Cadmium Succinate and Cadmium Malate Stability ConstantsRevisited
Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, Quai Ernest-Ansermet 30,CH-1211 Geneva 4, Switzerland
Raewyn M. Town
School of Chemistry, David Keir Building, The Queens University of Belfast, Stranmillis Road,Belfast BT9 5AG, Northern Ireland
Mercedes Garca Bugarn
Departamento de Qumica Inorganica, Universidad de Vigo, Calle Torrecedeira 86, E-36208 Vigo, Spain
The complexes formed in the cadmium(II) succinate (suc2-) hydrogen ion and in the cadmium(II) malate(mal2-) hydrogen ion systems in aqueous solution at 37 C and I ) 150 mmoldm-3 (NaCl) have beencharacterized by means of glass-electrode potentiometry. The succinate and malate protonation constantswere found to be 5.187 ( 0.001, 9.135 ( 0.002 and 4.618 ( 0.001, 7.804 ( 0.002, respectively. The formationconstants for the complexes Cdsuc, CdsucH+, and Cdmal were found to be 1.63 ( 0.02, 6.26 ( 0.06, and1.25 ( 0.05, respectively. Particular attention has been paid to the evaluation of the effect of possiblesystematic errors on the constant values determined. Reliable standard deviation estimations have beenmade by applying a Monte Carlo calculation technique. Cyclic voltammograms and differential pulsepolarograms for both cadmium(II) systems were consistent with formation of weak, labile complexes.
Succinic acid (butanedioic acid, ethane dicarboxylic acid),HOOC-CH2-CH2-COOH, and malic acid (hydroxybu-tanedioic acid, monohydroxysuccinic acid), HOOC-CHOH-CH2-COOH, are naturally occurring ligands present inmany organisms. Succinic acid is an important intermedi-ate in the tricarboxylic acid cycle, where it is formed fromR-ketoglutaric acid. It is used via reactions in the tricar-boxylic cycle and in the glyoxylate cycle for the synthesisof amino acids and carbohydrates. The S-isomer of malicacid is also an intermediate both in the tricarboxylic acidcycle, being formed by hydration of fumaric acid andconverted into oxaloacetic acid by malate deshydrogenase,and in the glyoxylate cycle. Succinate is present, in free orbound form, especially as calcium and potassium succi-nates, in unripe fruits, algae, fungi, and lichens. Malateplays several metabolic roles in plants, for example in thediurnal acid rhythm of the Crassulaceae. Malic acid isfound free in sour apples, quinces, and berries. Succinateand malate are used in the preparation of drugs and inflavorings. Malic acid is also used to impregnate packingmaterials for foods.
Despite their biological significance, values of the stabil-ity constants for metal succinate and malate systems inaqueous solution have rarely been determined underconditions of temperature and ionic strength close to thoserelevant for biological fluids.
Determination of stability constants for weak complexes,as in the present case for the cadmium succinate and
malate systems, is not straightforward because the ana-lytical signals are only slightly perturbed in the presenceof complex formation. This situation is common to manybiological, and environmental, systems. For such systems,the effect of experimental errors on model selection andon the constant values obtained can be very important andmust be carefully checked. Failure to adequately considerthese aspects may be a source of the disparity amongpublished stability constant values.
In the present study, two different analytical techniquesare applied, glass potentiometry and voltammetry. Par-ticular attention is paid to the evaluation of the effect ofpossible systematic errors on the constant values deter-mined, and reliable standard deviation estimations aremade by applying a Monte Carlo calculation technique.Comparison of the values obtained with previously pub-lished values allows discussion of the validity and limita-tions of some of the existing values.
Experimental SectionPotentiometric Studies. A. Reagents. Analytical grade
reagents were used throughout. All solutions were preparedusing demineralized water (Millipore system), which hadbeen boiled and cooled under nitrogen, and stored underan atmosphere of purified nitrogen.
