Complexlng of Ni(1l) and Co(l1) by PMA
433
Complexing of Nickel(l1) and Cobalt(l1) by a Polymethacrylic Acid Gel and Its Linear Polyelectrolyte Analog la W. M. Anspachlb and J. A. Marinsky* Chemistry Department, State University of New Yo& at Buffalo, Buffalo, New York 14264 (Received June 28, 1974)
An earlier study of the interaction of trace concentrations of M(I1) ions with polyacids reported by Marinsky has been extended to consider the complexation behavior of Co(I1) and Ni(I1) in metal-crowded systems of a cross-linked polymethacrylic acid (PMA) gel and its linear polymer analog. Potentiometric, polarographic, and spectral measurements have been made to facilitate the experimental program. Concepts, shown to be valid in the earlier research, have been used to correct for the effect of the large and variable electric field a t the surface of the polyion in different experimental situations on the number distribution of the mobile ions a t the site of the complexation reaction. The earlier observation that the dominant complex species in these systems is an ion pair, MA+, has been confirmed. The stability constant determined for CoA+ in both the PMA gel and its linear analog duplicate the value obtained in the earlier studies after appropriate corrections are made for the effect of the bulk electrolyte used to fix the ionic strength of the systems studied. The stability of the CoA+ and NiA+ complex is identical, within the experimental error range of the measurements.
Introduction It was pointed out earlier by Marinsky2 that the study of metal-ion binding in polyelectrolyte systems has been hampered by the lack of a generalized analytical treatment of data obtained with such systems. The problem originates from inability to assess the concentration of mobile ions at the surface of the polyion at the site of the complexation reaction. Accurate estimate of the concentration of ligand and complex species is not straightforward as well. In their examination of M(I1)-PMA systems Gregor and coworkers3 and Mandel and Leyte4 sought only to overcome the second of these problems. The extended Henderson-Hasselbach equation
was used by Gregor, et al., for this purpose. This equation has been shown to give an empirical representation of the titration curve for many polyelectrolytes, K,, corresponding to the intrinsic dissociation constant of the polyacid and the constant corrective parameter n accounting for deviation of the system from ideality a t a selected acid concentration and ionic strength as the degree of dissociation of the acid, a , is varied. By determining Ka and n for the polyacid in the absence of the complexing ion, the value of [A-] for the metal-polyacid interacting system could be calculated by an iterative procedure using
where the term [A-]/([AtJ - [A-1) is substituted for a/1 a in eq 1 to correct for the functional groups bound to the metal ion, At representing the total polyacid concentration (dissociated, associated, and metal-bound). Mandel and Leyte4 used a more direct approach to the evaluation of [A-1. A titration curve of the polyacid in the presence of neutral salt was transformed into a plot of p([H+]/[HA]) us. p[A-]. This plot was then used to estimate the concentration of [A-] for the metal-ion containing
solutions a t the polyacid and neutral salt concentration of the reference system. With the value of [A-] available by either of these approaches the average ligand coordination number, 7, of M(II), the metal ion in the system under investigation, was computed by use of
-j
= --[At1 - [HA1 - [A"] Mt
If both the numerator and denominator of eq 3 are divided by M(II), the concentration of mobile M(I1) ion
