Acid-dissociation constant polyprotic acids

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. 

The standard notation for successive acid dissociation constants of a polyprotic acid is Kt, K2, K2, and so on, with the subscript a usually omitted. We retain or omit the subscript as dictated by clarity. For successive base hydrolysis constants, we retain the subscript b. The preceding examples illustrate that Kal (or K ) refers to the acidic species with the most protons, and Kbl refers to the basic species with the least number of protons. Carbonic acid, a very important diprotic carboxylic acid derived from COz, is described in Box 6-4. 

The equilibrium constant, K , is called the acid dissociation constant. Similarly for a polyprotic acid (i.e. phosphoric acid), the equilibrium... 

The equilibrium constants to be determined in this example are protonation constants, introduced in Chapter 20. The protonation constant of a base L is the reciprocal of the acid dissociation constant Kg for the corresponding conjugate acid HL. For a polyprotic acid, the general expression for the protonation constant is given by equation 22-5. 

Note that the acid-dissociation constants are labeled ol and K 2- The numbers on the constants refer to the particular proton of the acid that is ionizing. Thus, K 2 always refers to the equilibrium involving removal of the second proton of a polyprotic acid. 

TABLE 16.3 Acid-Dissociation Constants of Some Common Polyprotic Acids... 

The acid-dissociation constants for common polyprotic acids are listed in T Table 16.3, and Appendix D provides a more complete list. The structure of citric acid illustrates the presence of multiple ionizable protons Figure 16.13. 

The successive acid-dissociation constants of a polyprotic acid are often labeled K. 2 etc. Provided the second reaction... 

Values for the successive acid-dissociation constants for several polyprotic acids are given in Appendix IV. 

Polyprotic bases, like polyprotic acids, also have more than one base dissociation reaction and base dissociation constant. 

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. 

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. 

Acids Bronsted-Lowry theory of, 21 common, concentration of, (T) 829 dissociation constants of, (T) 832 hard. 54 ionisation of, 20 Lewis, 22 polyprotic, 20... 

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... 

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. 

For multiple equilibria dissociation constants (such as polyprotic acids), K for the overall reaction is the product of the equilibrium constants for the individual reactions. Therefore,... 

Titrations curves for polyprotic acids have an inflection point for each hydrogen in the formula if the dissociation constant (Ka) for each hydrogen is very different from the others and if any dissociation constant is not too small. The titration curves of the polyprotic acids H2S04 and H3P04 are shown in Figures 5.6 and 5.7. Sulfuric acid has essentially one inflection point (like hydrochloric acid—compare with Figure 5.1(a)), while phosphoric acid has two apparent inflection points. Both hydrogens on the... 

As you know, polyprotic acids have more than one hydrogen atom that dissociates. Each dissociation has a corresponding acid dissociation constant. How can you calculate the pH of a solution of a polyprotic acid ... 

All polyprotic acids, except sulfuric acid, are weak. Their second dissociation is much weaker than their first dissociation. For this reason, when calculating [HsO" ] and pH of a polyprotic acid, only the first dissociation needs to be considered. The calculation is then the same as the calculation for any weak monoprotic acid. In the Sample Problem, [HP04 ] was found to be the same as the second dissociation constant, Ka. The concentration of the anions formed in the second dissociation of a polyprotic acid is equal to... 

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. 

Acids that contain more than one dissociable proton are called polyprotic acids. Polyprotic acids dissociate in a stepwise manner, and each dissociation step is characterized by its own acid-dissociation constant, Kal, Ka2, and so forth. For example, carbonic acid (H2C03), the diprotic acid that forms when gaseous carbon dioxide dissolves in water, is important in maintaining a constant pH in human blood. It undergoes the following dissociation reactions ... 

For polyprotic acids such as H3PO4 or H3As04, there is usually a factor of approximately 105 difference in successive Ka values. Phosphoric acid has dissociation constants that have the values Kal = 7.5 x 10-3, Ka2 = 6.2 x Itr8, and Ka3 = 1.0 x 10-12. This is because the first proton comes from a neutral molecule, the second from a -1 ion, and the third from a -2 ion. As a result of electrostatic attraction, it is energetically less favorable to remove H+ from species that are already negative. When considering the first and second ionization... 

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

Acids that contain more than one ionizable hydrogen atom per molecule are called polyprotic acids. These acids ionize in steps. The second (or third) proton has a much lower dissociation constant than does the prior proton because it is harder to remove a hydrogen ion the more negatively charged the Brpnsted acid (Table 19.4). Also, the prior ionization produces hydronium ions that repress the further ionization, in accord with LeChatelier s principle. Any acid ionizes less in the presence of a stronger acid (see Example 19.20). Thus, the hydronium ion in a solution of a polyprotic acid comes mainly from the first step in the ionization. 

Polyprotic acids ionize in steps, each having its own value for the dissociation constant. 

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