2594
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979
2. LibuS and H. Tialowska
Thermodynamic Properties and Solution Equilibria of Aqueous Divalent Transition Metal Trifluoroacetates and Magnesium Trifluoroacetate Zofla Llbul" and Hanna Tlalowska Department of Physical Chemistry, Technical Unlverslty of GdaAsk, 80952 Gdahk, Poland (Received April 9, 1979)
Osmotic coefficients for MII(CF~COO)~, CO(CF~COO)~, Ni(CF3C00)2,CU(CF~COO)~, Zn(CF3C00)2,and Mg(CF3C00)2in aqueous solution have been determined by the isopiestic method at 25 "C, and the activity coefficients are derived. Changes in the UV and visible absorption spectra induced by changing the concentration have been followed for Ni(CF3C00)2,CO(CF~COO)~, and CU(CF~COO)~, and are compared with those observed in the mixed solutions of the respective metal perchlorates and CF3COONa. Spectral results indicate very small inner-sphere coordination of the CF3COO- anion in Ni(CF3C00)2,larger coordination in CO(CF,COO)~, with the largest coordination in CU(CF~COO)~, only the monotrifluoroacetato complex being formed in each case. Strong ionic association of the outer-spheretype must therefore be assumed to account for the osmotic coefficients of Ni(CF3C00)2being markedly lower than those of Mg(CF3C00)2,and even slightly lower, within the range of high molalities, than those of CO(CF~COO)~ This conclusion is confirmed by an auxiliary spectrophotometric comparison of the overall association of the CF3COO-anion with metal cations, and an essential role of hydrogen bond formation in outer-sphere association is inferred.
Introduction Aqueous bivalent transition metal salts involving the same anion but different cations display, in general, a large variety of thermodynamic behavior. Illustration is provided by the divergent osmotic and, accordingly, activity coefficient curves of the chlorides1 and bromidesa2This behavior contrasts that of bivalent transition metal perchlorates, which display closely similar r$(rn) dependences up to the highest molalities ac~essible.~ At the same time, the lack of change in the visible spectra of the colored metal perchlorates indicates the persistence of intact hexaaquo cations in the respective solutions. Most significant, in this connection, is the fact that magnesium perchlorate exhibits closely similar (though perceptibly lower) osmotic and activity coefficients as the transition metal perchlorates. These facts clearly show that it is not differences in hydration of the cations, at least not in the direct sense, but differences in ionic association that are responsible for the diversity of behavior observed among the other transition metal and magnesium salts. For colored transition metal chlorides and bromides changes in the visible spectra indicate inner-sphere coordination of the respective anion, with the slightest for nickel(II), stronger for cobalt(II), and strongest for ~ o p p e r ( I I ) .It ~,~ follows that the formation of inner-sphere complexes is the main factor responsible for the lowerings in the osmotic and activity coefficients compared with a hypothetical nonassociated electrolyte. However, a closer examination of the results and, in particular, comparison of the data for NiC12 and NiBr2 with those of the respective magnesium salts indicated that outer-sphere association of halide anions with hexaaquo cations also is of importance. At the same time, the stronger outer-sphere association in the nickel(I1) halides than in the respective magnesium halides, as shown by the lower osmotic and activity coefficients, indicated a marked contribution of specific non-Coulombic interactions to the stability of outer-sphere ion pairs in the systems studied. Hydrogen bond formation between the halide anions and the hexaaquo cations, dependent on the acidity of the latter, seemed to provide a consistent explanation for the experimental finding^.^^^ An independent confirmation of the relative contributions of outer-sphere and inner-sphere associations in the overall process was also obtained from the dependences of the first step association constants on water activity in the re0022-3654/79/2083-2594$0 1.OO/O
spective metal perchlorates forming the ionic mediaa5 In view of the above inferences it seemed worthwhile to study further systems in order to obtain estimations of the relative importances of outer-sphere and inner-sphere ion associations in determining the thermodynamic properties of divalent transition metal salts. Trifluoroacetates have been chosen for the present study, as it seemed probable that the trifluoroacetate anion might show a higher tendency to outer-sphere association than the other anions studied so far. To our knowledge no osmotic and activity coefficient data have been reported in the literature so far for these salts.
Experimental Section Materials. The metal trifluoroacetates, obtained by dissolving the corresponding metal carbonates in trifluoroacetic acid, and potassium chloride were purified by several crystallizations. Heating above 32 "C was avoided during recrystallization of Mn(CF3C00)2to prevent decomposition. To depress hydrolysis, the Zn(CF3C00)2 stock solution was additionally acidified by trifluoroacetic acid to the equivalence point by potentiometric titration, and the CU(CF~COO)~ stock solution was acidified to ca. 0.005 M acid concentration. Perchlorates of Mg(II), Mn(II), Co(II), Ni(II), Cu(II), and Zn(I1) were obtained by dissolving the corresponding metal carbonates in perchloric acid. The materials were further purified by repeated crystallizations. Stock solutions of C O ( C F ~ C O O )Ni(CF3C00)2, ~, CU(CF~COO)~, C O ( C ~ O Ni(C104)2, ~)~, and C U ( C ~ Owere ~)~ analyzed for the corresponding metals by standard electrogravimetric methods. Manganese, zinc, and magnesium in the Mn(CF,C00)2, Zn(CF3C00)2,and Mg(CF3C00)2 solutions, respectively, were determined gravimetrically in the form of M2P2O7or as ZnNH4P04in the case of Zn(II), and by EDTA titration as well. The differences in the results obtained by these two methods did not exceed 0.25%. The arithmetic means were used in further calculations. The concentrations of the M I I ( C ~ O ~ ) ~ , Zn(C104)2,and Mg(C104)2stock solutions were determined by EDTA titrations. Potassium chloride concentration was determined by drying weighed amounts of the solution at 180 "C, and the concentration of CF3COONa was determined by the flame-photometric method. All chemicals used in this work were reagent grade quality. 0 1979 American Chemical Society
Thermodynamic and Solution Properties of M(CF3COO)2
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979 2595
