In the Laboratory
Rigorous Potentiometric Determination of Metal Complexes Stability Constants An Undergraduate Laboratory Practice Graciela M. Escandar Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Suipacha 531, 2000 Rosario, Argentina Luis F. Sala* Departamento de Química Física, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Suipacha 531, 2000 Rosario, Argentina The development of the new fields of environmental, bioinorganic, and ecological chemistry has promoted changes in undergraduate chemistry curricula. Therefore, in recent years, topics related to coordination chemistry in biological systems have become relevant in chemical subjects. The magnitude of the interaction between chelating agents and metal ions is defined by the corresponding equilibrium constants, and classical methods for determining them have been widely described in the literature (1–4). Now, with the advent of the computer, more accurate and rapid determinations of equilibrium constants can be obtained. In most biological systems, the degree of complex formation is sensitive to pH, and therefore potentiometric methods are important tools for determining complex equilibrium constants (5). In the present work we describe both experimental and computational methods used in potentiometric determination of equilibrium constants. This experiment is an example of integration between laboratory instruments and computational analysis of data, and at the same time familiarizes the students with the field of coordination chemistry. The procedure is designed to be carried out in three parts: • • •
preparation and standardization of solutions (1 laboratory hour) potentiometric runs (2 laboratory hours) computational work (2 hours)
Selected System As an example of a straightforward potentiometric determination of stability constants, the detailed procedure for the determination of stability constants of the system formed by D-galacturonic acid and Cu(II) ion is now described. COOH O
OH H
OH
H
H
OH
(H,OH)
D-galacturonic
D-Galacturonic
Experimental Procedure
Reagents and Experimental Conditions It is important that all reagents used in this experiment be of the highest possible purity (ACS reagent grade or equivalent). The concentration of metal ion (preferably as nitrate or chloride) in the potentiometric cell is on the order of 1 or 2 × 10{3 M. It is appropriate to prepare a more concentrated stock solution of the metal ion and standardize it by classical methods. If the ligand is stable in aqueous solution, a stock solution may be prepared. The ligand used in this work, D-galacturonic acid, is stable enough in aqueous solution so that potentiometric measurements can be safely carried out. However, it is not advisable to use solutions that have not been recently prepared. An alternative, as in this case, is to weigh out the required amount of ligand for each potentiometric run (see Table 1).
Table 1. Determination of Equilibrium Constants of Cu(II) Ion–D-Galacturonic Acid Complexes, 1:5 Molar Ratio Parameter or Reagent
Value or Amount
Final volume
100.00 mL
Temperature
20.0 °C
Ionic strength
0.100 M
Cu(NO3)2
10.00 mL of 0.02050 M a
D-Galacturonic
acid
acid is a uronic acid characterized by a terminal carboxylate group able to bind most of the transition metal ions (6, 7). Although at the beginning of the 20th century the interaction between metal ions and carbohy-
*Corresponding author.
drates was already known, only from 1970 to date has this study become important (8). This is so because these interactions were found to be relevant as models of metabolic mechanisms, ion detoxification, processes and biological catalysis. Specifically, D -galacturonic acid, present in plant cells, activates the solubilization of metal ions through complex formation, mobilizing them from insoluble salts (9).
acid monohydrate
0.2175 g (Sigma) b
NaNO3
10.0 mL of 1.00 M c
CO2-free NaOH titrant
0.1110 M d
Double-distilled water
—
a
Prepared by dissolving Cu(NO 3)2 (Sigma) in double-distilled water and titrimetrically standardized with EDTA (12 ). b The purity of this ligand was checked by elemental analysis and pH titration. c Prepared by weighing out NaNO3 (Mallinckrodt). d Prepared from 17 M NaOH solution and standardized with potassium biphthalate.
Vol. 74 No. 11 November 1997 • Journal of Chemical Education
1329
In the Laboratory The concentration of the ligand in the experimental solution is selected according to the system under investigation. Generally, several metal :ligand molar ratios are checked with the purpose of finding complexes with different metal– ligand stoichiometries.
