J. Phys. Chem. 1993,97, 62894291
6289
Transport Measurements in Aqueous Sodium Sulfate. Evidence for Like-Ion Pairs in Concentrated Solutions H. Weingiirtner’ Institut f i r Physikalische Chemie und Elektrochemie der Universitiit Karlsruhe, Kaiserstrasse 12, D- 7500 Karlsruhe, Germany
W. E. Price,’ A. V. J. Edge,* and R. Mills Atomic and Molecular Physics Laboratories, The Australian National University, Canberra, ACT 2600, Australia Received: January 11, 1993
Precise self-diffusion and conductance data are reported for aqueous solutions of sodium sulfate at 25 O C in the general concentration range 0.1 mol dm-3 to saturation. These data in conjunction with mutual diffusion, transference, and activity coefficient data enable the calculation of velocity correlation coefficients, fa,,, and closely related transport coefficients, which may serve as sensitive probes for ion configurations in solution. Evidence is found for like-ion pairs a t concentrations above 0.1 mol dm-3.
Introduction
TABLE I: Equivalent Conductance of Aqueous Nafi04 at 25 Oca
Recently there has been much progress in our understanding of interionic interactions in electrolyte solutions.’ One of the central objects of study has been the association of ions due to Bjerrum-type electrostatic ion pairing, and much work has been directed toward the determination of pair association constants from the propertiesof dilute solutions.lS2 Little is however known of association in concentrated solutions, where larger ion clusters and like-ion pairs may be present.lJ Owing to their relation to activation-controlled electron-transfer reactions, such like-ion configurationsare of rather wide interest in chemistry.l.3 Also, electrolyte thermodynamics is strongly affected by interactions between ions with the same sign of charge.’ Modern statistical mechanics gives methods for calculating these ion distributions from interionic potentials for model electrolytes.1J There remains the problem of finding experimentalproperties which are sufficientlysensitiveto these ion codigurations. Recent work has shownc7that certain pair interaction coefficientsderived from conductance and diffusion data may be uniquely useful for probing such configurations. These coefficients, denoted as velocity correlation coefficients (vcc), fab, or distinct diffusion coefficients, Dabd, were promoted in several studies from our laboratories.s*6 Here, we apply this approach to the study of ion associationin the Na2S04+ H2O system. N a B 0 4is an important constituent of many natural brines and a typical representative of 1:2 electrolytes. There is evidence for ion pairing in dilute solutions with an association constant of about 5 dm3 mol-1.8 Theory relates thef.b to solvent-averaged potentials of mean force between the ions, but apart from a brief report7bon the conductance and transference of a 1:l electrolyte conforming to K2SO4, no model calculationshave been reported hitherto for 1:2 electrolytes. Information on ion associationcan however be gained from a somewhat more qualitative analysis536 of the A b .
C
A
C
A
C
A
0.098 0.2144 0.3140 0.3911 0.6254
82.13 71.89 66.44 63.24 55.53
0.6953 0.8008 0.9161 1.010 1.195
53.80 51.16 48.64 46.72 43.32
1.313 1.424 1.473 1.683 1.800
41.30 39.54 38.81 35.73 34.05
TABLE II: Self-Diffusion Coefficients of the Na, SO,, and H20 Constituents in Aqueous Nafi04 at 25 O c a C
0 0.1008 0.2485 0.5281 0.7361 0.8140 0.8141 1.002 1.518 (I
10% 1.334 1.213 1.132 1.031 0.951 0.934 0.945 0.860 0.720
c 0 0.1020 0.2514 0.4921 0.7651 1.004 1.005 1.501 1.752
c
105~~0, 1.064 0.973 0.901 0.816 0.708 0.638 0.641 0.499 0.437
0 0.100 0.251 0.530 0.981 1.001 1.480
1 0 3 ~ ~ ~ 2.30 2.19 2.06 1.88 1.61 1.59 1.36
Units are as follows: C, mol dm-3;D, cmz s-1.
with solutions made from the Merck “suprapur” salt and distilled and deionized water (18 rS cm-1). The estimated accuracy is &0.05%. Literature data&10agree fairly well with our data, but are more scattered. Results for the self-diffusion coefficients of the Na+ and S O P constituentsobtained by diaphragm cell measurements6 with the radiotracers 22Na+ and 3sS042(The Radiochemical Center, Amersham, U.K.) are given in Table 11. Self-diffusioncoefficients of water determined by the NMR spin-echotechnique11 are also given. The estimated accuracy of all data is fl%. Our results disagree largely from older datal2for Na+ and S042-self-diffusion (see also ref 13) and to a minor degree from more recent data for the self-diffusion of Sod2- and water.14
Experimental Results Table I gives equivalent conductances A (S cm2 equirl) for aqueous NapS04 at 25 OC measured using standard techniques7
* To whom correspondence should be addressed.
t Resent address: Department of Chemistry, University of Wollongong,
P.O.Box 1144, Wollongong. NSW 2500, Australia.
t Resent address: Department of Physics, University College, UNSW, Australian Defense Force Academy, Campbell, ACT 2600, Australia.
