Acid-base equilibria polyprotic acids

Some of the problems at the end of the sections on Acids and Bases, Hydrolysis, Polyprotic Acids, and Buffers involve multiple equilibria. They may be omitted in a simplest treatment of ionic equilibrium. 

In addition, the equilibria on the left hand side of eqn (8.20) can sometimes be defined by the dissociation constants Kdissj (j = 1, 2,. .., m), that are very familiar from acid-base reactions (the acidity constants Kgj for polyprotic acids are in fact dissociation equilibrium constants). The relationships between all these constants are given by the sets of eqn (8.21). In certain cases, it is more convenient to use one type of equilibrium constants or another, and the choice is typically made based on the simplicity of the mathematical equations describing a system of interest. Definitions and uses of all equilibrium constants in determination of concentrations of all species present in a complex system are given in many monographs on coordination chemistry. ... 

Weltin, E. Galculating Equilibrium Goncentrations for Stepwise Binding of Ligands and Polyprotic Acid-Base Systems, ... 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base by using the reaction stoichiometry to recognize what stage we have reached in the titration. We then identify the principal solute species at that point and the principal proton transfer equilibrium that determines the pH. 

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. 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base (see Toolbox 11.1). First, we have to consider the reaction stoichiometry to recognize what stage we have reached in the titration. Next we have to identify the principal solute species at that point and the proton transfer equilibrium that determines the pH. We then carry out the calculation appropriate for the solution, referring to the previous worked examples if necessary. In this section, we see how to describe the solution at various stages of the titration our conclusions are summarized in Tables 11.3 and 11.4. 

In the 1920s, Johannes Bronsted and Thomas Lowry recognized that acids can transfer a proton to bases regardless of whether an OH" ion accepts the proton. In an equilibrium reaction, the direction of proton transfer depends on whether the reaction is read left to right or right to left, so Bronsted acids and bases exist in conjugate pairs with and without a proton. Acids that are able to transfer more than one proton are called polyprotic acids. 

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. 

Changing the pH of a solution shifts the positions of all acid-base equilibria, including those involving polyprotic acids. Acid-base equilibrium expressions and equilibrium constants are used to calculate the amount of the change. For example, the two equilibria that apply to solutions containing H2CO3, HCOJ, and... 

We saw in the following section how polyprotic acids are capable of providing more H ions in several steps and we saw how pH ay be calculated in solutions of polyprotic acids. In connection with this we looked briefly at acid and base properties of salt and on how pH may be calculated in such salt solutions. In connection with the influence of foreign ions on the equilibrium conditions in chapter 4 we looked briefly at ion effects and its influence on pH conditions. 

The acidity or basicity of a solution is frequently an important factor in chemical reactions. The use of buffers of a given pH to maintain the solution pH at a desired level is very important. In addition, fundamental acid-base equihbria are important in understanding acid-base titrations and the effects of acids on chemical species and reactions, for example, the effects of complexation or precipitation. In Chapter 6, we described the fundamental concept of equilibrium constants. In this chapter, we consider in more detail various acid-base equilibrium calculations, including weak acids and bases, hydrolysis, of salts of weak acids and bases, buffers, polyprotic acids and their salts, and physiological buffers. Acid-base theories and the basic pH concept are reviewed first. 

Vt (aq) in a polyprotic acid solution comes from the first dissociation step, the pH can usually be estimated satisfactorily by considering only Weak bases include NH3, amines, and the anions of weak acids. The extent to which a weak base reacts with water to generate the corresponding conjugate acid and OH is measured by the base-dissociation constant, JCj. Kh is the equilibrium constant for the reaction B(aq) -H H20(/) HB (aq) -I- OH aq), where B is... 

Weak Acids and Weak Bases—A weak acid or weak base ionizes to a limited extent in water. The extent of their ionization can be related to the ionization constants Ka and Kt, or their logarithmic equivalents pKa = -log Ka and pKt, = -log Kt, (Table 16.4) by setting up and solving an equilibrium calculation. Calculations involving ionization equilibria are in many ways similar to those introduced in Chapter 15, although some additional considerations are necessary for polyprotic acids. 

Solutions of Salts of Polyprotic Acids 17-6 Acid-Base Equilibrium Calculations A Summary... 

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 ... 

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