Table 2. Computer Output of Program BEST for the 1:5 Cu(II)–D-Galacturonic Acid System Cu(II)-GALACTURONIC ACID (1:5): INITIAL VOLUME NORMALITY OF BASE MILLIMOLES ACID NUMBER DATA POINTS PH CORR. INCLUDED
100.0000 0.1110 0.0000 52 0.0000
Potentiometric Measurements
COMPONENTS: 1 Cu(II) 2 galactu 3 H+
0.20500 1.02500 1.02500
SPECIES: LOG BETA 0.0000 {7.5300 0.0000 3.1894 2.0848 {3.7474 0.0000 {13.7800
1 2 3 4 5 6 7 8
1 Cu(II) 1 Cu(II) 0 Cu(II) 0 Cu(II) 1 Cu(II) 1 Cu(II) 0 Cu(II) 0 Cu(II)
0 galactu 0 galactu 1 galactu 1 galactu 1 galactu 1 galactu 0 galactu 0 galactu
0 H+ {1 H+ 0 H+ 1 H+ 0 H+ {1 H+ 1 H+ {1 H+
SIGMA PH FIT = 0.01136 VB
A
PH
PHCALC
DIFF
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
.000 .200 .400 .600 .800 1.000 1.200 1.400 1.600 1.800 2.000 2.200 2.400 2.600 2.800
.000 .108 .217 .325 .433 .541 .650 .758 .866 .975 1.083 1.191 1.300 1.408 1.516
2.620 2.630 2.650 2.670 2.710 2.730 2.750 2.770 2.790 2.820 2.850 2.880 2.900 2.930 2.960
2.609 2.633 2.656 2.680 2.705 2.792 2.754 2.780 2.806 2.832 2.858 2.884 2.911 2.938 2.966
:
:
:
0.011 {0.003 {0.006 {0.010 0.005 0.001 {0.004 {0.010 {0.016 {0.012 {0.008 {0.004 {0.011 {0.008 {0.006
36 7.000 3.790 37 7.200 3.899 38 7.400 4.007 39 7.600 4.115 40 7.800 4.223 41 8.000 4.332 42 8.200 4.440 43 8.400 4.548 44 8.600 4.657 45 8.800 4.765 46 9.000 4.873 47 9.200 4.981 48 9.400 5.090 49 9.600 5.198 50 9.800 5.306 51 10.000 5.415 52 10.200 5.523 SIGMA PH FITa = 0.011361
:
:
3.700 3.760 3.820 3.880 3.940 4.020 4.110 4.220 4.340 4.500 4.750 5.060 5.380 5.650 5.840 5.990 6.110
3.684 3.734 3.789 3.849 3.914 3.988 4.072 4.170 4.291 4.445 4.657 4.953 5.289 5.796 5.796 5.994 6.181
:
0.016 0.026 0.031 0.031 0.026 0.032 0.038 0.050 0.049 0.055 0.093 0.107 0.091 0.080 0.044 {0.004 {0.071
a
The equation for this is
Σ w pHobs – pHcalc N
σ fit =
2
i =1
Σw N
i =1
N = number of potentiometric equilibrium points and w = 1/(pH i+1 – pHi–1)2.
1330
Both the temperature and the ionic strength of the solution should be carefully established. The former is controlled by circulating water through a thermostated jacket. The ionic strength can be fixed by adding an inert electrolyte such as the potassium or sodium salt of nitrate or chloride. To avoid possible oxidation reactions and acidification of the medium, oxygen and carbon dioxide should be removed by circulating a stream of nitrogen or argon. Table 1 shows the experimental materials and solutions employed in the present example. Although a 1:5 metal : ligand molar ratio was used, only 1:1 complexes were found.
