2388
The Journal of Physical Chemistry, Vol.
J. C. T.
82,No. 22, 1978
Kwak and R. W. P. Nelson
Mean Activity Coefficients for the Simple Electrolyte in Aqueous Mixtures of Polyelectrolyte and Simple Electrolyte. 4. The Systems Nickel Chloride-Nickel Poly(styrenesulfonate), Zinc Chloride-Zinc Poly(styrenesulfonate), and Cadmium Chloride-Cadmium Poly(st yrenesulfonate) Jan C. T. Kwak” and Richard W. P. Nelson Department of Chemlstry, Dalhousle University, Halifax, Nova Scotia, Canada, and Laboratory for Nectrochemistry, Unlverslty of Amsterdam, The Netherlands (Received February 75, 1978) Publlcation costs assisted by the National Research Councll of Canada
Mean molal activity coefficients of the simple electrolyte in aqueous solutions of the Ni, Zn, and Cd salts of poly(styrenesu1fonic acid) (PSA) with added NiC12,ZnC12,or CdC12are reported. Mono-molal concentrations of PSA vary between 0.005 and 0.05 equiv of sulfonate/kg of H20 and at each polyion concentration the ratio of PSA to C1- is varied between 0.25 and 16. An electrochemical cell, with a cation exchange membrane in the appropriate ionic form and an AglAgCl electrode, is used in all three systems. The results show that for all three salts y+/y*O, where y+O is the activity coefficient of the pure added salt at the same concentration as in the polyelectrolyte-simple electrolyte mixture, is within e#xperimentaluncertainty independent of the polyion concentration at a given polyion to coion concentration ratio. The results for y*/y*O of ZnC1, are virtually identical with the MgCl, and CaCl, mixtures studied earlier, while NiCl, and CdClzyield values only slightly lower. The results are compared to Manning’s limiting laws and to the additivity rule.
In previous publi~ationsl-~ (papers 1-3 in this series) we have reported mean molal activity coefficients of the added electrolytes in solutions of polystyrenesulfonate (PSA) salts with added simple electrolyte. Counterions used were Na+, K’, Mg2+, and Ca2+. One of the results was that the activity coefficients of added CaCl, or MgCl, in single counterion systems CaC12-CaPSA or MgC12-MgPSA can be described very closely by the mobile ion-mobile ion interaction corrected form of Manning’s limiting law,214v5 better in fact than is the case in systems with univalent counterions. A similar behavior was reported for salts of carboxymethylcellulose.6 A number of recent papers have focused on the “state of binding” of multivalent metals by polyelectrolytes and especially by biopolymers containing ionic g r o ~ p s , ~and - l ~have pointed out the importance of the long-range Coulombic forces (as opposed to short-range exchange forces). To further study the interaction between polyions and multivalent counterions, and to investigate the possible influence of specific interactions between the polyion functional group and the metal ion over and above the already so important long-range electrostatic effect, we determined the mean activity coefficient of three transition metal chlorides in mixtures with the polystyrenesulfonate salt of the same metal. Only a very limited number of similar studies on polyelectrolyte solutions containing transition metal ions are available, of course partially caused by the fact that only a few POlyanions yield soluble transition metal salts. Constantino et al.ll measured the sodium ion activity in sodium poly(methacry1ic acid) solutions to which divalent metal chloride was added, and from this deduced differences in the interaction of the polyion with the metal ions. Oman and DolarL2measured single ion activity coefficients of Zn, Cd, and P b ions in their respective poly(methy1styrenesulfonic acid) salts. Reddy, Marinsky, and Sarkar13 measured osmotic coefficients of a number of divalent metal salts of PSA. Free energies of binding of divalent metal ions by maleic acid copolymers, derived from potentiometric titration curves, were given by Paoletti, Delben, and Crescenzei.14 The mean activity coefficient 0022-365417812082-2388$0 1.OOlO
of the polyelectrolyte salt itself (CdPSA in salt free solution) as determined from measurements on concentration cells was reported by Vesnaver, Span, and D01ar.l~ We report mean activity coefficients of NiC12,ZnCl,, and CdC12in the mixtures NiCl,-NiPSA, ZnC12-ZnPSA, and CdC12-CdPSA, as measured with the galvanic cell technique described earlier.lv2 A strip of cation-exchange membrane in the appropriate ionic form is used in conjunction with an AgJAgC1electrode. A study of such mixtures is essential for the interpretation of data in multi-ionic mixtures containing both univalent counterions and transition metal ions.
