In the Laboratory
Acid–Base Titration of (S)-Aspartic Acid: A Circular Dichroism Spectrophotometry Experiment
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Ana M. V. Cavaleiro* and Júlio D. Pedrosa de Jesus Department of Chemistry, University of Aveiro, 3810-193 Aveiro, Portugal; *
[email protected] Titrations are commonly included in the laboratory portion of chemistry courses. A solution of a reagent, of known concentration, is gradually added to a sample solution until, ideally, all the substance in the sample has reacted. This simple procedure is fundamental in chemical analysis, but may be used with different objectives, such as the determination of the stoichiometry of a reaction or of equilibrium constants. Even if titrations are routinely taught to students in all kinds of laboratory courses, in practice they are not at all a matter of routine, requiring procedures adapted to each problem (1). Students will benefit in realizing that the same basic principles may be put to work in different contexts and in finding that this may lead to different types of information. In this paper we discuss the titration of (S)-aspartic acid with base and the determination of the ionization constant of the protonated amino group, using circular dichroism (CD) spectrophotometry to monitor the course of the reaction. The work shows the use of a less usual technique to determine the end points of an acid–base titration, which is possible because the analyte is a chiral molecule. It is a study in solution chemistry that will be equally appropriate in analytical, organic, and physical chemistry as well as biochemistry laboratory courses. It is suited for intermediate or advanced laboratory courses, when students have the background to integrate the information obtained by different processes, and where a CD spectrophotometer may be more accessible. Acid–Base Reaction Monitoring by Circular Dichroism Spectrophotometry Aspartic acid, HOOC–CH2–CH(NH2)COOH, was chosen because it provides an interesting example of some complexity. Starting with the fully protonated form, HOOC–CH2–CH(NH3+)COOH (H3A+), three acid–base equilibria may be considered, with ionization constants pKa = 1.99, pKa = 3.90, and pKa = 9.90 at 25 °C and I = 0 (2). Values for the ionization constants of aspartic acid at different ionic strength are known (3–5). In aqueous solutions with pH near 3 the zwitterionic form HOOC–CH2–CH(NH3+)COO᎑ (H2A) predominates, although significant amounts of ᎑OOC–CH2–CH(NH3+)COO᎑ (HA᎑) and H3A+ may be present. The monoanion HA᎑ is predominant at pH between 5 and 9; the fully deprotonated anion ᎑OOC–CH2–CH(NH2)COO᎑ (A2᎑) is only important in more basic solutions. Potentiometric titrations of aspartic acid show one or two equivalence points, depending on acid concentration (6 ). In the concentration range suitable for performing the CD spectrophotometric titration the second equivalence point is not detected. The circular dichroism (CD) spectra of aqueous solutions of (S)-aspartic acid show only one positive band with maxima that vary with pH in the 190–210-nm range (7–9). The observed CD, at a fixed wavelength in the 210–220-nm 1
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2
3
range, increases with the rise of pH. This allows us to use CD spectrophotometry to monitor the acid–base titration of aspartic acid. A plot of the CD against concentration of base, in the conditions of the experiment, represents a spectrophotometric titration curve. Two equivalence points are defined that allow quantitative determination of the concentration of the acid. Determination of the Equilibrium Constant pK a
