In the Laboratory edited by
The Microscale Laboratory
R. David Crouch Dickinson College Carlisle, PA 17013-2896
Determination of Acidity Constants by Gradient Flow-Injection Titration
W
António C. L. Conceição* Centro de Química Estrutural, Complexo Interdisciplinar, Instituto Superior Técnico, 1049-001 Lisboa, Portugal; *
[email protected] Manuel E. Minas da Piedade Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
Since its introduction in the 1970s (1–3), flow-injection analysis (FIA) has developed into a powerful analytical technique, allowing fast analysis with a high degree of automation and with relatively inexpensive equipment (4, 5). A variety of undergraduate experiments have been reported to illustrate the applications of FIA techniques, including acid– base titrations (3, 6, 7), quantitative analysis based on redox reactions (8), protein assay (9), gravimetric analysis (10), and chemiluminescence detection (11). In all these applications, a sample of a solution containing an unknown concentration of the species under study is injected into a continuously moving non-segmented carrier stream propelled by a peristaltic pump, and the stream is then passed directly, or after combination with appropriate reagents, through a detector that quantitates the quantity of analyte present. This detector may be, for example, a spectrophotometer or a potentiometer. However, no experiments have been proposed that make use of the gradient chamber flow-injection titration method (GCFIT) (12–14). In the GCFIT, the transition between the carrier and sample solutions is monitored following dispersion in a gradient chamber. Here, we present a three-hour laboratory experiment, designed for an advanced undergraduate course in instrumental analysis, that illustrates the application of the GCFIT
Figure 1. Scheme of the apparatus: S1 and S2 are the flasks containing the solutions.
www.JCE.DivCHED.org
•
method with spectrophotometric detection to determine acidity constants. The procedure involves the use of an acid–base indicator to obtain the relation between the pH and the absorbance of the solution throughout the titration, which constitutes a new approach to the determination of pKa’s by GCFIT. Two monoprotic weak acids were selected: acetic acid and benzoic acid. Although the main goal of the experiment is the illustration of the GCFIT method it can also serve to demonstrate the implementation of automated analytical procedures at the microscale level and a rigorous analysis of an acid–base titration. Experimental
Reagents Six solutions labeled S1–S6 are used. Their compositions are as follows: solution S1: sodium acetate (5.00 × 10᎑3 M), HCl (5.00 × 10᎑3 M), NaCl (0.1 M), and bromocresol green (9.95 × 10᎑7 M); solution S2: identical to S1 except for the concentration of HCl (1.40 × 10᎑3 M); solution S3: sodium benzoate (5.00 × 10᎑3 M), HCl (4.00 × 10᎑3 M), NaCl (0.1 M), and bromocresol green (9.95 × 10᎑7 M); solution S4: identical to S3 except for the concentration of HCl (6.00 × 10᎑4 M); solution S5: HCl (3.00 × 10᎑4 M), NaCl (0.1 M), and bromocresol green (9.95 × 10᎑7 M); and solution S6: identical to S5 except for the concentration of HCl (1.00 × 10᎑5 M). The HCl present in solutions S1–S4 serves to generate acetic or benzoic acids, from sodium acetate or sodium benzoate. We find this method advantageous when compared with the direct preparation of the solutions from acetic or benzoic acids, since sodium acetate is odorless and easier to handle than acetic acid, and sodium benzoate is easier to dissolve in water than benzoic acid. Equipment A scheme of the GCFIT system used in this experiment is shown in Figure 1 (see Supplemental MaterialsW for details). The gradient chamber consists of a magnetically stirred cylindrical vessel made of Perspex, with an internal volume of 471 mL. The experiments are carried out at room temperature (20–25 ⬚C). The students are asked to monitor the room temperature throughout the laboratory session. Typically the fluctuation is smaller than 1 ⬚C.
Vol. 83 No. 12 December 2006
•
Journal of Chemical Education
1853
In the Laboratory
Hazards There are no unusual hazards associated with this experiment. Concentrated HCl solutions are corrosive and skin contact should be avoided in the case of bromocresol green. The proper handling and disposal of the solutions used should be observed. Method and Results
Figure 2. Scheme of a titration curve obtained with the GCFIT apparatus described in this work: ti represents the initial time, tb corresponds to the rotation of the valve, to is the time at which the second solution reaches the gradient chamber, and tf corresponds to the end of the titration.
start n
tot
HCl
HCl
S5
tot
HInd1− + H2O
S6
( At , t1 ) , … ( At , t x ) , … ( At , tn ) 1
x
n
−
tot tx
tot
= HCl
( HCl
A(calc)t x =
tot S6
S6 tot
− HCl
exp (t o − t x )
S5
F V
a H3 O
+ tx
At =
+ b 2
Dx 2 = Atx − A(calc)t x x = x +1
x > n
no
yes n
M =
∑ D
x
2
x =1
M = minimum
no
yes F , t o , a, b V end
Figure 3. Algorithm used in the determination of the a and b parameters in eq 1 from the titration curve obtained in the calibration.
