Polybasic acids dissociation constants

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. 

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 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. 

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... 

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. 

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. 

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

Bjerrum N, Unmack A (1929) Electrometric measurements with the hydrogen electrode on mixtures of acids and bases with salt. The dissociation constants of water, phosphoric acid, citric acid and glycine. Kgl Danske Videnskab Selskab Math Fys Medd 9 5-206 Timberlake CF (1964) Iron-malate and iron-citrate complexes. J Chem Soc 5078 5085 Litchinsky D, Purdie N, Thomson MB, White WD (1969) A rigorous solution to the problem of interfering dissociation steps in the titration of polybasic acids. Anal Chem 41 1726 1730... 

Strengths of oxoacids can be affected by many variables. For example, you may wonder how acidity depends on oxidation number, or how it varies across a row of the Periodic Table. There is also the question of the relationship between the first, second, etc., dissociation constants of polybasic acids. 

Pauling s first rule relates to successive dissociation constants of a polybasic acid. From simple electrostatic considerations, it is easy to predict that successive ionization steps will take place less readily (for example, you might argue that it is easier to lose a proton from a neutral species like H3PO4 than from one, such as H2P04, that already carries a negative charge). The value of the rule is that it allows us to quantify the relationships between successive dissociation constants. 

Use Pauling s first rule to predict (approximately) the dissociation constants for each step in the dissociation of polybasic acids. (Questions 11.5, 11.8 and 12.2)... 

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