2173
J . Phys. Chem. 1984,88, 2173-2178
barely perceptible in the emission of (+)-NEA in the same medium (Figure 5 ) . Similarly, the single-exponential fluorescence lifetime (A& = 375 nm) of (-)-NEA is some 27% longer than that due to (+)-NEA. The corresponding difference at = 395 nm is 19%. Since there is no difference between the fluorescence lifetimes of (-)-NEA and (+)-NEA in the absence of P-cyclodextrin in 60:40Me2SO:H20,entrapment and concomitant formation of NEA-@-cyclodextrin-Me2S0complexes (2) provide the required environment for discrimination. Observation of more pronounced stereoselectivity in these complexes = 375 and 395 nm) than less organized systems (detected at lower wavelengths) is not surprising.
The present study clearly illustrates the stringent requirements for diastereomeric recognition. Tight interacting, close proximity, and appropriate solvent microenvironment all contribute to stereoselectivit y.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for their support of this research. Registry No. (-)-NEA, 10420-89-0; (+)-NEA, 3886-70-2; a-cyclodextrin, 10016-20-3; fl-cyclodextrin, 7585-39-9; y-cyclodextrin, 1746586-0.
Unusual Behavior of Transport Coefficients in Aqueous Solutions of Zinc Chloride at 25 OC H. Weingartner,* K. J. Muller, H. G. Hertz, Institut for Physikalische Chemie und Elektrochemie der Universitat Karlsruhe, 0-7500 Karlsruhe, West Germany
A. V. J. Edge, and R. Mills Diffusion Research Unit, Research School of Physical Sciences, The Australian A.C.T. 2600, Australia (Received: August 5, 1983; In Final Form: September 28, 1983)
'niversity, Canberra,
Conductance, viscosity, and tracer-diffusion measurements are reported for aqueous ZnC12 at 25 O C . The effects of ion association in aqueous ZnC12 are discussed by comparison with aqueous MgC12 and CdC1,. The ZnCI2-H20 system is characterized by unexpectedly fast molecular motions and a "dip" in the concentration dependence of the equivalent conductance, viscosity, and self-diffusion coefficient of water, which have not yet been observed for other systems.
Introduction The application of recent theoretical developments such as the velocity correlation formalism' has stimulated our interest in obtaining isothermal transport coefficients in concentrated electrolyte solutions. This paper is concerned with diffusion, conductance, and viscosity data in the system ZnC12-H20. Although comprehensive sets of such data exist for solutions of alkali and alkaline-earth halide^,^^^ little work has been done on aqueous solutions of the transition-metal salts. Exceptions are the studies of Paterson et a1.4-9on Cd12, ZnCI2, and Zn(C104)2and recent work on solutions of NiC12,10,11CdC1,,12 and CdI,13 published by some of the present authors. Solutions of CdC12 and CdI, exhibit pronounced differences in the behavior of their transport properties (1) H. G. Hertz, Ber. Bunsenges. Phys. Chem., 81, 660 (1977). (2) H. G. Hertz, K. R. Harris, R. Mills, and L. A. Woolf, Ber. Bunsenges. Phys. Chem., 81, 664 (1977). (3) H. G . Hertz and R. Mills, J . Phys. Chem., 82, 952 (1978). (4) R. Paterson, J. Anderson, S. S . Anderson, and Lutfullah, J. Chem. SOC., Faraday Trans. I , 73, 1773 (1977). (5) R. Paterson and Lutfullah, J . Chem. SOC., Faraday Trans. 1,74, 103 (1978). ( 6 ) Lutfullah and R. Paterson, J . Chem. SOC., Faraday Trans. 1,74, 484 (1978). (7) A. Agnew and R. Paterson, J. Chem. SOC., Faraday Trans. 1,74,2885 (1978). ( 8 ) A. Agnew and R. Paterson, J. Chem. SOC., Faraday Trans. I, 74,2896 (1978). Faraday Trans. I, 76, 1052 (9) R. Paterson and C . Devine, J . Chem. SOC., (1980). (10) R. H. Stokes, S. Phang, and R. Mills, J . Solution Chem., 8, 489 (1979). (11) A. Geiger, H. G. Hertz, and R. Mills, J . Solution Chem., 10, 83 (1981). (12) R. Mills and H. G. Hertz, J. Chem. SOC.,Faraday Trans. 1,78, 3287 (1982). (13) H. G. Hertz, A. J. V. Edge, and R. Mills, J . Chem. Soc., Faraday Trans. 1, 79, 1317 (1983).