With M(I1)-monomeric ligand systems the activity of M(I1) is maintained constant by the use of a fixed concentration of simple electrolyte which does not complex the M(I1) ion. The expression for 7 can then be used to deduce the value of bj for any sequence of complex species that may form in the system since the values of /3j will be uniquely defined a t the experimental ionic strength.5 With M(I1)-polyligand systems, however, only the use of simple electrolyte a t a very high level of concentration can maintain the activity of M(I1) ion invariant a t the site of the reaction. Since insolubility of the polyelectrolyte is usually a consequence of this experimental condition the concentration level of simple electrolyte in such studies is most often insufficient to shield effectively the electric field a t the surface of the polyion &e., a t the site of complexation) which can vary considerably with varying experimental conditions. Neglect of its effect on the activity of the mobile M(I1) ions prevents the resolution of uniquely invariThe Journal of Physical Chemistry, Vol. 79, No. 5, 7975
434
W. M . Anspach and J. A. Marinsky
ant p, values.2 Inability to analyze the effect of the electric zene and PMA), also received from the Rohm and Haas field a t the surface of the polyion on the activity of the moCo., was first treated with HCl. After complete removal of bile M(II) ions has been the important deterrent to the the acid was assured by exhaustive washing with deionized meaningful interpretation of metal-ion binding in polyelecwater the resin was air dried for 48 hr prior to storage in a trolyte systems such as those carried out by Gregor, et ~ 1 . , ~ sealed polyethylene bottle. Ethylenediaminetetraacetic acid dihydrate (EDTA and Mandel and L e ~ t e . ~ 2H20, Baker Analyzed Reagent) used in the standardizaScatchard and coworkers6 in their studies of the binding of small ions to proteins have attempted to correct for such tion of Ni and C O S Osolutions ~~ was dried for 60 hr at 80° perturbations in their systems by estimating the electric to ensure correct water c ~ n t e n t .Glycine ~ hydrochloride, field a t the surface of the protein which is assumed to have supplied by the Eastman Organic Chemical Division, was its charge uniformally distributed over a spherical surface. purified by two recrystallizations from 95% methanol. However, even this approach to the problem is inadequate Water first distilled and then passed through two multibed ion-exchange columns (Ilco-Way Research Model) was since accurate estimate of this variable term for the evaluastored in sealed polyethylene bottles to minimize the prestion of the effective concentration of mobile ions a t the site of complexation is most difficult to achieve because of unence of Cog. Prior to use it was boiled to remove any traces certainty with respect to the actual conformational properof coz. ties of the protein molecule in the course of experimentaThe chemicals listed below were used as received: NiS04, tion. COS&, and Murexide were Baker Analyzed Reagents; glacial acetic acid, concentrated HC1, and concentrated Recently an experimental method for the evaluation of NH40H were from Baker and Adamson, Inc.; NaOH (0.1 the number distribution of mobile metal ions a t the sites of complexation reaction was proposed by Marinsky.2 It was N ) , NazS04, and (2.5 N ) were Fisher Certified Resuggested that the potential difference between the surface agents; HCl (0.1 N ) was obtained from Will Scientific of a polyion and the region of the solution in which the poCorp.; Titron X-100, lot no. 3998, was from the Rohm and tential vanishes can be measured by a chemical reaction Haas Co. which involves mobile ions competing with the metal ions ( b ) Potentiometric Titrations. ( 1 ) M(II)-PMA Gel Sysfor the ionized groups fixed on the polymer. A reaction of tems. Periodic pH surveillance showed that a 40-day interthis type that can be easily monitored potentiometrically is val was required for representative gel-solution systems to the neutralization of weak polyacids or polybases which is reach equilibrium and it was necessary to work with indidescribed by the well-known equation vidual samples to facilitate the completion of meaningful potentiometric titration curves. Four sets for each of the cy pH = pK + log metals investigated were consequently prepared for this 1 - a purpose. Each set consisted of a t least ten 100.0-ml samples which contained an identical amount of the hydrogen-form resin (0.100 f 0.0005 g = 1 mequiv) a t degrees of neutralization varying from 0.1 to 0.9. The metal to initial acid molar ratio was made 0:1, 1:2, 1:4, and 1:6 in the respective corresponding to the potential at the surface of the posets to examine coordination