Analytical Chem istry - DePauw University

252 Analytical Chemistry 2.0We can use a multiprotic weak acid to prepare buffers at as many differentpH’s as there are acidic protons, with the Henderson–Hasselbalch equationapplying in each case. For example, using malonic acid (pK a1 = 2.85and pK a1 = 5.70) we can prepare buffers with pH values ofCpH = 285 . + logCCpH = 570 . + logC−HMHM 22−M−HMwhere H 2 M, HM – and M 2– are malonic acid’s different acid–base forms.Although our treatment of buffers relies on acid–base chemistry, wecan extend the use of buffers to equilibria involving complexation or redoxreactions. For example, the Nernst equation for a solution containing Fe 2+and Fe 3+ is similar in form to the Henderson-Hasselbalch equation.+oFeE = E3+ +− . log [ 2]20 05916Fe / Fe3+[ Fe ]A solution containing similar concentrations of Fe 2+ and Fe 3+ is bufferedto a potential near the standard state reduction potential for Fe 3+ . We callsuch solutions redox buffers. Adding a strong oxidizing agent or a strongreducing agent to a redox buffer results in a small change in potential.6H.2 Representing Buffer Solutions with Ladder DiagramsA ladder diagram provides a simple graphical description of a solution’spredominate species as a function of solution conditions. It also providesa convenient way to show the range of solution conditions over which abuffer is effective. For example, an acid–base buffer exists when the concentrationsof the weak acid and its conjugate weak base are similar. Forconvenience, let’s assume that an acid–base buffer exists when110−[ CH COO ]3≤≤[ CH COOH]Substituting these ratios into the Henderson–Hasselbalch equation1pH = pK+ log = pK−1aa1010pH = pK+ log = pK+ 1aa13shows that an acid–base buffer works over a pH range of pK a ± 1.Using the same approach, it is easy to show that a metal-ligand complexationbuffer for ML n exists when101