S’ did not improve two-component accuracy without serious degradation of one-component results.
CONCLUSIONS
This work demonstrates that a binary pattern classifier can be used to detect the presence of doublet peaks in stationary electrode polarography under widely varying conditions of peak height ratio, peak separation, and n-value. The overlap tested here for theoretical reversible systems was so severe that visual subjective interpretation from second-derivative data was not possible. The method greatly exceeds the limits of conventional derivative peak detection (5). Better than 90% prediction accuracy was obtained with overlapping reduction peaks as close as 6 mV. Good prediction could be obtained though complete convergence was not realized. A large number of representative curves were necessary in training to achieve successful prediction when any n-values between 1 and 3 electrons were allowed. By combined methods of feature elimination, only 22 of the 133 features investigated were necessary to implement the classifier. The computerized pattern classification scheme demonstrated here for the detection of signal multiplicity is applicable to many analytical measurement techniques. Inherent in this scheme is the selection of features from the observed signal. This selection would be tailored to the technique in question. No prior information about the data is necessary other than category for training purposes, and this situation
was assumed for the work presented here. The features which predominate in the empirical classification problem could be investigated for fundamental relationships to the experimental phenomenon being measured. However, this is not to say that only important relationships are retained. Since the features used here are certainly not intended to include every possibility, the results presented are only relative to the features chosen for investigation. Other features could be devised, other normalization procedures used, and different pattern classification rules applied (32), that might improve upon the results presented here. However, this work is a step toward that goal. The investigation of real analytical data is the important next step. ACKNOWLEDGMENT
The authors thank F. E. Lytle and J. E. Davis for their helpful comments.
RECEIVED for review March 6,1972. Accepted July 20,1972. This work was presented in part by the authors at the 163rd National Meeting of the American Chemical Society, Boston, Mass. April 9, 1972. This work was supported by the National Science Foundation, Grant No. GP-21111. L. B. S. gratefully acknowledges Fellowships granted by Hercules, Inc., SOHIO, the Purdue Research Foundation, and the Analytical Division of the American Chemical Society sponsored by DuPont’s Instrument Products Division.
Stability Constants of Some Polyamine and Polyaminocarboxylate Complexes in Methanol-Water Mixtures by Differential pH Potentia1 Titrimetry +-
D. B. Rorabacher, B. J. Blencoe, and D. W. Parker Department of Chemistry, Wayne State Uniaersity, Detroit, Mich. 48202 Stability constants of Cu(ll), Zn(ll), and Cd(ll) complexes with the polyamines triethylenetetramine (trien) and tetraethylenepentamine (tetren) were determined in methanol-water solvent mixtures containing 40, 65, 80,90 (trien only), 95, and 99% methanol (by wt) at 25 O C , p = 0.1M by means of a differential pH*-potential titrimetric approach em ploying a me rcu r y-g lass-ca lo me1 electrode system. For these complexes the stability constant values exhibit an accelerating increase with increasing methanol content in the solvent, the net gain being 1000-fold or greater on going from water to 99% methanol. By contrast, the stability constants of ethylene glycol bis(paminoethy1 ether) N,N,N’,N‘tetraacetate ion (EGTA) with Mg(ll), Ca(ll), Co(ll), and Cd(ll) and frcms-1,2-diaminocyclohexane-N,N,N’,N‘-tetraacetate ion (CDTA) with Mg(ll), Ca(ll), and Ni(ll) in 99% methanol fail to show notable increases relative to aqueous values, despite the more favorable electrostatic contribution as the solvent dielectric is decreased. The analytical implications are discussed.
involving the influence of solvent on the kinetics of metalcomplex formation (2-4) has led us to obtain information in this area. Much of the current interest is centered on the use of alcoholic solvents-particularly methanol and methanolwater mixtures. In a recent paper we reported on the determination of ligand protonation constants for polyamine and polyaminocarboxylate species as a function of solvent composition in methanol-water solvent mixtures (5). In the current paper, we report the determination of stability constants for some complexes formed by these ligands utilizing, in part, the protonation constant data which are now available. Previous work on stability constant measurements in methanol appears to be limited and the methods employed are
THE STUDY OF COORDINATION REACTIONS in nonaqueous solvents and the development of analytical methods based on such reactions have been hindered by the lack of available thermodynamic data ( I ) . Recent interest in this laboratory
(2) W. J. MacKellar and D. B. Rorabacher, J. Amer. Chem. SOC., 93,
4379 (1971).
(3) F. R. Shu and D. B. Rorabacher, Znorg. Chem., 11, 1496 (1 972).
(4) D. B. Rorabacher and F . R. Shu, Inorg. Chem., submitted for
publication.