Procedures. The osmotic coefficients were determined by the isopiestic method following the procedure described p r e v i ~ u s l y . ~A~massive ~ ~ ~ ~ ' vacuum-tight brass vessel with 18 depressions for sample cups was used as the isopiestic apparatus. The cups were made of gold-plated silver. Weighed portions ( 1g) of the investigated solutions of known initial concentrations were usually placed in four cups, while six cups contained reference solution. The brass vessel containing the investigated samples was slowly evacuated at the beginning of each isopiestic run. After evacuation the apparatus was immersed in the thermostated water bath (25 f 0.01 "C) where it remained for 3-25 days, depending on concentration. In order to diminish the time necessary to attain equilibrium, slow rotation of the isopiestic apparatus inclined at an angle of 45O was applied. After equilibrium had been reached, the brass vessel was removed from the bath, air was slowly admitted, and lids were placed on the cups as soon as possible. The equilibrium concentrations of the solutions were calculated from the initial concentrations and final weights of the cups. The measurements were performed in the concentration range from 0.1 to -4 mol kg-' with the exception of CU(CF~COO)~ solutions, where the highest concentration was 2.5 mol kg-l. It was not possible to attain isopiestic equilibrium above this limit, probably because of hydrolysis, producing the volatile trifluoroacetic acid. Absorption spectra of the solutions were determined with Perkin-Elmer Model 323 or Zeiss VSU 10 spectrophotometers, both equipped with thermostated cell compartments, using quartz cells of widths varying within the range 0.01-5 cm. The temperature was kept at 25 f 0.1 "C. Calculations. The osmotic coefficients were calculated as follows: vr mr4r $=3m where m and $ are molality and the osmotic coefficient, respectively, of the investigated solution, while v,, mr, and $r are the number of ions, molality, and the osmotic coefficient, respectively, of the reference solution. KC1 and Mg(ClO,), solutions were used as standards. Values for their osmotic coefficients were found by interpolation of the data of Hamer and Wu8 (KC1) and Robinson and Stoked (Mg(C104),). The derived $ values have been approximated by the polynomials and by Pitzer's e q ~ a t i o n .Its ~ form for 2:l electrolytes and the best values of the parameters (4/3)p(O), (4/3)p('), and (25/2/3)C+obtained for the molality range 0.1- -2 mol kg-' by the use of the least-squares method are listed in Table 111. These values were used in the calculation of the mean molal activity coefficients for m I 1.8 mol kg-l, using Pitzer's e q ~ a t i o n : ~
-
1.358m1I2 - 1.307 In (1 2.078m1/2) 1 + 2.078m1I2 2(4/3)$O)m + (1/6)(4/3)/3(')[1 - e-3.464m1'2(1 3.464m1/2 - 6m)l (25/2/3)C+(1.5)m2
lny=-
+
+
+ +
For m > 1.8 mol kg-' the polynomials listed in Table IV were used in calculations. Effects in the UV and Visible Absorption Spectra Solutions of C O ( C F ~ C O O ) ~Figure . 1 shows visible absorption spectra of CO(CF,COO)~in aqueous solution of varying concentration, as well as the respective curve for C O ( C ~ O ~As ) ~is. seen, the spectral changes brought about by increasing the concentration are small, but
IW
0 ~ " " " " " " ' " 450 500
550
Xhm) Figure 1. Absorption spectra of Co(CIO,), (curve 1, 0.1023 M) and CO(CF,COO)~in aqueous solution at 25 O C . The concentrations of CO(CF,COO)~was as follows: (2)0.1010M; (3)0.5066 M; (4)0.9972 M; (5)1.4894 M; (6)1.8605 M; (7)2.8384 M.
distinct. They indicate a slight coordination of the trifluoroacetate anion in an octahedral configuration, as outer-sphere association does not usually influence the d-d bands. No absorption band was found in the spectral range above 600 nm, characteristic of tetrahedral cobalt(I1) complexes. It would not be realistic to analyze the spectra shown in Figure 1for the number of light absorbing species because of the small differences in absorption between the successive curves. Therefore, we tried to obtain this type of information, in an indirect way, from the spectra of + three-component system of C O ( C ~ O+~ CF3COONa )~ HzO. It might be expected that complexes formed in these latter solutions at low and medium concentrations of CF3COONa should be the same as those formed in the two-component system Co(CF3C00)2 + H20. Figure 2 shows the visible absorption spectra of solutions containing a small and constant concentration of cobalt(I1) perchlorate and a varying concentration of CF3COONa. As is seen, up to -4 M, changes in the spectrum are very + similar to those observed in the system CO(CF~COO)~ H20. In order to determine the number of the light absorbing species appearing in the whole concentration range, the spectra were analyzed by using Coleman's test.1° It has been found that the absorbances satisfactorily fulfill the expected linear relations for two absorbing species. It follows that only one coordination complex with the trifluoroacetate anion is formed in the solutions now under consideration, most probably [ C O ( O H ~ ) ~ ~ C F ~ C the OO]+; other absorbing species obviously was the hexaaquo cation, [ C O ( O H ~ ) ~This ] ~ + .we take as an indication that the first trifluoroacetato complex is formed in the CO(CF~COO)~ + H2O two-component solution as well. Since outer-sphere association is known to have practically no effect on d-d bands, the above analysis detects different coordination complexes of cobalt(II), irrespective of their possible participation in outer-sphere association. Therefore, outer-sphere association of the trifluoroacetate anions with the [ C O ( O H ~ ) ~or] ~[CO(OHZ)~_,CF~COO]+ + cations may also take place in these solutions. Solutions of Ni(CF3C00)2. Absorption spectra of Ni(CF3C00)2in aqueous solution, as well as the reference spectrum of Ni(C10J2, within the short-wavelength and long-wavelength bands are shown in Figures 3 and 4, respectively. As is seen, changes in absorption with increasing concentration of the salt up to its highest accessible concentration are very small, indicating very slight
2596
2. Lib& and H. Tlalowska
The Journal of Physical Chemistry, Vol. 83,No. 20, 1979
L
8
i
600
700
800
Ah) Flgure 4. Absorption spectra of Ni(C104)2(curve 1, 1.0221 M) and Ni(CF3C00)2in aqueous solution at 25 OC. The concentratlon of Ni(CF3C00)2was as follows: (2) 1.4935 M; (3) 1.9325 M; (4) 2.6507 M.
0
450
550
500
Xhm)
+
Flgure 2. Absorption spectra of the CO(CIO~)~CF,COONa aqueous solutions at 25 OC. The concentrationof Ca(C104)2ranged from 0.0777 to 0.0787 M; the concentration of CF,COONa was as follows: (1) 0.0 M; (2) 0.806 M; (3) 1.55 M; (4) 2.37 M; (5) 3.04 M; (6) 3.98 M; (7) 4.70 M; (8) 5.47 M; (9) 6.29 M; (10) 7.16 M.
IW 350
400 Xnm)
450
+
Flgure 5. Absorption spectra of the Ni(CIO& CF,COONa aqueous solutions at 25 OC. The concentrationof Ni(C104)2ranged from 0.0763 to 0.0770 M; the concentration of CF,COONa was as follows: (1) 0.0 M; (2) 1.57 M; (3) 2.34 M; (4) 3.03 M; (5) 3.87 M; (6) 4.72 M; (7) 5.34 M; (8) 6.22 M; (9) 7.19 M.