behavior as a function of liglyion. By knowing the intrinsic dissociation constant, K,, and concentration. The concentration of NazS04, the neufor the reaction, the fraction of reacted and unreacted tral salt employed, was 0.05 M in each sample. The samples groups and the chemical potential of the mobile Hf ions were shaken a minimum of 40 days at the ambient temperwhere no electrostatic field is encountered, the deviation ature of 24 f 2O prior to potentiometric investigation of the from ideality a t the site of reaction, pAK, is available a t supernatant solution. every experimental situation. In gel systems a Donnan poAll pH measurements were made with a glass-saturated tential term supplements the electrostatic contribution to calomel combined electrode system at the ambient temperpAK? Examination of this reaction during complexation of ature using a Radiometer Model 4 pH meter. The electrode M(I1) ion by a weak polyacid by measuring pH yields the was adjusted with standard buffer solutions (pH 4.00, 7.00, following information. and 10.00) over the pH range of the experiment. [HA][K,]/[H'] = [A-IAK-' (7 ) (2) M(II)-PMA Systems. The component concentrations It has been experimentally shown2B8 that a t equilibrium that were employed for the M(I1)-PMA gel systems were M(I1) ion present at trace-level concentration in both PMA essentially duplicated in this parallel investigation of M(I1) and polyacrylic (PAA) acid is exposed to the same potenion binding by the linear analog of the cross-linked PMA tial, as the Hf ion in the metal-polyion ion pair comgel. Since equilibration times were reasonably short the plex, MA+, that is dominant in these systems and that the course of the potentiometric titration for a given experiterm (AK-1)2 provides an accurate assessment of the demental condition was followed on a single sample, care viation from ideality of the M(I1) ions at the site of reacbeing taken to exclude COz from the system by covering tion. the sample with a stream of Nz. It was the objective of this research to demonstrate fur( 3 ) Calibration of Combined Glass-Calomel Electrode. ther the validity of this observation in metal-crowded PMA Potentiometric titrations of glycine hydrochloride and acegels and their linear polymer analog. tic acid were carried out according to the method of Eger, Anspach, and Marinskylo to refine the preliminary calibraExperimental Section tion of the glass electrode that was effected with standard buffers. During the course of calibration, the absence of ( a ) Chemicals. A 23% solution of polymethacrylic acid COz in the solutions was ensured as before with presaturat(PMA), molecular weight 5800, was used as received from ed Nz and the temperature of the system was maintained the Rohm and Haas Co., Philadelphia, Pa. The approxiconstant at 25 f 0 . 1 O . The reproducible behavior of the mately 1%cross-linked PMA gel (copolymer of divinylbenThe Journal of Physical Chemistry, Vol. 79, No. 5, 1975
Complexingof Ni(l1) and Co(ll) by PMA
435
TABLE I: Potentiometric Titration Dataa 0.0000121 cos04 M(II)/A, = o
0.00486121 C0S04 Co(II)/A, = 1/2
0.00243M C0S04 Co(II)/A, = 1/4
0.00164M C0S04 CO(II)/A, = 1/6
-
b
PHmew
PHcnrr
PHme,
PHcorr
PHme,
PHcon
PH,
PHcnrr
0.0 0.1
4.048 4.896 5.414 5.758 6.032 6.279 6.518
4.077 4.917 5.427 5.765 6.033 6.274 6.507 6.813 7.096
3.961 4.709 5.127 5.367 5.597 5.822 6.026 6.232 6.479 6.862
3.992 4.732 5.145 5.381 5.607 5.827 6.027 6.228 6.469 6.842
4.012 4.788 5.214 5.579 5.764 6.005 6.264 6.522 6.813
4.042 4.810 5.23 1 5.589 5.771 6.006 6.259 6.511 6.794
3.994 4.981 5.258 5.557 5.816 6.069 6.318 6.592 6.900 7.352
4.024 5.001 5.274 5.568 5.822 6.069 6.312 6.579 6.879 7.318
0.2 0.3 0.4 0.5 0.6 0.7
0.8 0.9
7.124
0.00486M NiS04 Ni(II)/A, = 1/2
0.00243M NiSO, Ni(II)/A, = 1/4
0.00163121 NiS04 Ni(II)/AT = 1/6
4.043 4.072 4.159 4.186 3.900 4.633 4.657 4.784 4.806 4.807 5.034 5.053 5.212 5.229 5.258 5.386 5.400 5.516 5.528 5.540 5.563 5.574 5.748 5.755 5.803 5.780 5.786 5.998 6.000 6.130 5.968 5.970 6.242 6.238 6.318 6.206 6.203 6.516 6.505 6.606 6.546 6.534 6.823 6.804 6.893 6.833 6.814 7.202 7.172 7.248 a 1.00 mequiv of PMA gel; 1.00 mequiv of NaOH; 0.05 M NaZS04; total volume = 100.00 ml after addition of 0.100 "zSO4.
