In the Laboratory
Determination of Equilibrium Constants of Metal Complexes from Spectrophotometric Measurements
W
An Undergraduate Laboratory Experiment Gabriela A. Ibañez, Alejandro C. Olivieri, and Graciela M. Escandar* Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas Universidad Nacional de Rosario, Suipacha 531, 2000 Rosario, Argentina; *
[email protected] In this report we provide a detailed description of the experimental conditions and computational method for the spectrophotometric determination of equilibrium constants. We describe a laboratory experiment designed to familiarize students with the use of spectrophotometric techniques and at the same time to apply computational methods (model fitting and parameter estimation) to obtain relevant thermodynamic results concerning stability constants. The latter information regarding metal complexes is needed in many applications in diverse areas of science and industry (1a). It is therefore interesting to know how complex formation constants are determined in real practice. These topics are becoming increasingly important as computer software acts as a critical interface between instruments and the chemical information obtained from them. With respect to the chemistry curriculum, the availability of microcomputers has exerted a profound influence in the laboratory practices in chemistry careers. Many classical methods have been revisited and optimized with the aid of computer methodologies. Several experiments have been described in this Journal with the object of illustrating such concepts (2, 3). When the degree of complex formation is sensitive to the hydrogen ion concentration, potentiometric pH measurements constitute one of the most convenient methods for complex equilibrium determinations (1b, 3). However, under special circumstances (low solubility of either the ligand or the chelate, high basicity of the ligand, etc.) potentiometry cannot be employed. The spectrophotometric method is an alternative that allows one to work with low concentrations of components and in a pH range where potentiometric determinations become inaccurate. Computer methods applied to spectrophotometric data referring to chemical equilibria have been reported (4, 5). We use the program Epsilon (6 ) developed in our laboratory. The main advantages of this computer program are mentioned below. The experiment described in this paper is regularly performed by students in the last year of the chemistry curriculum. Selected System As an example of a spectrophotometric determination of equilibrium constants, 2-hydroxybenzoic acid (salicylic acid) was studied in aqueous solution in the presence of Cu(II) ion.
COOH OH Salicylic acid (LH2)
Salicylates are in wide use as antiinflammatory drugs for the treatment of rheumatoid arthritis and other diseases, and their determination in biological fluids is important for monitoring the illness (7). Analytically, salicylic acid (LH2) is used as an indicator in the titration of several metals (8a). This is possible because it contains a carboxylate and a hydroxy functional group, both of which are able to bind transition metal ions (9). Specifically, it forms colored species with Cu(II) ion that are suitable for a spectrophotometric study. Salicylic acid is commercially available with a high degree of purity. Time Requirement The experiment is designed to be carried out in approximately 4 hours, apportioned as follows: • • •
preparation and standardization of solutions (1 laboratory hour) spectrophotometric run (2 laboratory hours) computational work (1 hour)
Experimental Procedure
Instruments Measurements of pH were performed with a Metrohm 713 pH meter equipped with a combination Metrohm glass electrode. The electrode was calibrated with HNO3 and acetate buffer at the same ionic strength as the experimental solutions. Thus, {log [H+] (pH) is read rather than hydrogen ion activity, and the calculation of “mixed” constants is avoided. Students are already familiar with glass-electrode calibration from previous analytical chemistry experiments. Spectral data were obtained with a Beckman DU 640 spectrophotometer using 1.00-cm quartz microcells. The computational work was performed on an 80486 PC microcomputer. Reagents and Experimental Conditions Table 1 shows the experimental materials and solutions employed in the present example. General conditions are described below. All reagents used in equilibrium constant determinations must always be of the highest possible purity
JChemEd.chem.wisc.edu • Vol. 76 No. 9 September 1999 • Journal of Chemical Education
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In the Laboratory
(ACS reagent grade or equivalent). The concentrations of the absorbing species in the experimental solution should be selected so that Beer’s law holds. In our work, the concentration of copper ion (as nitrate or chloride) in the experimental cell was on the order of 2.00 × 10{3 M, prepared from a 0.0100 M stock solution of the metal ion, previously standardized by EDTA titration (see Table 1). Since the ligand is stable in aqueous solution, a stock solution can be prepared and the final required amount is measured from this solution. An alternative, as in this case, is to weigh the required amount of salicylic acid so that the ligand concentration in the experimental cell is about 7.00 × 10{3 M. In coordination chemistry studies several metal–ligand molar ratios can be checked with the purpose of finding complexes with different metal–ligand stoichiometries. Usually, the molar ratios between metal ion and ligand are selected according to the particular system being investigated (coordination sites on the ligand and nature of the metal ion). For the present work, it is already known that both 1:1 and 1:2 complexes are formed (10), and students work with concentrations of ligand larger than those stoichiometrically required (see above). Both the temperature and the ionic strength (µ) of the solution should be fixed. The temperature is controlled during both the pH and spectrophotometric measurements using thermostated cells. The ionic strength can be established by the addition of an inert electrolyte such as the sodium or potassium salt of chloride or nitrate. To avoid redox reactions and acidification of the medium, oxygen and carbon dioxide should be removed by bubbling a stream of argon or nitrogen through the solution.
