After working in industrial analytical laboratories for twenty years, I became an academic and taught analytical chemistry. I wondered why this should include calculating titration curves, since I had never had occasion to do so as an analyst. I have since taught hundreds of analytical students and thousands of introductory students to do such calculations, but still see no purpose in it for either course. The calculations do not help students to understand titrimetry. Students concentrate their attention on learning the algorithms but still fail to understand the basic principles. They do not understand the effect of equilibrium at the equivalence point, nor the usefulness of logarithmic relationships. It is an example of the principle asserted by Moore (1) that students who can answer numerical questions do not necessarily understand their chemistry. It provides an exercise in equilibrium calculations for which they otherwise have little use (2, 3). Consider:
At the equivalence point the concentration of analyte must change from small to negligible after the addition of one increment of titrant (similarly, the concentration of titrant must change from negligible to small). If the reaction reverses too readily, then near the equivalence point the reverse reaction produces a significant quantity of analyte. Then the change in concentration of the analyte from small to negligible takes several increments of titrant and the end point is difficult to detect so that tricks must be used to find the equivalence point.
One cure is to use a more powerful titrant such as CH3CO2H2+ in acetic acid instead of H3O+ or C2H5O- in ethanol instead of OH-. Another is to remove the reaction product so that the reaction cannot reverse.
Another trick uses a logarithmic monitor such as a potentiometric electrode with an output that is linear with the logarithm of the concentration. In the theoretical limiting case where the reaction actually does go to completion, the concentration of the analyte becomes zero at the equivalence point and its logarithm becomes minus infinity. The change in the logarithm of the analyte concentration with one increment of titrant is then infinite. In real cases, the reaction merely approaches completion. Near the equivalence point where the analyte concentration is low and the concentration of reaction product is high, the reaction has some tendency to reverse. Then the logarithm of the change between a low concentration and a negligible one is not infinite but it is substantial. The sharpest change in the logarithm is at the equivalence point or as near to it as makes no difference (except in special extreme cases that are not discussed in undergraduate courses; ref 4). When the point of sharpest change is unclear then the recourse is to plot the derivative or the second derivative.
None of this reasoning is helped by calculating the titration curve. Worse, calculating the curve devotes attention to unimportant parts of the titration.
Decades ago when titrimetry was the almost exclusive method of quantitative analysis, it was sometimes necessary to calculate multiple equilibria to design a titrimetric method that avoided interferences. These were the subject of graduate courses in analytical chemistry and did require the calculation of titration curves. It would be very rare in the 21st century for such calculations to be useful.
Calculation of titration curves should not be taught in undergraduate analytical courses and a fortiori not in introductory chemistry. There are more important subjects on which students should spend their study time (5).
Literature Cited
- Moore, J. W. J. Chem. Educ. 2004, 81, 7.
- Hawkes, S. J. J. Chem. Educ. 2003, 80, 1381.
- Lewis, D. L. J. Chem. Educ. 2004, 81, 1265.
- Roller, P. S. J. Amer. Chem. Soc. 1928, 50, 1.
- Hawkes, S. J. J. Chem. Educ. 2005, 82, 1615.
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