Xnm)
Flgure 3. Absorption spectra of Ni(C104)2(curve 1, 0.1128 M) and Ni(CF3COO)2in aqueous solution at 25 OC. The concentration of Ni(CF3C00)2was as follows: (2) 0.5049 M; (3) 1.4935 M; (4) 2.6507 M.
coordination of the trifluoroacetate anion in the octahedral configuration. Again, absorption spectra of the threecomponent solution Ni(C10J2 + CF3COONa + HzO were studied in order to obtain some indirect information as to the nature of complexes to be expected in the pure solutions of nickel(I1) trifluoroacetate. Respective sets of absorption curves of solutions containing a fixed small amount of Ni(C104)zand varying amounts of CF3COONa in the short- and long-wavelength bands are shown in Figures 5 and 6, respectively. As is seen, up to -3 M CF3COONa,the spectra are very similar to those observed in the system Ni(CF3C00)2+ HzO. The number of light absorbing species formed is two, as indicated by Coleman's test.1° One of them is the hydrated cation, [Ni(OHZ),I2+,
IW
600
700 1Inm)
800
+
Figure 6. Absorption spectra of the Ni(C104)* CF,COONa aqueous solutions at 25 OC. The concentrationof Ni(C104)zranged from 0.0763 to 0.0770 M; the concentration of CF,COONa was as follows: (1) 0.0 M; (2) 1.57 M; (3) 2.34 M; (4) 3.03 M; (5) 3.87 M; (6) 4.72 M; (7) 5.34 M; (8) 6.22 M; (9) 7.19 M.
and the other, most probably, the monotrifluoroacetate complex, [Ni(OHz)6-,CF3COO]+. It seems that the same complexes should be formed in the system Ni(CF3C00)z
Thermodynamic and Solution Properties of M(CF3COO)2
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979 2597
A
,
X(nml
Figure 7. Absorption spectra of CU(CIO~)~ (curve 1, 0.1100 M) and CU(CF,COO)~ in aqueous solution at 25 OC. The concentration of Cu(CF,COO), was as follows: (2)0,1099M; (3)0.5033M; (4)1.0137 M; (5)1.6335 M; (6)2.0029 M; (7)2.3123 M; (8)3.0422M; (9)3.7336 M.
800 1000 X(nm1
600
I
J
1200
Figure 9. Absorption spectra of the CU(CIO,)~ iCF,COONa aqueous solutions at 25 OC. The concentration of CU(CIO,)~ ranged from 0.0369 to 0.0375 M the concentrationof CF3COONawas as follows: (1) 0.0 M; (2)0.700M (3)1.58 M; (4)2.35 M (5)3.11 M; (6)3.89 M; (7)4.73 M; (8)5.48 M; (9)6.28 M; (10)7.22 M.
TABLE I: Mean Molar Absorption Coefficients of Cu(I1) in Cu(ClO,), t M(ClO,), Mixtures Containing CF,COONa for Two Total Concentrations, ct, of the Metal Perchlorates at 25 C h,nm Mg Mn Co Ni Cua Zn .
-
M;CCu(CIO,),/Ct = 0.061; CCF,COON~= 0.098 M;CHClO, = 0.01 M ~t =
Ah)
Flgure 8. Absorption spectra of CU(CIO,)~(curve 1, 0.1047 M) and CU(CF,COO)~ in aqueous solution at 25 OC. The concentration of CU(CF,COO)~ was as follows: (2)0.1099 M; (3)0.5033 M;(4)1.0137 M; (5)1.6335 M; (6)2.0029M; (7)2.3123 M; (8)3.0422M; (9)3.7336 M.
1.598
267.5 270 275
4.69 3.59 2.05
4.05 3.89 3.10 3.03 1.80 1.77
3.85 2.99 1.80
2.81 2.13 1.20
3.78 2.88 1.61
270 275
6.62 3.86
4.61 4.39 2.73 2.61
4.26 2.54
1.80 1.06
4.67 2.78
CCu(ClO,),/Ct
= 1.
spectral changes in the range of small and medium concentrations of CF,COONa are similar to those observed for the two-component solutions. Coleman's testlo HzO. Of course, outer-sphere association between cation demonstrated the existence of two absorbing species. This and anion may also take place in these solutions. confirms the above conclusion of the existence of two Solutions of C U ( C F ~ C O OThe ) ~ set of absorption curves absorbing complexes only in the two-component system of CU(CF,COO)~in aqueous solution together with the Cu(CF3C00)2 + H2O. curve for C U ( C ~ Oare ~ )shown ~ in the Figures 7 and 8. As Taking into account the known ability of copper(I1) to is seen, the intensity of the d-d band characteristic of form dimeric complexes with carboxylate anions, we deoctahedral complexes of copper(I1) increases markedly with termined the spectra of two solutions with the same high increasing concentration and, unlike the other systems, the concentration of CF3COONa (4.69 M) and different band undergoes a slight blue shift from -820 nm in concentrations of Cu(C104)z(0.0214 and 0.2031 M). The C U ( C ~ Oto~ -790 ) ~ nm in 3.7336 M CU(CF,COO)~.The spectra proved to be the same, within experimental error, changes indicate extensive coordination of the trifluorothus excluding the possibility that the complex formed is acetate anion. The large increase of intensity within the dimeric. Respective curves are shown in Figure 10. It charge-transfer band confirms