~
(1) A. Ringbom, “Complexation in Analytical Chemistry,” Interscience, New York, N.Y., 1963, p 14.
( 5 ) D. B. Rorabacher, W. J. MacKellar, F. R. Shu, and M. Bona43, 561 (1971). vita, ANAL.CI-IEM.,
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
2339
generally inapplicable for complexes of high stability (2,6, 7). The large stability constants of polyamine and polyaminocarboxylate complexes indicate the desirability of utilizing a competition method. In the present work, application of the mercury electrode as an electrode-of-the-third-kind for pH-potential titrimetric measurements has proved to provide satisfactory data in the alcoholic solvents. Since the requisite standard electrode potentials for the Hg(I1)-Hg(0) couple are unavailable in the various solvent compositions employed, comparative potential measurements for two solutions-with and without a second metal ion present-have been used to calculate the stability constant values. In addition to circumventing the need for determining the standard electrode potential value in each solvent composition, this differential titrimetric approach also averts the necessity of determining values for the Hg(IIb ligand complex stability constant and the activity coefficient for the Hgi2 ion. Under ideal conditions, pH dependence may also be bypassed, thereby making the method applicable for solvent systems in which no reliable acidity scale is available. Stability constant values for complexes of the analytically useful polyamines, triethylenetetramine (trien) and tetraethylenepentamine (tetren), with Cu(II), Zn(II), Cd(II), and Ni(I1) (trien only) were successfully obtained in 40, 65, 80, 90 (trien only), 95, and 99% methanol (by wt). Despite solubility problems with polyarninocarboxykte complexes in alcoholic solvents, values are reported for complexes of ethylene glycol bis(6-aminoethyl ether) N,N,N‘,N‘-tetraacetate ion (EGTA) with Mg(lI), Ca(II), Co(II), and Cd(I1) and for trans-l,2-dkminocyclohexane-N,N,N’,N’-tetraacetate ion (CDTA) complexes of Mg(II), Ca(II), and Ni(I1) in 99 % methanol. The solvent trends of the resultant values are discussed. In addition to demonstrating the feasibility of this method for determining stability constant values in nonaqueous solvents, the results imply the analytically significant possibility that metal ions may, in some cases, compete more favorably with the proton for the ligand in intermediate alcohol-water mixtures than is the case in either pure solvent. EXPERIMENTAL
Apparatus. Nonaqueous pH measurements referenced to the standard state in each solvent composition, designated as pH*, were based on the standard buffer solutions established by deLigny and coworkers (8) using a Corning Model 12 expanded-scale pH meter with a glass-calomel electrode system as previously described (5). For the potential measurements, a Reilley-type mercury electrode (Sargent) was employed using fresh triply-distilled mercury for each titration. To minimize problems of sluggish response and erratic potentials, the mercury electrode was stored in an oven between titrations to prevent moisture condensation on the contact wire; also, the platinum wire was frequently cleaned with H N 0 3 and bent well up into the mercury pool with care taken to prevent the formation of air pockets around the wire on filling. Reagents. Perchlorate salts of the metal ions were used exclusively to minimize competitive complexation. To prepare these compounds (9),perchloric acid (73.6%, G. F. Smith (6) G. Popa, C. Luca, and V. Magearu, J. Chim. Phys, 60, 355 (1963). (7) E. C. Romanenko and N. A. Kostromina, Zlz. Neorg. Khim., 13, 2955 (1968); Rim. J. Zttorg. Clzem., 13, 958 (1968). (8) C. L. deligny, P. F. M Luykx, M. Rehbach, and A. A. Wieneke, Rec. Truc. Cltim. Pays-Bus, 79, 713 (1960). (9) “Perchlorates: Their Properties, Manufacture and Uses,”
J. C . Schumacher, Ed., Reinhold Publishing Corp., New York, N.Y., 1960. 2340
