Dibasic acids dissociation constants

A frequently encountered pH-rate profile exhibits a bell-like shape or hump, with two inflection points. This graphical feature is essentially two sigmoid curves back-to-back. By analogy with the earlier analysis of the sigmoid pH-rate curve, where the shape was ascribed to an acid-base equilibrium of the substrate, we find that the bell-shaped curve can usually be accounted for in terms of two acid-base dissociations of the substrate. The substrate can be regarded, for this analysis, as a dibasic acid H2S, where the charge type is irrelevant we take the neutral molecule as an example. The acid dissociation constants are... 

Some compounds exhibit pH behavior in which a bell-shaped curve is obtained with maximum instability at the peak [107]. The peak corresponds to the intersection of two sigmoidal curves that are mirror images. The two inflection points imply two acid and base dissociations responsible for the reaction. For a dibasic acid (H2A) for which the monobasic species (HA-) is most reactive, the rate will rise with pH as [HA-] increases. The maximum rate occurs at pH = (pA) + pK2)/2 (the mean of the two acid dissociation constants). Where an acid and base react, the two inflections arise from the two different molecules. The hydrolysis of penicillin G catalyzed by 3,6-bis(di-methylaminomethyl)catechol [108], is a typical example. For a systematic interpretation of pH-degradation profiles, see the review papers by van der Houwen et al. [109] and Connors [110]. 

The bipyridines are dibasic, and the two acid dissociation constants Ki and K2, for all the bipyridines have been determined. Typical values are recorded in Table I. There has been considerable interest in the first dissociation constants Ki of 2,2 -bipyridine and substituted 2,2 -bipyridines because of their use as metal complexing agents. In general, the order of relative basic strengths of derivatives of 2,2 -bipyridine is as expected. Electron-attracting substituents reduce the basicity, whereas electron-donating substituents increase the basicity of the molecule. " The dissociation constants of several substituted bipyridines correlate well with the Hammet equation. 2,2 -Bipyridines with an electron-donating substituent at position 4 are monoprotonated at N-1 and not at... 

Dibasic acids dissociate in two steps, and both dissociation equilibria can be characterized by separate dissociation equilibrium constants. The dissociation of the dibasic acid H2A can be represented by the following two equilibria ... 

The third acid dissociation constant, pKa, represents the removal of the imino proton. The bis complexes of these ligands have been examined and found to behave as dibasic acids the acidity arises from the dissociation of the imino proton from each ligand. The acid dissociation constants for the iron(II) complexes of these ligands are shown in Table III. 

Davidson and Hantzsch (1898) and later Engler and Hantzsch (1900) investigated this system on the supposition that it corresponds to that of the common dibasic acids. From conductivity measurements they calculated basic dissociation constants for the diazohydroxides, but it is now known that their assumptions were incorrect. In fact, at the turn of the century it was practically impossible to reach the right solution. On the one hand, Hantzsch did not have at his disposal the current poten-tiometric technique for protolytic equilibria, and on the other hand, the system of Scheme 5-1 is a special case for a dibasic acid, the principle of which was not grasped in Hantzsch s time. 

In deriving theoretical equations of the current-potential (or time) curves of ion transfer of an acid we shall make essentially the same assumptions as the assumption 1-6 above. It is noted here that theoretical equations of the more general case, that is, of a dibasic acid, such as expressed by AH2 = AH + H, AH = A + H, can be derived [24], but are not included here, to save space. The formal formation constant, and formal dissociation constant,, in the a phase is defined by... 

The above treatment of moderately dilute acids and dibasic acids can be used for analogous cases of bases. Table 1.7 lists examples of dissociation constants of bases in aqueous solutions. 

It has been found experimentally [see Edsall and Wyman (1958), p. 485] that the monoester of dicarboxylic acid has a value of the dissociation constant nearly half of the Ki iss value of the dibasic acid. This is equivalent to saying that the binding constant ks to the monoester is nearly the same as the second intrinsic binding constant for the dicarboxylic acid, i.e., kg = k n. 

The cis- and trans-isomers of [Pt MeNH(OH) 2(NH3)2] have been synthesized and potentiometric titrations show that both are dibasic.161 The difference between consecutive dissociation constants is much greater for the cis-isomer, which is attributed to ds-interaction of the ligands. In addition [PtCl2(NHMeOH)4] was shown to be tetrabasic, the titration curve behaving as though two dibasic acids were present. 

If the dissociation constants for any two. successive stages are sufficiently different it is sometimes feasible to apply the methods employed for monobasic acids the conditions under which this is possible will be considered with reference to a dibasic acid, but the general conclusions can be extended to more complex cases. If H2A is a dibasic acid for which Ki, the dissociation constant of the first stage, ... 