this conclusion. The seems most probable that it is the [CU(OH~)~,CF~COO]+ long-wavelengthabsorption curves were analyzed by using pseudooctahedral ion. Coleman's test,1° with the result that there are only two Comparison of Stabilities of MCF,COO+ Complexes. In absorbing species in the whole concentration range. This order to compare the stabilities of MCF3COO+ type means that only one trifluoroacetate complex of Cu(I1) is formed, in addition to the hexaaquo cation, [ C U ( O H ~ ) ~ ] ~ + .complexes, we measured the absorbance of Cu(I1) within the UV band due to the CuCF3COO+complex in equiIn order to further check on the number and nature of complexes formed between the Cu2+and CF3COO-ions, molar mixtures of C U ( C ~ Owith ~ ) ~the other transition the spectra of the three-component solutions C U ( C ~ O ~ ) ~metal perchlorates containing CF,COONa at a small + CF3COONa + H 2 0 were also measured. In all these constant concentration. The acidity of the solutions was kept constant due to small controlled additions of per~ ) ~small and solutions the concentration of C U ( C ~ Owas chloric acid. In these experiments, copper(I1) acted as an approximately constant (-0.037 M), and the concentration indicator of the concentration of free trifluoroacetate ions. of CF3COONa varied from 0.0 to 7.22 M. The resulting Light absorption due to the noncomplexed Cu2+and other spectra are shown in Figure 9. As in previous cases,
+
2598
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979
TABLE 11: Isopiestic Molalities, m, and Osmotic Coefficients, Cu(CF,COO),, Zn(CF,COO),, and Mg(CF,COO), Solutions
m 0.1050 0.1979 0.2173 0.2492 0.3023 0.4061 0.4844 0.5385 0.5651 0.7051 0.9909 1.2978
6 Mn(CF,COOL vs. KC1 lo. 8 7 56 0.8905 0.8901 0.9020 0.9086 0.9354 0.9548 0.9730 0.9849 1.0157 1.1099 1.1814
msa
0.1500 0.2915 0.3205 0.3734 0.4578 0.6351 0.7734 0.8762 0.9305 1.1961 1.8161 2.4900
Mn(CF,COO), vs. Mg(C10,), 1.4967 1.8436 1.9021 2.0060 2.3217 2.3340 2.6101 2.6116 2.8488 3.0391 3.2574 3.4868 4.0717
1.2351 1.3214 1.3346 1.3598 1.4295 1.4348 1.4891 1.4900 1.5376 1.5741 1.6147 1.6523 1.7382
1.2575 1.5038 1.5432 1.6141 1.8186 1.8279 1.9983 2.0007 2.1419 2.2512 2.3746 2.4995 2.8029
Co(CF,COO), vs. KCl 0.1077 0.1229 0.1507 0.2184 0.2360 0.2966 0.3432 0.3972 0.4137 0.4243 0.4259 0.4342 0.4550 0.4912 0.5352 0.5640 0.57 5 1 0.6254 0.6622 0.6991 0.7220 0.7921 0.7949 0.9062 0.9090 0.9289 1.0497 1.0758 1.0921 1.0986 1.1229 1.1450 1.2073 1.2423 1.2527 1.2557 1.2619 1.3032 1.3049 1.3158 1.3252 1.3400 1.3521 1.3634 1.4131 1.4197 1.4463
0.8655 0.8715 0.8744 0.8856 0.8891 0.9044 0.9174 0.9327 0.9366 0.9370 0.9353 0.9394 0.9465 0.9582 0.9740 0.9786 0.9826 0.9960 1.0058 1.0201 1.0261 1.0439 1.0427 1.0727 1.0791 1.0790 1.1153 1.1284 1.1299 1.1310 1.1372 1.1485 1.1626 1.1733 1.1773 1.1786 1.1832 1.1897 1.1905 1.1930 1.1970 1.2015 1.2009 1.2030 1.2239 1.2250 1.2314
0.1523 0.1754 0.2169 0.3205 0.3482 0.4470 0.5257 0.6193 0.6479 0.6648 0.6661 0.6821 0.7202 0.7871 0.8717 0.9228 0.9448 1.0411 1.1127 1.1906 1.2361 1.3772 1.3803 1.6122 1.6265 1.6608 1.9293 1.9959 2.0273 2.0409 2.0948 2.1539 2.2912 2.3745 2.4009 2.4062 2.4286 2.5163 2.5208 2.5455 2.5708 2.6068 2.6274 2.6523 2.7858 2.8004 2.8627
Z. Lib& and H. Tlalowska @,
of Mn(CF,COO),, Co(CF,COO),, Ni(CF,COO),,
m
@
msa
1.4529 1.5493 1.6093 1.6270 1.6529 1.6663 1.6748 1.6901 1.7541 1.7740 1.7898 1.8188 1.8222 1.9038 1.9255 2.0494 2.0567 2.0759 2.0817 2.1529 2.1736
1.2340 1.2620 1.2704 1.2800 1.2869 1.2900 1.2926 1.2989 1.3151 1.3189 1.3237 1.3274 1.3339 1.3504 1.3600 1.3930 1.3924 1.4027 1.3979 1.4185 1.4282
2.8806 3.1207 3.2501 3.3056 3.3739 3.4025 3.4248 3.4676 3.6278 3.6749 3.7154 3.7793 3.8026 4.0018 4.0642 4.3874 4.3990 4.4642 4.4619 4.6552 4.7225
Co(CF,COO), vs. Mg(ClO,), 1.1264 1.4050 1.4115 1.6791 1.7615 1.7635 1.9229 2.1292 2.2246 2.2682 2.2883 2.3158 2.3174 2.3598 2.4383 2.4471 2.5994 2.7660 2.7766 2.8202 3.0254 3.0352 3.1058 3.1513 3.1725 3.3862 3.4309 3.5446 3.5697 3.8073 3.9280
1.1433 1.2204 1.2244 1.2971 1.3177 1.3202 1.3630 1.4121 1.4394 1.4499 1.4504 1.4602 1.4630 1.4686 1.4916 1.4891 1.5243 1.5640 1.5693 1.5780 1.6288 1.6221 1.6499 1.6526 1.6579 1.7031 1.7192 1.7412 1.7364 1.7803 1.8106
0.9816 1.1949 1.2023 1.4006 1.4571 1.4597 1.5741 1.7132 1.7789 1.8069 1.8186 1.8378 1.8426 1.8662 1.9192 1.9230 2.0216 2.1258 2.1362 2.1603 2.2898 2.2898 2.3399 2.3618 2.3746 2.4998 2.5315 2.5987 2.6044 2.7364 2.8111