Chemical Co.) was added in slight excess to a slurry of the appropriate metal or metal compound-as indicated belowin distilled-deionized water. The resultant metal perchlorate solutions were boiled to expel COz (in the case where carbonates were used), evaporated to near saturation, and cooled. The resulting crystalline needles of metal perchlorate salt were filtered, washed with ether, and air dried (with the exception of the Zn(I1)- and Hg(I1)-perchlorate salts which were used as generated in solution without subsequent filtration). Metal compounds used as starting materials (and sources) include : nickel carbonate, cobalt(I1) carbonate, cadmium oxide, and zinc metal (J. T. Baker Chemical Co.); basic cupric carbonate and mercuric oxide (Allied Chemical Co.); and basic magnesium carbonate (Fisher Chemical Co.). Reagents used were, in all cases, reagent grade or better and used without further purification. All methanol-water solvent mixtures, computed as weight per cent methanol, were prepared from distilled-deionized water and 99.98 % methanol (J. T. Baker “Analyzed Reagent” grade). All ligand and metal perchlorate solutions were prepared by dissolving the respective compounds in the appropriate solvent compositions with the water content of the 95 % and 99 methanol solutions being subsequently checked by the Karl Fischer Titrimetric method. All metal perchlorate solutions were standardized potentiometrically against EDTA using the mercury electrode with Hg(I1)-EDTA as indicator (IO), the methanolic solutions being first diluted with water so that all standardization titrations were carried out in essentially aqueous media. A direct titration in acetate buffer was used for Zn(I1) while Ni(II), Cu(II), Cd(II), and Hg(I1) were standardized by a back-titration of excess EDTA with Zn(I1). Direct titrations of Mg(I1) and Ca(I1) were performed in triethanolamine (TEA) buffered solutions ; Co(I1) was first deaerated with nitrogen before utilizing a direct titration in ammonia buffer. Solutions of EGTA and CDTA (reagent grade, LaMont Laboratories, Dallas, Texas) were standardized by direct titrations against standard Ca(I1) (TEA buffer) and standard Zn(I1) (acetate buffer), respectively. The purification, preparation, and standardization of trien, tetren, and sodium methoxide solutions were the same as previously described (5). Procedure. The procedural details for obtaining pH*potential titration curves were essentially identical to those employed by Reilley and Holloway to study polyamine complexes in aqueous solution (11) with the exception that sodium methoxide solutions were used as titrants to increase the maximum attainable pH* (i.e.,basicity) of the methanolic solutions. To establish the reference base-line curves for the Hg(I1)ligand solutions (designated as Limiting Curve 11), a solution containing 1.000mM Hg(C10&, 2.000mM ligand, and 0.10M NaC104 (for ionic strength control) was prepared. For the stability constant determinations, identical solutions were prepared which contained additionally 2.000rnM of the competing metal ion, M+m. (In preparing these solutions, the order of addition was to mix the two competing metal ions first, followed by additional HC10, prior to introducing the ligand since the ligands were stored in basic solution and the possible precipitation of metal hydroxides upon ligand addition was thus averted.) Although not essential to the stability constant determinations, the titration of a solution containing only 1.000mM Hg(C10& and 0.10M NaC104 (designated as Limiting Curve I) was also run in some solvent compositions as an additional reference curve representing the potential response for Hg(I1) in equilibrium with the HgO precipitate. To avoid COz absorption, nitrogen, which was first passed through concentrated HrSOa followed by two solvent washes, was bubbled into the solution for a few minutes prior to commencing each titration and then swept over the solution sur(10) R. W Schmid, Cltemist-Amlyst, 51, 56 (1962). (11) C. N. Reilley and J. H. Holloway, J. Amer. Cltem. Sor., 80, 2917 (1958).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
face throughout the course of the titration. Sodium methoxide in an identical solvent composition was used as the titrant and the pH*-potential behavior was followed using the glass us. calomel and mercury us. calomel electrode systems, respectively. Rapid switching between the two modes was facilitated by connecting all electrode leads to a rotary switch adapter mounted in an aluminum box, the box being grounded and the output leads to the pH meter shielded. The titration vessel consisted of a 200-ml tall-form beaker fitted with a stopper into which holes had been drilled for the three electrodes, the buret, and the nitrogen inlet. This vessel was thermostated at 25.0 i 0.1 “C by inserting it into a hollow brass jacket through which water was circulated from a constant temperature bath. Petroleum ether filled the small space between the jacket wall (designed to hold 250-mi beakers) and the titration vessel to act as a heat conductor while providing insulation from any stray ac leakage from the water bath. Stirring was provided by a magnetic stirrer with the stirring speed kept constant throughout the titration.
