Diprotic Buffers

Multiprotic weak acids can be used to prepare buffers at as many different pH s as there are acidic protons. For example, a diprotic weak acid can be used to prepare buffers at two pH s and a triprotic weak acid can be used to prepare three different buffers. The Henderson-Hasselbalch equation applies in each case. Thus, buffers of malonic acid (pKai = 2.85 and = 5.70) can be prepared for which... 

Suppose we are titrating the triprotic acid H P04 with a solution of NaOH. The experimentally determined pH curve is shown in Fig. 11.13. Notice that there are three stoichiometric points (B, D, and F) and three buffer regions (A, C, and E). In pH calculations for these systems, we assume that, as we add the hydroxide solution, initially NaOH reacts completely with the acid to form the diprotic conjugate base... 

At point A, the system is in the first buffer region and pH = pKa). Once all the acid H,P04 molecules have lost their first acidic protons, the system is at B and the primary species in solution are the diprotic conjugate base and sodium ion—we have a solution of NaH2P04(aq). Point B is the first stoichiometric point, and to reach it we need to supply 1 mol NaOH for each mole of H P04. 

Figure 11.14 shows the pH curve of a diprotic acid, such as oxalic acid, H2C204. There are two stoichiometric points (B and D) and two buffer regions (A and C). The major species present in solution at each point are indicated. Note that it takes twice as much base to reach the second stoichiometric point as it does to reach the first. 

A buffer made from a diprotic (or polyprotic) acid is treated in the same way as a buffer made from a monoprotic acid. For the acid H2A. we can write two Henderson-Hasselbalch equations, both of which are always true. If we happen to know [H2A] and [HA ], then we will use the pA, equation. If we know [HA ] and [ A2 ], we will use the pK2 equation. 

Go back and read the Example Preparing a Buffer in a Diprotic System" on page 187. See if it makes more sense now. 

Point C in Figure 11-4 shows where the intermediate form of a diprotic acid lies on a titration curve. This is the least-buffered point on the whole curve, because the pH changes most rapidly if small amounts of acid or base are added. There is a misconception that the intermediate form of a diprotic acid behaves as a buffer when, in fact, it is the worst choice for a buffer. 

At high buffer concentrations, positive curvature may be observed in buffer dilution plots, indicating that the general acid and base are simultaneously participating in the rate-determining step.27 In such a case, the rate law must be expanded by third-order terms. Furthermore, plots of buffer slopes versus xHb may be nonlinear, when the unstable tautomer is a diprotic acid as, for example, the aci-nitro tautomer of nitrobenzene.28... 

Bicarbonate is much more suitable as a major environmental water pH buffer. Its parent acid is H2C03, which is diprotic (Fig. 1.11). The dissociation of carbonic acid is described as follows ... 

If Product M, a diprotic base, is to be analyzed in its neutral form, the higher of Product M (which is 5.3) needs to be considered because the other of 3.3 is less basic. Let us use to try to determine at what wpH the analyte would be in its neutral form at eluent conditions of 30v/v% MeCN and 70 v/v% acidic buffer. 

Titration and buffer calculations for weak diprotic and triprotic acids are done exactly as shown earlier for weak monoprotic acids. The only new consideration is which Kc or pKa value to use Very simply, we use the appropriate constant that describes the equilibrium between the species we are dealing with. For example, Figure 1-4 shows the titration of a weak diprotic acid with OH (p/ a, = 4, pKo, = 7). The pH at any point along the titration curve is given by ... 

The common amino acids are simply weak polyprotic acids. Calculations of pH, buffer preparation, and capacity, and so on, are done exacdy as shown in the preceding sections. Neutral amino acids (e.g., glycine, alanine, threonine) are treated as diprotic acids (Table l-l). Acidic amino acids (e.g., aspanic. acid, glutamic acid) and basic amino acids (e.g., lysine, histidine, arginine) are treated as triprotic acids, exactly as shown earlier for phosphoric acid. 

The HCOs/COa system is one of the pvo major blood buffers. Carbonic acid ionizes as a typical weak diprotic acid ... 

Figure 3.10. Equilibrium composition, buffer intensity, and titration curve of diprotic acid-base system, (a) Species distribution, (b) Buffer intensity, (c) Titration curve. The equivalence points, x, y, and z (a), are representative of the composition of pure solutions of H2L NaHL, and Na2L respectively, and correspond to minima in the buffer intensity. The smaller the buffer intensity, the steeper is the titration curve.