Ni( CF,COO), vs. KCl 0.1063 0.1175 0.1512 0.1552 0.2360 0.2959 0.3445 0.3894 0.3928 0.3993 0.4156 0.4262 0.4347 0.4570 0.4926 0.5168 0.5385 0.5658 0.5772 0.6277 0.6647
0.8643 0.8674 0.8715 0.8670 0.8891 0.9066 0.9140 0.9234 0.9254 0.9278 0.9324 0.9328 0.9383 0.9424 0.9555 0.9591 0.9680 0.9755 0.9791 0.9940 1.0020
0.1500 0.1668 0.2169 0.2215 0.3482 0.4470 0.5257 0.6009 0.6075 0.6193 0.6479 0.6648 0.6821 0.7202 0.7871 0.8288 0.8717 0.9228 0.9448 1.0411 1.1127
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979 2599
Thermodynamic and Solution Properties of M(CF,COO)2
TABLE I1 (Continued)
m 0.7024 0.7253 0.7807 0.7964 0.7975 0.9080 0.9146 0.9277 1,0526 1.0828 1.0943 1.1030 1.1237 1.2101 1.2466 1.2553 1.2577 1.2649 1.3058 1.3316 1.3420 1.3480 1.3548 1.3664 1.4232 1.4536 1.4589 1.5533 1.6126 1.6307 1.6614 1.6709 1.6796 1.7248 1.7588 1.7849 1.7987 1.8104 1.8173 1.8323 1.9276 2.0567 2.0647 2.0845 2.1602 2.1861
6 1.0153 1.0214 1.0290 1.0383 1.0393 1.0717 1.0725 1.0803 1.1122 1.1211 1.1276 1.1265 1.1364 1.1599 1.1693 1.1749 1.1767 1.1804 1.1897 1.1913 1.2013 1.1943 1.1985 1.2000 1.2221 1.2252 1.2289 1.2587 1.2678 1.2770 1.2821 1.2864 1.2890 1.3012 1.3116 1.3108 1.3172 1.3172 1.3181 1.3265 1.3585 1.3880 1.3870 1.3969 1.4137 1.4200
Ni(CF,COO), vs. Mg(ClO,), 1.1417 1.2195 1.2233 1.2954 1.3161 1.4340 1.4490 1.4636 1.4652 1.4892 1.4872 1.5168 1.5275 1.5792 1.6182 1.6430 1.6484 1.6434 1.6825 1.6946 1.7056 1.7340 1.7733 1.7975 1.8020 1.8246 Cu(CF,COO), vs. KCl 0.1026 0.8566 0.1194 0.8536
1.1280 1.4060 1.4128 1.6813 1.7637 2.2320 2.2695 2.3104 2.3653 2.4422 2.4503 2.5655 2.5940 2.8181 3.0425 3.1190 3.1508 3.1689 3.3187 3.3999 3.4298 3.5746 3.7838 3.9376 3.9467 4.0925
m,(l 1.1906 1.2361 1.3388 1.3772 1.3803 1.6122 1.6265 1.6608 1.9293 1.9959 2.0279 2.0409 2.0948 2.2912 2.3745 2.4009 2.4062 2.4286 2.5208 2.5708 2.6098 2.6068 2.6274 2.6523 2.8004 2.8627 2.8806 3.1207 3.2501 3.3056 3.3739 3.4025 3.4248 3.5384 3.6278 3.6749 3.7154 3.7378 3.7525 3.8026 4.0642 4.3874 4.3990 4.4642 4.6552 4.7225 0.9816 1.1949 1.2023 1.4006 1.4571 1.7789 1.8069 1.8378 1.8662 1.9192 1.9230 2.0007 2.0216 2.1603 2.2898 2.3399 2.3576 2.3618 2.4544 2.4993 2.5215 2.6044 2.7220 2.8029 2.8111 2.8864 0.1433 0.1668
m
6
msa
0.1545 0.1580 0.2044 0.2431 0.3095 0.3171 0.3579 0.3761 0.4346 0.4456 0.4568 0.5178 0.5665 0.5966 0.6097 0.6644 0.7063 0.7509 0.7774 0.8333 0.8519 0.9809 1.0054 1.0662 1.1475 1.1961 1.2068 1.2325 1.3081 1.3744 1.3824 1.3826 1.3896 1.3971 1.4476 1.4704 1.4882 1.4888 1.5009 1.5149 1.5838 1.5903 1.6250 1.6337 1.7463 1.8178 1.8386 1.8963 1.9081 1.9260 1.9592 2.0291 2.0447 2.0890 2.2240 2.2273 2.3881 2.3884 2.4316 2.4372 2.5421 2.5754
0.8529 0.8516 0.8621 0.8631 0.8668 0.8783 0.8797 0.8784 0.8916 0.8922 0.8929 0.9090 0.9202 0.9252 0.9269 0.9376 0.9430 0.9498 0.9530 0.9641 0.9706 0,9910 0.9969 1.0096 1.0202 1.0316 1.0296 1.0361 1.0509 1.0606 1.0647 1.0667 1.0650 1.0687 1.0731 1.0789 1.0786 1.0829 1.0818 1.0827 1.0919 1.0937 1.0960 1.0974 1.1196 1.1247 1.1327 1.1335 1.1346 1.1398 1.1455 1.1531 1.1587 1.1635 1.1786 1.1757 1.1992 1.1952 1.1968 1.1946 1.2013 1.2053
0.2169 0.2215 0.2915 0.3482 0.4470 0.4644 0.6257 0.5518 0.6479 0.6648 0.6821 0.7871 0.8717 0.9228 0.9448 1.0411 1.1127 1.1906 1.2361 1.3388 1.3772 1.6122 1.6608 1.7790 1.9293 2.0273 2.0409 2.0948 2.2467 2.3745 2.3966 2.4009 2.4062 2.4286 2.5208 2.5708 2.6068 2.6098 2.6274 2.6523 2.7858 2.8004 2.8627 2.8806 3.1207 3.2501 3.3056 3.4025 3.4248 3.4676 3.5384 3.6749 3.7154 3.8026 4.0669 4.0642 4.3990 4.3874 4.4619 4.4642 4.6552 4.7225
0.1009 0.1054 0.1068 0.1171 0.1223 0.1453 0.1990 0.2507 0.3062 0.3232 0.3560 0.3873 0.3901
Zn(CF,COO), vs. KCI 0.8711 0.8717 0.8728 0.8704 0.8758 0.8756 0.8855 0.8966 0.9096 0.9136 0.9239 0.9284 0.9318
0.1433 0.1500 0.1523 0.1668 0.1754 0.2092 0.2915 0.3734 0.4644 0.4927 0.5494 0.6009 0.6075
2600
Z.Libus and H. Tialowska
The Journal of Physical Chemistry, Vol. 83,No. 20, 1979
TABLE I1 (Continued) m
cp
msa
m
cp
m,a
0.4197 0.4245 0.4856 0.5128 0.5669 0.6126 0.7160 0.7355 0.7946 0.8386 0.8587 0.9070 0.9260 0.9951 1.0675 1.0747 1.1424 1.2146 1.3011 1.3135 1.5296 1.5544 1.5867 1.7984 1.8026 1.9105 2.0000
0.9413 0.9383 0.9610 0.9665 0.9818 0.9955 1.0257 1.0311 1.0482 1.0598 1.0674 1.0815 1.0852 1.1052 1.1270 1.1295 1.1511 1.1688 1.1916 1.1951 1.2593 1.2642 1.2707 1.3260 1.3288 1.3477 1.3778