Malic and succinic acids were purchased from Merck.They were potentiometrically assayed and found to besufficiently reliable to be used without further purification.Ligand solutions were freshly prepared daily by directweighing.
Stock solutions of cadmium were prepared from theirchloride salts and were made slightly acidic by adding* Corresponding author. E-mail: email@example.com.
1009J. Chem. Eng. Data 1999, 44, 1009-1019
10.1021/je990048w CCC: $18.00 1999 American Chemical SocietyPublished on Web 08/18/1999
hydrochloric acid to prevent hydrolysis and adsorption ofcarbon dioxide. The metal content of the solutions wasdetermined against EDTA using xylenol orange as indica-tor (Vogel, 1971). Their mineral acid content was deter-mined by titration with standard alkali (Gran, 1988) andthe concentration verified by using the MAGEC program(May et al., 1982).
Carbonate-free sodium hydroxide solutions were pre-pared from Merck standard volumetric solutions. Alkalititer and absence of carbonate were checked by means ofGran plots (Gran, 1988) using potassium hydrogen phtha-late (Merck) as the acid.
B. Technique and Experimental Conditions. Forma-tion constants were determined from potentiometric titra-tions. A Radiometer PHM93 millivoltmeter was used tomonitor the emf of cells of the type
where G.E. denotes a glass electrode (Orion 91-01) and R.E.a double-junction silver/silver chloride reference electrode(Orion 90-02). Successive aliquots of sodium hydroxide wereadded to the solution by means of a Metrohm Multi-dosimat 665 autoburet. A versatile computer-controlledsystem for data acquisition was used throughout. Allexperiments were carried out in a titration cell thermo-stated at (37 ( 0.02) C by circulating thermostated water.Titrations were performed in a nitrogen atmosphere.
Sodium chloride (150 mmoldm-3) was used to maintainthe ionic strength constant and to ensure isotonicity withblood plasma. Although, from the thermodynamic view-point, the conditions used are not ideal due to the possibleassociation of chloride with metal ions (Daniele et al.,1985), the advantage is that constants obtained in this saltsolution implicitly account for the influence of the biologicalmedium.
The electrode system was calibrated in terms of hydrogenion concentrations by performing strong acid versus strongbase titrations (Linder et al., 1984). The logarithm of theconcentration quotient for water dissociation under thesame experimental conditions was found to be -13.36, ingood agreement with literature values (Pettit and Powell,1997).
The cadmium and ligand solutions used were acidifiedsuch that all the ligand donor groups were protonated atthe beginning of each titration. Titrations were performedover the wider range of metal-to-ligand ratios allowed bythe working ionic strength. Data were recorded over thewidest possible -log[H] range. Replicate titrations weredone to check reproducibility.
Titration data used for calculating formation constantsare summarized in Table 1.
C. Calculation Procedures. The general equilibriainvolving metal M2+, ligand L2- (i.e. deprotonated succinicacid ) suc, deprotonated malic acid ) mal), and H+ ionscan be written as
Signs are omitted for simplicity. The overall formationconstant is denoted by pqr.