by means of the reciprocal mole fraction concept n CLL =
[ZLI/[L]
=
j=O
BH~~*(uH*)I
(6)
where aH*is the molal activity of the solvated hydrogen ion referenced to the standard state in the same solvent composition (8) and BH,”* represents the cumulative mixed-mode protonation constant
based on the definitions (5)
KHom*E 1 Substitution of Equation 6 into Equation 5 yields
RESULTS
Theoretical Considerations. The original suggestion for the mercury electrode method, a member of the general class of competitive methods, has been attributed to Schwarzenbach and coworkers (12,13) but the details of the theory and operation are due to Reilley and coworkers (11, 14, 15). Basically the method depends on the effect of ligand complexation upon the potential of the half-reaction
+ 2.2 = Hg
HgA2
(1)
as described by the Nernst equation (at 2 5 “C)
E
=
EH,’*
+ 0.0296 log aag-2*
(2)
where aHe’**represents the molar activity of the mercuric ion and Ea,O* represents the standard electrode potential for half-reaction 1 in the solvent under consideration. In the presence of a ligand which forms only a 1 :1 complex with the mercuric ion Hgi2
+ L-’
S HgL+2-b
(3)
the potential of the mercury electrode is dependent on the concentration of free ligand present (an electrode-of-thesecond-kind) and the stability constant of the complex (defined here as a molar concentration constant)
Substitution of Equation 4 into Equation 2 yields
where [HgLd2-’] and [L-’3 represent the molar concentrations of the mercuric complex and the unprotonated, uncomplexed ligand, respectively, and YI~,’Z* represents the activity coefficient of the solvated mercuric ion in the solvent being studied. The value of [L-’1 may be related to the total concentration of uncomplexed ligand (charges omitted), [ZL]
=
[L]
+ [HL] f
.
.
+ [HjL]
(12) G. Schwarzenbach, R. Gut, and G. Anderegg, Helc. Cl7im. Acta, 37, 937 (1954). (13) G. Schwarzenbach and G. Anderegg, ibid., p 1289. (14) R. W. Schmid and C . N. Reilley, J. Amer. Cliem. SOC.,78, 5513 (1956). (15) J. H. Holloway and C. N. Reilley, ANAL.CHEM.,32, 249 (1960).
which then describes the pH* behavior of the potential in the presence of ligand (Limiting Curve 11). When a second metal ion, M+”, is added to the Hg(I1)ligand system, the resulting competitive equilbrium HgL+Z-b
+ M+m
ML+m-b + Hg+2
(8)
is dependent on the relative stability constants of the two complexes, i.e., (for molar concentration constants),
-K H -L - [ML+”-’l[Hg+2] KEa~ [HgL+2-b][M+”]
(9)
which, upon substitution into Equation 2 yields
This describes the potential behavior of the mercury electrode as an electrode-of-the-third-kind (M+mcurves). In aqueolis systems containing known concentrations of HgL+2-b, M+m,and MLfm-’, where the value of E H , ’ is known and K H ~isLeither known or can be evaluated under the conditions of Equation 7, the potential of the mercury electrode is directly related to KHL,the stability constant of the complex under consideration, in a pH region where a significant amount of the complex ML+m-’ is formed. Under the proper conditions (KMI,< K H ~ Linitial ; concentrations: e.g., 2[Hg+2] = [Mim] = [L-’1) a pH-independent plateau is established when ML+m-b complexation occurs since the presence of excess Mtm essentially removes the effect of proton competition for the ligand upon the value of [Hg+2]. In this manner, Reilley and coworkers have utilized Equation 10 to calculate the stability constants of a wide variety of ligands, assuming a value of unity for ytie-: (11, 14, 15). The application of Equation 10 to nonaqueous solvents is hampered by the lack of suitable values for EH,”*, which is known to be solvent dependent. The possibility of estimating this constant for nonaqueous conditions is disputable. Amis (16) and Corsaro and Stephens (17) have reported some solvent systems for which Eqvalues appear to be linearly related to the reciprocal of the dielectric constant. However, in the latter study the percentages of nonaqueous component (16) E. S. Amis, J. Elecrroaiial. Cliem., 8,413 (1964). (17) G. Corsaro and H. L. Stephens, J. Electrocl7em. SOC.,104, 512 (1957).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1 9 7 2
2341
so0
so0
'
400
300
400
.
300
li
uVI
200
=.