0.6606 0.6661 0.7804 0.8288 0.9305 1.0194 1.2255 1.2650 1.3869 1.4777 1.5229 1.6265 1.6648 1.8161 1.9791 1.9959 2.1539 2.3162 2.5163 2.5455 3.0776 3.1347 3.2092 3.7378 3.7525 4.0018 4.2519
0.3521 0.3796 0.3876 0.4141 0.4782 0.5059 0.5286 0.5569 0.6881 0.7008 0.7191 0.7773 0.8176 0.8390 0.8849 0.8998 0.9690 1.0363 1.0439 1.1054 1.1488 1.1741 1.2075 1.2461 1.2590 1.2708 1.2783 1.4697 1.4985 1.7222 1.7273
0.9341 0.9473 0.9378 0.9541 0.9759 0.9797 0.9912 0.9994 1.0408 1.0479 1.0547 1.0715 1.0871 1.0925 1.1085 1.1168 1.1350 1.1606 1.1629 1.1896 1.1966 1.2092 1.2138 1.2304 1.2314 1.2352 1.2379 1.3106 1.3113 1.3847 1.3868
0.5494 0.6009 0.6075 0.6606 0.7804 0.8288 0.8762 0.9305 1.1961 1.2255 1.2650 1.3869 1.4777 1.5229 1.6265 1.6648 1.8161 1.9791 1.9959 2.1539 2.2467 2.3162 2.3869 2.4900 2.5163 2.5455 2.5647 3.0776 3.1347 3.7378 3.7525
1.3620 1.6147 1.6897 1.7988 1.8437 2.0332 2.1890 2.2123 2.3206 2.3284 2.6246 2.6411 2.6485 2.8696 2.8703 2.9777 2.9828 3.0628 3.1300 3.1935 3.2381 3.2512 3.4618 3.5848 3.6936 3.8411 4.0115 4.0384 4.0705 4.1969 4.2972 4.3550 4.3777 4.4241 4.4459 4.6073
Mg(CF,COO), vs. Mg(ClO,), 1.2689 1.3488 1.3779 1.4113 1.4215 1.4788 1.5298 1.5325 1.5672 1.5651 1.6483 1.6500 1.6530 1.7172 1.7152 1.7442 1.7459 1.7649 1.7839 1.8059 1.8066 1.8142 1.8665 1.8908 1.9182 1.9440 1.9908 1.9955 2.0042 2.0252 2.0512 2.0600 2.0661 2.0697 2.0857 2.1060
1.2023 1.4006 1.4597 1.5432 1.5741 1.7132 1.8279 1.8426 1.9192 1.9230 2.1258 2.1362 2.1408 2.2898 2.2899 2.3576 2.3618 2.4132 2.4544 2.4998 2.5215 2.5315 2.6645 2.7364 2.8111 2.8864 2.9967 3.0125 3.0328 3.1020 3.1650 3.1927 3.2073 3.2299 3.2513 3.3320
Zn(CF,COO), vs. Mg(C10,), 1.1460 1.2233 1.2244 1.2955 1.3186 1.3206 1.3574 1.3747 1.4107 1.4446 1.4522 1.4634 1.4822 1.4797 1.5054 1.5165 1.5513 1.5539 1.5540 1.6056 1.6294 1.6429 1.6707 1.6744 1.6789 1.7030 1.7206 1.7374 1.7791 Mg(CF,COO), vs. KCl 0.8711 0.1009 0.8712 0.1070 0.8751 0.1224 0.8762 0.1452 0.8918 0.1976 0.8950 0.2161 0.9053 0.2483 0.9168 0.2996 0.9189 0.3031 0.9289 0.3179 a Molality of the reference solution. 1.1238 1.4017 1.4116 1.6812 1.7603 1.7630 1.9309 1.9843 2.1314 2.2765 2.3346 2.3681 2.4537 2.4628 2.5715 2.6128 2.7885 2.8045 2.8172 3.0690 3.1962 3.2902 3.4519 3.4937 3.5132 3.6397 3.7553 3.9012 4.1972
0.9816 1.1949 1.2023 1.4006 1.4571 1.4597 1.5741 1.6141 1.7132 1.8069 1.8426 1.8662 1.9192 1.9230 1.9954 2.0216 2.1258 2.1362 2.1408 2.2898 2.3618 2.4132 2.4998 2.5215 2.5315 2.6044 2.6645 2.7364 2.8864 0.1433 0.1523 0.1754 0.2092 0.2915 0.3205 0.3734 0.4578 0.4644 0.4927
transition metal cations in this spectral range is very small, and was compensated by the respective composition of the reference probes. The results are listed in Table I. Obviously, decreasing (increasing) mean molar absorption
coefficient of copper(I1) indicates a decreasing (increasing) concentration of the free CF3COO- ion and, in turn, increasing (decreasing) stability of the trifluoroacetato complex of the other metal ion constituting the equimolar
The Journal of Physical Chemlstry, Vol. 83,Y
Thermodynamic and Solution Properties of M(CF,COO),
:O, 1979 2001
TABLE 111: Derived Values of Parameters in Pitzer's Eauation
( 4 / 3)P'O'
a
( 4 / 3 P
(25'2/3)C@
Mn(CF,COO), 0.537815 2.309316 0.535459 2.20951 1 Co(CF,COO), 0.536673 2.120484 Ni(CF,COO), 0.444655 2.049311 Cu(CF,COO), 0.542524 2.236630 Zn( CF,COO), 2.206060 0.575934 Mg(CF,COO)* The maximum molality for which the listed parameters may be used.
-0.066400 -0.060021 -0.062313 -0.071 300 -0.063924 -0.056601
mrnaxa
Ub
2.0 1.8 1.8 1.8 2.0 2.0
0.004 0.002 0.002 0.002 0.002 0.002
The standard deviation of fit.
TABLE IV: Coefficients for the Osmotic Coefficient Polynomials @ = a , t a,m t a,mz + a,m3 + a,m4 + a,m5 Zn(CF,COO), Cu(CF,COO), Mn(CF,COO), Co(CF,COO), Ni(CF,COO), Mg(CF,COO), a, a,
a, a, a4
a, a
8.4212 X lo-' 1.8401 X 10'' 1.3907 X lo-' -7.9174 X lo-' 1.8808 X lo-' -1.6934 x lo-, 8.02 X loT6
8.5250 X lo-' 1.5539 X lo-' 1.7528 X lo-' -1.0411 X lo-' 2.4893 x lo-' -2.2049 x lo-' 1 - 3 5x 10-5
8.3865 X 1 O - I 1.8995 X 10'' 1.2104 X l o - ' -6.4524 X lo-' 1.4202 X lo-' -1.2032 x lo-, 1.40 x 10-5
8.5028 -1.8520 3.7626 -3.0504 1.0979 -1.5121 8.02 X
X X X X X X
lo-' lo-' lo-' lo-' lo-' lo-'
8.4937 X lo-' 1.6653 X l o - ' 1.6106 X l o - ' -8.8133 X lo-' 1.9130 X lo-' -1.5578 X loh3 6.67 X
8.4215 X lo-' 2.2885 X l o - ' 1.2846 X l o - ' -6.4727 X lo-' 1.2922 X lo-' -9.6772 X 1.11x 10-5
Residual variance.