The titration data were processed with the ESTA com-puter program library (May et al., 1985, 1988; May andMurray, 1988a, 1988b) by following our previously de-scribed approach (Filella et al., 1987a, 1987b; GarcaBugarn et al., 1989; Garca-Tasende et al., 1991a, 1991b)involving optimization and simulation in successive steps.The initial models were obtained from the experimental
protonation, deprotonation and formation curves. Proto-nation curves are obtained by plotting the average numberof protons bound to each ligand, Zh H, as a function of-log[H]
where TH, TL and TOH ) total concentrations of strong acid,ligand, and hydroxide, respectively and n ) number oftitratable protons of the ligand. Deprotonation curves areobtained by plotting Qh as a function of -log[H], Qh beingdefined as
Table 1. Summary of Titration Data Used in theFormation Constant Calculations: Number of TitrationPoints, Initial Total Concentrations of Cadmium(II) (TM),and Ligand (TL) in mmoldm-3, and -log[H] RangeInvestigated
system titrationno. ofpoints TM TL
suc-H+ 1 48 5.1 2.30-8.502 46 5.1 2.30-6.063 50 9.6 2.29-6.544 50 9.6 2.29-6.555 48 14.9 2.28-6.496 49 14.9 2.28-8.677 45 15.39 2.28-6.958 59 15.39 2.29-6.529 53 19.25 2.28-6.22
10 53 19.25 2.28-6.2211 55 19.86 2.28-6.3712 47 19.86 2.28-6.37
mal-H+ 1 45 4.85 2.27-5.622 46 4.85 2.27-6.163 44 5.17 2.26-5.074 48 5.17 2.27-6.325 42 10.08 2.24-6.086 52 10.08 2.23-5.977 53 10.34 2.23-5.938 57 14.94 2.21-5.769 43 14.94 2.20-5.75
10 63 19.98 2.18-7.0211 56 19.98 2.18-6.04
Cd2+-suc-H+ 1 42 0.8554 12.36 2.79-5.372 42 0.8554 12.36 2.79-5.373 43 0.8554 16.29 2.74-5.504 42 0.8554 17.30 2.74-5.285 41 0.8554 17.30 2.73-5.236 51 0.8554 26.21 2.68-6.017 52 0.8554 26.21 2.68-6.188 44 1.711 7.616 2.68-5.509 51 1.711 17.40 2.61-5.84
10 49 1.711 17.40 2.61-5.6511 49 1.711 26.03 2.56-5.7312 49 1.711 26.03 2.57-5.7413 52 3.421 7.62 2.44-5.7914 50 3.421 26.03 2.39-5.67
Cd2+-mal-H+ 1 50 0.8554 16.17 2.46-5.952 45 0.8554 17.06 2.46-4.933 43 1.711 7.33 2.52-4.974 47 1.711 17.06 2.40-4.995 47 1.711 17.06 2.70-4.996 52 1.711 17.54 2.39-5.337 55 1.711 17.4 2.39-5.918 48 1.711 25.70 2.32-5.139 46 1.711 25.70 2.31-4.96
10 51 3.421 7.33 2.38-5.2811 52 3.421 17.37 2.28-5.1412 53 3.421 17.37 2.29-5.2313 54 3.421 25.70 2.24-5.71
G.E.|Cd2+, ligand, H+, NaCl (150 mmoldm-3)|R.E.
pM + qL + rH h MpLqHr (1)Zh H )
TH + nTL - TOH + [OH] - [H]TL
* - THTM
1010 Journal of Chemical and Engineering Data, Vol. 44, No. 5, 1999
where TH* is the calculated total concentration of protons
in the system at the observed -log[H]. Metal complexformation curves show the variation of the average numberof ligands bound per metal ion Zh M, as a function of-log[A]
and TM ) total metal concentration.The shapes of these curves were used to predict the
stoichiometry of the possible complexes present in thesystem as well as to obtain rough estimates for theirformation constants. Formation constants were estimatedinitially by using the BETA task of ESTA (May et al., 1988).This task calculates the formation constant values for asingle species from the emf reading at each titration pointby assuming that this is the only species formed. Modelselection was based on five criteria: (i) search for theminimum value of the objective function being minimized,(ii) good internal consistency of the data as reflected bysmall standard deviations of formation constants, (iii) bestfit between experimental and calculated graphical visual-izations of the data (protonation and formation curves) for
the different models tested, (iv) calculation of the degreeof formation of each species (complexes not reaching 10%of the total metal concentration over a range of points inmore than one titration were regarded as dubious), and(v) application of chemical common sense.