Polyprotic Systems In the same fashion as equation 91 has been derived, expressions for the buffer intensity of polyprotic acid-base systems can be developed. In Table 3.8, the buffer intensity of a diprotic acid-base system is derived. A polyprotic acid can be treated the same way as a mixture of indi-... 

A reference book states that a saturated aqueous solution of potassium hydrogen tartrate is a buffer with a pH of 3.56. Write two chemical equations that show the buffer action of this solution. (Tartaric acid is a diprotic acid with the formula H2C4H40g. Potassium hydrogen tartrate is KHC4H4O5.)... 

Where is the total concentration of acid species and A, and K2 are the first and second stepwise dissociation constants of the acids. This equation can be used to compute the buffer index of a polyprotic acid as long as successive dissociation constants differ by at least 20 times (this assures a calculation error of 5% or less). In other words, for a diprotic acid K2fK should be less than 0.05 (cf. Butler 1964). Thus, for example, Eq. (5.114) may be used to compute the buffer index due to species of carbonic acid, for which A = 10 and K2 = 10" °, or/ for species of silicic acid, for which a , = lO- and K, = 10... 

Please note that equations (4.8-5) through (4.8-7), (4.8-12) through (4.8-14), (4.8-19) through (4.8-21), and (4.8-26) through (4.8-28) are identical when the concentration fractions are written merely as a2i a1) and a0j where a2 is the concentration fraction of the fully protonated form (H2A for a dipro -tic acid, HA+for a diprotic amino acid, H2B2+for a diprotic base), a0 that of the fully deprotonated form, while is the concentration fraction of the intermediate form. For the buffer strength of the solution of a diprotic acid and/ or its conjugate bases we then have... 

Literature proposed CZE methods for phenols and derivatives using test mixtures based on aqueous buffered systems (phosphate-borate and borate " ), volatile electrolytes (ammonium hydrogencarbonate, diethylmalonic acid/dimethylamine in isopropanol and L-cysteic acid, 3-amino-1-propanesulfonic acid, aminomethanesulfonic acid, and diethylmalonic acid ), andnon-aqueous media (ammonium acetate in ACN/acetic acid in MeOH acetate, bromide, chloride, and malonate in ACN and diprotic acids/tetrabutylammonium hydroxide and maleate in MeOH ). 

If this were a diprotic acid titration, the same methods as used in (a) to (d) would apply. There would of course be two buffer ranges and two equivalence points. Take care that you use the proper pK value in the buffer equation. The calculation at the intermediate equivalence point calls for the formula for an amphiprotic salt, pH = MpK j + pKg2). 

The diagrams shown here contain one or more of the compounds H2A, NaHA, and Na2A, where H2A is a weak diprotic acid. (1) Which of the solutions can act as buffer solutions (2) Which solution is the most effective buffer solution Water molecules and Na ions have been omitted for clarity. 

Several aspects of these equilibria are notable. First, although carbonic acid is a diprotic acid, the carbonate ion is unimportant in this system. Second, one of the components of this equilibrium, CO2, is a gas, which provides a mechanism for the body to adjust the equilibria. Removal of CO2 via exhalation shifts the equilibria to the right, consuming H ions. Third, the buffer system in blood operates at a pH of 7.4, which is fairly far removed from the pK i value of H2CO3 (6.1 at physiological temperatures). In order for the buffer to have a pH of 7.4, the ratio [base]/[acid] must have a value of about 20. In normal blood plasma the concentrations of HCOs and H2CO3 are about 0.024 M and 0.0012 M, respectively. As a consequence, the buffer has a high capacity to neutralize additional acid, but only a low capacity to neutralize additional base. 

Between the two buffer regions there is an end-point, or equivalence point, where the pH rises by about two units. This end-point is not sharp and is typical of a diprotic acid whose buffer regions overlap by a small amount p/fa2 p ai is about three in this example. (If the difference in p. values were about two or less, the end-point would not be noticeable.) The second end-point begins at about pH 6.3 and is sharp. This indicates that all the protons have been removed. When this is so, the solution is not buffered and the pH rises steeply on addition of a small amount of strong base. However, the pH does not continue to rise indefinitely. A new buffer region begins at about pH 11 (p/fw - 3), which is where self-ionization of water becomes important. 

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