3.932 4.829 5.274 5.551 5.809 6.128 6.312 6.593 6.872 7.217
0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
electrode used over the period of the experimental program was demonstrated to be within 0.01 pH unit by repeated calibrations at spaced time intervals. ( 4 ) Polarographic Analysis of M ( I I ) in Equilibrated M ( I I ) - P M A Gel Systems. The equilibrium concentrations of the M(I1) ion remaining in solution above the gel samples were determined polarographically with a Radiometer polariter P04. The Ni(I1) and Co(I1) equilibrium solutions were made 1.0 M in NH40H and NH4C1 and 0.02% in Triton X-100 to effect fairly well-defined reversible waves (E112" = -1.30 V; E1,/zNi= -1.09 V)." ( c ) Spectral Investigations. A Cary Model 14 recording spectrophotometer was employed to examine spectral features of the Ni-PMA and Co-PMA systems at various degrees of neutralization and at the specified metal to acid ratios in the wavelength region of maximum absorption for each of these ions. Because of the low absorption coefficient of these metal ions, samples were more concentrated by a factor of 2 than in the potentiometric studies. Results a n d Discussion ( a ) T h e Stability of N i ( I I ) and Co(II)-PMA Gel Complexes. The representative potentiometric data that were obtained during investigation of the Ni(I1)- and Co(I1)PMA gel systems selected for study are presented in Table I. The symbol b at the head of the first column of the table refers to the fractional neutralization value of standard alkali added to each sample. These data were employed in eq 7 to evaluate the term [A-] AK-l. The value of K,, the intrinsic dissociation constant of the repeating monomer unit of the PMA gel that was used for this computation, was obtained by extrapola-
4.0 I
0.2
I
I
0.4
I
I
0.6
,
,
,
0.0
a
Figure 1. Potentiometric study of polymethacrylic acid system: 0.01 M PMA in 0.05 M Na2S04.
tion of the potentiometric data obtained for the linear PMA analog of the gel in 0.05 M NaS04 as shown in Figure 1. The extrapolation of the upper curve is by a straight line extension of the data as it should be in this region of low charge density where the Debye-Huckel approximation is valid. The long extrapolation of the lower line must be The Journal of Physical Chemistry, Vol. 79, No. 5, 1975
W. M. Anspach and J. A. Marinsky
436
TABLE 111:Evaluation of the Formation Constant of the Ni(I1)-PMA Gel Complex
TABLE 11: Analysis of Potentiometric and Polarographic Data
A,/Ni b
[A'] A T '
a0
0.8 0.9
AT/Ni(II) = 2 6.042 X 0.973 1.341 X lo-' 0.885 2.613 X lom2 0.808 3.344 x 10-2 0.733 4.542 X low2 0.658 5.551 X 10" 0.577 7.121 x lom2 0.540 1.017 x lo-* 0.427 9.693 X 0.362
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
8.530 2.013 3.510 5.075 7.437 1.029 1.428 1.895 2.211
0.3 0.4 0.5 0.6 0.7
AT/Ni(II) = 6 3.701 x lo-' 0.628 5.748 X lo-' 0.466 9.987 X lo-' 0.361 1.221 x 10-1 0.230 1.785 x 10" 0.168
0.1 0.2 0.3 0.4 0.5 0.6 0.7
AT/Ni(II) = 4 0.904 10" 0.792 10" 0.663 lom2 0.575 10-2 0.408 lo-* 0.333 lo-' 0.246 lo-' 0.184 10-1 0.137
x lom3 X
x x x x x X
x
2
A,/Ni = 4
1 - a,
4.593 9.687 9.093 10.894 11.444 13.207 11.963 13.196 18.178 8.02 13 .O 14.5 14.6 19.5 19.4 21.4 23.4 28.5 15.9 20.0 17.7 27.4 27.8
slightly curved to reach the same intercept value. Such curvature is to be expected in the higher charge density region.12 The K , of 1.48 X that is determined from this analysis of the potentiometric data is in good agreement with the dissociation constant reported for isobutyric acid, the repeating monomer unit of this polymer, duplicating a similar potentiometric examination of PMA by Arnold and 0~erbeek.l~ The fraction of total M(II), ao, present as free M(I1) ion in the various equilibrium mixtures was obtained directly from polarographic analysis, as described in the Experimental Section, and permitted evaluation of the term
(1 - a,)/a,AK-'[A~] The results of these computations are presented in Table I1 for the Ni(I1)-containing systems. A similar analysis of the data is obtained with the Co(I1)-containing system. Since it was shown earlier by Marinsky2 that