1854
Journal of Chemical Education
Ind2− + H3O+
can be neglected in the mass balances for the determination of the acidity constants of the acids. The detection is set to 616 nm, which corresponds to the wavelength of maximum absorbance of Ind2− in the visible (15, 16). At this wavelength the contribution of the acid form of the indicator, HInd1−, to the absorbance of the solution is negligible. The relation between the absorbance of the solution at a given time t, At, and the corresponding [H3O+] is (see the Supplemental MaterialW):
guess F , to a, b, V x = 1 H3 O +
The determination of the acidity constants of acetic and benzoic acids involves monitoring of the concentration of H3O+ inside the gradient chamber as a function of time. This is indirectly achieved by following the corresponding change in the concentration of the basic form of bromocresol green, Ind2−, using spectrophotometry. The total concentration of the indicator is ca. four orders of magnitude smaller than the total concentration of the acetic acid–sodium acetate or benzoic acid–sodium benzoate systems. Hence the equilibrium
•
a H3 O +
t
+ b
(1)
where a and b are constants. The determination of a and b involves a calibration experiment where the solution S5 is titrated with the solution S6. The general procedure can be illustrated using the titration of acetic acid as an example. A similar method is followed in the titration of benzoic acid and in the calibration experiment. Figure 2 shows a typical titration curve. During the initial period (between ti and tb ), a steady flow of the solution S1 is maintained through the system, and a constant value of absorbance is recorded. The injection valve is rotated at tb, stopping the flow of S1 through the chamber and initiating the flow of solution S2, which, except for the concentration of HCl is identical to S1. The S2 solution reaches the gradient chamber at to and, as a result, in the period between to and tf (the end point of the experiment) the absorbance of the mixture inside the gradient chamber varies reflecting the acid–base equilibrium of the acetic acid–sodium acetate system. If the inflowing concentration of a species in solution (acetic acid in this example) changes from a constant CS1 to a constant CS2 at time to, its concentration inside the gradi-
Vol. 83 No. 12 December 2006
•
www.JCE.DivCHED.org
In the Laboratory
ent chamber at a time t, Ct, is given by (12, 17): C t = C S2 − (C S2 − C S1 ) exp (t o − t )
start
F V
n, a, b, K w
(2)
where V is the volume of the chamber and F is the flow rate. The algorithms used to determine the optimum values of the parameters in eq 1, or the values of Ka, from the corresponding titration curves are summarized in Figures 3 and 4 (see Supplemental MaterialW for details). In both cases, the data treatment involves the use solver tool of MS Excel 2003 to minimize the sum of the squares of the deviations, Dx, between the values of the absorbance directly obtained in the titration experiments and those calculated from eqs 1 and 2, and the set of equations defining the appropriate mass balances and equilibrium conditions (see Supplemental MaterialW). The mean values of the pKa of acetic and benzoic acids obtained by this method from nine independent titrations each were pK a (CH 3 COOH) = 4.58 ± 0.02 and pKa(C6H5COOH) = 3.95 ± 0.04 at 24 ± 1 ⬚C and ionic strength, I = 0.1 M. The uncertainty quoted corresponds to tσ where σ is the standard deviation of the mean and t = 2.306 the corresponding Student’s t factor. These values agree within the experimental error with pKa(CH3COOH) = 4.56 ± 0.03 and pKa(C6H5COOH) = 4.01 ± 0.02 at 25 ⬚C and I = 0.1 M, cited in the literature (18), showing that the reliability of the present method is comparable to that of more traditional techniques.
