Dissociation of polyprotic acids

Since [H + ][OH ] = Kw (the ionic product of water), we have Kb = KJKa 

The values of Ka and Kb for different acids and bases vary through many powers of ten. It is often convenient to use the dissociation constant exponent pK defined by 

The larger the pKa value is, the weaker is the acid and the stronger the base. 

For very weak or slightly ionised electrolyes, the expression a2/( 1 — a) V = K reduces to a2 = KV or a = fKV, since a may be neglected in comparison with unity. Hence for any two weak acids or bases at a given dilution V (in L), we have a1 = y/K1 V and a2 = yjK2V, or ol1/ol2 = Jk1/ /K2. Expressed in words, for any two weak or slightly dissociated electrolytes at equal dilutions, the degrees of dissociation are proportional to the square roots of their ionisation constants. Some values for the dissociation constants at 25 °C for weak acids and bases are collected in Appendix 7. 

When a polyprotic acid is dissolved in water, the various hydrogen atoms undergo ionisation to different extents. For a diprotic acid H2A, the primary and secondary dissociations can be represented by the equations  

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Diphenylcarbazide as adsorption indicator, 358 as colorimetric reagent, 687 Diphenylthiocarbazone see Dithizone Direct reading emission spectrometer 775 Dispensers (liquid) 84 Displacement titrations 278 borate ion with a strong acid, 278 carbonate ion with a strong acid, 278 choice of indicators for, 279, 280 Dissociation (ionisation) constant 23, 31 calculations involving, 34 D. of for a complex ion, (v) 602 for an indicator, (s) 718 of polyprotic acids, 33 values for acids and bases in water, (T) 832 true or thermodynamic, 23 Distribution coefficient 162, 195 and per cent extraction, 165 Distribution ratio 162 Dithiol 693, 695, 697 Dithizone 171, 178... 

The only common strong polyprotic acid is sulfuric acid. Nevertheless, it is strong only for the first dissociation. Like the second dissociation of other polyprotic acids, the second dissociation of sulfuric acid is weak. 

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. 

Weak polyprotic Bronsted-Lowry acids are those that possess more than one dissociable H+. Examples of polyprotic acids include carbonic acid (H2C03, a diprotic acid) and phosphoric acid (H3P04), a triprotic acid (Table 1.17). In the case of phosphoric acid, the following dissociation steps can be demonstrated ... 

The addition of a NEW Section 19.5 on Polyprotic Acids, with Table 19.4 on Selected Dissociation Constants of Polyprotic Acids . 

Table 19.4 Selected Dissociation Constants of Polyprotic Acids...

The common ion effect is also important in solutions of polyprotic acids. The production of protons by the first dissociation step greatly inhibits the succeeding dissociation steps, which also produce protons, the common ion in this case. We will see later in this chapter that the common ion effect is also important in dealing with the solubility of salts. 

There is a close similarity between the working of Example 16.8 and an acid-base calculation. The first step (the assumption that the reaction goes to completion and is followed by a small amount of back dissociation) is analogous to the procedure for dealing with the addition of a small amount of a strong acid to a solution of a weak base. The subsequent calculation of the successive dissociation steps resembles the calculation of polyprotic acid equilibria in Example 15.12. The only difference is that in complex-ion equilibria it is conventional to work with formation constants, which are the inverse of the dissociation constants used in acid-base equilibria. 

Titrations of polyprotic acids will have more than one equivalence point and more than one half equivalence point. For the MCAT, assume that the first proton completely dissociates before the second proton begins to dissociate. (This assumption is only acceptable if the second proton is a much weaker add than the first, which is usually the case.) Thus we have a titration curve like the one shown below. 

Hardcastle, J.E. and Jano, I. (1998) Determination of dissociation constants of polyprotic acids from chromatographic data. Journal of Chromatography B, 717, 39-56. 

For polyprotic acids (acids where more than one proton can be removed), each successive proton becomes more difficult to remove. In H SO, the first proton readily dissociates, forming the HSO/ ion. The additional electron density on the ion has a stronger hold on the additional hydrogen ion, so it is heldmuchmore tightly. Therefore, for polyprotic acids, the anions formed by the dissociation of the acidic hydrogen are always less acidic than their parent molecule. 

Fortunately, there is such a method, which is both simple and generally applicable, even to mixtures of polyprotic acids and bases. It is based on the fact that we have available a closed-form mathematical expression for the progress of the titration. We can simply compare the experimental data with an appropriate theoretical curve in which the unknown parameters (the sample concentration, and perhaps also the dissociation constant) are treated as variables. By trial and error we can then find values for those variables that will minimize the sum of the squares of the differences between the theoretical and the experimental curve. In other words, we use a least-squares criterion to fit a theoretical curve to the experimental data, using the entire data set. Here we will demonstrate this method for the same system that we have used so far the titration of a single monoprotic acid with a single, strong monoprotic base. 

For many polyprotic acids Kai is much larger than subsequent dissociation constants, in which case the H iaq) in the solution comes almost entirely from the first ionization reaction. As long as successive values differ by a factor of 10 or more, it is usually possible to obtain a satisfactory estimate of the pH of polyprotic acid solutions by treating the acids as if they were monoprotic, considering only Kai-... 

CT is a (complementary against PT) technique, applied for determination of stabihty constants of complexes and proto-complexes, in particular. The knowledge of physico-chemical parameters related to dissociation of mono- and polyprotic acids H L in electrolytic systems is important both from cognitive and analytical viewpoints. Dissociation of the acids in such systems is characterized by pK = -logKj values for acidity parameters. In binary-solvent systems, the acidity parameters at the ends of x-scale (i.e., x = 0 and 1) are called as acidity constants," referred to solutions in pure (mono-component) solvent SI (pKjsi), S2 (pK s2), and W (pK ), where SI, S2 - organic solvents, W - water. We refer later to the solvents characterized by mutual miscibility, in all proportions, within the pairs W+Sl, W+S2, and S1+S2. 

Monoprotic weak acids, such as acetic acid, have only a single acidic proton and a single acid dissociation constant. Some acids, such as phosphoric acid, can donate more than one proton and are called polyprotic weak acids. Polyprotic acids are described by a series of acid dissociation steps, each characterized by it own acid dissociation constant. Phosphoric acid, for example, has three acid dissociation reactions and acid dissociation constants. 

A more challenging problem is to find the pH of a solution prepared from a polyprotic acid or one of its conjugate species. As an example, we will use the amino acid alanine whose structure and acid dissociation constants are shown in Figure 6.11. 

From a chemical point of view, the common amino acids are all weak polyprotic acids. The ionizable groups are not strongly dissociating ones, and the degree of dissociation thus depends on the pH of the medium. All the amino acids contain at least two dissociable hydrogens. 

Buffer mixtures are not confined to mixtures of monoprotic acids or monoacid bases and their salts. We may employ a mixture of salts of a polyprotic acid, e.g. NaH2P04 and Na2HP04. The salt NaH2P04 is completely dissociated ... 

Polyprotic acids (or mixtures of acids, with dissociation constants AT, K2, and AT3) and strong bases. The first stoichiometric end point is given approximately... 

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. 

It will be noted that there is a factor of approximately 105 between successive dissociation constants. This relationship exists between the equilibrium constants for numerous polyprotic acids, and it is sometimes known as Pauling s rule. This rule is also obeyed by sulfurous acid, for which ffj = 1.2 X 10 2 and K2 = 1 X 10 7. 

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