when compared with other 2:l electrolytes such as MgC12."J4 This has been attributed to the well-known property of autocomplex formation in the cadmium halide systems. In spite of these anomalies, velocity correlation coefficients could be derived successfully from the experimental data by applying the usual method of eva1uation.l In fact, the presence of complex species such as CdX+, CdX,, CdX3-, ..., where X = C1-, I-, has been supported by the large positive values for the CdX and XX velocity correlation c ~ e f f i c i e n t s . ' ~ J ~ At first sight, aqueous solutions of zinc and cadmium halides appear to exhibit many similar properties such as, for example, the negative transference numbers observed in these s y s t e m ~ . ~ J ~ J ~ It was decided therefore, in the first instance, to measure the tracer-diffusion coefficients of all three constituents for the ZnC12-H20 system in order to use these, in conjunction with other transport data in the literature, to calculate velocity correlation coefficients. With application of the normal procedure for the evaluation of these c~efficientsl-~ unexpected values were obtained which were not sensible even at concentrations greater than 2 M. Such behavior has not been observed before for other electrolytes in water. A critical reexamination of the various sets of transport data for ZnC1, in the literature led to the observation that there were consistent anomalies in these data which were not present in the corresponding data for other electrolyte solutions. For example, it was observed that in ZnC1, solutions there was a peculiarity in the concentration dependence of the self-diffusion coefficients of water which were measured as part of our original program. At concentrations below 0.5 M, DH20exhibits the typical behavior of a 2:l electrolyte such as MgC1,. At concentrations of ca. 4 M, the magnitude of DHIOis markedly higher than that (14) S. Phang and R. H. Stokes, J . Solution Chem., 9, 497 (1980). (1 5) A. C. Harris and H. N. Parton, Trans. Faraday Soc., 35,758 (1939). (16) A. J. McQuillan, J . Chem. SOC.,Faraday Trans. 1 , 70, 1558 (1974).
0022-3654/84/2088-2173$01.50/00 1984 American Chemical Society
2174
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
TABLE I: Tracer-Diffusion Coefficients of the Zn and C1 Constituents in Aqueous ZnC1, at 25 “C
Zn
cl
Weingartner et al. TABLE 11: Self-DiffusionCoefficients of Water in Aqueous ZnC1, at 25 “C Determined by the NMR Spin-Echo Technique
c1
(mol dm-3)
109D/ (m2 s-’)
0.0492 0.0980 0.143 0.203 0.505 0.898 1.946 2.828 3.631 3.896 4.571
0.714 0.7 18 0.700 0.698 0.679 0.660 0.590 0.510 0.434 0.415 0.334
cl (mol dm-j) 0.0492 0.143 0.272 0.474 1.210 1.871 2.435 4.075 4.079 4.471
mal
10’Dl (mZs-’) 1.902 1.755 1.633 1.496 1.075 0.839 0.703 0.431 0.430
0.362
observed for 2:1 electrolytes, approaching the values observed for 1:1 electrolytes. In the intermediate concentration range the transition is characterized by a “dip” in the concentration dependence of DHQ A similar behavior had been observed in the concentration dependence of proton and deuteron magnetic relaxation rates in the ZnC12-H20 and ZnCl2-DZ0systems.” We anticipated that other transport coefficients would also reflect this peculiar behavior. Then a close examination of viscosity data for the ZnCl2-HZO system in the literature18-20revealed that similar inflections could be observed in the same concentration range 0.1-1 M by careful replotting of the data. Hitherto, authors who reported these sets of data had drawn smoothed curves through them. Paterson’s data8 for the conductance of ZnC12also indicate an inflection at low concentration. Note that similar anomalies are observed in equilibrium properties such as osmotic coefficients of the zinc halides.21 It was decided then to repeat the viscosity measurements carefully in the region concerned and also to extend the conductivity measurements to lower concentrations. Experimental Section and Results Tracer-Diffusion Experiments. For the tracer-diffusion experiments, ZnC12was obtained from Alpha Products (Danvers, USA) and was of “ultrapure” grade. It was dried at 70 “ C under vacuum for 3 days. Stock solutions and all dilutions were made up by weight. Suitably diluted portions were analyzed by titration of Zn2+ against EDTA and of C1- against AgNO,. Duplicate titrations agreed to better than 0.1% and the overall accuracy is estimated to be better than f0.1%. Water used in the experiments was passed through an ion-exchange column and distilled. Its C2-l cm-’. specific conductance was -1 X Tracer-diffusioncoefficients D,, D, of the Zn and C1 constituents were measured by the diaphragm cell technique as developed by Mills and Woolf.22 The radiotracers used were 65Zn and 36Cl. Results are shown in Table I and in Figure 3. The limiting values at zero salt concentration, as calculated from the limiting ionic for Zn2+and 2.033 X m2 s-l conductances, are 0.705 X for C1-. The observed value of D, at the lowest concentration measurable with the diaphragm cell technique (which is about 0.05 M) is about 3% higher than the limiting value. It follows that D, possesses a small maximum in its concentration dependence. The observed effect is only small but seems to be outside the limits of experimental error. Self-diffusion coefficients of water have been determined by the N M R spin-echo method using procedures similar to those described by Harris et al.23 All values are based on a calibration (17) K. J. Miiller, to be submitted for publication. (18) E. Hatschek, ”Die Viskositat der Fliissigkeiten”, Dresden-Leipzig, 1929, p 117, cited in “Gmelin, Handbuch der Anorganischen Chemie”, Vol. 32 (Zn), Supplementary Issue, Verlag-Chemie, West Berlin, p 859. (19) D. J. Mead and R. M. Fuoss, J . Phys. Chem., 49, 480 (1945). (20) J. Timmermans, ’The Physico-Chemical Constants of Binary Systems in Concentrated Solutions”, Interscience, New York, 1960, p 840. (21) R. H. Stokes and J. M. Stokes, Trans. Faraday SOC.,41, 688 (1945). (22) R. Mills and L. A. Woolf, “The Diaphragm Cell”, ANU Press, Canberra, 1968.