The calibration of the electrodes can be performed with standard buffers at an ionic strength equal to those of the experimental solutions. For example, HNO3, acetic acid, and NaOH standard solutions should be employed. Thus, {log [H+] is read rather than hydrogen ion activity, and the calculation of “mixed” constants is avoided. The first experimental run is designed to determine the deprotonation constant of the D -galacturonic acid. Usually, standard base solution is added in small increments to the acid solution of the ligand, and each pH value is read. The procedure is repeated so as to provide 50–60 pH values for each potentiometric run. To keep the ionic strength constant, the standard base added to the solution should be made to the same concentration as the supporting electrolyte. The standard base solution is added through a capillary tip below the surface of the reaction mixture and is measured by a piston buret that permits reading small volumes (0.01 mL or less). Commercial automatic titrators and data collectors are available, but in the work described here such devices were not used. The reason is that it is extremely difficult to program an automatic titrator to determine with reasonable certainty whether equilibrium has been achieved at each titrating point. We emphasize that equilibrium conditions should be obtained before proceeding with the next step. Attainment of equilibrium is determined by a pH drift of less than 0.01 pH unit in 5 min. The profile of pH vs. a (mol of base added per mol of ligand) is used to calculate the protonation constant of the ligand. At the same time the purity of the ligand can be checked. For computation of the equilibrium constant of the metal complexes, a similar run is performed, but with a solution that also contains the metal ion. In this case, a represents moles of base added per mole of metal ion.
Instrumentation The equipment necessary to carry out the experiment is very simple. In our case, measurements of pH were performed with a Corning 125 pH meter equipped with glass and calomel reference electrodes. The computer-fitting work was performed on an 80486 PC microcomputer. Computations Both the deprotonation constant for the ligand and the equilibrium constants for the metal chelates are determined by using the program BEST (5). This program was elaborated for refinement of the stability constants from potentiometric data measured on systems containing any number of interacting components. The input for BEST consists of the components and their concentrations, the estimates of the equilibrium constant for each species considered to be present in terms of these components, and finally the
Journal of Chemical Education • Vol. 74 No. 11 November 1997
In the Laboratory 12
100
10
80 Cu
-log [H+]
8
(a)
2+
60 % species
6
40 (b)
4
+
CuL
20
2
CuH-1L
precipitate
0 2.5
0 0
1
2
3
4 a
5
6
7
8
3.5
4.5
5.5
- log [H+]
Figure 1. Potentiometric equilibrium curves of (a) D -galacturonic acid and (b) 1:5 Cu(II)-D-galacturonic acid system. µ = 0.10 M (NaNO 3), t = 20.0 °C, CM = 2.050 × 10 {3 M, C L = 1.025 × 10{2 M.
Figure 2. Species distribution in Cu(II)- D-galacturonic acid system as a function of {log[H+] at 20.0 °C and µ = 0.10 M (NaNO3). CM = 2.050 × 10 {3 M, C L = 1.025 × 10{2 M.
potentiometric equilibrium data experimentally determined. With this program simultaneous mass-balance equations are set up for all components present at each increment of base added and, with initial assumptions for the equilibrium constants, the concentration of each species and the pH at each data point are calculated. Equilibrium constants are changed to minimize the sum of the square of the differences between the calculated and observed values of {log [H+], and a close approximation of the experimental curve is obtained (see Table 2). Several examples of processing data with this program are cited in scientific literature (5, 10). The book cited in ref 5 contains a diskette with the compiled program BEST. Another alternative to process data for single systems can be found in ref 11.
In the system under study, the student can note that the postulated model is consistent with the shape of the titration curve obtained. The jump in a = 5 corresponds to the neutralization of the carboxylic protons (take into account the 1:5 metal-ligand ratio used in the experiment). The Cu(II) ion coordinates with the carboxylate group (eq 1), while an excess of L{ remains in the solution. The second inflection suggests that more protons are released in the complex formation. However, this occurs in a pH zone where the solid phase is present, precluding the equilibrium computations. Since only the soluble region of the curve was processed, only the CuH {1L complex (eq 2) was included in the refinement (further deprotonation would occur in a nonanalyzed alkaline region). The release of noncarboxylic protons from the complex can be attributed either to the sugar hydroxyl groups or to the coordinated water molecules, though it is not possible to distinguish between the above processes on the basis of potentiometric results. However, a previous knowledge of the behavior of sugar acid–metal systems suggests that the released proton should correspond to the most acidic one on the carbon chain (the OH of C-2). Table 2 shows the computed results for the 1:5 Cu(II)-Dgalacturonic acid system. An additional feature of BEST is that it computes the complete species distribution consistent with the current data base (Fig. 2). These are important tools for the chemist, since they allow verification using the concentration data if the suggested model is in agreement with the experimental observations (e.g., precipitation of the metal hydroxide on increasing the pH). Since potentiometry does not yield microscopic information on the metal coordination sites, this can be obtained by spectroscopic analyses such as 13C and 1 H-NMR, UV-vis absorption, and IR (13, 14). Therefore, in order to complete the coordination studies, other laboratory experiments should be programmed. In sum, we feel that the experiment shown in this report helps students to appreciate the advantage of using computer analysis in the optimization of chemical methods and in the acquisition of critical results.