Discussion The fab approach to describe transport, as well as some fundamental aspects of ion association in relation to this, has been discussed in detail el~ewhere.”~We describe transport by pair interaction coefficients which characterize the coupled diffusive motions of pairs of species a-b, which may be of the same or of different kind. This results in three coefficients for
0022-3654/93/2091-6289s04.0~/00 1993 American Chemical Society
6290 The Journal of Physical Chemistry, Vol. 97, No. 23, 1993
Weinglrtner et al. view is corroborated on a quantitative level by the AltenbergerFriedman-Zhong (AZF) transport theory which relates the fat, to the equilibrium spatial distributions of ions by expression of the form7
-01 0
05
10
15
210
-
4-i
25
Figure 1. Cation-anion velocity correlation coefficients,f+, of aqueous solutions of Na2S04, ZnS04,and MgC12 plotted against the square root of the ionic strength. Units are as follows: f+ cm2 5-1; Z, mol dm-3. 0310 5 1..
t 0201-
'.._ '4
-0
0
05
10
15
2:o
-
Ji-
2'5
Figure 2. Cationqtion velocity correlation coefficients,f++,of aqueous solutions of NazS04, ZnSO,, and MgCl2 plotted against the square root of the ionic strength. Units are as follows: f++,om2 s-I; Z, mol dm-3.
-0&+ 0
05
10
15
2'0
-t
2'5
fi
Figure 3. Anion-anion velocity correlation coefficients,f- -,of aqueous solutions of Na2SO4, znso4, and MgC12 plotted against the square root cm2 s-l; I, mol dm-3. of the ionic strength. Units are as follows: the ionic interactionsf++,f--,and f+-. The measured transport coefficients(conductance, transference number, mutual and selfdiffusion coefficients) may be expressed in terms of thefab. Theory relates thefib to solvent-averagedpotentialsof mean force between the ions? so that experimental Jab may serve to discriminate between different model potentials and to parametrize the potentials. The subsequent discussion aims at providing the data base for future calculations of this type, as well as at contributing to the qualitative understanding of ion association phenomena. To assist the discussion of the work reported here, we restate the most important observations on the behavior of the fpbaS7 Attractive interactions between the a and b ions cause the fab to be positive due to correlated motions of the respective pairs of species, while negativevaluesareobtained if repulsiveinteractions are dominant. An example shown in Figure 1-3 is MgC12 H20, where almost complete dissociationis thought to be present even in the molar concentration range. Therefore, the negative f++ and f--and positivef+-of this system have repeatedly been considered as being representative for strong electrolytes.s.6This fL,
+
where gab@) is the equilibrium pair correlation function for a-b pairs.ls Hence, positive fab are obtained just when expected, namely, when a-b pairs cause g(r) to have a large peak.16 Obviously, the formation of ion pairs and higher ion clusters will have a profound influence on thefab. In particular, close like-ion configurations may yield positivef++orf--,which makes the fab uniquely suited for probing like-ion pairsn3 For example, for auto-complex-formingtransition-metal halides like CdClz the Cl-Cl coefficient is predominantly positi~e.~ More important in the present context is the observation6 of positivef++ and f--in aqueous ZnS04, as is displayed in Figures 2 and 3. These imply the existence of marked peaks in the Zn-Zn and so4304 distributions, predicted' by model calculations. We have calculated the fab for Na2S04 + H20 in Figures 1-3 from the conductance and self-diffusion data in Tables I and 11, in conjunction with reported tran~ference,'~ mutual diffusion,'* and activity coefficient data.I9 The data in Figure 1 are plotted against the square root of the conventional ionicstrength, I , based on molar concentrations. Limitations of the diaphragm cell technique impose a lower bound for the determination of selfdiffusion coefficients at a molar concentration, C, of about 0.1 mol dm-3, but by extrapolation, and in conjunction with other transport coefficient data for dilute solutions,8J*JO reasonable estimates of thefab can be obtained down to about 0.01 mol dm-3 or even lower. Data have also been calculated for other, closely related sets of generalized transport coefficients, Le., the /ab of Miller:' and the distinct diffusion coefficientDabdof F~iedman'h~~ and these are listed in the Appendix. We can predict that the stability of cation-anion pairs, e.g., evidenced by conductance data in the dilute regime,8should reveal itself by large and positive values off+-. This is just what is observed in Figure 1, wheref+-for Na2S04 shows exceptionally large values, not yet