(mol kg-’)
0
0.0999 0.299 0.499 0.749 0.997 1.49 2.00 a Molality.
cbl
ma/
1 o 9 D ~ , ~(mol , drn‘j) (m2 s - l ) kg-’) 0 2.30 2.49 0.0995 2.25 2.99 0.297 2.10 3.49 0.493 2.00 3.98 0.735 1.91 4.96 0.971 1.81 6.97 1.43 1.69 8.98 1.88 1.58 Molarity. (mol
cb/
(mol 1 0 9 0 ~ , 0 , dm-3) (mZs - l )
2.30 2.71 3.10 3.47 4.18 5.48 6.60
1.49 1.40 1.31 1.23 1.07 0.790 0.567
using water as a reference with a value of 2.30 X lo-’ mz s-’ at 25 0C.24 Furthermore, the accuracy of our technique was tested by comparing self-diffusioncoefficients in solutions of MgC12 and CdC12 with tracer values reported by Mills and co-workers.10,12 The tracer results could be reproduced to within f1.5%. All values reported are an average of at least four measurements which in general agreed to better than 2%. HTO tracer measurements have also been performed at two representative concentrations using the diaphragm cell technique. The two data points are 2.2% and 1.9% lower than values, at the same concentrations, interpolated from the N M R data. Millsz4observed a ratio of 1.03 between DH20and DHToin pure water, so that, taking this isotopic effect into account, tracer and N M R data agree to better than 1.5%. Thus, the overall accuracy of our data which are shown in Table I1 and also in Figure 3 is estimated to be better than 2%. Selfdiffusion of water in electrolyte solutions including ZnC12 has also been investigated by McCall and D o u g l a s ~Nakamura ,~~ et a1.,26 and Yagodarov and K h r a m ~ v , ~all’ using the N M R method. In every case the experimental accuracy was not high enough to detect the very specific effects being investigated here. Viscosity Measurements. The aqueous ZnC12solution for these measurements was prepared from Merck analytical-grade anhydrous salt. An 8 m solution of ZnC12was prepared by weight and this served as a stock solution from which other solutions were prepared by dilution with water. For each ZnC12 solution the density was determined at 25 “ C by using an Anton Parr densimeter and the resulting values were compared with Miller and Rard’s data2*for the density of ZnC12solution at 25OC to obtain an accurate estimate of the molality of the prepared solution. The viscosity measurements were made by using an Ostwald type viscometer having a capillary with flared ends in order to minimize kinetic corrections. All measurements were made with the viscometer immersed in a water bath controlled at 25 f 0.005 OC. Efflux times were measured at least 3 times for each solution and agreed to within 1 0 . 2 s (i.e., f 0.04% in the worst case). The viscometer was calibrated by using four liquids having well-known but widely differing viscosities at 25 OC, namely, benzene, water, ethanol, and n-hexane. The efflux times ( t ) , density ( p ) , and viscosity (7)from the literature were fitted to the equation q / p = at - b / t where a and b are constants for the viscometer, b being a very small kinetic correction coefficient. Results for the viscosity of aqueous ZnC1, at 25 “C are shown in Table 111. Conductance Measurements. The aqueous ZnC12stock solution used for these measurements was prepared by a method described by Stokes involving the direct reaction of stoichiometric quantities of zinc and hydrochloric acid. Using conductivity water freshly (23) K. R. Harris, R. Mills, P. Back, and D. S. Webster, J . Magn. Reson., 29, 473 (1978). (24) R. Mills, J . Phys. Chem., 77, 685 (1973). (25) D. W.McCall and D. C. Douglass, J . Phys. Chem., 69,2001 (1965). (26) Y. Nakamura, S. Shimokawa, K. Futamata, and M. Shimoji, J. Chem. Phys., 77, 3258 (1982). (27) V. P. Yagodarov and A. S. Khramov, Russ. J . Phys. Chem. (Engl. Transl.), 51, 169 (1977). (28) J. A. Rard and D. G. Miller, J . Chem. Eng. Dam, in press. (29) R. H. Stokes, J . Am. Chem. SOC.,65, 1242 (1962).
