Polybasic acids dissociation

This system of nomenclature has withstood the impact of later experimental discoveries and theoretical developments that have since the time of Guyton de Morveau and Lavoisier greatiy altered the character of chemical thought, eg, atomic theory (Dalton, 1802), the hydrogen theory of acids (Davy, 1809), the duahstic theory (Berzehus, 1811), polybasic acids (Liebig, 1834), Periodic Table (Mendeleev and Meyer, 1869), electrolytic dissociation theory (Arrhenius, 1887), and electronic theory and modem knowledge of molecular stmcture. 

Chelating agents that are polybasic acids give two or more hydrogen ions per molecule. The four stages of dissociation of EDTA, eg, are represented by the equations... 

The definition of pH is pH = —log[H+] (which will be modified to include activity later). Ka is the equilibrium constant for the dissociation of an acid HA + H20 H30+ + A-. Kb is the base hydrolysis constant for the reaction B + H20 BH+ + OH. When either Ka or Kb is large, the acid or base is said to be strong otherwise, the acid or base is weak. Common strong acids and bases are listed in Table 6-2, which you should memorize. The most common weak acids are carboxylic acids (RC02H), and the most common weak bases are amines (R3N ). Carboxylate anions (RC02) are weak bases, and ammonium ions (R3NH+) are weak acids. Metal cations also are weak acids. For a conjugate acid-base pair in water, Ka- Kb = Kw. For polyprotic acids, we denote the successive acid dissociation constants as Kal, K, K, , or just Aj, K2, A"3, . For polybasic species, we denote successive hydrolysis constants Kbi, Kb2, A"h3, . For a diprotic system, the relations between successive acid and base equilibrium constants are Afa Kb2 — Kw and K.a Kbl = A w. For a triprotic system the relations are A al KM = ATW, K.d2 Kb2 = ATW, and Ka2 Kb, = Kw. 

Moreover, many hydrogen compounds, when dissolved in such solvents, ionize more or less completely lo give solvated protons and anions, In the case uf polybasic acids, ionization constants are reported for each step in this dissociation. 

Sometimes the acid-base reaction involved is more complex than that indicated in scheme (19). The two most frequently observed complications are participation of proton-donors other than hydroxonium ion and dissociation of two or more protons. Participation of various proton-donors is demonstrated by the dependence of the height of the kinetically controlled wave on the nature and concentration of the buffer with the usual type of buffers, a pH-dependence of wave f in the shape of a deformed dissociation curve is obtained. For polybasic acids several po-larographic dissociation curves are observed at various pK -values under certain conditions the slopes of these curves may differ. 

The examples cited above illustrate the difficulties of deciding the state of hydration of the species involved in an equilibrium on the basis of solvent isotope effects. This discussion has certain parallels in problems of reaction mechanism where the degree of involvement of water in the transition state (distinction between A-l and A-2 reactions) is at issue. By analogy with the conclusions reached for the dissociation of polybasic acids we may anticipate that it will similarly not be easy to settle such questions by the measurement of rate constants in H20-DzO mixtures. 

Polybasic adds dissociate in more steps, yielding more than one hydrogen ion per molecule, Sulphuric acid is a dibasic acid and dissociates in two steps ... 

Dissociation Constants of Polybasic Acids Conductance Method.— A polybasic acid ionizes in stages, each stage having its own characteristic dissociation constant for example, the ionization of a tribasic acid HsA, such as phosphoric acid, may be represented by ... 

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... 

It follows, therefore, that in a polybasic acid system, or in a mixture of approximately equivalent amounts of different acids, the neutralization of a particular stage or of a particular acid may be regarded as commencing effectively when the pH is equal to pA n+i 3, where pkn+i is the dissociation of the (n -f l)th stage or acid at this point the pH-neutraliza-tion curve for the mixture will commence to diverge from that of the previous stage of neutralization. Similarly, when an acid is 99.9 per cent neutralized,... 

In polybasic acids, the effect of chelation appears between later /C s. For example, in ethylenediaminetetra-acetic acid the first two hydrogen ions can dissociate readily, but the third and later ionizations axe greatly hindered by H bonding. 

The procedure just described has been used for the determination of the dissociation constants of a number of weak monobasic acids. It has also been extended to the study of polybasic acids and amino-acids. 

In all but a few situations, the assumption of a single principal equilibrium, as invoked in Examples 15-4 and 15-5, provides a satisfactory estimate of the pH of buffer mixtures derived from polybasic acids. Appreciable errors occur, however, when the concentration of the acid or the salt is very low or when the two dissociation constants are numerically close to one another. A more laborious and rigorous calculation is then required. 

Polybasic acids. The second dissociation step of a polybasic acid may be described in the following manner ... 

Each dissociation step has an associated equilibrium constant (acid dissociation constant), and it is general for polybasic acids that Aia(l) > K 2), and so on it is more difficult to remove H from an anion than from a neutral species. Values of equilibrium constants may be temperature-dependent, and the inclusion of the temperature to which... 

The stability constant given in Eq. 4 is an association constant. A dissociation constant is numerically equal to the reciprocal of the corresponding association constant. It is common practice to quote dissociation constants for acids (particularly organic acids), while association constants are used for complexes. For a monobasic acid, HL. there are no further complications. But for polybasic acids, the numerical order of the two sets is reversed. For example, for a dibasic acid, the first stepwise dissociation constant is equal to the reciprocal of the second stepwise association constant and vice versa. 

The Lewis acidity level is denoted by pM, the negative logarithm of the concentration of a metal ion M, just as the pH is used as a measure of the Bronsted acidity level. Further, it is necessary to consider stepwise formation constants in metal complex equilibria just as is done with calculations involving polybasic Bronsted acid dissociations. Just as those calculations are systematized and simplified by the use of aC to describe the concentrations of all species, so too is the definition of a set of a values that represent the fractions of the total concentration present as each metal complex species in these cases. 

Dibasic acids, polybasic acids, and proteins, with two or more ionizable groups, give more complex titration curves than the sinqile monobasic adds (Schulz, 1994). Consider the titration curve of a simple amino acid which has no charge in its side chain. In aqueous solution, a monoamino, monocarboxylic add is distributed between three species, namely the fully protonated acid, the zwitterion, and the fully dissociated base ... 

J. Th. G. Overbeek, The Dissociation and Titration Constants of Polybasic Acids. Bull Soc. Chim. Belg., 57,252-261,1948. 

Polybasic acids like HP3O4 dissociate in stages—the first atom of hydrogen ionizes easily, but HP2O4 is a weak acid and ionizes slowly, and HPO4 is a very weak acid. 

Let us now consider titration curves of polybasic acids which can donate more than one proton and can consequently possess more than one pK corresponding to the successive dissociation of each of the protons. A good example is afforded by phosphoric acid, H PO, for which three ionization steps and there corresponding pK are... 

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