0
-100
E
1
100
w
0
2
4
8
6
IO
-100
12
PH'
Figure 1. pH*-potential curves for triethylenetetramine (trien) complexes in 99% methanol. Limiting Curve I represents a solution containing only 1.000mM Hg(I1) whereas Limiting Curve I1 contains additionally 2.000mM trien. All other curves ( M + m curves) contain these same quantities of Hg(I1) and trien plus 2.000mM metal ion. Curves are for 25 "C, p = 0.1M (NaC104) did not exceed 32.2% methanol, 40% ethanol, or 30% dioxane while Amis does not give solvent compositions but indicates that deviations from linearity increase as the nonaqueous component becomes predominant. By contrast, Strehlow (18) notes that the variation of Eo* with changing solvent composition is generally not simple and our related kinetic studies on other metal ions in methanol-water mixtures (2-4, 19) lead us to conclude that deviations in the value of Eapo*will depend on the composition of the inner coordination sphere of the solvated mercuric ion as well as on the dielectric effect. Therefore, no reasonable basis for estimating EHRo*values in solvents of high methanolic content can be formulated on the basis of present information. To circumvent the need for independent determinations of EaRo*in each desired solvent composition, we have utilized a differential approach, described mathematically by subtracting Equation 7 from Equation 10 to yield
In Equation 11 the subscripts 1 and 2 refer to the relevant values for the system described by Equation 7 (Limiting Curve 11) and Equation 10 (MCmcurve), respectively. It is t o be noted that the terms for EH,O*and K H ~dL o not appear in Equation 11 nor does the activity coefficient term, Y ~ ~ + ~Thus * . a comparison of the potential values of two (18) H. Strehlow in "The Chemistry of Nonaqueous Solvents," Vol. I, J. J. Lagowski, Ed., Academic Press, New York. N.Y., 1966. (19) D. B. Rorabacher and R. W. Taylor, Abstracts, 3rd Inter-
national Conference on Non-Aqueous Solvents, East Lansing, Mich , July 1972. 2342
-200
t
\
Limiting (Hg
' \
- Tetren)
I
x\
I I
2
4
6
6
PH*
Figure 2. pH*-potential curves for tetraethylenepentamine (tetren) complexes in 99 % methanol. All conditions same as for Figure 1 mercury(I1)-ligand solutions, with and without added metal ion, may be used to calculate the only remaining unknown quantity, KYL, providing that the protonation (acid dissociation) constants for the ligand in the specific solvent composition are available for the calculation of cyL. Since these values have now been determined for several polyamines and polyaminocarboxylates in methanol-water solvents ( 5 ) , stability constants for complexes of these ligands can be determined. In practice, even the dependence on protonation constant information may be eliminated if a pH*-independent potential can be established for the HgL+*-' system (Limiting Curve 11) at high pH* where CLL = 1.0, provided further that the formation of mixed hydroxide complexes does not interfere. This behavior appears to be exhibited by the mercury (11)-polyamine systems, yielding improved stability constant values relative to the polyaminocarboxylate systems where pH*-independent potentials were not obtained under the conditions used. Precipitate Formation. As is to be anticipated for solvents of lower dielectric, many ionic species exhibited decreased solubility in the methanolic solvents as evidenced by the appearance of precipitates. Since the formation of these precipitates agected the measured potentials, a n understanding of their nature and effect is pertinent to establishing the significance of the observed behavior. At least five different types of precipitates occurred, singly or together, in the systems studied. These can be identified according to their physical appearance and the potentiometric behavior of the system after precipitate formation. HgO. A yellow precipitate of mercuric oxide formed in all systems at higher pH* after which potential readings typical of Limiting Curve I were obtained. The appearance of this precipitate had no influence on the calculated stability constant values.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
500
500
-
\
450
400
350
w
x
-
300
> VI
>
250
W
200
I50
100
50
2
4
8
6
10
12
PH*
Figure 3. pH*-potential curves for trans-1,2-diaminocyclohexane-N,N,N',N' tetraacetate ion (CDTA) complexes in 99 methanol. All conditions same as for Figure 1
-
Hg. The appearance of a black precipitate occurred in rare instances. In such cases, the addition of chloride ion t o the stock Hg(C104)?solution revealed a positive test for Hg(1) which presumably disproportionated upon the addition of the strong ligand to yield elemental mercury. The Hg(C10& solution was then discarded and a new solution prepared. M(OH)? or M(OCH&. A gelatinous precipitate occurred at higher pH* values in many systems causing the potential, although steady, to decrease gradually with increasing pH* with a slope frequently paralleling that of the limiting curves. These observations imply the formation of metal hydroxides or methoxides. Depending on the constancy of the potential readings prior to the appearance of such a precipitate, it was sometimes feasible to evaluate or estimate K M L in such cases. Hgl'[Hgl*L]. In a few polyaminocarboxykdte systems, a finely divided white precipitate formed in the region of pH*4, redissolving at higher pH* and causing a potential behavior similar t o that observed upon metal hydroxide formation. The behavior and appearance of this precipitate was essentially identical to that observed in aqueous media by Schmid and Reilley for ethylenediaminetetraacetate ion (EDTA) (14) and by Aikens and Bahbah for CDTA (20)-both sets of workers indicating that the compound was a Hg(1) salt of the Hg(I1)ligand complex. MH,L(?). In the singular case of Cd(1I)-EGTA in 99% methanol, a coarse granular precipitate was observed to form which caused the potential of the system to increase suddenly to that of Limiting Curve I, thus indicating the sudden conversion of all mercury to the uncomplexed state. In view of the concentration levels of reagents present, the most logical assignment of this species would seem to be CdH:EGTA. (20) D. A. Aikens and F. J . Rahbah, ANAL.CHEM., 39, 646 (1967).