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984 2175
Unusual Behavior of Transport Coefficients TABLE 111: Viscosity of Aqueous ZnC1, Solution as a Function of Concentration at 25 "C
mal
(mol kg-') 0
0.09964 0.1968 0.3980 0.5920 0.7870 1.2324 1.965 2.956 3.930 4.91 1 5.902 7.106 7.933 a Molality.
cbl
103vdi
(mol dm-3) (g cm-') (Pa s) v/q0 0.997 07 8.904 1 0 1.04200 1.009 30 9.278 0.0991 9 1.08053 0.1 9564 1.021 00 9.621 1.1543 1.044 24 10.278 0.394 26 1.2202 1.065 36 10.865 0.5836 1.2817 1.085 51 11.41 0.7715 1.1907 1.4158 1.12852 12.61 1.6202 1.193 26 14.43 1.8493 1.9236 1.273 06 17.13 2.6825 1.344 67 20.35 2.2858 3.4415 1.411 05 24.23 2.7209 4.1515 1.472 94 29.07 3.2650 4.81 77 4.1077 5.5614 1.54215 36.58 4.8294 6.0386 1.585 57 43.00 Molarity. Density. Viscosity.
TABLE IV: Equivalent Conductance of Aqueous ZnCI, Solution as a Function of Concentration at 25 "C C"Z/
Ai'
(mol (a-' cm2 Cbl mal (mol dm-') dm-s)1'2 equiv" ) (mol kg-') 0,001 644 0.04054 120.33 0.001 647 0.09065 1 1 1.46 0.008 21 7 0.008 200 0.1 280 106.34 0.016 39 0.01 6 44 0.082 25 0.2868 91.31 0.08258 0.1654 0.4067 82.89 0.166 18 0.254 61 0.5046 76.46 0.256 39' a Molality. Molarity. This solution served as stock solution. prepared in the laboratory, we diluted an amount of 35% wf w Univar hydrochloric acid to about 0.5 mol dm-3. The exact molality of the acid was determined condu~timetrically.~~ A few granules of zinc (AnalaR grade, 99.95% minimum purity) were weighted out and wrapped in a weighted platinum gauze. An exact amount of the approximately 0.5mol dm-3 hydrochloric acid was weighed out and allowed to react with the zinc. When the reaction was complete, the mixture was reweighed in order to determine the exact concentration of the ZnC1, solution, which was then taken to be the stock solution for the conductivity measurements, other solutions being prepared by dilution with conductivity water. The pH of the stock solution was 3.5. Dilution of the stock solution would clearly increase the pH but none of the diluted solution showed any evidence of turbidity due to zinc oxychloride precipitation. The conductance cells had platinized platinum electrodes, those being used for the very dilute solutions being only very lightly platinized to minimize ionic adsorption effects. A Jones-Dyke ac bridge was used for the measurement of the electrical resistance across the electrodes of the cell which was immersed in an oil bath set to control at 25 f 0.005 OC. In making measurements, care was taken to eliminate Soret effects,30and allowance was made for the resistance of the leads from the bridge to the cell and for the conductivity of water. It was established experimentally that the frequency dependence of the resistance across the cell was negligibly small in the region of the frequency used for measurements, Le., 1000 Hz. The measured values of the equivalent conductance of zinc chloride are given in Table IV. The concentration dependence of the equivalent conductance, resulting from our data and the data reported by Agnew and Paterson,8 is shown in Figure 1. In the overlapping concentration range both sets of data agree excellently.
Discussion In the literature, there are many conjectures as to the species present in aqueous ZnC1,. During the course of this work it
Figure 1. Plot of equivalent conductance (A) vs. c'/~ for aqueous ZnCI2 solutions at 25.0 "C in comparison with values for MgClz and CdClZ: (0)this work; (0) data of Agnew and Paterson.' The MgC1, data were reported by Phang and Stokes.I4 The CdC1, data were reported by McQuillanI6(0.15-5 M) and Mathie~on~~ (0.00015-0.1 M). Abscissa: (c/(mol dm-3))1/2.Ordinate: A/(10-3 n-' m2 equiv-I).
became evident that there exists no simple model to describe all the observations but it is hoped that the measurements now made will aid in identifying the species in such solutions. In this connection, it should be instructive to compare the various transport coefficients of ZnCl,, in turn, with the corresponding ones of the two 2:l electrolytes MgC1, and CdCl,. MgC1, is thought to be completely dissociated up to high concentration^'^^^^ whereas complex formation in CdC1212J6,31 is well established. Conductances. In the very dilute concentration range, the behavior of the conductance of 2:l electrolytes should be predictable from the Onsager conductance theory and its extension^.^' In Figure 1 are plotted conductance data for ZnCI,, MgCI,, and CdCl, over a large range of concentration. It will be noted that the curves for MgC1, and ZnC1, become indistinguishable below 0.1 M. However, the curve for CdClz is qualitatively very different right down to the highest dilution, even though the three limiting ionic conductances are very ~ i m i l a r . ~ I Robinson J~ and Stokes33 have proposed a conductance equation which in favorable cases represents the conductance data in normal electrolytes up to 0.1 M31
where Bl, B2,and K are the conventionalparameters of the Onsager theory and a is the ion size parameter. Stokes et a1.I0 found a = 4.8 A for aqueous NiCI,, where ion association is thought to (31) R.A. Robinson and R. H. Stokes, "Electrolyte Solutions", 2nd ed., Butterworth, London, 1968. (32) B. B. Owen and G. W. Gurry, J . Am. Chem. SOC., 60, 3074 (1938). (33) R. A. Robinson and R. H. Stokes, J . Am. Chem. SOC.,75, 4563 (1953).