Experimental Section Sodium poly(styrenesulfonate), molecular weight 500 000, was purified in the way described earlier.2 The acid form was converted to the Ni, Zn, or Cd form by addition of NiC03, ZnC03, or CdO, and the excess carbonate or oxide filtered off. Concentrations of the stock solutions were determined by complexometric titration with EDTA, using Snazoxs (G. F. Smith Co., Columbus, Ohio) or eriochrome black as indicator; these determinations are accurate to f0.1% , NiC12,ZnCl,, and CdClz were analytical grade and were used without further purification. Concentrations were again determined by complexometric titration. All mixtures were prepared by weight from stock solutions of polyelectrolyte and of simple electrolyte. The AgCl electrodes, the membrane cell, and the ionexchange membrane were the same as described beforea2 Potentials were measured directly on a calibrated digital electrometer (160 B, Keithly Instruments, Cleveland, Ohio), The potential measurement is accurate to f10 pV. The measurement temperature is 25.0 f 0.1 OC. Activity coefficients of the reference solutions were interpolated from the data given in Harned and Owen.16 The NiClz curve below 0.1 m was taken as equal to the CaClz curve. The ZnClz curve below 0.005 m was taken as equal to the CaC1, curve. The CaC12 curve below 2 X m was extrapolated to the Debye-Huckel limiting slope. The ac0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No.
Simple Electrolyte Activity Coefficients
1
t \
ro;
22, 1978 2389
0.10
-1ogYt
0.20
-
ja20 -logy+ 0.30
A 0
0.30-
0.40
t 1
4
-1
a
0.50
2
0 0
Flgure 1. Mean molal activity coefficients of NiCI, in mixtures of NiClz-NiPSA: (0) mp = 0.05; (0) mp= 0.02;(A) mp= 0.01; (V)mp = 0.005; (X) yhamean value, error bar indicates range from four mp values; solid line, eq 4; broken line, eq 3 with rpp = 0.06.
0.60 0 I
1
I
1
1
k
I
I
I
4
Figure 3. Mean molal activity coefficients of CdCI, in mixtures of CdCI,-CdPSA: (tl)mp = 0.05; (0) mp = 0.02;(A)mp = 0.01; (V) mp = 0.005; (X) y+' mean value, error bar indicates range from four mp values; solld line, eq 4; broken line, eq 3 with qip = 0.06.
i'"
-logy?:
0.20
0.30
1
X
wo
P
1/23
4
b
Flgure 2. Mean molal activity coefficients of ZnCI, in mixtures of ZnCI,-ZnPSA: (0) mp= 0.05; (0) mp = 0.02;( 0 )mp = 0.014; (A) mp = 0.01; (V)mp = 0.005; (X) y+' mean value, error bar indicates range from four mp values; solid line, eq 4; broken line, eq 3 with q5
= 0.09.
tivity coefficients used should have an error of less than f0.002 units. The Nernst slopes observed for the reference solutions were 87.5 mV/decade of activity for NiC12, 87.0 mV for ZnClz, and in the case of CdC12a slight curvature was observed, with the Nernst slope varying from 87.5 to 89.5 mV between 2 X and 0.1 m. Repeatability of individual potential measurements after changing the unknown or the reference solution was better than f0.3 mV.
