by Czapski and Dorfman is (3.5 + 2.0)x 10 mole.l. . ... 

Extensive data are given in the Uterature for the potentiometric titration of polymer acids which may be used to study the behaviour of polyelectrolyte systems under different conditions. For poly(a-D) galacturonic acid there are few data of this kind, especially in connection with the occurrence of a conformational transition induced by pH variations, or with the effect brought about by the addition or the exchange of counterions. Since for a polyacid not exhibiting a conformational transition in the course of titration, pK K denoting the apparent dissociation constant) increases monotonously with degree... 

Generally, the results of the measurements indicated that, where dissociation constants were determined by conductometry and also potentiometric titration, they were in agreement with each other further, KHX is low, e.g., about 10 4-10 6moll 1 for aromatic sulphonic acids and 10 13-10 16 moll-1 for carboxylic acids, Xhx2 is high, e.g., 102-104, and KBis low again, e.g., 10 5-10 6 for aliphatic amines and 10 10 for aromatic amines. 

With the dibasic sulphonphthaleins the situation becomes much more complex, as there are at least six equilibrium constants involved. Fig. 4.16 shows the titration of 3.000 ml of 0.01140 M bromocresol green with 0.0855 M TMG in 1,2-DCE. It appears that, once KPH = l/AdBH+ is known, the other constants can be found, as each of the four regions in the titration curve enables the possibility of determining one dissociation constant, viz., in ... 

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