HA 1
tot
n
guess F , to , Ka V x = 1 HA
tot tx
HA
− A−
tot tx
tot
HA
=
=
S2
tot S2
MA
tot
− A
2
tot
− Ka
tx
9
tot
K w + K a HA
H3 O +
tot
−
3
F V
tx
tot tx
tot A− tx
tx
q = −
−
exp (t o − t x )
S1
HA
−
K w + K a HA p = −
tot
HA
−
− Ka
3 3
tot A− tx
+ Ka −
27
tx
= 2
A(calc )t x =
Ka Kw
1 cos −1 3
p cos
tot tx
−
2 q p
3
+ Ka
3 a
H3 O +
tx
+ b 2
Dx 2 = Atx − A(calc)t x x = x +1
x > n
no
yes n
M =
∑ D
x
2
x =1
M = minimum
no
yes F , to , Ka V
Supplemental Material
A list of chemicals, details of the apparatus and experimental procedure, details of the data treatment and underlying theory, and notes for the instructor are all available in this issue of JCE Online.
www.JCE.DivCHED.org
MA
S2
x
A−
The experiment described in the present article is fast, involves a simple experimental procedure, and yields accurate results. It is also easy to fully automate the GCFIT setup by using an automated switching valve. The method can be applied to other monoprotic systems provided an adequate indicator is selected. Finally, although this is not the point of this experiment, the technique can also, in principle, be extended to polyprotic acids, but this involves a more complex experimental approach or data-treatment procedure. For example, if the two pKa’s of a diprotic acid are sufficiently different (typically Ka1兾Ka2 ≈ 104), they may be determined by using two independent titrations, each with a different indicator. If they are similar a single titration with one indicator may be used. However, in this case, a more complex mass balance is involved and the determination pKa1 and pKa2 requires fitting a four parameter equation (F兾V, to, Ka1, and Ka2) to the experimental titration curve.
tot
HA
S1
( At , t1 ) , … ( At , t x ) , … ( At , tn )
Conclusion
W
tot
•
end
Figure 4. Algorithm used in the determination of Ka from the titration curves.
Vol. 83 No. 12 December 2006
•
Journal of Chemical Education
1855
In the Laboratory
Literature Cited 1. Ruzicka, J.; Hansen, E. H. Anal. Chim. Acta 1978, 99, 37– 76. 2. Betteridge, D. Anal. Chem. 1978, 50, 832A–846A. 3. Hansen, E. H.; Ruzicka, J. J. Chem. Educ. 1979, 56, 677– 680. 4. Karlberg, B.; Pacey, G. E. Flow Injection Analysis: A Practical Guide; Elsevier: Amsterdam, 1989. 5. Trojanowicz, M. Flow Injection Analysis: Instrumentation and Applications; World Scientific Pub. Co.: River Ridge, NJ, 2000. 6. Carroll, M. K.; Tyson, J. F. J. Chem. Educ. 1993, 70, A210– A216. 7. McKelvie, I. D.; Cardwell, T. J.; Cattrall, R. W. J. Chem. Educ. 1990, 67, 262–263. 8. Rios, A.; Luque de Castro, M. D.; Valcárcel, M. J. Chem. Educ. 1986, 63, 552–553.
1856
Journal of Chemical Education
•
9. Wolfe, C. A. C.; Oates, M. R.; Hage, D. S. J. Chem. Educ. 1998, 75, 1025–1028. 10. Sartini, R. P.; Zagatto, E. A. G.; Oliveira, C. C. J. Chem. Educ. 2000, 77, 735–737. 11. Economou, A.; Papargyris, D.; Stratis, J. J. Chem. Educ. 2004, 81, 406–410. 12. Turner, D. R.; Knox, S.; Whitfield, M.; Santos, M.; Pescada, C.; Gonçalves, M. L. Anal. Chim. Acta 1989, 226, 229–238. 13. Turner, D. R.; Knox, S.; Whitfield, M.; Santos, M.; Pescada, C.; Gonçalves, M. L. Anal. Chim. Acta 1989, 226, 239–246. 14. Conceição, A. C. L.; Gonçalves, M. L. S. S.; Santos, M. M. C. Anal. Chim. Acta 1995, 302, 97–102. 15. Ramette, R. W. J. Chem. Educ. 1963, 40, 252–254. 16. Vithanage, R. S.; Dasgupta, P. K. Anal. Chem. 1986, 58, 326– 330. 17. Tyson, J. F. Anal. Chim. Acta 1986, 179, 131–148. 18. Smith, R. M.; Martell, A. Critical Stability Constants; Plenum Press: New York, 1989; Vol, 6, Supplement 2.
Vol. 83 No. 12 December 2006
•
www.JCE.DivCHED.org