Discussion Figure 1 shows the potentiometric profiles corresponding to both the D -galacturonic acid alone and the 1:5 Cu(II)D -galacturonic acid system. An examination of the latter curve shows a first jump at a = 5 and another at a = 6.8. Since Cu(OH)2 precipitation occurs at about pH 5.5 and equilibrium analysis in the presence of solid phase is difficult, the constants computation was performed in acid medium. The coordination reaction can be explained by postulating that two 1:1 complexes are formed, in agreement with eqs 1 and 2: Cu2+ + L{ = CuL+ +
CuL = CuH {1L +
H+
(1) (2)
where the subscript to the H atom in eq 2 represents the noncarboxylic proton released in the formation of the complex. Notice how H stoichiometry is preserved in eq 2. The species considered to be present in the experimental solutions are those whose formation would be predicted according to established principles of coordination chemistry: the nature of donor groups, the electronic configuration of the metal ion, and similar metal complex systems previously known. An important aid for selection of the proposed species is the shape of the pH profile. When the system is very complex the model selection is sometimes a matter of judgment and chemical intuition. However, it is preferable to introduce the minimum number of species necessary to explain the potentiometric results and to avoid the temptation of inventing complexes to cover cases for which a satisfactory fit cannot be achieved with a reasonable model.
Literature Cited 1. Martell, A. E.; Calvin, M. Chemistry of the Metal Chelate Compound; Prentice-Hall: Englwood Cliffs, NJ, 1952. 2. Chaberek, S.; Martell, A. E. Organic Sequestering Agents; Wiley: New York, 1959.
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In the Laboratory 3. Rossotti, F. J. C.; Rossotti, H. The Determination of Stability Constants; McGraw-Hill: New York, 1961. 4. Chelating Agents and Metal Chelates; Dwyer, F. P.; Mellor, D. P., Eds.; Academic: New York, 1964. 5. Martell, A. E.; Motekaitis, R. J. Determination and Use of Stability Constants, 2nd ed.; VCH: New York, 1992. 6. Escandar, G. M.; Sala L. F. Can. J. Chem. 1992, 70, 2053. 7. Tajmir-Riahi, H. A. J. Inorg. Biochem. 1986, 26, 23. 8. Burger, K. Biocoordination Chemistry: Coordination Equilibria in Biologically Active Systems; Ellis Horwood: New York, 1990.
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9. Leppard, G. G.; Ramamoorthy, S. Can. J. Bot. 1975, 53, 1729. 10. Motekaitis, R. J.; Martell, A. E. Can. J. Chem. 1982, 60, 2403. 11. Freiser, H. Concepts and Calculations in Analytical Chemistry. A Spreadsheet Approach; CRC: Ontario, 1992. 12. Schwarzenbach, G. Complexometric Titrations; Interscience: New York, 1960; p 82. 13. Escandar, G. M.; Olivieri, A. C.; Gonzalez Sierra, M.; Sala L. F. J. Chem. Soc. Dalton Trans. 1994, 1189. 14. Escandar, G. M.; Olivieri, A. C.; Gonzalez Sierra, M.; Frutos, A. A.; Sala L. F. J. Chem. Soc. Dalton Trans. 1995, 799.
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