0
600
1
I
I
800
1000
1200
Xhml
+
Flgure 10. Absorption spectra of Cu(CIO,), CF,COONa in aqueous and CF,COONa were solution at 25 OC. The concentration of CU(CIO~)~ respectively, (-) 0.0214 and 4.69 M and ( X X X ) 0.2031 and 4.70 M.
mixture. Thus, inspection of the data shows that stabilities of the MCF3COOt complexes, apart from their nature, follow the sequence Mg < Mn S Co 5 Ni < Cu (1) The position of Zn depends on the molality of the metal perchlorates forming the ionic medium, but it is always Mg < Zn < Cu. Osmotic and Activity Coefficients Isopiestic equilibrium molalities of the investigated anu reference solutions and the calculated osmotic coefficients of the former are listed in Table 11. The maximum error in is estimated to be 0.6%. The values of 6 and y at rounded concentrations, calculated with the aid of Pitzer's equationsg (Table 111) or from the polynomials of Table IV, are listed in Table V. Plots of the osmotic and activity coefficients vs. molality for all investigated systems are shown in Figures 11 and 12, respectively, The pattern of 6(m)curves determined presently for the divalent transition metal trifluoroacetates differs markedly from those for aqueous solutions of transition metal salts involving other anions (Clod-, Sod2-,C1-, and BY).^-^ Osmotic coefficients at molalities not exceeding 1mol kg-l are very nearly the same for Mn(CF3C00)2,CO(CF,COO)~, Ni(CF3C00)2,and Zn(CF3C00)2and markedly lower for CU(CF~COO)~. At the same time the values of 6 for
I
I
lo
20
m h o 1 kg'l
30
40
50
Figure 11. M o l a l i dependences of the osmotic coefficient for aqueous Ni(CF,COO),, Cu(CF,COO),, solutions of Mn(CF,COO),, Co(CF,COO),, Zn(CF,COO),, and Mg(CF,COO), at 25 'C.
3.0
I
OD
ID
ZC
30
LD
5.0
m(rnol kg-1)
Flgure 12. Molality dependences of the mean molal activity coefficient for aqueous solutions of Mn(CF,COO),, Co(CF,COO),, Ni(CF,COO),, Cu(CF&OO),, Zn(CF3C00),, and Mg(CF,COO)2 at 25 OC.
Mg(CF3COO), are markedly higher. If there were no coordination and association, the osmotic coefficients should be the same for all the salts, including Mg(CF3COO)2,in analogy to what was observed in the systems
2802
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979
TABLE V: Osmotic Coefficients,:~4 Mn(CF,COO),
2. Llbus and H. Tialowska
and Activity Coefficients, 7: of M(CF,COO), a t Even Molalities (25 “ C )
Co(CF,COO),
Ni(CF,COO),
Cu(CF,COO),
m
4J
Y
4J
Y
4J
Y
4J
Y
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.o 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5
0.8712 0.8882 0.9114 0.9367 0.9631 0.9904 1.0182 1.0462 1.0744 1.1025 1.1580 1.2119 1.2633 1.3118 1.3593 1.4668 1.5658 1.6573 1.7303
0.538 0.503 0.494 0.495 0.503 0.515 0.529 0.547 0.566 0.588 0.636 0.691 0.751 0.815 0.885 1.080 1.310 1.578 1.862
0.8677 0.8838 0.9068 0.9323 0.9592 0.9872 1.0158 1.0448 1.0741 1.1034 1.1617 1.2188 1.2739 1.3265 1.3798 1.5036 1.6200 1.7281 1.8170
0.533 0.496 0.487 0.488 0.495 0.506 0.521 0.539 0.559 0.581 0.630 0.687 0.750 0.819 0.896 1.119 1.392 1.721 2.085
0.8648 0.8801 0.9029 0.9284 0.9554 0.9834 1.0121 1.0411 1.0703 1.0995 1.1575 1.2139 1.2682 1.3197 1.3752 1.4991 1.6137 1.7190 1.8092
0.529 0.491 0.481 0.481 0.488 0.499 0.513 0.530 0.550 0.571 0.619 0.674 0.735 0.801 0.876 1.093 1.356 1.669 2.023
0.8531 0.8584 0.8713 0.8870 0.9041 0.9221 0.9405 0.9592 0.9778 0.9963 1.0322 1.0658 1.0965 1.1237 1.1507 1.2014
0.517 0.469 0.450 0.441 0.439 0.440 0.443 0.448 0.455 0.463 0.481 0.501 0.522 0.544 0.567 0.621
Zn(CF,COO), 0.8693 0.8862 0,9098 0.9357 0.9630 0.9911 1.0199 1.0490 1.0782 1.1074 1.1653 1.2216 1.2757 1.3270 1.3778 1.4904 1.5899 1.6790 1.7540
Mg(CF,COO),
Y
4J
Y
0.535 0.499 0.490 0.492 0.500 0.512 0.527 0.545 0.566 0.588 0.639 0.696 0.760 0.829 0.904 1.114 1.358 1.636 1.941
0.8717 0.8919 0.9191 0.9489 0.9802 1.0126 1.0457 1.0793 1.1132 1.1472 1.2151 1.2821 1.3473 1.4104 1.4717 1.6161 1.7487 1.8724 1.9875 2.0882
0.537 0.504 0.499 0.504 0.516 0.532 0.553 0.576 0.603 0.632 0.699 0.777 0.865 0.963 1.073 1.399 1.809 2.319 2.946 3.682
a Values of 4~ and y in the molality range 0.1-1.8 mol kg-’ were calculated from Pitzer’s equations (see text and Table 111), and for the higher molalities with the polynomials listed in Table IV.
