Weak 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. 

This approach can be used to sketch titration curves for other acid-base titrations including those involving polyprotic weak acids and bases or mixtures of weak acids and bases (Figure 9.8). Figure 9.8a, for example, shows the titration curve when titrating a diprotic weak acid, H2A, with a strong base. Since the analyte is... 

Certain weak acids are polyprotic they contain more than one ionizable hydrogen atom. Such acids ionize in steps, with a separate equilibrium constant for each step. Oxalic acid, a weak organic acid sometimes used to remove bloodstains, is diprotic ... 

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. 

The parent acids of common polyprotic acids other than sulfuric are weak and the acidity constants of successive deprotonation steps are normally widely different. As a result, except for sulfuric acid, we can treat a polyprotic acid or the salt of any anion derived from it as the only significant species in solution. This approximation leads to a major simplification to calculate the pH of a polyprotic acid, we just use Kal and take only the first deprotonation into account that is, we treat the acid as a monoprotic weak acid (see Toolbox 10.1). Subsequent deprotonations do take place, but provided Kal is less than about fCal/1000, they do not affect the pH significantly and can be ignored. 

Any anion of a weak acid, including the anions of polyprotic acids, is a weak base. The acid-base properties of monoanions of polyprotic acids are complicated, however, because the monoanion is simultaneously the conjugate base of the parent acid and an acid in its own right. For example, hydrogen carbonate anions undergo two proton-transfer reactions with water ... 

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. 

STRATEGY The primary solute species in a solution of a polyprotic acid is the acid itself, in this case, H2S. We can find the pH of the solution by assuming that the acid loses only one proton and treat it as a monoprotic weak acid. Set up an equilibrium table as described in Toolbox 9.1 and determine the H3CU molarity by using the first acidity constant, Kal. 

We can calculate pH titration curves using the principles of aqueous solution equilibria. To understand why titration curves have certain characteristic shapes, let s calculate these curves for four important types of titration (1) strong acid-strong base, (2) weak acid-strong base, (3) weak base-strong acid, and (4) polyprotic acid-strong base. For convenience, we ll express amounts of solute in millimoles (mmol) and solution volumes in milliliters (mL). Molar concentration can thus be expressed in mmol/mL, a unit that is equivalent to mol/L ... 

Definition of Acids and Bases 222 Conjugate Acid-Base Pairs 222 Amphoteric Species 224 Strong Acids 225 Strong Bases 225 Weak Acids 226 Weak Bases 226 Polyprotic Acids 227 Acid and Base Strength Ka and Kb 228 Acid/Base Strength of Conjugate Acid-Base Pairs 230 Acid-Base Reactions 231... 

Buffer Capacity of a Buffer Solution Containing a Polyprotic Weak Acid or Weak Base and Its Conjugate Base or Acid... 

Acid-Base Catalyzed Hydrolysis of Polyprotic Weak Acids and Weak Bases... 

The dependence of the equilibrium constants of polyprotic weak acids and weak bases on ionic strength allows them to be treated in exactly the same manner as monoprotic weak acids and weak bases. The first, second, and third ionization constants for triprotic weak acids in terms of activity coefficient are given by ... 

The titration curve of a polyprotic acid can be obtained by using the same approach as for monoprotic weak acids or weak bases. The mass and charge balance equations... 

In the same manner as described in Section 2.2.5, mathematical expressions for the buffer capacity of polyprotic weak acid/base systems can be developed. When one adds a strong base such as NaOH to an aqueous buffer solution containing a polyprotic weak acid (HnA), the electroneutrality would be ... 

Substituting Equation (2.157), Equation (2.158), and Equation (2.159) gives the general equation for the buffer capacity of a polyprotic weak acid. 

If the drug is a polyprotic weak acid or weak base, the inclusion complexation process can be described as (e.g., a diprotic weak base) ... 

Equation (5.164) can be rearranged for mono- and polyprotic weak acids (or weak bases) as follows ... 

There are a few main types of titrations a strong acid titrated with a strong base (or a strong base titrated with a strong acid) a weak acid titrated with a strong base a weak base titrated with a strong acid and a polyprotic acid titrated with a strong base. Each one of these produces characteristic results and will need to be discussed separately. For the solutions of weak acids and bases, the process is complicated by the common-ion effect. 

Drugs may also have more than two pKa values, such as polyprotic or polybasic compounds (e.g., minocycline), and such drugs exhibit a complex pH solubility profile. It is essential to know per se pH of the drug solution during preformulation studies. The pH is measured or theoretically calculated if the pKa and drug concentration C are known. The pH of a weak acid or the salt of a weak base and a strong acid can be calculated using the equation... 

Other common species that have an effect on the pH and buffering capacity of natural systems include phosphates, borates, amino acids, and some organic compounds (generally weak acids). Phosphoric acid is a polyprotic acid that liberates one proton in each of its three dissociation steps, leaving a weaker acid... 

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