Proton from polyprotic acids

Acids with more than one ionizable proton are polyprotic acids. In a solution of a polyprotic acid, one proton at a time dissociates from the acid molecule, and each dissociation step has a different K. For example, phosphoric acid is a tripro-tic acid (three ionizable protons), so it has three values ... 

The acid-dissodation constants for a few common polyprotic acids are listed in Table 16.3 . A more complete list is given in Appendix D. The stmctures for ascorbic and dtric acids are shown in the margin. Notice that the values for successive losses of protons from these acids usually differ by a factor of at least 10. Notice also that the value of K i for sulfuric add is listed simply as "large." Sulfuric add is a strong add with respect to the removal of the first proton. Thus, the reaction for the first ionization step lies completely to the right ... 

The values for K, listed here have been calculated from pK, values with more significant figures than shown so as to minimize rounding errors. Values for polyprotic acids—those capable of donating more than one proton—refer to the first deprotonation. 

Suppose we need to estimate the pH of an aqueous solution of a fully deproto-nated polyprotic acid molecule. An example is a solution of sodium sulfide, in which sulfide ions, S2-, are present another example is a solution of potassium phosphate, which contains P04 ions. In such a solution, the anion acts as a base it accepts protons from water. For such a solution, we can use the techniques for calculating the pH of a basic anion illustrated in Example 10.11. The K, to use in the calculation is for the deprotonation that produces the ion being studied. For S2, we would use Ki2 for H2S and, for P043-, we would use Kai for H3P04. 

H2 CO3] =0.050 M [H3 0+]= 1.5 X IO M [HCO3] = 1.5 x lO" M What happens if we add a base to this solution The strongest acid donates protons preferentially, but the concentration of hydronium ions is so small that this ion is rapidly consumed. Then the next strongest acid, H2 CO3, reacts with added base. Generalizing, when a base is added to a solution that contains both a polyprotic acid and its anion, the base accepts protons preferentially from the neutral acid. Only after the neutral acid has been consumed completely does the anion participate significantly in proton transfer. Example provides molecular pictures of this feature. 

Sulfuric acid is a far stronger acid than the hydrogen sulfate ion, because much more energy is required to remove a proton from a negatively charged ion. The strength of a polyprotic acid decreases as the number of hydrogen atoms that have dissociated increases. 

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. 

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... 

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 (Section 19.5) ionize stepwise, and the hydronium ion from each step represses the ionization of later steps. The second (and third) steps are essentially weaker because it is harder to remove a proton from a negatively charged species than from a neutral one. However, polyprotic acids follow the usual rules of equilibrium. For example, LeChatelier s principle can be used to predict and explain their behavior. 

Table 7.3 pK values at 25 °C of some acids and bases (upper section) and some large organic zwitterions (lower section) commonly used in buffer solutions. For polyprotic acids, where more than one proton my dissociate, the p/fa values are given for each ionization step. Only the trivial acronyms of the larger molecules are provided their full names can be obtained from the catalogues of most chemical suppliers... 

The example shown in Figure 14-10 illustrates the use of Select Case to calculate the pfCa value of a polyprotic acid. Since data at or near the equivalence points cause large calculation errors, the pKa is calculated only for n-bar values in the range 0.2 - 0.8, 1.2 - 1.8, 2.2 - 2.8 or 3.2 - 3.8. The expression used to calculate the piCa from the n-bar parameter depends on the number of protons... 

In the case of a polyprotic acid for which the individual ionizations are well separated (ideally, by at least 3 log units), values for the individual constants can be calculated from data points in the appropriate regions of the titration curve. If the individual ionizations overlap, the Bjerrum fi (n-bar) method may be used. This mathematical approach was introduced by Bjerrum for the calculation of stability constants of metal-ligand complexes, but it can also be applied to the determination of proton-ligand equilibrium constants. 

There are a number of computer programs available for the determination of stability constants from pH titration data. The most general of these perform a least-squares fit of the data to a calculated titration curve. The programs are able to handle protonated complexes, polynuclear systems, etc. In this example least-squares curve fitting is applied to a somewhat simpler case, a polyprotic acid in which the equilibria overlap extensively. The method is that used in the... 

The first step in the ionization of H2SO4 is complete in dilute aqueous solution. The second step is nearly complete in very dilute aqueous solutions. The first step in the ionization of a polyprotic acid always occurs to a greater extent than the second step, because it is easier to remove a proton from a neutral acid molecule than from a negatively charged anion. 

Polyprotic acids have more than one ionizable proton, but in solution, essentially all the HaO comes from the first dissociation. 

Note that Ka2 for sulfurous add is much smaller than fC . Because of electrostatic attractions, we would expect a positively charged proton to be lost more readily from the neutral H2SO3 molecule than from the negatively charged HSO3 ion. This observation is general It is always easier to remove the first proton from a polyprotic acid than to remove the second. Similarly, for an add with three ionizable protons, it is easier to remove the second proton than the third. Thus, the values become successively smaller as successive protons are removed. 

This principle applies equally well to polyprotic acids and bases. In these cases, the concentration terms in the PBE are multiplied by the number of protons consumed or released in the formation of the species in question from the starting material. 

Carbon dioxide from air dissolves in water to make carbonic acid, which has two acidic protons. Later in this chapter, we explore potential effects of dissolving massive amounts of this acid in the ocean. Carbonic acid from CO2 and amino acids from proteins are examples of polyprotic acids—those having more than one acidic proton. 

Polyprotic acids, such as H2SO3, have more than one ionizable proton. These acids have add-dissociation constants that decrease in magnitude in the order ai > a2 > n3- Because nearly all the H (aq) in a polyprotic acid solution comes from the first dissociation step, the pH can usually be estimated satisfactorily by considering only Kai-... 

We see from Reactions (5.15b) and (5.16) that H2CO3 (carbonic acid) contributes two protons to water. Substances that contribute more than one proton to water are called polyprotic acids. Other polyprotic acids are H2C2O4 (oxalic acid), H3PO4 (phosphoric acid), and H2SO3 (sulfurous acid). 

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