2
4
IO
I2
pH*
Figure 4. pH*-potential curves for ethylene glycol bis(p-aminoethylether) N,N,N',N'-tetraacetate ion (EGTA) complexes in 99 % methanol. All conditions same as for Figure 1 Equilibration of potential readings tended to be very slow in the presence of precipitates and the observation of such behavior was generally interpreted as the first evidence of precipitate formation. With the exception of HgO, and in some instances M(OH)2, precipitate formation generally precluded the possibility of obtaining trustworthy stability constant values. In the absence of precipitates, stable readings of 10.005 pH* unit and i1.O mV were achieved in 2-3 minutes in the lower percentage methanol solvents (except at higher pH* regions), but equilibration times up to 15 minutes were required for each titration point as the methanolic content increased due to the sluggish behavior of the glass electrode in the alcoholic media. In the case of the nickel polyamine systems, however, even slower response times were observed, presumably due to the slow kinetics of complex formation ( 4 ) and attempts to obtain a pH*-potential curve for the nickel tetren system were finally abandoned. Examples of the various types of potential behavior are to be seen in Figures 1-4 for the trien, tetren, CDTA, and EGTA systems, respectively. In these figures, the broken or dotted curves represent the behavior observed ajier the formation of a precipitate. In those instances where precipitate formation preceded the establishment of a potential plateau [e.g., Co(II), Cu(II), Zn(II), and Cd(I1) in Figure 31, no attempt was made to estimate a stability constant value. Calculation of Stability Constants. Stability constant values were calculated using Equation 11 by assuming that, in the region of the potential plateaus for the M-" curves, the values of [HgL+2-b]i,[HgLt2-*I?,[M-%, [ELIi, and [ML,+m-bl? were each equal to 1.000 X lO-3M under the conditions used for these measurements. The E? value was taken as the
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
2343
Table I. Stability Constants for Trien Complexes in Methanol-Water Solvents at 25 “C, p = 0.1M (NaC104)
z
Wt CHsOH 0 40 65 80 90
95 99
Ni(I1) 14.la 14.62b 13.13b 13.31b ... 11.55b 13.84b
log KYL Cu(I1) Zn(I1) 20.15 11.9a 19.31 12.94 20.7 12.26 21.42 13.23 21.79 13.85 22.60 14.33 23.26 14.61
Cd(I1) 10.8a 11.95 12.05 12.76 13.21 13.60 13.96
a C. N. Reilley and R. W. Schmid, J. Elisha MitcheN Sci. Soc., 73, 279 (1957).
Values for Ni(I1)-trien are questionable because of relatively slow formation kinetics (ref. 4 ) . Table 11. Stability Constants for Tetren Complexes in Methanol-Water Solvents at 25 OC, p = 0.1M (NaC104) Wt log KXL CH3OH CU(I1) Zn (11) Cd(I1) 0 22.9a 15.4O 14 Oa 40 23.15 15.72 14.8 65 23.80 15.61 16.2(?) 80 24.54 17.12 15.70 95 25.90 18.55 16.78 99 26.05 19.00 17.44 a Ref. 11.
and Senzel (23, 24) and by Carr and Swartzfager (25, 26). The nonaqueous protonation constant measurements in the presence of sodium ion indicate that such complexes become more stable with increasing methanol content (5). Since, in the measurement of the pH*-potential curves, sodium ion is present in a 50-fold excess over the metal ion, it is probable that the potential measurements for some polyaminocarboxylate systems a t high pH* are influenced by sodium complexation with the ligand. However, since the same sodium concentration level is present in both the measurement of Limiting Curve I1 and the M+m curves, and 0.10M sodium ion was also present during the determination of the protonation constants (5), any effects due to sodium ion should cancel. The competitive equilibrium illustrated in Equation 8 is also complicated by the possibilities of protonated and hydroxy (or methoxy) metal-ligand complex species as represented by the scheme
z
Table 111. Stability Constants for CDTA Complexes in Methanol-Water Solvents at 25 “C, p = 0.1M (NaC10J
z
Wt CH3OH 0
99
log KXL
Mg(I1) 10.3a 10.2
Ca(I1) 12.3a 9.4, 9.6*
Ni(I1) 19.4a 15.9, 15.5, 13.8(?)*
L. G. Sillin and A. E. Martell, “Stability Constants,” Special Publication No. 17, The Chemical Society, London, 1964. More than one potential plateau observed.