3
CD instruments are modified absorption spectrophotometers that measure the difference in absorbance (∆A) of the two circularly polarized beams as a function of wavelength (10–14). For data that conform to the Beer–Lambert law, ∆A = ∆εbc (b is the sample width and c is the concentration of the absorbing species; ∆ε represents the difference in molar absorptivities, ∆ε = εL – εR, where εL and εR are the molar absorptivities for left- and right-polarized light, respectively). ∆A and ∆ε may take positive or negative values. The absorbance of a solution containing several absorbing species corresponds to the summation of the absorbance of each species. Similarly, circular dichroism values are additive. For a given solution, the circular dichroism at a fixed wavelength can be represented by eq 1 (considering b = 1 cm) if the Beer–Lambert law is obeyed. This can be simplified to eq 2 when pH > 8. For these pH values, the concentration of each predominant species may be translated by the expressions 3 and 4, respectively (Ca = total concentration of aspartic acid in solution). Combination of expressions 2, 3 and 4, leads, finally, to eq 5, that can be used for the determination of the value of pK a . 3
∆A = ∆εH A+[H3A ] + ∆εH A[H2A] + ∆εHA᎑[HA᎑] + ∆εA ᎑[A2᎑] (1) +
3
2
2
∆A = ∆εHA᎑[HA ] + ∆εA ᎑[A ] ᎑
2᎑
(2)
[HA ] = Ca[H ]/([H ] + Ka )
(3)
᎑
2
+
+
3
2᎑
+
[A ] = Ca Ka /([H ] + Ka ) 3
pH = pKa + log 3
3
∆ A – ∆εHAC a ∆εAC a – ∆ A
(4) (5)
Experimental Procedure Stock solutions of (S)-aspartic acid (0.02 mol/L), NaClO4⭈H2O (3 mol/L), and NaOH (0.01 mol/L, standardized) + NaClO4⭈H2O (3 mol/L) were prepared. Solid NaClO4⭈H2O and standard 0.05 mol/L NaOH were used to prepare the last solution. These stocks were used to prepare 12 solutions of (S)-aspartic acid (2 × 10᎑3 mol/L) with variable amounts of NaOH (between zero and 10 × 10᎑3 mol/L), at constant ionic strength. Circular dichroism (at λ = 215 nm) and pH values of those solutions were measured. Aspartic acid should not be dissolved directly in the NaClO4 solution.
Journal of Chemical Education • Vol. 77 No. 9 September 2000 • JChemEd.chem.wisc.edu
In the Laboratory 2.5
12
2.0
1.5
pH
∆A / 10
−3
11
1.0
10
0.5 9
0.0 0
1
2
3
4
5
6
C b / Ca Figure 1. Variation of the CD values of (S)-aspartic acid with the addition of base: λ = 215 nm, Ca = 2.003 × 10᎑3 mol/L, I = 2.7 mol/L (NaClO4).
8 −1.0
− 0.5
0.0
0.5
1.0
log X Figure 3. Example of representation of eq 5 for the determination of pK a 3: λ = 215 nm, Ca = 2.003 × 10᎑3 mol/L, I = 2.7 mol/L (NaClO4).
2.5
Hazards To prepare the stock solutions containing sodium perchlorate adequate safety conditions are needed, namely, an empty fume cupboard with a metal or ceramic tray. It is advisable that students do not prepare these solutions. Use of the aqueous solutions of this compound in the experiment offers no risk, but adequate cleanliness should be ensured.
1.5
∆A / 10
−3
2.0
1.0
Results and Discussion 0.5
0.0 0
2
4
6
8
10
12
14
pH Figure 2. Plot of the CD values of the solutions of (S)-aspartic acid versus pH: λ = 215 nm, Ca = 2.003 × 10᎑3 mol/L, I = 2.7 mol/L (NaClO4).
To simplify the procedure, the experiment was conducted at ambient temperature. Laboratory temperatures were in the range of 18–20 °C.
Equipment This experiment requires the use of a CD spectrophotometer. This equipment is relatively expensive ($60,000– 70,000), particularly the latest models that make measurements in the UV down to 165–170 nm. At least one spectrophotometer maker used to sell a CD attachment. The results presented here were obtained on a Jobin–Yvon dichographe IV, using 1-cm round quartz cells.
