Peter E. Sturrock Georgia Institute of Technology Atlanta, Georgia 30332
I 1
Is a Weak Arid Monopntir? A new look at titration curves
In most introductory treatments of acid-base titrations, the titration curves for weak diprotic acids are described as having two distinct breaks provided the consecutive dissociation constants differ by a factor of lo4. While this statement is correct, it is insufficient because it gives the impression that two breaks are always obtained, but may not be sufficiently sharp to allow titration to two endpoints. Often, however, the titration curves of diprotic acids do not have any detectable break a t the first equivalence point of the titration, and Auerbach and Smolczyk' have shown that there should be no such inflection if K I / K ~I 16. The lack of a break at the first equivalence point may make it diicult to decide whether an acid is monoprotic or diprotic. However, this distinction can be made on the basis of the slope of the mid-region of the titration curve. For the titration of a weak monoprotic acid, HA, the pH of the region between the initial point and the equivalence point is given by the familiar equation pH = pK.
[A-I + lag [HA1
In eqn. (I), [A-] and [HA] are the molar concentrations of the salt and acid, respectively, and activity effects are neglected. At the one-fonrth titration point the acid concentration is three times that of the salt while at the three-fourths titration point the relative concentrations are reversed. Substituting these conditions into eqn. (1)
- 0.477
(2)
+ log 3 = pK. + 0.477
(3)
pH,/, = pK, - log 3 = pK, pH./, = pK.
Thus for a monoprotic acid the change in pH between the one-fourth and three-fourths titration points is seen from eqn. (4) to be 0.95 pH units. The diprotic acid titration curve can be elucidated most conveniently by application of Bjerrum's formation f u n c t i ~ n a. , ~ For a diprotic acid a, the average number of bound protons per acid anion, is given by eqns. (5) and (6).
Presented before the Division of Chemical Education at the 153rd National Meeting of the American Chemical Society, April 1967, in Miami Beach, Fla.
'AOERBACH, F., AND SHOLCZYK, E., 2. phys. chern. llOA, 65 (1924). Formation in Aqueous Solul B ~ ~ J.,~ "Metal ~ ~ Ammine x , tion," Dissertrttion, Copenhagen, 1941. AD AM^, E. Q.,J. Am. Chern. Sac., 38, 1503 (1916). 4 GANE, R.,AND INGOLD, C. K., J . Chem. Sac., 2153 (1931). 258
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journal of Chemical Education
(6)
In eqn. (5), CH and CA are the analytical concentrations of protons (dissociated and combined with acid anions) and acid, respectively. Except for very dilute solutions, the approximation in eqn. (5) is valid and then a is experimentally obtained from the fraction titrated. For example, a is 1.50 a t the titration point and 0.50 at the a/4 titration point. As pointed out by Bjerrum and Adamq3 the ratio between consecutive dissociation constants is determined partly by statistical effects. Considering only statistical effects,the ratio, KJKz would be 4.0. For any real case the ratio will be greater. The lowest ratio found in the literature, by the present author, is 7.2 for azelaic acid.' By use of eqn. (6) it is found that for the statistical case (KI/Kz = 4.0) the change in pH from the l/ath to 3/4th titration points (ApH) is 0.954, exactly the value for a monprotic acid. For azelaic acid (KJKs = 7.2) the ApH value is calculated to be 1.09 and for adipic acid (Kl/Kz = 9.8) the ApH value is calculated to be 1.18.
Theoretical titration curves of diprotic acids. o, KI/K~ = 4; b, K1/K2 = 16 (pH axis shifted 1 unit); c, K3/K1 = 50 (pH oxir shifted 2 units); d, K , / K ~ = 100 IpH axis shifted 3 mild.
The figure shows theoretical titration curves, calculated by use of eqn. (6) for K JK2 of 4, 16, 50, and 100. For the case of KJKz = 50, a small break is evident a t a = 1 in the theoretical titration curve. This break is small enough that it might easily be overlooked in an experimental curve unless the data were of the highest quality. However, the ApH value for this case is greater than 2.0 and thus the slope of this curve is more than twice that of a monoprotic acid. For a triprotic acid statistical effects lead to minimum ratios, Kl/Kz = Kz/K3 = 3.0. Using an extended form of eqn. (6) it is again found that ApH = 0.954 for the statistical case and higher for any real case.
The Experiment
I n view of the above considerations, it is suggested that experimental values of ApH may be employed as a simple, yet sensitive, criterion t o determine whether an unknown acid is monoprotic. Of course activity effects will cause some change in the ApH value from that predicted by eqn. (6), but such influences are usually not sufficiently pronounced to mask the distinction. This diagnostic criterion has been employed for two years in the sophomore analytical laboratory of the Georgia Institute of Technology. In this course, each student performs a potentiometrio titration of an unknown organic acid with standard hydroxide solution. From the titration data he calculates the equivalent weight of the acid, determines whether or not the acid is monoprotic and then calculates approximate values of the dissociation constant(s). Using these data he then identifies the acid from a list of about twenty acids. The acids, used as unknowns, include citric, fumaric, malic, succinic, and tartaric which show no inflection a t
Typical Student Results and Conclusions
Acid
pHL/,
pHa/r
ApH
Conclusion
Barbituric Benzoic Citric Fumsric Malic Salicylic Succinic Sulfmilic Tsrtsric
3.35 3.08 3.55 2.60 3.10 2.95 4.10 2.25 3.05
4.30 4.05 5.70 3.85 4.90 3.80 5.53 3.15 4.25
0.95 0.97 2.15 1.25 1.80 0.85 1.43 0.90 1.20
Monoprotic Monoprotic Polyprotic Polyprotic Polyprotic Monoprotic Polyprotic Monoprotic Poly~rotic
the half titration point of the experimental titration curve. However, the students do very well on this experiment and with the aid of the APH criterion have little difficulty in distinguishing between these acids and monoprotic acids such as barbituric, benzoic, salicylic, and sulfanilic acids. The most serious difficulty in this experiment comes with a relatively insoluble acid such as uric acid. I n such a case the experimental titration curve exhibits an abnormally low slope.
Volume 45, Number 4, April 1968
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