(30) R. H. Stokes, J . Phys. Chem., 65, 1277 (1961).
(34) R. A. Mathieson, private communication.
2176
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
Weingartner et al.
TABLE V: Maximum of the Specific Conductancea in Aqueous Solutions of Various 2:l Electrolytesat 25 "C
cmaxi
(mol dm'')
MgC4 CaC1, NiC1, COC1, CdC1, a
2.15 2.5
2.3 2. I 1
ZnC1, 2.5 Approximate values.
Krnaxi' (i2-l
cm-')
0.34 0.20 0.33 0.14 0.028 0.105
ref
0.4
14 41 10
41 16 8
be negligible. A value of a = 4.9 A is obtained if the recent conductance data of Phang and Stokes14in aqueous MgClz are fitted to eq 1. For the ZnC12-H20 system the experimental data given in Table I could be represented up to 0.1 M, choosing a = 5.3 A. It is a straightforward conclusion that the conductance of aqueous ZnC12 below 0.1 M does not indicate marked contributions from incomplete dissociation. The conductance data for CdC124 at low concentrations however do not fit eq 1 without allowance for complex species being made. Above 0.1 M the equivalent conductance in ZnC1, becomes markedly lower than in MgC12. Experience shows that in normal electrolytesdeviations from the Onsager limiting slope are positive. This implies that in a A vs. c1I2 plot the curve is convex toward the abscissa. This behavior is observed in ZnCl, below 0.1 M and it is also observed above 1 M. In the intermediate concentration range, however, a curvature concave toward the abscissa is found; Le., there are two points of inflection at about 0.1 and 1 M, respectively. As a result, there is a small dip in the concentration dependence of the equivalent conductance. In a large-scale plot, as in Figure 1, this dip is not obvious but is more clearly seen if the data are replotted on a larger scale over the concentration range 0.1-1 M. Turning to higher concentrations it is noteworthy that the specific conductance in ZnCl, passes through a maximum at about 2.5 M. Similar maxima have been observed in other 2:l electrolytes: MgC12,14CaC12,35NiClZ,I0C O C ~ , and , ~ ~CdC12.16 As noted recently,I0the existence of such maxima does not imply the presence of ion associates, unless they occur at low concentration or the conductance at the maximum is low. A summary of the properties of the conductance maxima for the various systems is given in Table V. The maximum for ZnC1, lies int he range of concentrations observed for normal electrolytes, but the conductance is lower than that observed in MgC12,NiC12, CoCl2, and CaC1,. In contrast, the maximum observed in CdC1, occurs at definitely lower concentrations than those observed in the other systems. It is also characterized by a low value. In order to interpret this behavior further measurements of this type are obviously necessary. At this point, it should be mentioned that cation transference numbers in ZnC1, as measured by Harris and Parton15 and Agnew and Patersonx become negative at about 2 M and this has usually been interpreted as due to the presence of anionic ZnC1< and ZnCldZ-complexes. One may conclude from the conductance evidence therefore that there is no appreciable complex formation in ZnCl, at low concentrations (1 M). The anomalous curvature in the conductance curve may well reflect the onset of complex formation. Viscosities. The viscosities measured in this work have been ~ c1j2 and are shown in Figure plotted as ( q / q o - 1 ) / ~ ' /against 2 together with the correspondingvalues for MgC1214and CdC1,.37 This function is based on the Jones-Dole equation3xand the low concentration slope yields the viscosity B coefficient. It will be (35) R.Haase and K. H. Ducker, Z . Phys. Chem. (Frankfurf am Main), 54. - , 319 - - (1967). (36) H. Wdingartner, unpublished data. (37) A. S . Chakravarti and B. Prasad, J . Indian Chem. Soc., 15, 479 (1938). (The CdCI2viscosities reported here are at 35 OC but serve to show the effect of complexation.) (38) G. Jones and M . Dole, J . Am. Chem. SOC.,51, 2950 (1929).
0.2
0
0.5
1.0
Figure 2. Jones-Dole plot of ( ? / t o I ) / C ' / ~ against c1l2 for ZnC12 solution at 25.0 OC compared with a similar plot for MgC12 solution also
at 25.0 "C and one for CdClzsolution at 35.0 O C . The MgClz data were reported by Phang and Stokes14and those for CdCI2by Chakravarti and Pra~ad.~'Abscissa: (c/(mol dm-3))'/z. Ordinate: ( ? / t-ol)/(c/(mol dm-3))1/2.