Results and Discussion Results for log y+(NiCl,) in NiCl,-NiPSA mixtures, for log y+(ZnClz) in ZnC1,-ZnPSA mixtures, and for log y+ (CdC12)in CdCl,-CdPSA mixtures are presented in Figures 1-3 and in Table I." In the case of the Cd and Ni systems series a t 4 mp values (mp = monomolal polyion concentration, moles of sulfonate/kg of H20), approximate mp values 0.005, 0.01, 0.02, and 0.05 monomolal/kg, with 7 X values between 0.2 and 16 ( X = mp/mcl)were measured. In the case of the Zn system an additional series of mp = 0.014 was determined. This series was prepared by dilution
from the mp = 0.05 series, whereas the other three Zn series were prepared from a different stock solution. From Figures 1-3 it is clear that the reproducibility of the NiC12 data is better than it is for the ZnC12and CdClz data. The reproducibility of individual potentials was better in the Ni and Zn systems than in the Cd system, and in the Cd system the cell potential took appreciably longer to come to equilibrium. In all three systems the data at different mp's can be reduced to a single curve by applying a correction for the activity coefficient of the added salt in the absence of p~lyelectrolyte:~~~ Y*c = Y+(exPt)/y*O
(1) where ykcis the corrected activity coefficient, y+(expt)the measured activity coefficient in the mixture, and y+O the activity coefficient of the pure salt at the same molality m, as in the polyelectrolyte mixture. The average value of yiCat a given X is indicated by a crossmark in Figures 1-3, the error bars indicate the range of actual y+cvalues obtained. The standard deviation u of the individual yhC's from the average values a t a given X is 0.005 in the case of NiClz (28 points), 0.009 in the case of ZnCla (35 points), and 0.013 in the case of CdCl, (25 points). The larger error in the Cd system is partially caused by the magnitude of the y+O correction, which is much larger than in the two other systems, but also by the scatter in a number of the data points, which may be attributable to the slower electrode response in this system. If we consider these results for yaCin conjunction with our earlier results for MgC1, and CaC1z,2we can draw the following conclusions. First of all, in all five systems the measured activity coefficients at various X and mp values can within measurement error be reduced to single yaCvs. X curves by applying the ykocorrection (eq 1). This in spite of the large differences in this y+O correction, as is evidenced, e.g., from the difference between the CdClz system and the ZnClz systems (Figures 2 and 3). In no case can we detect an mpdependence in the yhCvs. X curves
2390
The Journal of Physical Chemistry, Vol. 82,No.
22, 1978
in the polyion concentration range employed. Interestingly enough, a barely significant mp dependence at higher X values was detected in NaCl-NaPSA,l but not in KC1KPSA., Significant mp dependences of y+cvalues were found in mixtures of LiCl with lithium dextransulfatels and NaCl with sodium d e x t r a n ~ u l f a t e , ~but ~ J ~not in mixtures KC1-potassium dextransulfate and CsC1-cesium dextransulfate.ls Secondly the ykccurves for the MgC12, CaCl,, and ZnC12 are identical within experimental error, and give an almost exact agreement with Manning’s limiting law The NiCl, and CdCl, curves are slightly below the limiting law prediction and thus below the three other systems studied, These two systems are virtually identical at the higher X values (see Table I, because of the different scales used this is not immediately obvious from the figures), however, below X = 4 the NiCl, curve again coincides with the limiting law and the three other systems, while the CdCl, curve seems to fall just slightly below these values. In view of the very large y+O correction especially for the CdC1, system in this range, we should probably not draw any conclusions about this slight deviation of CdCl, a t low X values. However it seems plausible to attribute the lower results for both NiC12 and CdCl, at