Procedure The reaction solution (Table 1) is made up in a thermostated potentiometric cell. NaOH solution is added to the weighed quantity of salicylic acid, for the purpose of easing its dissolution. An excess of alkali should be avoided, since copper hydroxide may precipitate in the initial solution upon the addition of the metal ion solution. The preparation of the experimental solution ends with the addition of a strong acid (HNO3 ca. 0.10 M), with the aim of evaluating a wide pH range, and of NaNO3 as an ionic strength adjustor. It is not necessary to know either the exact concentration of the NaOH (used for ligand dissolution and as titrating agent) or of the HNO3, because the data used in the computational process are the pH values read at each experimental point. To the stirred acid solution prepared as described above, base solution is added in known increments (0.05–0.1 mL). For each experimental pH point a known aliquot of solution (e.g., 0.60 mL) is extracted and its spectrum in the absorption region is obtained. The absorbance is read at a fixed wavelength (usually at a maximum). Equilibrium conditions are established before proceeding with the next step. Attainment of equilibrium is determined by a pH drift of less than 0.01 pH units in 5 minutes. The procedure is repeated so as to provide more than 15 pairs of absorbance and pH values for each experimental run. Thus, a profile of absorbances vs pH is obtained for each experiment. The experimental run should be conducted at least in duplicate.
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Table 1. Reagents and Conditions for Determining Equilibrium Constants of Cu(II)–Salicylic Acid Complexes Reagent or Parameter
Amount or Value
Salicylic acid
0.0468 g (Aldrich, AC)
CO2-free NaOH
4 mL of ~ 0.1 Ma
Cu(NO3)2
10.02 mL of 0.0106 Mb
HNO3
2 mL of ~ 0.1 Mc
NaNO3
5.00 mL of 1.00 Md
Doubly-distilled water
–
Final volume
49.69 mL
Temperature
20.0 °C
Ionic strength
0.10 M
CO2-free NaOH titrant
~ 0.1 Ma
aPrepared from 17 M NaOH solution. It is not necessary to know the exact concentration of this solution (see text) bPrepared by dissolving Cu(NO ) (Sigma) in doubly distilled water 3 2 and titrimetrically standardizing with ethylenediaminetetraacetic acid (EDTA) (8b). cPrepared from concentrated HNO (Merck). It is not necessary to 3 know the exact concentration of this solution (see text). dPrepared by weighing solid NaNO (Mallinckrodt). 3
Computations The equilibrium constants for the metal chelates were determined by using the program Epsilon (6 ),W which was designed to work with experimental results obtained from this experiment. However, other programs could also be used for similarly designed experiments (5). Epsilon was developed for the refinement of both equilibrium constants and extinction coefficients from spectrophotometric pH titration data on systems containing any number of interacting components. It allows an easy treatment of the data through windows and handles graphics very efficiently. The general structure of Epsilon can be summarized as follows: 1. input of data, 2. calculation of concentrations of all intervening species at each pH value, 3. refinement of extinction coefficients and stability constants to minimize the sum of the squares of the differences between the calculated and observed values of absorbances and to obtain a close approximation to the experimental curve, 4. plotting of both the spectrophotometric titration curve and the species distribution as a function of pH during refinement (in order to judge on the relative importance of species), and 5. estimation of standard deviations for the refined parameters.
Discussion Figure 1 shows the spectra observed in the course of a typical spectrophotometric titration of Cu(II)–salicylic acid system. Since the absorbance changes are largest at the maximum located at about 400 nm, this wavelength was chosen to obtain the most accurate data for the computation of equilibrium constants. Table 2 illustrates the computer input of program Epsilon, showing the parameters and data used in determining the equilibrium constant of Cu(II)–salicylate
Journal of Chemical Education • Vol. 76 No. 9 September 1999 • JChemEd.chem.wisc.edu
In the Laboratory Table 2. Computer Input to Program Epsilon for the Cu(II)–Salicylate System
Species and Parameters ε
pK
0
0
0
7.38
0 0 0
Ligand
H+
1
0
1
0
0 {1
0 {2.81
0
1
0
0
1
13.4
0
1
1 {1
100
3
1
1
{1
180
8
1
2
{2
Metal
Data Vol/mL
Figure 1. Absorbance of Cu(II)–salicylic acid system at indicated pH values. Initial analytical concentrations: c L = 6.78 × 10 {3 M , c M = 2.12 × 10{3 M; t = 20.0 °C, µ = 0.10 M (NaNO3).