and that j = 1 in these systems when trace concentration levels of M(I1) are used,2J?division by AK-l of the experimental term listed in Table I1 should yield a number that is constant and equal to the value of P I , the formation constant of the dominant ion-pair species, MA+, that is to be expected on this basis. In order to obtain the value of AK-l at each experimental situation the concentration of MA+ was first computed by subtracting the measured concentration of free M(I1) ion in the equilibrated systems from MT, the total metal concentration employed. This number added to the conThe Journal of Physical Chemistry, Vol. 79, No. 5, 7975
=
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Av Std dev (a) Probable error (0.674~)
0.708 1.057 0.726 0.884 0.841 0.939 0.802 0.678 1.106 0.860 0.127 0.086
A,/Ni
1 - an
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.756 0.976 0.904 0.855 0.934 0.825 0.776 0.746 0.892 0.852 0.077 0.052
= 6
1 - a,
0.3 0.4 0.5 0.6 0.7
1.033 1,090 0.702 1.065 0.883 0.955 0.145 0.097
centration of undissociated polyacid, [HA,], calculable from stoichiometric consideration, was subtracted from AT, the total initial concentration of polyacid, to obtain the concentration value of [A-] for division into the experimentally determined [AK-l] [A-] value. The results of this treatment of the data are presented in Table 111. The precision range of the pH measurements is believed to be 0.03 pH units, introducing the possibility of a 14% error interval in the computed (AK-1)2[A-] term. Additional uncertainty introduced to this term in the computation of AK-' by the f0.25% error possible in the analysis of [AT] and [HA,], respectively, and the f2% error limit in the polarographic analysis of free metal ion is no more than an additional 1-2%. The potential error range in the value of (1 - ao)/ao due to the 4% uncertainty limit in the analysis of free metal ion, however, is slightly greater than 4% when this term is somewhat larger than unity, 8%at unity, and as much as 15% when its value decreases to as low as 0.03. On the basis of this analysis an error range of -30% that is possible at the lowest a! value is expected to be narrowed to -20% over the rest of the polyacid-neutralization range studied. Although there is sizeable scatter in the (1 - ao)/ UO(AK-~)~[A values ] that are resolved in Table I11 for the Ni(I1)-PMA gel systems studied standard deviation from the constancy expected in each set of measurements (15,9, and 15%)is approximately the error range projected for the evaluation of this term. In addition, almost 50% (44%) of the experimental numbers fall within the "probable error" range. From statistical considerations this result is to be expected in the measurement of a constant term. The estimate that ion pairing is predominant in these metal-crowded systems as it is in the trace-metal-polyacid systems studied earlier298 is fully supported by this correlation of the data. This result is further supported in Figure 2. The ordinates of this plot, (1 - U ~ ) / U O ( A K - ~ ) ~and [ A - [A-l-l, ]~ obtained by dividing both sides of eq 8 by [A-] should yield a straight line with a slope of PI, and an intercept of Pz. The straight line of slope 0.95 ((31) that is drawn through the data points obtained for all three systems intercepts the or-
Complexlng of Ni(1l) and Co(I1) by PMA
437
TABLE IV: Comparison of Free.Ligand Concentration Computations
0.00163M NiS04
0.00243M NiS04
0.00486M NiS04
P[A'l
piA-1
pLA-1
P[A'l
(stoich)
(M-L)
P[A'l (stoich)
P[A'l
b
(M-L)
(s toich)
(M-L)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
3.072 2.836 2.618 2.504 2.402 2.324 2.248 2.190 2.130
3.041 2.788 2.655 2.536 2.383 2.336 2.225 2.197 2.175
3.093 2.821 2.659 2.527 2.448 2.355 2.286 2.221 2.161
3.060 2.817 2.668 2.570 2.460 2.376 2.293 2.234 2.196
3.031 2.835 2.683 2.567 2.476 2.404 2.321 2.283 2.229
3.155 2.930 2.747 2.68 2.597 2.543 2.473 2.398 2.395
TABLE V: Evaluation of the Formation Constant of the Co(I1)-PMA (Linear) Complex
iul9
Co/A, = 1/6 b
* e/
/
/
I
[PI - ' X ! O - ~
Flgure 2. Graphical analysis of polarographic and potentiometric study of NI(II)-PMA gel system.