higher X values to special polyion-counterion interactions operative in these two systems but not in the three others. Given the remarkable agreement with the limiting law of the MgCl,, CaCl,, and ZnCl, systems, and the easy qualitative explanation of the only slightly lower y+ccurves observed for NiCl, and CdC1, in terms of the expected influence of short-range attractive polyion-counterion interactions, one may wonder whether it is necessary to search for alternative descriptions of the experimental results. We shall still proceed to do so, if only to indicate how two rather different equations can both be used to successfully reproduce the data. The additivity rule, originally proposed by Mock and Marshall for the pH of mixtures of an acidic polyelectrolyte with HC1,20can be formulated in a number of ways21,22 when used to describe y+ data. Central in our comparisons will stand the observed fact that within experimental error the y+cvalues do not exhibit an mp dependence. Thus, if we formulate the additivity rule as a+ = up + CZ+O,~~ where a+ is the counterion activity in the mixture, ap the counterion activity in the pure polyelectrolyte, and a+O the counterion activity in the pure simple electrolyte, and introducing the additional relation y-=!y for the co-ion activity coefficient?l we can compare the result for our case of a divalent counterion and a univalent co-ion directly to log Y + ~ because , we find log y+/y+o = 3-’ log Mrp/r*02)X
+ 11(X+ 11-1 (2)
where we have used the Bates convention for the single ion activitie~,,~ y+ = y+,,y- = y+lI2. Alexandrowicz employed a slightly different form of the additivity rule,22 which for our case can be formulated as log y+/y*o = 3-1 log
($px+ 1)(X+ 1)-1
(3)
Alexandrowicz stated that y+O should be taken not at m,, but at m, + mp, where 4p is the osmotic coefficient of the pure polyeyectolyte. This leads to predicted values for log y+ in mixtures with an excess of polyelectrolyte which are far too low, both in systems with univalent counterionsl and in the systems considered here. We shall employ yho at m, in both eq 2 and 3. Finally, it is interesting to compare these equations to the limiting law, which in its form corrected for mobile ion-mobile ion interactions (eq 1) can be written as2
J.
C. T. Kwak and R. W. P. Nelson
log y+/y*o = 3-1 log ([(24)-1X
+ 1](X + 1)-1] 0.109(X + 34)-1 (4)
In comparing eq 2 and 3 with eq 4 we should keep in mind that for a divalent counterion the limiting laws (but also the Lifson-Katchalsky theory24)predict that 4 = (44)-l, and the limiting laws predict a relation y = 2e-lh4 where We wil! see that Loth eq the cell model assumes yp = 4 and 3 can give an excellent representation of the data in the MgCl,, CaCl,, and ZnC1, systems, eq 3 by employing 4 = 0.09, a value identical with (44)-l for the PSA polyion. ?phus it becomes clear that there is a very close relation between these equations: the second term on the righthand side of eq 4 in fact has numerically the same influence as replacing (24)-l in the logarithmic term by (44)-l. On the other hand, the y+O term on the right-hand side of the eq 2 introduces an mp dependence in this equation for log Y+/y+Owhich is not observed experimentally. This predicted mp dependence is larger than the experimental error in all divalent counterion cases, but is especially noticeable in the CdCl, case, where eq 2 predicts a difference between log y+/y+O at mp = 0.005 and at 0.05 of as much as 0.045 (in the case of ZnCl, the maximum difference predicted is about 0.020). Of course the use of eq 3 in the way originally proposed by Alexandrowicz would lead to similar differences. It is for this reason also mp. A final that we employ yaoat m,, and not at m, difficulty in using the additivity relations is tke choice to be made for yp or 4p. Single ion activity coefficient measurements for the Zn and Cd counterion in poly(methylstyrenesulfonate) are available from the measurements of Oman and Dolar.12 At mp = 0.01 these