complexes. The notation in Table 2 representing the different species is that normally used in coordination chemistry: the species present in the solution are formed by components. Each component is assigned a number that corresponds to (i) the stoichiometric coefficient when the component is the ligand or the metal, and (ii) the number of released or captured protons from a given reference level when the component is the proton itself. Since the salicylate monoanion (LH{, salicylic acid without the carboxylic proton) is the dominating ligand species in the pH working range, this species is taken as the ligand reference level. It is represented by the notation 0 1 0, while the species denoted as 0 1 1 and 0 1 {1 are salicylic acid (LH2) and the completely deprotonated ligand (L2{), respectively (Table 2). The latter is obtained when the phenolic proton is released in addition to the carboxylic one. The initial guesses for ε (extinction coefficient) and pK of the complexes are made according to the spectra and known values for similar systems. Neither the protonated nor the deprotonated forms of salicylic acid absorb at the selected wavelength so that ε = 0 in Table 2. As seen in Table 2, literature values for the protonation (LH{ + H+ LH2) and deprotonation (LH{ L2{ + H+) of salicylic monoanion are used as input data for the calculation (10). The copper ion hydrolysis is also considered and its equilibrium constant value is that corresponding to the literature (11). However, the concentration of the hydrolytic [Cu(OH)]+ species is lower than 1% over the pH range investigated. It should be noted that Epsilon allows the introduction of any number of hydrolytic species. For example, [Cu(OH)]+ is represented, using the nomenclature described above, as 1 0 {1. After defining the system on the basis of the equilibrating species, their extinction coefficients and pK values, it is necessary to enter the data of pH, absorbance, and micromoles of both ligand and metal ion (calculated from their initial concentrations and taking into account the amount extracted for each spectrophotometric reading) at each experimental point. To decrease the differences between the calculated and experimental titration curves (measured through the σFIT value, see footnote of Table 3) it was necessary to consider
Amount/10{6 mol
Absorbance
Metal
pH
Ligand
49.09
0.0009
104
333
3.278
48.89
0.0086
103
329
3.534
48.59
0.0182
102
325
3.830
48.29
0.0441
100
321
4.344
47.79
0.0710
98.9
317
4.552
46.79
0.0883
96.4
308
4.754
46.29
0.1545
95.1
304
5.121
45.79
0.1903
93.9
300
5.320
45.29
0.2251
92.6
296
5.545
44.74
0.2470
91.3
292
5.680
44.19
0.2612
90.0
288
5.845
43.64
0.2720
88.8
284
6.038
43.09
0.2996
87.5
280
6.309
42.54
0.3180
86.2
276
6.599
41.99
0.3388
85.0
272
6.887
41.44
0.3541
83.7
268
7.110
40.89
0.3701
82.4
264
7.296
the formation of the following complexes: Cu2+ + LH{ [CuL] + H+ 2+
{
2{
(1) +
Cu + 2LH (2) [CuL2] + 2 H Therefore, the species 1 1 {1 and 1 2 {2 were introduced in the model. This notation symbolizes 1:1 and 1:2 metal– ligand complexes in which one and two protons, respectively, have been released in the complex formation. The protons removed would correspond to the phenolic ones. Table 3 shows the results obtained after the refinement of the data presented in Table 2. If the above-mentioned species are not taken into account, the calculated absorbances show a poor fit with respect to the experimental spectrophotometric results. At this point, one should emphasize that it is essential to avoid the temptation to increase the number of species in the model in order to produce a slightly better fit. In general, it is preferable to postulate the minimum number of species necessary to explain the experimental data. As can be seen in Figure 2, the discrepancies between the calculated and experimental curves are very small and would indicate that a good equilibrium description of the systems was achieved. This is confirmed by the small value of the overall σFIT (4 × 10{3) and by the standard deviation of the refined parameters (see Table 3). The fact that the error
JChemEd.chem.wisc.edu • Vol. 76 No. 9 September 1999 • Journal of Chemical Education
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In the Laboratory
obtained for the [CuL2]2{ complex is rather large is due to precipitation of Cu(OH)2 above pH 7, which competes with the complex formation. Thus, the soluble region where this complex is present is not completely adequate for refining both its extinction coefficient and equilibrium constant. This problem is reflected in the standard deviation, even when the σFIT is very small. Nevertheless, the equilibrium constant values obtained are in good agreement with those reported in the literature (see Table 3). In addition to the equilibrium constants and extinction coefficients, the computer program Epsilon offers a complete species distribution for all the titration points (Figure 3). In a separate laboratory experiment not discussed here, students may compare the spectrophotometric results with those obtained by potentiometric methods. A potentiometric experiment of equilibrium constant determination of this type was recently described in this Journal (3). In conclusion, this experiment is an example of the integration of spectroscopic and computer-fitting work. As such, it is ideally suited for advanced undergraduate students, since it helps them to appreciate what research chemists do in real practice. Acknowledgments Financial support from the University of Rosario, Fundación Antorchas, and CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas) is gratefully acknowledged. G.A.I. thanks CONICET for a fellowship. Note W
The program Epsilon and instructions for running it can be obtained through JCE Online at http://jchemed.chem.wisc.edu/Journal/issues/ 1999/Sep/abs1277.html.