2
4
Figure 3. Plot of the self-diffusion coefficients (D)of HzO, Zn, and C1
constituents in aqueous ZnCI2vs. concentration (c) at 25.0 OC in comparison with similar plots for MgC12and CdC1, solutions also at 25.0 O C . The CdC12data were reported by Mills and Hertz,lzand those for MgC1, by Harris et a1.39*z3 Abscissa: c/(mol drn-"). Ordinate: D/(10-9 mz s-I). seen from the figure that these slopes are identical, the resulting B coefficients for ZnC12being 0.372. The CdClz viscosity function shown in Figure 2 differs markedly from the other two at the lower concentrations. At higher concentrations (>0.1 M) there are usually positive deviations from the Jones-Dole linear plot and these can be characterized by higher order terms in the Jones-Dole expansion. This is indeed observed for MgC12. For ZnClz above 0.1 M we observe a negative deviation from the limiting slope; Le., the rate of increase of viscosity with molarity is a decreasing
Unusual Behavior of Transport Coefficients quantity. Only at about 0.7 M is passes through a minimum and thereafter becomes a steadily increasing quantity. Again if our new viscosity data for ZnCl, are simply plotted against concentration, an inflection is clearly seen in the region 0.1-1 M. So the viscosity data reinforce the conclusions reached in the conductance studies that the onset of complex formation occurs in the above concentration range. Tracer-Diffusion Coefficients. The tracer-diffusion coefficients of all three species in ZnCl, as given in Tables I and I1 are shown in Figure 3. Also shown in this figure are corresponding data for MgC1, and CdC12. Dealing first with the low concentration region, the self (tracer)-diffusion coefficientsof water for the three salts are shown as the top three curves in Figure 3. It will be noted that the water self-diffusion coefficients for all three curves are identical within experimental error up to about 0.2 M. The anionic tracer coefficients (shown in the middle of the figure) again show coalescence in the case of MgC1, and ZnC1, at about 0.1 M but the CdCl, data are separate. The cationic tracer coefficients are shown at the bottom of the figure and here a distinct departure from the behavior patterns outlined above will be noted. The Onsager limiting law for tracer diffusion predicts a cl/, dependence characterized by a negative slope in a D vs. c 1 / 2plot.31 Though we expect deviations from the limiting law at concentrations of the order of 0.1 M, the general shape of the curve is expected to be retained as is the case for MgC12.38 In contrast, the cationic tracer-diffusion coefficient, D, (Zn2+),at the lowest concentration measurable with the diaphragm technique (Le., 0.05 MZ2)is about 3% higher than the limiting value derived from the limiting ionic cond~ctance.~'A similar maximum in the concentration dependence of Dc has been observed in aqueous CdClzlZand Cd12.13 These maxima have been ascribed to Cd-halide complexes which are presumed to move faster than the hydrated Cd2+ ion. Of course, it would be a straightfoward conclusion to explain the maximum of Dc in aqueous ZnC1, by the same arguments, Le., formation of Zn-Cl complexes. It is however not easy to reconcile these findings with the statements on complete dissociation of ZnC12in this concentration range, derived from the other transport coefficients. Looking now at the higher concentration ranges, the most striking feature derived from the diffusion data is the finding of unexpectedly fast diffusive motions. For example, at 4 M the self-diffusion coefficient of water is more than twice that of MgCl, and approaches the order of magnitude observed for 1:l electrolytes. Also in aqueous CdC12, enhancement of water selfdiffusion relative to its value in MgC1,12 has been found. In fact, Mg2+ is regarded as a strongly hydrated ion, exhibiting "structure-making" properties. In contrast, complexes such as ZnC1+ or anionic complexes such as ZnC1,- or ZnC14,- may act only as weak structure formers, or even as structure breakers with respect to viscosity and water self-diffusion, as judged from extensive studies on complex ions of similar valency and shape.38 Also the viscosity lies between the ranges of values expected for normal 2:l and 1:l electrolytes, respectively. The tracer-diffusion coefficients of zinc and chloride constituents in ZnCl, become almost equal at about 4 M, which means that the motions of the ionic constituents are strongly coupled. A similar behavior was observed in CdCl,, whereas in MgCl, the anionic mobility is more than twice that of the cation.39 Again, the high mobility of the ionic constituents in ZnCl,, as compared with those in CdCl, and Mg2+in MgCl,, is striking. As mentioned earlier, the negativity of transference numbers in ZnCl, at about 2 M is usually interpreted by the presence of anionic ZnC13- and ZnC14Z-complexes. It follows then from the behavior of the ionic tracer-diffusion coefficients that the very high mobility must be ascribed to these complexes. It has been noted by Mills and Hertz(, that the conventional interpretation of the CdC1, trans(39) K. R. Harris, H. G. Hertz, and R. Mills, J . Chim. Phys. Phys.-Chim. Bid., 75, 391 (1978). (40) H. G. Hertz and G. Engel, Ber. Bunsenges. Phys. Chem., 72, 808
(1968).