authors report yp to be 0.11 for Zn and 0.99 for Cd. Although the difference between these two numbers is a significant quantity, it is not certain whether the absolute value of these single ion coefficients can be used directly. Osmotic coefficient measurements by Reddy, Marinsky, and Sarkar yielded 4pvalues of 0.11 for CaPSA, 0.12 for ZnPSA and CdPSA, and 0.17 for NiPSA, all at mp = 0.05. This trend cannot easily be reconciled with the y+ data reported here, or the yp data reported by Oman and Dolar, and points out the problem in equating 4pto yp. It may well be that the influence of the hydration effects on (bP, at least in the concentration range of interest here, invalidates the rationale behind this equality, where after all the water is assumed to be a continuum. For these reasons it seems preferable by far to use the factor $p in eq 3 as an adjustable parameter which should conform to the fairly wide constraints given by direct yp measurements. The additivity rule then becomes an empirical mixture rule which attempts to represent the data by a single adjustable parameter. This procedure also seems preferable because in this way the additivity rule loses the theoretical significance it might otherwise be thought to have. Such a theoretical interpretation of the additivity rule has been criticized.* In Figures 1,2, and 3 the broken lines represent the “best fit” values of eq 3 to the observed values for log y*/y+O. The $p values employed are 0.06 for CdC12 and NiC12, and 0.09 for ZnC1,. Similarly, our earlier data for MgC1, and CaC12 can be fitted to eq 2 by using 4p values respectively of 0.08 and 0.085 where we should realize that this small difference is within the standard deviation of the two sets of experimental data. The difference between on the one hand the 4 values obtained for CdCl, and NiC12 (0.06 f 0.01), an$ on the other hand for MgCl,, CaCl,, and ZnCl, (0.085 f 0.01) is significant, and is in reasonable agreement with the difference in yp values reported by Oman and Dolar. For PSA, 4 = 2.8 and the limiting law value for 4p = (44)-’ is
+
Charge Transfer Complexes of Bromine with Pyridines
The Journal of Physical Chemistry, Vol. 82,No. 22, 1978 2391
0.089, and thus the limiting law value for yp is 0.108. In conclusion, we can interpret the mean activity measurements of the added salt in mixtures of polyelectrolyte and simple electrolyte as showing an influence of short range attractive interactions between the polyion and Ni2+ and Cd2+counterions, but not for Mg2+,Ca2+, and Zn2+counterions. However, in all cases the major part of the lowering of the mean activity coefficient of the divalent metal chloride is caused by nonspecific electrostatic interactions. In all cases studied so far the experimental curves of *ti vs. X a t various polyion concentrations can be reduced to single curves by applying a simple correction for yho,the activity coefficient of the added salt without polyelectrolyte. In three of the five cases studied these single curves coincide within measurement error with the limiting law for activity coefficients derived by Manning and they do so a t all polyion to coion concentration ratios. In the CdClz and NiClz cases the Tic curves fell significantly below the limiting law curve a t high polyion to coion concentration ratios, but the difference is still small compared to the already major effect of the nonspecific Coulombic effects described by Manning's limiting laws. Acknowledgment. The hospitality of the assistance of the Laboratory for Electrochemistry of the University of Amsterdam to J. C. T. K. is gratefully acknowledged. This research was supported by the National Research Council of Canada. Supplementary Material Available: Table I containing the mean molal activity coefficients for the simple elec-
Raman Intensity Study of the with Pyridines
vBr-Br
trolyte in aqueous mixtures of polyelectrolyte and simple electrolyte (1page). Ordering information is available on any current masthead page.
