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178 Modern Analytical Chemistry

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with a formation constant of 1.5 ´10 . Derive an equation, 23. A redox buffer contains an oxidizing agent and its conjugate
similar to the Henderson–Hasselbalch equation, which relates reducing agent. Calculate the potential of a solution
3+
2+
pM to the concentrations of L and ML. What will be the pM containing 0.010 mol of Fe and 0.015 mol of Fe . What is
for a solution containing 0.010 mol of M and 0.020 mol of L? the potential if sufficient oxidizing agent is added such that
3+
2+
What will the pM be if 0.002 mol of M are added? 0.002 mol of Fe is converted to Fe ?
6O SUGGESTED READINGS

A lucid discussion of Berthollet’s discovery of the reversibility of Gordus, A. A. “Chemical Equilibrium VI. Buffer Solutions,”
reactions is found in J. Chem. Educ. 1991, 68, 656–658.
Roots-Bernstein, R. S. Discovering. Harvard University Press: Gordus, A. A. “Chemical Equilibrium VII. Precipitates,” J. Chem.
Cambridge, MA, 1989. Educ. 1991, 68, 927–930.
The following texts and articles provide additional coverage of Gordus, A. A. Schaum’s Outline of Analytical Chemistry. McGraw-
equilibrium chemistry and the systematic approach to solving Hill: New York, 1985.
equilibrium problems. Olivieri, A. C. “Solution of Acid–Base Equilibria by Successive
Butler, J. N. Ionic Equilibria: A Mathematical Approach. Addison- Approximations,” J. Chem. Educ. 1990, 67, 229–231.
Wesley: Reading, MA, 1964. Ramette, R. W. Chemical Equilibrium and Analysis. Addison-
Butler, J. N. Solubility and pH Calculations. Addison-Wesley: Wesley: Reading, MA, 1981.
Reading, MA, 1973. Thomson, B. M.; Kessick, M. A. “On the Preparation of Buffer
Chaston, S. “Calculating Complex Equilibrium Concentrations by Solutions,” J. Chem. Educ. 1981, 58, 743–746.
a Next Guess Factor Method,” J. Chem. Educ. 1993, 70, Weltin, E. “Are the Equilibrium Concentrations for a Chemical
622–624. Reaction Always Uniquely Determined by the Initial
Fernando, Q.; Ryan, M. D. Calculations in Analytical Chemistry, Concentrations?” J. Chem. Educ. 1990, 67, 548.
Harcourt Brace Jovanovich: New York, 1982. Weltin, E. “A Numerical Method to Calculate Equilibrium
Freiser, H. Concepts and Calculations in Analytical Chemistry, CRC Concentrations for Single-Equation Systems,” J. Chem. Educ.
Press: Boca Raton, 1992. 1991, 68, 486–487.
Freiser, H.; Fernando, Q. Ionic Equilibria in Analytical Chemistry, Weltin, E. “Calculating Equilibrium Concentrations,” J. Chem.
Wiley: New York, 1963. Educ. 1992, 69, 393–396.
Gordus, A. A. “Chemical Equilibrium I. The Thermodynamic Weltin, E. “Calculating Equilibrium Concentrations for Stepwise
Equilibrium Concept,” J. Chem. Educ. 1991, 68, 138–140. Binding of Ligands and Polyprotic Acid-Base Systems,”
Gordus, A. A. “Chemical Equilibrum II. Deriving an Exact J. Chem. Educ. 1993, 70, 568–571.
Equilibrium Equation,” J. Chem. Educ. 1991, 68, 215–217. Weltin, E. “Equilibrium Calculations are Easier Than You
Gordus, A. A. “Chemical Equilibrium III. A Few Math Tricks,” Think— But You Do Have to Think!” J. Chem. Educ. 1993, 70,
J. Chem. Educ. 1991, 68, 291–293. 571–573.
Gordus, A. A. “Chemical Equilibrium IV. Weak Acids and Bases,”
J. Chem. Educ. 1991, 68, 397–399.

6P REFERENCES

1. (a) Runo, J. R.; Peters, D. G. J. Chem. Educ. 1993, 70, 708–713; (c) Bates, R. G. Determination of pH, 2nd ed. Wiley-Interscience: New
(b) Vale, J.; Fernandez-Pereira, C.; Alcalde, M. J. Chem. Educ. 1993, York, 1973, p. 73.
70, 790–795. 4. Lambert, W. J. J. Chem. Educ. 1990, 67, 150–153.
2. Van Slyke, D. D. J. Biol. Chem. 1922, 52, 525–570. 5. Kolthoff, I. M.; Lingane, J. J. Phys. Chem. 1938, 42, 133–140.
3. (a) Bower, V. E.; Bates, R. G. J. Res. Natl. Bur. Stand. (U. S.) 1955, 55, 6. Davies, C. W. Ion Association. Butterworth: London, 1962.
197–200; (b) Bates, R. G. Ann. N. Y. Acad. Sci. 1961, 92, 341–356;