Formation constants were refined by using the ESTAoptimization module (May et al., 1988). The ESTA objectivefunction can be minimized with respect to either total ionconcentrations (OBJT) or emf (OBJE). The objective func-tion based on unit-weighted residuals in total analyticalconcentrations (OBJT) was used throughout the modelselection procedures. Optimization of the best set ofspecies was performed by applying the weighting schemeproposed by May and Murray (1988a) on the emf-basedobjective function. The weight at each titration point wasbased on errors of 0.2% in analytical concentrations, 0.005cm3 in titer and 0.05 mV in emf. Results based onunweighted total ion concentration residuals (OBJT) andon weighted emf residuals (OBJE) are given in Table 2.OBJE results should be considered as being the best setof constants, but it should be borne in mind that weightedfunctions are not directly comparable among differentchemical systems because they depend on estimates oferrors and on how the weighting is done. It is because ofthis that unweighted OBJT values are also given.
Ionic strength may vary to some extent over the courseof a titration when the background supporting electrolyteis maintained constant at relatively low concentrations, asis the case in the present study. The ESTA computerprogram library allows the data to be corrected for thisfactor by calculating ionic strength values at each titrationpoint (May et al., 1985). This correction is based on the
Table 2. Formation Constants, pqr, Determined in This Study at 37 C and I ) 150 mmoldm-3 NaCl (pqr )[MpLqHr]/[M]p[L]q[H]r)
system p q r log pqr SDa OFb Rc nd
suc-H+ OBJT 0 1 1 5.1772 0.0002 4.14E-10 0.001 6110 1 2 9.1268 0.0002
OBJE 0 1 1 5.1787 0.0002 0.58 0.0020 1 2 9.1283 0.0002
DHCe 0 1 1 5.1875 0.0002 0.62 0.0020 1 2 9.1360 0.0003
best valuesf 0 1 1 5.187 0.001 0.250 1 2 9.135 0.002
mal-H+ OBJT 0 1 1 4.6108 0.0002 4.07E-10 0.001 5490 1 2 7.7971 0.0002
OBJE 0 1 1 4.6109 0.0002 0.366 0.0010 1 2 7.7976 0.0002
DHCe 0 1 1 4.6183 0.0002 0.282 0.0010 1 2 7.8043 0.0002
best valuesf 0 1 1 4.618 0.001 0.310 1 2 7.804 0.002
Cd2+-suc-H+ OBJT 1 1 0 1.669 0.005 1.07E-09 0.001 6571 1 1 6.293 0.010
OBJE 1 1 0 1.662 0.006 0.77 0.0021 1 1 6.298 0.012
DHCe 1 1 0 1.630 0.006 0.62 0.0021 1 1 6.259 0.012
best valuesf 1 1 0 1.63 0.02 0.011 1 1 6.26 0.06
Cd2+- mal-H+ OBJT 1 1 0 1.328 0.010 2.35E-09 0.002 643OBJE 1 1 0 1.331 0.010 1.49 0.002DHCe 1 1 0 1.244 0.011 1.48 0.002best valuesf 1 1 0 1.25 0.05 0.01
a Standard deviations as given by the program. b OF, in OBJE output ) [w(EMFio - EMFic)2]/(N - np); in OBJT output ) [(Tio -Tic)2]/(N - np), where N ) number of points, np ) number of refined parameters, and Ti ) total concentrations. See the CalculationProcedure section for an explanation of why both OBJT and OBJE results are given. c R ) Hamilton R factor. d Number of points usedin the calculations. e Values corrected for variations in ionic strength along the titrations as described in the text (weighted OBJE optionwith Debye-Huckel corrections applied). f Formation constants calculated by applying the Monte Carlo technique described in the text(number of Monte Carlo cycles ) 99). The OBJE weighted optimization option with correction for variations in ionic strength along thetitrations has been used.
Zh M )
TL - [A](1 + n
[A] )TH - [H] + [OH]
Journal of Chemical and Engineering Data, Vol. 44, No. 5, 1999 1011
extended Debye-Huckel equation for the calculation of theactivity coefficient for each component and complex. Whenthe Debye-Huckel parameters for all components andcomplexes are not introduced, default values implementedin the ESTA computer program library are used (Linderand Murray, 1982). All complexes and anionic...