<p> Chapter 8</p><p>Titration Curves For Complex Acid/Base Systems</p><p>Objectives The aim of this chapter is to describe methods for constructing titration curves for complex acid/base systems. This chapter describes polyfunctional acid and base systems, including buffer solutions and acid salts. Calculations of pH and titration curves are also described.</p><p>Complex Acid/Base Systems Complex systems include on of the following solutions: (1) two acids or two bases of different strengths. (2) an acid or a base that has two or more acidic or basic functional groups. (3) an amphiprotic substance, which is capable of acting as both an acid and a base.</p><p>In this chapter, we will limit our discussion to the polyfunctional acids and bases as an example on complex systems.</p><p>Polyfunctional Acids and Bases Phosphoric acid is a typical polyfunctional acid. In aqueous solution, it undergoes the following three dissociation reactions: When we add two adjacent stepwise equilibria, we multiply the two equilibrium constants to obtain the equilibrium constant for the resulting overall reaction.</p><p>+ 2 2- K = Ka1Ka2 = [H3O ] [HPO4 ]/[H3PO4]</p><p>= 7.11 X 10-3 X 6.32 X 10-8 = 4.49 X 10-10</p><p>For the reaction; + 3- H3PO4 ↔ 3H3O + PO4</p><p>-22 K = Ka1Ka2 Ka3 = 2.0 X 10</p><p>When carbon dioxide is dissolved in water, a dibasic acid system is formed by the following reactions:</p><p>Buffer Solutions Involving Polyprotic Acids Two buffer systems can be prepared from a weak diprotic acid and its salts. The first consists of free acid H2A and its conjugate base NaHA, and the second consists of the acid NaHA and its conjugate base Na2A. The pH of the latter system is higher than that of the former because the – acid dissociation constant for HA is always less than that for H2A.</p><p>- For a buffer prepared from H2A and NaHA, the dissociation of HA to yield A2- is neglected, and the calculation is based only on the first dissociation.</p><p>For a buffer prepared from NaHA and Na2A, the second dissociation will ordinarily predominate, and the hydronium ion concentration can be calculated from the second dissociation constant. Example 1 Calculate the hydronium ion concentration for a buffer solution that is 2.00 M in phosphoric acid and 1.50 M in potassium dihydrogen phosphate.</p><p>+ - + - H3PO4 + H2O ↔ H3O + H2PO4 , Ka1 = [H3O ][H2PO4 ]/[H3PO4] = 7.11 X 10-3</p><p>+ - [H3O ] = Ka1[H3PO4]/[H2PO4 ] = 7.11 X 10-3 X 2.00/1.50 = 9.48 X 10-3 M</p><p>Example 2 Calculate the hydronium ion concentration of a buffer that is 0.0500 M in potassium hydrogen phthalate (KHP) and 0.150 M in potassium phthalate</p><p>(K2P).</p><p>- + 2- + 2- - -6 HP + H2O ↔ H3O + P , Ka2 = [H3O ][P ]/[HP ] = 3.91 X 10</p><p>+ - 2- [H3O ] = Ka2 [HP ]/[P ] = 3.91 X 10-6 X 0.0500/0.150 = 1.30 X 10-6 M</p><p>Calculation of pH of an Acid Salt Solution (NaHA) Acid salts are salts that contain hydrogen, they can act as an acid or a base (amphiprotic substances). They are formed during the titration of polyfunctional acids or bases. The pH of acid salt solution is determined by two equilibria:</p><p>- 2- + + 2- - HA + H2O ↔ A + H3O , Ka2 = [H3O ][A ]/[HA ]</p><p>- - - - HA + H2O ↔ H2A + OH , Kb2 = Kw/ Ka1 = [H2A][OH ]/[HA ]</p><p>A solution of NaHA will be acidic or basic depending on the relative magnitude of the equilibrium constants for these processes:</p><p>If Kb2 is greater than Ka2 the solution is basic; otherwise it is acidic. The pH of a solution of NaHA can be calculated from the relation: This equation is not valid for very dilute solutions of NaHA or when Ka2 or Kw/ Ka1 is relatively large.</p><p>- - If the ratio [HA ]/Ka1 is much larger than unity, and Ka2[HA ] is greater than Kw, the equation simplifies to:</p><p>Example 3 -3 Calculate the hydronium ion concentration of a 1.00 X 10 M Na2HPO4 solution.</p><p>2- Ka2 and Ka3 are used since they both contain [HPO4 ]. Their values are 6.32 X 10-8 and 4.5 X 10-13 respectively. Note that (1.00 X 10-3 )/(6.32 X -8 - 10 ) is much larger than 1. However, Ka2[HA ] is not much greater than Kw. Therefore we use a partially simplified version of equation:</p>