Chemical Education Today
Letters In Partial Defense of Calculating Titration Curves After writing four editions of a comprehensive analytical chemistry textbook, I set out to write a lower-level, abbreviated textbook. I needed to eliminate half the content of the comprehensive book and decrease mathematical demand. In agreement with Prof. Hawkes, I eliminated titration curve calculations for EDTA and redox reactions, but I retained acid– base titration curves. There are more important subjects for a student whose only formal exposure to analytical chemistry will be this one course and whose primary interest is likely to be outside of chemistry (such as life sciences). Surely, separation techniques are more important than calculating titration curves. The empirical result of my experiment in the first edition of Exploring Chemical Analysis (1) was a resounding cry from users to include EDTA and redox titration calculations— which I did in subsequent editions. Whether or not a practicing chemist ever calculates a titration curve, there is value in learning the theory. Calculations do help many students understand titrimetry and, more importantly, the underlying chemistry. Students who memorize algorithms instead of understanding basic principles do not benefit. When we break a titration curve into regions in which different approximations apply, we must be cognizant of the chemistry occurring in each region in order to apply the appropriate approximation. In practice, when I need to compute a titration curve, I use a spreadsheet—not the approximations that were appropriate for a calculator. However, approximations are important in teaching about titrations, because they force us to know which part of the titration reaction is occurring and, therefore, to understand the underlying chemistry. One practical use of calculating titration curves is to fit experimental data to find equilibrium constants. Buffers are important to anyone who uses chemistry in a laboratory. Understanding a titration curve is equivalent to understanding how buffers work. Buffer capacity is the change in pH or pM or pε with respect to volume of titrant. I have seen people use the intermediate form of a diprotic acid as a buffer “because it always has pH ≈ ½(pK1 + pK2)”. In fact, the titration curve shows that the intermediate form of a diprotic acid has minimum buffer capacity, not maximum, and is usually a poor choice for a buffer.
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Computing titration curves allows us to select an appropriate end-point indicator and to estimate the titration error in using that indicator. The equilibrium constant and stoichiometry are used to derive the equation for a Gran plot, which is one of the best, practical ways to find the end point and the equilibrium constant. It is not necessary for students to carry out tedious calculations with activity coefficients, but chemistry students should be aware that a next, better approximation requires activity coefficients. Some professors favor teaching equilibrium in analytical chemistry because equilibrium is not taught in any depth in any other part of the curriculum. This argument carries weight only if equilibrium is more important than other subjects competing for attention. I hope that our courses never become standardized to the point where we all teach the same set of subjects. One reason why textbooks are so large is that different professors choose to emphasize different topics, so a large selection of topics needs to be in the textbook if it is to be widely useful. For non-chemistry majors taking one analytical chemistry course, I think acid–base titration curves are enough to teach some chemical equilibrium and the theory of titrations. Like Prof. Hawkes, I suggest that time could be better spent in the rest of the course teaching subjects other than titrations. Literature Cited 1. Harris, D. C. Exploring Chemical Analysis; W. H. Freeman: New York, 1997.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Apr/abs498_2.html Full text (HTML and PDF) with links to cited URLs and JCE articles Daniel C. Harris Naval Air Systems Command Stop 6303 China Lake, CA 93555
[email protected] Journal of Chemical Education • Vol. 85 No. 4 April 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
Chemical Education Today
Letters
Hawkes replies: Teachers demand that texts include what they have always taught, but this is not a criterion for what they ought to teach. I have sympathized elsewhere (1) with the need of textbook authors to meet the demands of the market. However, we should persuade teachers to demand the curriculum that students need rather than what our profession wants to teach. If teaching something that is otherwise valueless provides an opportunity to emphasize something that is taught in another part of the curriculum, this is an advantage; but the teacher may question whether the advantage outweighs the time spent learning that otherwise valueless subject. Calculating a titration curve is an unnecessarily complicated method of explaining how a buffer works. Buffers consist of a conjugate acid–base pair in equilibrium with hydronium ion. The equation for this equilibrium makes it obvious that addition of a small quantity of an acid or base will not alter the hydronium concentration significantly. Even if the added acid or base is a strong one that is neutralized by the buffer components, which in practice it usually is not, it will cause only slight alteration in the concentrations of the acid or base in the pair, and hence small alteration in the concentration of hydronium ion and hence of pH. Students, especially sub-average students, should not be confused by relating buffer action to titrimetry. Buffer capacity is the change of pH with respect to the number of moles of strong acid or base added per liter of buffer, rather than “with respect to the volume of titrant”. This is more directly related to the usefulness of a buffer than the slope of a
titration curve. Buffer capacity is given by δ(mole acid or base added per liter)/δ pH = (ln10)/(1/[salt]+1/[base]). Choosing an indicator for an acid–base titration requires only calculation of the pH of the salt solution that is formed at the end point. Calculating the whole titration curve merely complicates the issue. In analytical practice, the correct indicator is usually already known. If it is not, the acid dissociation constant is often also unknown, so the calculation is impossible. In the rare case that the pH at the end point is not already known, in practice it is found experimentally, so that the ability to calculate it is merely an academic exercise. Similar considerations apply to other kinds of titration. Equilibrium calculations are grossly over-emphasized in chemistry teaching, as has been discussed elsewhere (2, 3). Literature Cited 1. Hawkes, S. J. J. Chem. Educ. 2005, 82, 1615. 2. Hawkes, S. J. J. Chem. Educ. 2003, 80, 1381. 3. Lewis, D. L. J. Chem. Educ. 2004, 81, 1265.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Apr/abs499.html Full text (HTML and PDF) with links to cited URLs and JCE articles Stephen J. Hawkes Department of Chemistry Oregon State University Corvallis, OR 97331-4003
[email protected] © Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 4 April 2008 • Journal of Chemical Education
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