median potential value along the potential plateau region of the M+m curve. For the polyamines, where the Limiting Curve I1 established a potential plateau at high pH*, the El value was taken as the median value in this region with the assumption that ( C Y L ) ~ = 1.0 (see, e . g . , Figure 2 ) . In such cases the entire calculation was independent of pH* readings and protonation constant values. Where no plateau was established for Limiting Curve I1 (see Figures 3 and 4), several El values were taken from the limiting curve and the respective values calculated via Equation 6 using the protonation constants previously reported (5). Interferences in Polyaminocarboxylate Systems. It should be noted that 0.10M sodium ion was present in all solutions as a result of the NaC104 used for ionic strength control. In the case of the polyaminocarboxylates, Schwarzenbach and Ackermann (21) originally noted that sodium forms a cornplex with EDTA in aqueous solution and Anderegg (22) has confirmed the generality of this behavior for a series of related ligands. Similar results have also been reported by Sudmeier (21) G. Schwarzenbach and H. Ackermann, Hell;. Chim. Acta, 30, 1798 (1947). (22) G. Anderegg, ibid., 50, 2333 (1967). 2344
(HgHzL+4-b
1
where OR- represents either OH- or CH30-. Most of these species have been reported previously for some aqueous systems. Aikens and Bahbah (20) describe the potentiometric behavior when HgHL and AlHL are the predominant species present. Holloway and Reilley (15) report a method for compensating the potential for the formation of Hg(0H)L in aqueous solution. The effect of MHL, MH2L, HgHL, and HgH2L on pH*-potential diagrams has also been shown by these same authors. Their findings indicate that the presence of these species causes pronounced deviations of the potential in the expected pH*-independent potential plateau region. For some polyaminocarboxylate systems included in this study, more than one potential plateau region was observed (Figures 3 and 4). These “extra” plateaus presumably indicate the formation of various species depicted in Equation 12. However, in the absence of other identifying information in the nonaqueous solvents, the nature of a species existing a t a particular plateau must remain speculative. In such cases we have chosen to list stability constant values calculated for each definitive plateau as if it represented the ML+m-b species. From the appearance of Limiting Curve I1 for Hg(I1)CDTA and -EGTA at high pH* values (Figures 3, 4), it is suggested that the species Hg(0H)L is implicated. Since potential readings in this region were not used for the stability constant calculations, however, this behavior did not influence the reported values for systems involving these ligands. Stability Constant Values. The logarithmic stability constant values calculated for all systems studied are listed in Tables I-IV for trien, tetren, CDTA, and EGTA, respectively. In the case of the latter two ligands, where the calculations were dependent on measured protonation constants, the stability constant values calculated using El values a t varying pH* show considerable variation, generally trending (23) J. L. Sudmeier and A. J. Senzel, ANAL.CHEM.,40, 1693 (1968). (24) J. L. Sudmeier and A. J. Senzel, J . Amer. Chem. Soc., 90, ‘ 6860 (1968). (25) J. D. Carr and D. G. Swartzfager. ANAL.CHEM.,42, 1238 ‘ (i970). (26) Zbid., 43, 583, 1520 (1971).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972
toward lower K M Lvalues when higher pH* readings were used. On the basis of similarly observed behavior for the polyamine systems, where presumably accurate KMLvalues were obtained at high pH*, a reasonably short extrapolation was made to obtain the values listed in the Tables on the assumption that similar behavior would be maintained as (CY L ) ~ approached unity. DISCUSSION
Stability Constant Trends for Polyamine Complexes. As noted in Tables I and 11, the stability constant values for the Cu(II), Cd(II), and Zn(I1) complexes of trien and tetren show a general increase with increasing methanol content of the solvent. In fact, taking experimental errors into account, the stability constant trends for these six complexes are remarkably similar with the rate of increase accelerating as anhydrous methanol is approached, the average increase amounting to more than 1000-fold on going from water to 99 % methanol. The different and seemingly erratic behavior of the Ni(I1)-trien complex may be attributable to the relatively slow formation rate of this complex ( 4 ) . As previously noted, this sluggish kinetic behavior precluded the measurement of the Ni(I1)-tetren stability constant altogether. With the exception of Ni(I1)-trien, the larger stability constants observed in the more methanolic solvents for the polyamine complexes indicate that such solvents may be used to analytical advantage for complexes of this type. From a practical standpoint, however, it is the values of the conditional stability constants [cy.,Schwarzenbach’s “apparent formation constants” (27)] which are of significance. Taking into account the side reactions with hydrogen and hydroxide (or methoxide) ions, the conditional stability constant may be defined as (28)
In the systems under consideration, the alpha coefficients (side reaction coefficients) involving the protonation and/or hydrolysis (or methanolysis) of the complex and the metal ion ( C Y M L and C Y M , respectively) cannot be calculated because of a lack of relevant thermodynamic data in the mixed solvents. By correlation to aqueous systems, however, it can be inferred that C Y M Lis approximately unity for these complexes except for very acidic or very basic media. Accordingly, the C Y M coefficient will be unity in acidic media but may increase significantly in basic media, particularly in the case of Cu(I1). For the basic ligands involved in this study, however, the most important variable is the CYLcoefficient defined by Equation 6. The logarithmic values of CYL for trien and tetren at integral pH* values are listed in Tables V and VI, respectively, for the solvent compositions considered in this work. These then permit the calculation of the conditional stability constants which take into account only the extent of ligand protonation (27, 28), viz.,
K M L=~ KML/CYL
(14)
Of particular analytical importance is the fact that, whereas the K M Lvalues for the trien and tetren complexes show a general increasing trend with increasing methanol content, the CYL values, for equivalent values of pH*, pass through a minimum in the region of 65-80 methanol reflecting the ~
(27) G. Schwarzenbach, “Complexornetric Titrations,” Methuen and Co., Ltd., London, 1957, p xvii. (28) A. Ringbom, “Complexation in Analytical Chemistry,” Interscience, New York, N.Y., 1963, pp 36-54.