Literature Cited
Table 3. Computer Optimized Output for Cu(II)-– Salicylate System σFIT = 4 × 10{3 a Parameter
Actual Value
SD
Lit (10)
ε of 11-1
150
±5
—
ε of 12-2
200
± 10
—
pK of 11-1
2.88
± 0.08
2.80
pK of 12-2
7.5
± 0.3
7.7
Absorbance
pH
Exptl
Calcd
∆
3.278
0.0009
0.0040
{0.0031
3.534
0.0086
0.0080
0.0006
3.830
0.0182
0.0163
4.344
0.0441
0.0483
0.0019 {0.0042
4.552
0.0710
0.0703
4.754
0.0883
0.0966
0.0007 {0.0083
5.121
0.1545
0.1547
{0.0002
5.320
0.1903
0.1872
0.0031
5.545
0.2251
0.2212
0.0039
5.680
0.2470
0.2392
0.0098
5.845
0.2612
0.2589
6.038
0.2720
0.2787
0.0023 {0.0067
6.309
0.2996
0.3015
{0.0019
6.599
0.3180
0.3221
{0.0041
6.887
0.3388
0.3409
{0.0021
7.110
0.3541
0.3538
0.0003
7.296
0.3701
0.3633
0.0068
a
σFIT =
N
Σ
m=1
2
A calcd(m) – A exptl(m) /N
where Acalcd and Aexptl are the calculated and experimental absorbances, respectively, m stands for each datum, and N is the total number of data.
1. (a) Martell, A. E.; Motekaitis, R. J. Determination and Use of Stability Constants, 2nd ed.; VCH: New York, 1992; pp 195–197.
Figure 2. Experimental (•) and calculated ( ––– ) values of absorbance vs pH for the Cu(II)–salicylic acid system. Initial analytical concentrations: c L = 6.78 × 10{3 M, c M = 2.12 × 10{3 M; t = 20.0 °C; µ = 0.10 M (NaNO3).
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Figure 3. Species distribution as a function of pH plotted with the equilibrium constants for the Cu(II)–salicylic acid system; % = percent of total concentration of metal (set at 100%). Initial analytical concentrations: c L = 6.78 × 10{3 M, c M = 2.12 × 10{3 M; t = 20.0 °C; µ = 0.10 M (NaNO3).
Journal of Chemical Education • Vol. 76 No. 9 September 1999 • JChemEd.chem.wisc.edu
In the Laboratory (b) Ibid., Chapters 3, 4. 2. Long, J. R.; Drago, R. S. J. Chem. Educ. 1982, 59, 1037. 3. Escandar, G. M.; Sala, L. F. J. Chem. Educ. 1997, 74, 1329. 4. Leggett, D. J. Computational Methods for the Determination of Formation Constans; Leggett, D. J., Ed.; Plenum: New York, 1985. 5. Leggett, D. J.; Kelly, S. L.; Shiue, L. R.; Wu, C.-D.; Kadish, K. M. Talanta 1983, 30, 579. 6. Araujo, C. L.; Ibañez, G. A.; Ledesma, G. N.; Escandar, G. M.; Olivieri, A. C., Comput. Chem. 1998, 22, 161. 7. Brewer, E. J. Drug Therapy: Juvenile Rheumatoid Arthritis; Saunders: Philadelphia, 1970; pp 180–188. 8. (a) Schwarzenbach, G. Complexometric Titrations; WileyInterscience: New York, 1960; pp 74, 77, 89. (b) Ibid., p 82. 9. Van Uitert, L. G.; Fernelius, W. C. J. Am. Chem. Soc. 1954, 76, 379. 10. Smith, R. M.; Martell, A. E. Critical Stability Constants, Vol. 6; Plenum: New York, 1989; p 366. 11. Baes, C. F. Jr.; Mesmer, R. E. The Hydrolysis of Cations; Krieger: Malabar, FL, 1986; p 269.
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