dinate at zero to show quite dramatically that 02 must, indeed, be small if the MA2 species does indeed exist. As expected the data scatter most severely a t the largest [A-l-l values which correspond to the lowest dissociation condition (a = 0.1). Additional corroborative evidence comes from the observation that in two of the three systems studied the estimate of [A-] with the use of the Mandel-Leyte reference plot method discussed earlier is in good agreement with our computations of [A-] that are based on the assumption of a dominant ion-pair species (Table IV). In the system where there is discrepancy between the two computed values of [A-] the initial ratio of Ni(I1) to AT is smallest. The apparent enhancement in this system of NiA2 that this result implies is unreasonable since a relatively lower concentration of ligand is available to the Ni(I1). This is a contradiction of the law of mass action. In addition, only 01 is resolvable from the binding data using the [A-] value derived from the Mandel-Leyte analysis. A t the apparent concentration level of NiAz that is indicated by the difference between the concentration of [A-] based on a stoichiometric balance assuming only the existence of NiA+ and the Man-
0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.80 Av Std dev (a) Probable error (0.674~)
Pi
*
0.956 0.902 1.093 0.935 0.832 0.704 0.729 0.830 0.837 1.052 0.887 0.121 0.082
CO/A, = 1/4 Pi
*
1.355 1.213 1.325 1.183 1.307 1.07 1.103 1.013 1.16 1.123
Co/A, = 1/2 P1*
1.41 1.436 1.39 1.37 1.347 1.45 1.43 1.39 1.235 1.227 1.30
del-Leyte analysis, 02 should have been easily resolvable. It must be concluded that in the most metal-crowded system of this study the Mandel-Leyte-based computation is not correct because of the introduction of conformational differences between the Ni(I1)-free and Ni(I1)-containing, but otherwise equivalent systems. Such conformational change would be expected to occur a t higher AJM(I1) ratios in the more flexible linear polyelectrolyte systems that are analyzed in the next section. ( b ) The Stability of Ni(ZI)-Co(ZZ)-PMA(Linear) Complexes. A direct analysis of the free, mobile metal ion in the linear PMA systems studied was not attempted in this part of the research program and it was necessary to use the Mandel-Leyte reference plot method to estimate the concentration of [A-]. By assuming once again that MA+ is the dominant complex species in these systems it was possible to compute a0 and evaluate the term (1 - ao)/ UO(AK-~)~[A-]. The results of these computations for the Co(I1)-PMA (linear) -Na2S04 systems studied are presented in Table V and are representative of the Ni(I1)-containing systems as well. In the least M(I1)-crowded system there is good agreement obtained between Pl(gel) and Pl(linear) and this result is again supportive of the model. As the metal to ligand concentration ratio becomes smaller, the value of 01 drifts slowly to an approximately 40% greatThe Journal of Physical Chemistry, Vol. 79, No. 5, 1975
W. M . Anspach and J. A. Marinsky
438
er value. Metal crowding of the polyelectrolyte apparently modifies the configuration of the macromolecule in such a way that the value of pA is predicted to be increasingly too small and the fraction of M(I1) bound increasingly too high by assuming no effect of metal-ion binding on the polyion configuration that the Mandel-Leyte approach implies. The effect of this configurational modification appears, as predicted above, at lower M(I1) to AT ratios in the linear molecule because of its higher flexibility. ( c ) Spectral Studies. The spectral properties of the Ni(I1)- and Co(I1)-containing systems in the presence and absence of PMA are not noticeably different. No shift in maxima is observed. A slight enhancement of the molar extinction coefficient is just detectable.
= &so4 (0.05)(675)2 = 0.023/3Mm4 (9) From this expression MMS04
= o*23/3MS04(MM(II,)
(10)
Since the sum of MS04 and free, mobile M(I1) ion ( Z:MM(II)~~,,,) is measured in the polarographic analysis of the equilibrated solution phase the concentration of free metal ion in these systems is 0*023&,W4(Mbl(11))+ M M ( I I )
CMM(II)soln
and
Concluding Remarks The validity of the experimental method used to assess the concentration of mobile ions at the site of the complexation reaction, confirmed earlier by trace-metal-polyacid complexation studies,* has been further supported, by this investigation. Unambiguous confirmation of the earlier demonstrations of the existence of an ion pair as the dominant complex species that is formed in the M(I1)-PMA systems studied has been made possible by its use. The formation constant of this complex species at a fixed ionic strength has been found to be identical in the cross-linked PMA gel and its linear polymer analog: also, @ c o ~=+@NiA+. In the method used to analyze the data, however, the evaluation of the concentration of free mobile M(I1) ions that are competing with free mobile H+ ions for ligand at the surface of the polyion