letters Equations for Potentiometric Titration
To the Editor: We have used the potentiometric titration experiment and the criteria suggested by Professor Sturrock [J. CHEX.EDUC.,45, 258 (1968)l with good success in an undergraduate course in analytical chemistry. Some difficulties arising from certain tacit assumptions in the derivation of the pHal, - pHil, criterion and in the treatment of the data to obtain the pKa of the weak acid deserve clarification, however. The rigorous equation for the hydrogen ion concentration during a titration of a monoprotic acid with a strong base, neglecting dilution, is [H+18 (Ka -t jCa)lH+l2 - lKX*I.l - f )
+
+
K.] [H+] - K,K.
=
0 (1)
where Ca is the analytical concentration of the acid and f is the fraction of the acid titrated The linear equation usually given for the titration and employed by Sturrock
is obtained by making several approximations in eqn. (I), namely that the first and last terms in the cubic equation are very small compared to the other terms, that K.C.(l - J) >> K., and that jC. >> K.. This last approximation causes deviations from the behavior predictedby eqn. (2) whenever K a becomes large compared to Ca, or when the ratio of Ca/Ka becomes small. Under these conditions the monoprotic acid criterion ApH = pH,,. - pH,,! = 0954 breaks down. The table below shows solutions of the rigorous eqn. (1) for ApH values for various values of Ca/Ka. ApH CJK.
= pHij, pH*/. 0 954
ApH = Ho 3 P& 0 954
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Note that the linear approximation only holds with reasonable accuracy for CJK. > lo2. Note also that because the approximation involves j, that the portion of the titration curve past the half-titration point is more accurately described by the linear approximation than the first half, and a criterion based on this portion, e.g., ApH = pHo 9 - pHsl2 or ApH = pHo pHo 8, holds over a wider range of CJK. values. The same reasoning also applies to the determination of pKa-values. For example, for salicylic acid, p K a = 2.98, at a C. = 0 01 M, the least squares line of pH versus log (f/1 - j) for 0.1 < j< 0 9 gives a slope of 0.708 (instead of the one expected from eqn. (2)) and a p K a = 3.18 The least squares line of the region 0.5 < J < 0 9 has aslopeof 0.918 and a pK. = 3.09, This experiment and the useful criterion suggested by Sturrock provide then the opportunity for allowing
the students to gain experience in using chemical equilibrium data to make decisions about chemical structure and to obtain useful thermodynamic data. The students should be aware, however, of the approximate nature of the derivation, and might be encouraged to devise alternate procedures for treatment of the data which =ill hold over a nider range of experimental conditions.
To the Editor: The ApH criterion was suggested as a simple way to distinguish between a monoprotic acid and a polyprotic acid. Under the conditions described by Lomax and Bard (C./Ka < lo2), the titration curve for a monoprotic acid is flattened and a ApH value of less than 0.95 is found. Thus the difference in ApH between such a monoprotic acid and a polyprotic acid is increased. The ApH criterion is still valid since no monoprotic acid will have a ApH greater than 0 95 and a volyprotic acid will not have a AÈ value less .. than 0.95 For obtaining the p K a value for a monoprotic acid, the method suggested by Lomax and Bard is clearly sunerior to simulv " takine the n H at the half titration point. Similar considerations apply to polyprotic acids as was pointed out in the original paper. Thus the suggestions, made by Lomax and Bard, undoubtedly lead to a closer agreement between theory and experiment. Still closer agreement could be obtained if activity effects were considered. However, it seems questionable whether or not the improvement is worth the additional complexity when teaching at the introductory level. s
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"Relating Science to People"
To the Editor: I n your editorial, "A Summons for Scientists" [J. CHEM.EDUC., 45, 4 (1968)l you stated; "It (this country) needs teachers who will show students how to use science and how to live with its by-products." In her letter to the editor [C. & 13. News, May 20, 19681 under the heading, "Science needs new perspectives" Elizabeth A. Eipper stated that, "The true crossroad, the one in most urgent need of thoughtful consideration, is that one which concerns the relationship of Volume 45, Number 9, September 1968
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