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984 2177
0.7 0.5 1.0 15 Figure 4. Plot of the osmotic coefficients (4) vs. m1/2for aqueous ZnC1, at 25.0 OC in comparison with values for MgC1,. For ZnCI2 the solid line represents values recommended by Goldberg4' and the dotted line
represents data reported by Stokes and Stokes.,] The dashed line refers Above 0.15 to values obtained by the equation of Pitzer and May~rga.~, m the dashed line coincides with the solid one. The MgClz data were ~~ (mlmol kg)'I2. recommended by Goldberg and N ~ t t a l .Abscissa: Ordinate: 4. ference numbers also implies an unusually high mobility of the CdC1,- ion. Summing up the tracer-diffusion section, there is one marked difference to the findings in the conductance and viscosity cases. This difference is that the Zn2+ tracer-diffusion coefficients do not behave in a fashion similar to Mgz+ coefficients at low concentrrations (C0.1M). In fact, there is more correspondence with the CdZ+coefficients implying some complexation at these concentrations. At higher concentrations the generally high mobilities for ZnC1, solutions can be reconciled with complex formation which accords with evidence from the conductance and viscosity results. If we, at this stage, compare the observed anomalies in detail, we find that the effect is most pronounced in the self-diffusion of water and is present only to a minor degree in the viscosity and the conductance. We therefore suppose that the presence of ion associates breaks the hydration structure and enhances the mobility of the water molecules causing a reduction of the viscosity. It is a general experience that the structure-breaking effect exhibits itself in a more pronounced way in the self-diffusion coefficients of water than in the viscosity. Thus, it is a tentative conclusion that the observed dip in the equivalent conductance stems from the behavior of the viscosity and is not a direct consequence of a varying number of charge carriers. It is, however, noteworthy that no related effects occur in aqueous CdC1, and CdI,. The peculiarity of the observed effects is also seen from the fact that, though inherent in the primary viscosity data which have been reported,'8-20 the respective authors have rejected the possibility of such an anomaly by drawing smoothed curves. Equilibrium Properties. It is now of interest to see whether the reculiar effects observed for transport phenomena are also present in equilibrium properties such as activity or osmotic coefficients. Pertinent work has recently been summarized by G ~ l d b e r g , ~who ' has listed recommended values for the mean activity and osmotic coefficients of ZnC1, at 25 "C in the range 0.001-23 m . The respective curve for the osmotic coefficient 4 up to 4 m is shown in Figure 4. We have also shown data as obtained by Stokes and Stokes,,' the smoothed curve based on the equation developed by Pitzer and Mayorga,", and the smoothed curve for MgCl, derived from the review of Goldberg and Nuttall.43 It is seen that the osmotic coefficients exhibit features (41) R. N. Goldberg, J . Phys. Chem. Ref Data, 10, 1 (1981). (42) K. S . Pitzer and G. Mayorga, J . Phys. Chem., 81, 2300 (1977).
2178 The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
similar to those of the transport coefficients, namely, a similarity to those of MgC12 at low concentrations and a very peculiar behavior above 0.1 M. It should, however, be noted that ”similar” does not mean “identical”, as there are marked differences in the osmotic coefficients of ZnC12and MgC12 at 0.05 m, whereas at are the same concentration the transport coefficients (except 0,) practically identical. Obviously, the osmotic coefficient is more sensitive to structural changes in solution than are the transport coefficients. One further remark should be added. Goldberg’s recommended values of osmotic and activity coefficients are based on primary data obtained from a considerable body of experimental work. We have examined the various primary references with respect to the behavior of osmotic and activity coefficients in the concentration range 0.1-2 M, where the transport coefficientsexhibit the most pronounced anomalies. In spite of the good overall agreement, the shapes of the various curves are markedly different. Agnew and Paterson8 have reported on mutual diffusion data which in principle could be included in the discussion of transport coefficients. However, in the analysis of mutual diffusion data the “driving force”
4 + m(d4/dm) has to be taken into account. It is well-known that calculation of the derivative may increase the error in the primary data by 1 order of magnitude. In fact, we believe that the anomalies observed in the conductance and viscosity may be present in the mutual diffusion coefficients if properly corrected by the driving force. However, the uncertainty in the above derivative is greater than is acceptable for calculations. General Information. A qualitative description only of our experimental findings has been given and it would now be. desirable to express these findings in terms of molecular structures. Conventionally, a set of stability constants for the stepwise equilibria Ki
K2
Zn2+ == ZnCl+ + ZnC1,
K3
K4
* ZnC1,- * ZnC1,2-