is based on the measured activity of H+ion in the solution away from the effect of the potential field at the site of complexation. For a comparable examination of the mobile M(I1) ions at the site of complexation, their effective concentration in the solution proper is needed in place of their measured or computed concentration; as a consequence the value of @MA,presented earlier in this work, needs to be modified as it was previouslys by taking this aspect into account. In the polarographic analysis of metal in the solution phase in equilibrium with PMA gel the correction procedure is complicated by the fact that total M(I1) present as the ion pair MS04, as well as free M(I1) ion, is measured. With the analogous linear PMA-M(I1) systems the total M(I1) is also obtained. In order to determine the effective concentration of free, mobile M(I1) ion in these systems (1) an appropriate correction for the presence of MS04 as well as (2) a reasonably correct estimate of the activity coefficient value for the net M(I1) ion in these solutions must be introduced into the computation. Analysis of the first of these problems can be achieved by consideration of the following equilibrium reaction of M(I1) ion M(I1)
+ SO4
cl MSOd
in 0.05 M Na2S04. The stability constant of c o s 0 4 and NiS04 in HzO at 25' has been reported14 to be 2.95 X lo2 and 2.5 X lo2, respectively. It can be assumed that the activity coefficient of the neutral ion pair is unity and that the mean activity coefficient of the dissociated electrolyte, M2+S042-, is calculable with sufficient accuracy by the Davies15 modification of the extended form of the DebyeHuckel equation at the ionic strength defined by the NazS04. With this approach y f M2+S04 = 0.675 and the ratio of MS04 to M(I1) is given by The Journal of Physical Chemistry, Vol. 79,No. 5, 1975
Its effective concentration is
With this analysis _ " I
L;Mco(rl)soln 7.985
(0.675) = 0 . 0 8 4 C M c , ( 1 1 ) ~ ~(13) ~~
and f l c o ~ += 0.9/0.084 = 11,in good agreement with /?CoA+ of 13 obtained in the earlier trace Co-PMA and PAA experiments after correction for the activity coefficient of Co(I1) in 0.1 and 0.4 M NaC104. The observation that an ion pair is a dominant species in the M(I1)-PMA systems studied here is in disagreement with reports in the literature of the presence in significant quantity of the MA2 species in parallel system^.^,^ This incorrect conclusion has been shown in this study to be a direct consequence of error in the assumption that the concentration of [A-] in these systems can be accurately ascertained by transferring exactly the nonideal properties of the metal-free polyacid to the metal-containing but otherwise equivalent polyacid system. Their evaluation of 7, the average coordination number of the metal ion on this basis, eventually exceeded unity and approached a value of 2. This led to the postulate of the existence of MA2 as a dominant complex species in their systems. Our examination of this approach to the evaluation of [A-] and 7 has shown that the value of [A-] deduced by this method of operation leads to the observation that each metal ion is increasingly bound to more than one [A-] as the ratio of M(I1) to AT is decreased in otherwise equivalent systems. It has been pointed out that this observation is a contradiction of the mass-action law. In the gel system where the fraction of free metal ion was available at every experimental situation and analysis of the data with eq 8 could be made using the value of [A-] obtained by the reference plot method to compute AK-l only @Mat was resolvable. Even though the increasing presence of MA2 that was indicated by the analysis of [A-] using the reference plot method of Leyte and Mande14 was sufficiently large to lead to resolution of P M A ~ by this analysis there was absolutely no indication of a second complex species. Acknowledgment. Financial support through Contract No. AT (30-1)-2269 with the United States Atomic Energy Commission is gratefully acknowledged.
Complexation of Cu ( I I) by Polyrnethacrylic Acid
References and Notes (1) (a) Presented in part at the Xth International Conference on Coordination Chemistry, Tokyo and Nikko, Japan, Sept 1967. (b) Abstracted in part from a dissertation submitted to the Faculty of the Graduate School of the State University of New York at Buffalo by W. M. Anspach in partial fulfillment of the requirements for the degree of Master of Arts, 1968. (2) J. A. Marinsky, "Equations for the Evaluatlon of Formation Constants of Complexed ion Species In Polyelectrolyte Systems," in "Ion Exchange and Solvent Extraction-A Series of Advance," Voi. IV, J. A. Marinsky and Y. Marcus, Ed., Marcel Dekker, New York, N.Y., 1973, Chapter 5. (3) H. P. Gregor, L. B. Luttinger, and E. M. Roebl, J. Phys. Chem., 59, 366 (1955). (4) M. Mandel and J. C. Leyte, J. Polym. Sci., Part A-2, 2663 (1964). (5)F. J. C. Rossotti and H. Rossotti, "The Determination of Stability Constants," McGraw-Hili, New York, N.Y., 1961.