Table IV. Stability Constants for EGTA Complexes in Methanol-Water Solvents at 25 “C, p = 0.1M (NaC104) Wt % CH,OH
log KML
Mg(I1) Ca(I1) Co(I1) Cd(1I) 0 5.4” 10.9 12.3a 16.7” 99 6.3* 11.1 13.5 =16.@ L. G. SillCn and A. E. Martell, “Stability Constants,” Special Publication No. 17, The Chemical Society, London, 1964. Two close-lying potential plateaus observed. e Precipitation interfered beyond the point of estimation. Table V. Log CYLValues for Trien in Methanol-Water Solvents at 25 “C, p = 0.1M. (Calculated from Equation 6)
PH* 0 % 0 29.54
1 25.54 2 21.57 3 17.68 4 14.27 5 11.17 6 8.22 75.60 8 3.44 9 1.60 100.40 11 0.05 12 0.01 13 0
40% 26.90 22.92 19.04 15.59 12.50 9.52 6.69 4.34 2.34 0.79 0.12 0.01
Table VI.
PH*
0%
0
35.61 30.63 25.76 21.30 17.28 13.68 10.53 7.52 4.62 2.20 0.63
1 2 3 4 5 6 7 8 9 10 11
12 13
0.08 0 0
0 0
log CYL 80% 26.58 22.61 18.81 15.48 12.43 9.45 6.67 4.36 2.38 0.83 0.15 0.02
65% 25.83 21.87 18.11 14.83 11.79 8.82 6.09 3.85 1.92 0.55 0.08 0.01 0 0
90% 28.21 24.22 20.33 16.83 13.73 10.72 7.82 5.32 3.23 1.43 0.34 0.05
0 0
0 0
95% 29.52 25.53 21.58 17.93 14.75 11.73 8.78 6.13 3.96 2.03 0.62 0.09 0.01 0
99% 32.50 28.50 24.52 20.67 17.26 14.18 11.18 8.28 5.75 3.64 1.78 0.50 0.07 0.01
Log CYLValues for Tetren in Methanol-Water Solvents at 25 “C, p = 0.1M. (Calculated from Equation 6)
40% 33.24 28.30 23.62 19.44 15.63 12.31 9.27 6.29 3.49 1.35 0.28 0.03 0 0
log f f L 65% 80% 32.38 32.84 27.89 27.40 23.18 22.58 18.98 18.40 15.00 15.32 11.94 12.15 8.94 9.11 5.97 6.15 3.20 3.32 1.18 1.20 0.23 0.23 0.03 0.03 0 0
0 0
95% 36.01 31.03 26.20 21.85 17.99 14.67 11.62 8.61 5.65 2.93 1.00 0.18 0.02 0
99% 38.64 33.67 28.88 24.57 20.58 16.94 13.76 10.73 7.74 4.80 2.23 0.63 0.09 0.01
minima in the K=jrn*values which were previously reported ( 5 ) . As a result, application of the (YL corrections to the KMLvalues according to Equation 14 yields values of KML! which, for comparable pH* values (below pH* lo), pass through a maximum in the region of 80% methanol. This is illustrated for Cu(I1)-tetren in Figure 5 where the pH* profile of log K M L t is plotted for each solvent composition relative to the corresponding aqueous values, ciz., A(1og K M L ~=) (log KMLT)mixed
solvent
- (log K M L ~ ) H(15) ~O
Since, as noted previously, the values of and CYML should be close to unity in neutral or slightly acidic solutions, (Equation L), 13) will also pass through the values of K . \ I ~ L ~ ( M a maximum in the region of 80% methanol for pH*