Weingartner et al. 0.48; K2 = 1.86;K3 = 0.56; K4 = 1.40. The disagreement among the various sets of data is obvious. On the other hand, the general conclusion that ZnC1, is more like a strong electrolyteat low concentrations and becomes strongly self-complexed at high concentrations is evident from most work published so far. Related arguments can, e.g., be found in the work of Paterson et al. cited in the Introduction. Also the evaluation of the transport coefficients measured by Paterson* in terms of the generalized transport coefficients of the thermodynamics of irreversible processes (li, coefficients) supports these conclusion^.^^ Nevertheless, the particular characteristics of this system have never been recognized in detail. Finally, some recent studies obtained in the Karlsruhe laboratory are quoted. Chemical shifts of water protons in zinc, cadmium, and magnesium halides and perchlorates, measured by one of the present authors,]’ are in general agreement with the conclusions derived from the transport coefficient data, Le., complete dissociation of ZnC12at dilute concentrations and beyond -0.1 M and sudden onset of complex formation. The potential utility of 35Cl and 81Brrelaxation and line-width measurements for studying the nature of transition-metal complexes in solution has been demonstrated by some of the present authors studying ion association in aqueous solutions of NiC12,18MnC12,50ZnBr2,51and CdBr2.51 In the case of ZnC12, investigations are complicated by the large line width of the 35Clresonance in the presence of ion associates. In preliminary measurements below 0.5 M, a 35Clresonance signal could be detected, which is attributable to symmetrical Zn(H20)2+ complexes. At larger concentrations the line widths seem to increase rapidly, leading to a disappearance of the resonance signal. Because the 36Clline width is determined by quadrupolar relaxation, which in turn depends on the symmetry of the charge distribution at the nucleus, one expects the sudden increase to be associated with the formation of Zn-C1 complexes. Further investigations in this area are in progress.
Conclusions We summarize the main observations as follows: (1) At dilute concentrations, ZnC1, seems to behave as a normal 2:l electrolyte with complete dissociation of ions. At higher concentrations it behaves more like a 1:l electrolyte, indicating the presence of Z n C P and ZnC1,- species. (2) The onset of complex formation acts differently with the various transport coefficients; Le., the various coefficients possess a different sensitivity of the formation of ion associates. (3) At high concentrations diffusive motions are unexpectedly fast. (4) The onset of complex formation above 0.1 M occurs rather suddenyl and causes inflections in the concentration dependence of the transport coefficients which have not been observed for other systems. (5) It is doubted whether stability constants can be found which represent all properties in the ZnCl-H20 system unambiguously.
is used to describe complex formation. We have, however, not yet succeeded in finding a set of constants which describes unambiguously the behavior of all properties discussed in this work. Therefore, only a tentative conclusion can be given. The absence of marked indications of ion association in most properties below 0.1 M suggests that the first stability constant must be small. On the other hand, there is evidence for anionic complexes above 1 M. Thus, the subsequent constants K3 and K4 may have comparatively large values. In aqueous CdC12 at about 1 M, the stability constants determined by Reilly and Stokes@indicate the presence of neutral CdC12 complexes, and these explain the low conductance observed in this system. It is a tentative conclusion that, in aqueous ZnCl,, K2 cannot have a large value, otherwise the conductance should be lower, as is the case with CdC12. Silldn and L i l j e q ~ i shave t ~ ~ derived the following constants (on the molarity scale): K1 = 0.65; K2 = 0.25; K3 = 1.4 (K4 was not included in their treatment). Paterson and co-worker~,~~ applying the procedure of Reilly and Stokes,44found K1 = 4.5 from emf data but admitted there was considerable ambiguity concerning this value. Maciel et al.,47analyzing chemical shift data of the 67Znmagnetic resonance, used the following set of values: K, =
Acknowledgment. H.W. thanks the Research School of Physical Sciences, Australian National University, Canberra, for a visiting fellowship. The Deutsche Forschungsgemeinschaft is thanked for financial support. Registry No. ZnC12, 7646-85-7; HzO,7732-18-5.
(43) R. N. Goldberg and R. L. Nuttall, J . Phys. Chem. Ref. Data, 7, 263 (1978). (44) P. J. Reilly and R. H. Stokes, Aust. J . Chem., 23, 1397 (1970). (45) L. G. SillCn and B. Liljequist, Acta Chem. Scand., 3, 539 (1949). (46) Lutfullah, H. S. Dunsmore, and R. Paterson, J . Chem. SOC.,Faraday Trans. I, 72, 495 (1976). (47) G. E. Maciel, L. Simeral, and J. J. H. Ackerman, J . Phys. Chem., 81, 263 (1977).
(48) D. G. Miller, “Proceedings of the 2nd Australian Thermodynamics Conference,” Royal Australian Chemical Institute, Melbourne, 1981, pp 490-509. (49) H. Weingartner, Ch. Muller, and H. G. Hertz, J . Chem. SOC., Faraday Trans. I , 75, 2712 (1979). (SO) L. Helm and H. G. Hertz, Ber. Bunsenges. Phys. Chem., 85, 158 (1981). (51) H. G. Hertz, Ber. Bunsenges. Phys. Chem, 65, 36 (1961).