Figure 1 represents the variation of the CD values of (S)aspartic acid with the addition of base, at a fixed wavelength. It is a titration curve of the linear segment type (6 ). The end points are obtained by the interception of straight lines, best defined by measurements in solutions away from the equivalence. Two end points were defined in the conditions of the experiment (Fig. 1) that allow quantitative determination of the concentration of the acid. Figure 2 represents the plot of the CD values of the solutions of (S)-aspartic acid versus pH. Between pH 5 and pH 8 the CD changes very little. These pH values correspond to the predominance of the anion HA᎑. The predominance of A2᎑ is only attained at very high pH values. This plot is used to determine the values of ∆ε for the species HA᎑ and A2᎑ (∆εHA᎑ and ∆εA ᎑, respectively) from the relation ∆A = ∆εbc. These are needed for the calculation of pK a . Equation 5 is used for the determination of pKa . Setting X equal to (∆A – ∆εHA᎑Ca)/(∆ ε A ᎑Ca – ∆A), a plot of pH against log X gives a straight line whose Y-intercept is pK a (Fig. 3). In the conditions described (I = 2.7 mol/L, NaClO4, T = 18 ± 2 °C) the value obtained was pK a = 9.56 ± 0.02. This may be compared with the following literature values: 9.56 (I = 1 mol/L, NaClO4, 20 °C) (5) and 9.59 (I = 1 mol/L, 2
3
3
2
3
3
JChemEd.chem.wisc.edu • Vol. 77 No. 9 September 2000 • Journal of Chemical Education
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In the Laboratory
KNO3, 30 °C) (3). As concentrations of the different species in solution, except for [H+], were indirectly used in the calculations, the determined pKa values should be considered as a mixed equilibrium constant (4a). This type of equilibrium constant is particularly useful for studies at relatively high ionic strength. Conversion to concentration constants may be performed using hydrogen ion activity coefficients, as proposed by Martell and Smith (4a). 3
Final Remarks The experiment described may be used with different objectives. It may be used to familiarize the students with CD spectrophotometry. It may be viewed as a particular case of a spectrophotometric titration or may be presented as a less common method for the determination of equilibrium constants. CD experiments are not very common in undergraduate laboratories. This may be due to the cost of the equipment, as this is not considered a standard instrumental technique; but there is also a lack of suitable simple experiments. CD spectrophotometry is used to gain information about the secondary structure of peptides and proteins, important biological macromolecules. It is also used in coordination chemistry, in the study of absolute configuration of ions and molecules, of stereoselective or stereospecific synthesis, etc. The experiment described here is a simple procedure that gives students contact with the use of CD spectroscopy and that needs no other background than the simple acid–base chemistry of amino acids. This CD spectrophotometric titration also exemplifies the use of a chiroptical property to determine the concentration of an optically active molecule. It stresses the point that a less usual technique may be well adapted to substitute for more common ones. The calculation of the equilibrium constant K a is an example of a possible simple spectrophotometric determination of an equilibrium constant. The advantage of using circular dichroism instead of conventional 3
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absorption spectrophotometry results from the highly favorable difference in values of ∆ε for the different species in equilibrium in solution and also from the fact that CD measurements of aqueous solutions in the 210–220-nm UV range have no particular interferences. W
Supplemental Material
Supplemental material for this article is available in this issue of JCE Online. Literature Cited 1. Winkler-Oswatitsch, R.; Eigen, M. Angew. Chem., Int. Ed. Engl. 1979, 18, 20. 2. CRC Handbook of Chemistry and Physics, 78th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1997–1998. 3. Sillen, L. G.; Martell, A. E. Stability Constants; Spec. Publ. 25, Suppl. 1; The Chemical Society: London, 1971. 4. (a) Martell, A.; Smith, R. Critical Stability Constants; Plenum: New York, 1974: Vol. 1. (b) Martell, A.; Smith, R. Critical Stability Constants; Plenum: New York, 1982; Vol. 5, Suppl. 1. 5. Perrin, D. D. J. Chem. Soc. 1958, 3125. 6. Skoog, D. A.; West, D. M.; Holler, F. J. Fundamentals of Analytical Chemistry, 7th ed.; Saunders: Fort Worth, TX, 1996. 7. Legrand, M.; Viennet, R. Bull. Soc. Chim. Fr. 1965, Part 1, 679. 8. Katzin, L. I.; Gulyas, E. J. Am. Chem. Soc. 1968, 90, 247. 9. Fowden, L.; Scopes, P. M.; Thomas, R. N. J. Chem. Soc., C 1971, 833. 10. Wong, K. P. J. Chem. Educ. 1974, 51, A573; 1975, 52, A9, A93. 11. Purdie, N.; Swallows, K. A. Anal. Chem. 1989, 61, 77A. 12. Fujita, J.; Shimura, Y. In Spectroscopy and Structure of Metal Chelate Compounds; Nakamoto, K., Ed.; Wiley: New York, 1968. 13. Circular Dichroism: Principles and Applications; Nakanishi, K.; Berova, N.; Woody, R. W., Eds.; VCH: New York, 1994. 14. Rodger, A.; Norden, B. Circular Dichroism and Linear Dichroism; Oxford University Press: Oxford, 1997.
Journal of Chemical Education • Vol. 77 No. 9 September 2000 • JChemEd.chem.wisc.edu