obtained with any other system. A further essential result is related to the behavior off++ and f--shown in Figures 2 and 3. Both are initially negative, but increase with higher concentrations, with f++becoming positive above 0.1 mol dm-3 and reaching exceptionally large values. f-- approaches zero and flattens out. We interpret this as strong evidence for cationsation pairs and to a minor degree also of anion-anion pairs. There is a certain analogy between these results and those reported previously for ZnS04 + H20. In the latter case the rationale was6 that large ionic clusters may stabilize close cationcation and anion-anion configurations. There are, however, some differences between the Na2S04and ZnS04 cases: f+-is positive in both cases, but much larger for Na2S04 than for ZnS04, as is f++.f--is large and positive for ZnS04, but not for Na2SO4. Also,f++ andf-- become negative for Na2S04 at concentrations below 0.1 moldm-3, andapproach thenegative theoretical limiting slope, while for ZnS04 the transition to negative values appears to occur at much lower concentrations, and for f--it cannot be seen from the data at all. The results suggest the following conclusions on the nature of ion association in concentrated Na2S04. Cation-anion pairing found at low salt concentrations persists up to the molar range, causing g+&) to have a large peak which is much more pronounced than found with ZnS04. Additionally, extensive cation4ation pairing, and to a minor degree also anion-anion pairs become detectable somewhere between 0.01 and 0.1 mol dm-3, and play an important role at molar concentrations. Such strong like-ion interactions may result from the formation of higher aggregates, but do not extend in the very low concentrations observed in 2:2
The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 6291
Transport Measurements in Aqueous Sodium Sulfate
TABLE Ilk Phenomenological Coefficients l*/N and
Distinct Diffusion Coefficients Ohdof Aqueous NafiO4 Solutions at 25 O C at Rounded Molar Concentrations0 C 10121++/N 10IZl+JN 101zI--/N 105D++dlO5D+-d 1.950 -0.128 0.128 4.972 0.172 0.01 -0.087 0.236 4.938 0.317 1.892 0.025 1.874 0.007 0.375 5.020 0.505 0.05 0.739 1.867 0.129 0.549 5.164 0.1 0.271 0.67 0.913 1.858 5.269 0.15 0.292 0.748 1.007 1.809 5.214 0.2 1.404 1.819 0.505 1.044 5.548 0.3 0.661 1.164 1.566 5.692 1.832 0.4 1.821 0.807 1.238 1.666 5.744 0.5 0.849 1.294 1.740 1.809 5.762 0.6 1.791 1.792 0.922 1.33 1 5.760 0.7 0.986 1.364 1.835 1.772 5.747 0.8 1.748 1.033 1.383 1.860 5.709 0.9 1.067 1.397 1.879 1.723 5.663 1 .o 1.112 1.393 1.873 1.659 5.502 1.2 1.142 1.375 1.850 1.591 1.4 5.320 1.155 1.368 1.562 1.840 5.240 1.5
lOSD--d -0.111 -0.149 -0.140 -0.095 -0.054 -0.051 0.033 0.1 1 1 0.175 0.215 0.258 0.294 0.324 0.350 0.386 0.419 0.414
d u n i t s are as follows: C, mol dm-3; l,b/N, molZ dm3 J-I cm-1 s-I equirl; Dabd,cm* s-I. b Unsmoothed data.
electrolytes.22 Thereby, N a S 0 4 - N a configurations appear to be preferred over S04-NaS04 configurations. The results allow some conclusions of the subtle behavior of the equivalent conductance given by4
where I+ and z- are the charge numbers of the ions, and all other symbols have their usual meaning. A pronounced decrease of A is expected from the large and positivef+-,as actually observed at low salt concentrations. Above 0.1 mol dm-3 this is obviously compensated by the like-ion termsf++andf--.Hence, the effect of cation-anion pairing upon the equivalent conductance is compensated by the formation of larger aggregates at high concentrations. This effect is well-known for solutions of 2:2 electrolytes,6where it is more pronounced, and has sometimes been interpreted as “redissociation”. The same interpretation may explain the subtle behavior of the cationic transference number, t+, in the Na2S04 + H20 system. At low concentration t+ decreases with increasing salt concentration, although the limiting law predicts an increase.20 This can be rationalized by cation-anion pairing. Above 0.1 mol dm-3 t+ remains essentially constant,17which appears to follow from the compensating effect of like-ion correlations. In conclusion, our results show that no satisfactory description of the properties of concentrated aqueous solutions of 1:2 electrolytes can be expected, unless allowance is made for likeion configurations in larger aggregates. Qualitatively, this behavior is quite similar to that observed6 for 2:2 electrolytes, which puts the 1:2 electrolytes in contrast to 2:l electrolytes like MgCl2. As pointed out by Friedman,’ the existence of these
like-ion configurations may have a strong effect on chemical reaction rates of reactions between ions of the same sign of charge.