References and Notes (1) J. C. T. Kwak, J . fhys. Chem., 77, 2790 (1973). (2) J. C. T. Kwak, M. C. O'Brien, and D. A. MacLean, J . fhys. Chem., 79. 2381 (197.5). (3) J. C. T. Kwak, N, J. Morrison, E. J. Spiro, and K. Iwasa, J . fhys. Chem., 80, 2753 (1976). (4) G. S. Manning, J . Chem. fhys., 51, 924 (1969). (5) J. D. Wells. R o c . R . SOC. London, Ser. 6 , 183, 399 (1973). (6) M. Rinaudo and M. Milas, Chem. fhys. Lett., 41, 456 (1976). (7) G. S. Manning, Biophys. Chern., 7, 95 (1977). (8) G. S.Manning, Biophys. Chem., 7, 141 (1977). (9) K. Iwasa, J . fhys. Chem., 81, 1829 (1977). (10) G. S. Manning, Biophys. Chem., submitted for publication. (11) L. Constantino, V. Crescenzi, F. Quadrifoglio, and V. Vitagliano, J. folym. Sci., A 2 , 5, 771 (1967). (12) S. Oman and D. Dolar, Z. fhys. Chem. (Frankfurtam Main), 56, 13 (1967). (13) M. Reddy, J. A. Marinsky, and A. Sarkar, J. fhys. Chem., 74, 3891 (1970). (14) S. Paoletti, F. Delben, and V. Crescenzi, J . fhys. Chem., 80, 2564 (1976). (15) G. Vesnaver, J. Span, and D. Dolar, Makromol. Chem., 178, 2429 (1977). (16) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolyte Solutions", 3rd ed, Reinhold, New York, N.Y., 1958. (17) See paragraph at end of text regarding supplementary material. (18) Y. M. Joshi and J. C. T. Kwak, Biophys. Chem., 8, 191 (1978). (19) M. Kowblansky, M. Tomasuia, and P. Ander, J . fhys. Chem., 82, 1491 (1978). (20) R. A. Mock and C. A. Marshall, J . folym. Sci., 13, 263 (1954). (21) F. Oosawa, "Polyelectrolytes",Marcel Dekker, New York, N.Y., 1971. (22) Z. Alexandrowicz, J . folym. Sci., 56, 115 (1962). (23) R. G. Bates, "Determination of pH", Wiley, New York, N.Y., 1964. (24) S. Lifson and A. Katchalsky, J. folym. Sci., 13, 43 (1954).
Vibration in Charge Transfer Complexes of Bromine
Guido Maes and TkLr6se Zeegers-Huyskens" Department of Chemistry, University of Leuven, 3030 Heverlee, Belgium (Received March 21, 1978) fubllcation costs assisted by the Belgjan Government
The frequency, intensity, and depolarization ratio of the YB,-B, Raman band of charge transfer complexes of bromine with several pyridine derivatives have been determined in dichloromethane solution at 296 K. The frequency shift AvBr-Br is linearly related to the pK, of the pyridines. Complex formation brings about an enhancement of the depolarization ratio and of the absolute intensitiesof the Q+B~ band. From these experimental data, the mean value aR' and the anisotropy derivatives YR' of the Br-Br bond have been calculated and it is shown that complexation induces a greater increase of YR' than of &R'. Further, the parallel (aR')iI and perpendicular (aR') I components of the bond polarizability derivatives have been calculated; the (aR'),, values are seen to increase by a factor of 2 or more and are related to the weight of the dative structure; the ( c I ~ ' ) ~ values become very low. These effects are discussed in terms of the variation of the Br-Br distance and of the vibronic effect.
Introduction The influence of molecular interactions on vibrational band parameters is one of the most important problems in molecular spectroscopy. The formation of charge transfer complexes is accompanied by distinct changes in the infrared spectrum of both the donor and acceptor molecules and more specifically the nu complexes formed between pyridine and halogens or mixed halogens have been extensively studied in the mid-infrared1-5 and farinfrared range.l@-10 At the present time however, very little 0022-3654/78/2082-239 1$0 1.OO/O
data exist concerning the Raman spectra of these complexes; the vBr-Br Raman band of complexes of pyridine with halogens has been observed in solution4J1and a t low temperature12 but so far, no absolute intensity data have been obtained for these nu complexes. In this work, we report the frequency, the absolute intensity, and the depolarization ratio of the vgr-Br Raman band of bromine complexed with several pyridine derivatives in dichloromethane solution. These molecular systems are suitable for Raman study because the interaction is strong (AHo 0 1978 American Chemical Society