The first stage dLSSociation constant of a dibasic acid is actually the sum of two constants consider, for example, the unsymmetrical dibasic acid HX X H, where X and X are different. This acid can dissociate in two ways, viz.,... 

The determination of the second dissociation constant of a dibasic acid also requires a knowledge of the equivalent conductance of the intermediate ion HA, and if the value of K2 is large enough to be determined from conductance measurements, the further dissociation of HA "... 

Dissociation Constants of Dibasic Acids by E.M.F. Measurement.— If the ratio of the dissociation constants of a dibasic acid, or of any two successive stages of ionization of a polybasic acid, is greater than about 10 or 10 , it is possible to treat each stage as a separate acid and to determine its dissociation constant by means of cells without liquid junction in the manner already described. In a mixture of the free dibasic acid H2A with its salt NallA, the essential equilibria are... 

When the dissociation constants of successive stages are relatively close together, a more complicated treatment becomes necessary. The dissociation constants of the first and second stages of a dibasic acid HjA may be written in a form analogous to that given above, viz.,... 

Since the X s and F s can be evaluated, as already described, the two dissociation constants of a dibasic acid can be determined from pairs of pH measurements. 

The activity coefficients have been omitted and the approximate functions ki and 2, for the two stages of dissociation of the dibasic acid, have replaced the corresponding thermodynamic constants. The quantity B is defined as... 

Dissociation Constants of Amino-Acids.—A very considerable simplification in the treatment of amino-acids can be achieved by regarding them as dibasic acids. Consider, for example, the hydrochloride of glycine, i.e., C1"" +NH3CH2C02H when this is neutralized by an alkali hydroxide, there are two stages of the reaction, corresponding in principle to the two stages of neutralization of a dibasic acid, thus... 

A titration curve of a dibasic add is essentially a composite of the titration curves of an equimolar mixture of two weak acids with dissociation constants and Ki- In the two buffer regions, where Equation (3-30) applies, the shape can be calculated directly if Aj. The hydrogen ion concentration at the first end point is given approximately by Vj, and at the second end point it is nearly the same as that for the titration of a monobasic weak acid with = 2- If is much larger than K2, the above approximations are no longer valid then the precision of the intermediate end point is so low that it is no longer of analytical value. The titration curve is too shallow for quantitative use unless KJK2 exceeds about 10 or 10 . ... 

Sulfuric acid is a dibasic acid and although regarded as a strong acid, the second dissociation constant is rather modest (—0.01 mol although care must be taken to consider the nonideality of electrolyte solutions when undertaking... 

Strictly, SO2 dissolves in water as (S02)aq with little forming sulfurous acid, H2S03(aq>, but it is usual to neglect the distinctions between these two species. The ionization equilibria are typically fast and in the case of the hydration of aqueous SO2 the hydration reaction proceeds with rate a constant of 3.4 X 10 s which allows the formation of the bisulfite anion to be exceedingly rapid. Although H2S03(aq) is a dibasic acid, the second dissociation constant is so small that the bisulfite anion (HSO ) dominates as the subsequent dissociation to the sulfite ion S03(aq> would not be important except in the most alkaline of solutions. At around pH 5.4 in a typical cloud with a gram of liquid water in each cubic meter, SO2 will partition equally into both phases, because of the hydrolysis reactions. 

Compormds with two or more acidic or basic functional groups will yield multiple endpoints in a titration, provided the acidic or basic groups differ sufficiently in strength. Computational techniques permit the derivation of reasonably accurate theoretical titration curves for polyprotic acids or bases, provided the ratio K1IK2 is above 103. Ki and K2 are dissociation constants. The titration curve of a dibasic weak acid with NaOH resembles that shown in Fig. 6. 

In the case of a dibasic acid two dissociation constants must be considered ... 

This equation has a number of uses. If [H+] is determined in two solutions of different concentrations of a given dibasic acid, two equations are obtained in which Ki and K2 are the only unknowns and from which the values of these dissociation constants are found very simply. 

It is possible, by conductance measurements or by electrometric methods, to obtain dissociation constants, which will be denoted by Ki and K2, for these two stages of ionization. It is the purpose of this section to consider the relations of the values of these constants to the molecular structures of the molecules. Adams11 has demonstrated that, from statistical considerations, the theoretical ratio of the two constants, K1/K2, is four. His reasoning is as follows. Representing a dibasic acid by HRR H in which R and R represent the two halves of the molecule to which the ionizable hydrogens are attached, the acid may have a primary dissociation in two different ways... 

As a matter of fact in all recent measurements of the ionization constants of dibasic acids the first dissociation constant has been found to be considerably greater than four times the second.14... 

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