Acknowledgment. W.E.P. thanks the Commonwealth Government of Australia for support through a Queen Elizabeth I1 fellowship award. Appendix Beyond the approach used in this work and in previous works from our laboratories, several other sets of closely related generalized transport coefficientsare used in pertinent work. The most common ones are the distinct diffusion coefficients Dabdof F r i e d m a ~ ~and ~ ~ gthe ~ phenomenological coefficients lab/N of Miller.21 Theory provides a connection between these sets of coefficients. In Table I11 we have listed these sets of coefficients for convenient comparison with other data in the literature expressed in terms of these alternative sets. Their adoption does not change the general conclusions. References and Notes (1) Friedman, H. L. Annu. Reu. Phys. Chem. 1981,32, 179. (2) See e.g.: Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1970. (3) Friedman, H. L. Faraday Discuss. Chem. Soc. 1988,85, 1 . (4) Hertz, H. G. Ber. Bunsen-Ges. Phys. Chem. 1977,81, 657. (5) See for example: (a) Mills, R.; Hertz, H. G. J. Chem.Soc., Faraday Trans. I 1982,78,3287. (b) Weingirtner, H.; Braun, B. M.; Schmoll, J. M. J. Phys. Chem. 1987, 91, 979 and references cited therein. (6) Price, W. E.; Weingirtner, H. J. Phys. Chem. 1991, 95, 8933. (7) (a) Altenberger, A. R.; Friedman, H. L. J. Chem. Phys. 1983, 78, 4162. (b) Friedman, H. L.; Raineri, F. 0.;Wood, M. Chem. Scr. 1989,29A, 49. (c) Zhong, E. C.; Friedman, H. L. J. Phys. Chem. 1988,92, 1685. (8) Jenkins, I. L.; Monk, C. B. J. Am. Chem.Soc. 1950,72,2695. Owing to the well-known difficulties in treating conductances of unsymmetrical electrolytes, other values may be found; we quote for example Fisher, F. H.; Fox, A. P. J. Solution Chem. 1975, 4,225. (9) For a comprehensivetabulation of transport coefficient data 8ee e.g.: Lobo V. M. M. Handbook of Electrolyte Solutions; Physical Science Data 41; Elsevier: Amsterdam, 1989; Part B. (10) (a) Valyashko, V. M.; Ivanov, A. A. Russ. J . Inorg. Chem. 1974,19, 1628. (b) Isono, T. J . Chem. Eng. Data 1984, 29, 45. (11) Holz, M.; Weingirtner, H. J. Magn. Reson. 1991, 92, 115. (12) Nielsen, J. M.; Adamson, A. W.; Cobble, J. W. J. Am. Chem. Soc. 1952, 74, 446. (13) Mills, R.; Lobo, V. M. M. Sel/Diffusion in Electrolyte Solutions; Physical Sciences Data 36; Elsevier: Amsterdam, 1989. (14) Tanaka, K. J. Chem. Soc., Faraday Trans. 1 1988,84, 2895. ( 15) Expressions of this type occur only in the electrophoreticcontributions to the f.a which appear however to be the dominant ones.’ (16) It should be noted that the factor r in the integrand of eq 1 tends to increase the contribution at large r beyond the direct core repulsion region, so that correlations over comparatively large distances may contribute, as would, e.g., be expected for like ions in clusters. (17) Braun, B. M.; WeingBrtner, H. J. Solution Chem. 1985, 14, 675. (18) Rard, J. A.; Miller, D. G. J. Solution Chem. 1979.8, 775. (19) Rard, J. A.; Miller, D. G. J. Chem. Eng. Data 1981, 26, 33. (20) Longsworth, L. G. J. Am. Chem. Soc. 1935,57, 1185. (21) Miller, D. G. J . Phys. Chem. 1985, 81, 1137. (22) Note that for MgCll and some other electrolytes the like-ion coefficients also turn up above 1 mol dm-”5b but the resulting effect is weak as compared with that observed here. Such an increase is expected at high concentrations from hydrodynamic arguments.