439 (6) G. Scatchard and W. T. Yap, J. Amer. Chem. SOC., 86, 3434 (1964). (7) J. A. Marinsky, "ion Exchange," Vol. I, J. A. Marinsky, Ed., Marcel Dekker, New York, N.Y., 1966, Chapter 9. (8) L. Travers and J. A. Marinskv. J. Polvm. Sci.. Part C. Svmoosium No. 47, in press. G. Schwarzenbach, "Compieximetric Titrations," interscience, New York, N.Y., 1957. C. Eger, J. A. Marinsky, and W. M. Anspach, J. lnorg. Nucl. Chem., 30, 1889 (1966). I. M. Kolthoff and J. J. Lingaine, "Polarography," Vol. 11, 2nd ed., Interscience, New York, N.Y., 1952, D. Olander and A. Holtzer, J. Amer. Chem. SOC.,90, 4549 (1968). R . Arnold and J. Th. G. Overbeek, Recl. Trav. Chem. Pays-Bas, 69, 192 (1950). T. 0. Denney and C. B. Monk, Trans. Faraday SOC.,47,992 (1951). C. W. Davies, J. Chem. SOC.,2093 (1938).
- .
Complexation of Copper(l1) by a Polymethacrylic Acid Gelia J. A. Marinsky* and W. M. Anspachlb Chemistry Department, State University of New York at Buffalo, Buffalo, New York 14214 (Received June 28, 1974)
The complexing of Cu(I1) by a polymethacrylic acid gel has been investigated. Potentiometric, polarographic, spectral, and magnetic susceptibility measurements have been employed to facilitate the experimental program. The spectral and magnetic data indicate that metal-metal interaction occurs at low degrees of neutralization. The stability constant of the CuAz species, predominant in the higher neutralization range, i s shown to be comparable in magnitude with the stability constant reported in the literature for copper (acetate)z. The quantitative evaluation of the stability constant is made possible by correcting for cornplication arising from the large and variable electric field at the surface of the polyelectrolyte in the polyion domain and by expressing the concentration of polymer species in terms of the measurable volume of the gel phase.
Introduction In recent s t u d i e ~ it~ has - ~ been shown that for the correct interpretation of complex formation of metal ions with the ionized functional groups of weakly acidic polymers it is necessary to (1) correct for deviation from ideality of these metal ions a t the highly charged surface of the reaction site and when more than a single ligand attaches to the metal ion to (2) express ion concentrations of polymer-contained species in moles/total volume, u, of the polymer which exists as a separate phase in the equilibrated system. The first of these requirements is satisfied by experimental measurement of such deviation from ideality by potentiometric study of the competing equilibrium between HCion and the functional group attached to the polymer's matrix. The potential difference between the surface of the polyion arid the region in which the potential vanishes is measured during pH measurement in the course of neutralization of the metal ion-containing polyacid and is the source of such information, the deviation from ideality of mobile H+ ions a t the site of the reaction being given by the well-known equation
where $(a) corresponds to the potential at the surface of the polyion, z is the charge of the proton, K , is the intrinsic
dissociation constant of the acid, and [A-] and [HA] correspond to the concentration of dissociated and undissociated acid.6 Since the free, mobile metal ions are exposed to the same field their deviation from ideality a t the reaction site, accounting for the valence, 2, of the metal ion, is equal to exp(-ZeJ.(a)lkT). In the metal-bound systems, however, the value of [A-] is not easily a ~ a i l a b l e ~and , ~ , only ~ the term [A-] exp( -tJ.(a)/hT)is accurately known. The second requirement is not easily resolvable because of inaccessibility of the domain volume of charged polymers in solution. The unavailability of such information has frequently led to the use of the incorrect concentration unit, moles per solution volume, V, for all species of the equilibrium solution. The resolution of formation constants based on such expression of the concentration of all species in these two phase systems has as a consequence interfered with a valid analysis of complexation in these systems. Only in the situation where the dominant complex species of the metal, polyacid system is an ion pair, MAZ-l, does this aspect become unimportant with use of this concentration unit. In this situation the volume dimension of the concentration unit cancels in the mass-action expression for PI, the ion-pair formation ~ o n s t a n t . ~When - ~ an additional species such as MA2Z-2 forms, however, use of the accessible but inappropriate concentration unit usually leads to sizable variation in the value of Pz with experimenThe Journal of Physical Chemistry, Vol. 79, No. 5 , 1975