M(C104)2+ H20.3 On the other hand, in systems involving coordinating anions (C1- and Br-) we observed the characteristic sequence of osmotic and activity coefficients, referred to as the “partly inverted Irving-Williams series”.1*2v6J1 Neither of these two patterns is observed for the trifluoroacetates. Within the range of low and moderate concentrations the sequence of osmotic coefficients is Mg > Mn Zn k Co k Ni > Cu (2) and above 2 mol kg-l it is Mg > Co > Ni > Zn > Mn > Cu (3)
-
Discussion A qualitative explanation of the characteristic pattern of the 4(m) curves displayed by bivalent metal trifluoroacetates seems possible in terms of overlapping outer-sphere and inner-sphere equilibria. All we need is to assume that, for a given valency type electrolyte, increasing hydration of ions, as well as of the association products, should result in increasing osmotic and activity coefficients, while increasing ionic association would induce an opposite effect. Further, taking into account the behavior of the bivalent transition metal perchlorates and magnesium perchlorate, we assume that in the absence of association the trifluoroacetates likewise would display closely similar $(m) dependences. Hence, apart from spectrophotometric evidence, the observed divergence of the 4(m)curves itself indicates extensive ionic association, at least for transition metal trifluoroacetates. Occurrence of ionic association in magnesium trifluoroacetate is less evident, although markedly lower osmotic coefficients of the latter compared with magnesium perchlorate make it highly probable. However, most significant for our purposes is the fact that nickel(I1) trifluoroacetate displays markedly lower osmotic coefficients than magnesium trifluoroacetate, despite the fact that inner-sphere association is essentially absent in the former, at least up to some 1 mol kg-l, as evidenced by the spectrophotometric results. It follows that outer-sphere association of ions must occur to a higher extent in nickel(I1) trifluoroacetate than in magnesium trifluoroacetate. Since the Coulombic contribution to the stability of an outer-sphere ion pair involving a given anion
for Ni2+should not be higher than for Mg2+,an essential contribution due to hydrogen bond formation between the anion and the hexaaquo cation must be assumed to account for the higher association in nickel(I1) trifluoroacetate. Higher acidity of the hydrated Ni2+cation than that of Mg2’ would, therefore, be responsible for the observed difference in association behavior toward the trifluoroacetate anion. The general conclusion at this point is that outer-sphere association of bivalent cations with the trifluoroacetate anion is not only Coulombic in nature, but also depends on the proton-donor strength of the hexaaquo cations. Similar conclusions arise from comparison between nickel(I1) and cobalt(I1) trifluoroacetates with respect to their $(m)behavior. As is seen from Figure 11,the two salts exhibit almost the same 4(m)dependence up to some 2.5 mol kg-l, and slightly lower 4 values are exhibited by the nickel(I1) salt at higher concentrations. At the same time, the visible spectral effects indicate marked innersphere association in the cobalt(I1) trifluoroacetate. Therefore, the conclusion must be drawn that outer-sphere association should be more extensive in the nickel(I1) salt. Again, the inferred difference in the extent of the outer-sphere association between nickel(I1) and cobalt(I1) would be accountable in terms of the higher acidity of the hydrated Ni2’ cation than that of Co2+. Unfortunately, existing literature data on the first step hydrolysis constants are too divergent to check this correlation.12 We may only note that the higher heat of hydration of Ni2+ than that of Co2+makes the higher acidity of the former cation in aqueous solution highly probable. Similar conclusions were inferred from a spectrophotometric study on the association of the picrate anion with divalent metal cations in aqueous s01ution.l~ It is difficult, from the experimental data available, to estimate the relative importance of the outer-sphere and inner-sphere associations in the remaining three trifluoroacetates, viz., those of manganese(II),copper(II),and zinc(I1). It is only clear that the latter association occurs in solutions of copper(I1) trifluoroacetate to the greatest extent, as evidenced by the visible absorption spectra and sequence (l),but nothing can be said of the outer-sphere association in this case. However, apart from this question, the present results taken together indicate a greater im-
Ionic Self-Diffusion in Polyelectrolyte Solutions
The Journal of Physical Chemlstiy, Vol. 83, No. 20, 7979 2603
portance of outer-sphere association in the presently studied trifluoroacetates than in the divalent transition metal halides. The above inferred positive contribution of hydrogen bond formation to the stability of the outer-sphere ion pairs involving the trifluoroacetate anion and the hexaaquo cations of the divalent transition metals apparently contradicts the relatively low ability of the anion to direct coordination. It seems that it is the spacial requirements of the carboxylic group in CF3COO-that may be responsible for its reluctance to enter the first coordination sphere of the metal cations in a regular octahedral configuration. At the same time formation of two hydrogen bonds with water molecules coordinated to the metal cation, as well as direct coordination to the cupric cation in a tetragonally distorted configuration, may not impose similar limitations. Acknowledgment. The authors are indebted to Professor w. Lib& for valuable suggestions and Mgr R.
Pastewski for programming the computer calculations.
References and Notes R. A. Robinsonand R. H. Stokes, “Electrolyte Solutions”, Butterworth, London, 1955. Z. Llbul, W. Maciejewski, and G. Kowalewska, Polish J . Chem., 52, 793 (1978). Z. LibuS and T. Sadowska, J . Phys. Chem., 73, 3229 (1969). Z. LlbuS, Polish J. Chem., in press; Inorg. Chem., 12, 2972 (1973). Z. LlbuS and H. Tlalowska, J . Solution Chem., 4, 1011 (1975). R. A. Robinson and D. A. Sinclair, J . Am. Chem. SOC.,56, 1830 11934). G. Scatchard, W; J. Hamer, and S. E. Wood, J. Am. Chem. Soc., 60, 3061 (1938). W. J. Hamer and Y.-C. Wu, J . Phys. Chem. Ref. Data, 1, 1047 (1972). K. S. Ptzer and G. Mayorga, J . Phys. Chem., 77, 268, 2300 (1973). J. S. Coleman, L. P. Varga, and S. H. Mastin, Inorg. Chem., 9, 1015 (1970). Z. LibuS and G. Kowalewska, Polish J. Chem., 52, 709 (1978). L. G. Sillen and A. E. Martell, “Stability Constants of Metal-Ion Complexes”, The Chemical Society, Burlington House, London, 1964. W. LibuS and H. Twardowska, Roc.?. Chem., 51, 499 (1977).
Conductivity and Ionic Self-Diffusion in Polyelectrolyte Solutions under Excess-of-Salt Conditions J. P. Meullenet, A. Schmitt, and
R. Varoqui”
CNRS, Centre de Recherches sur les Macromolcules, 67083 Strasbourg Cedex, France (Received April 9. 1979) Publication costs assisted by Centre National de la Recherche Scientiflque
Measurements of the “excess conductivity” of a linear polyelectrolyte (an alternating copolymer of maleic acid and ethyl vinyl ether) dissolved in aqueous solutions of NaBr are presented. On the basis of a previous theoretical study and of recently published electrophoresis data, a correlation is established with the Manning theory of self-diffusion of small ions. No quantitative agreement is reached, and the validity of the Debye-Huckel approximation is questioned.
Introduction To describe and understand the equilibrium and dynamic properties of aqueous solutions of flexible polyelectrolytes is a difficult task, which is far from accomplished. Some progress has been made recently in the field of polyelectrolyte conf~rmation,l-~ and the line-charge model introduced by Manning4 allows most colligative properties to be described almost q~antitatively.~ In recent articles,g8 we developed a phenomenological approach t o the description of linear irreversible processes occurring in polyelectrolyte solutions. Transport parameters were expressed as a function of binary friction coefficients, and we discussed the significance of these coefficients in relation to hydrodynamic and electrostatic interactions. The importance of electrostatic interactions was emphasized, and we showed how the binary coefficients of friction of the polyion with ions of its atmosphere can be evaluated by using molecular theories of the self-diffusion of small ions. The purpose of the present paper is to check the validity of the Manning theory9under excess-of-saltconditions, where direct measurement of the reduced ionic self-diffusion coefficients remains problematic because of the lack of experimental precision. However, the problem can be approached indirectly by studying the “excess conductivity” due to the added polyelectrolyte. We first briefly recall the theoretical background established in a previous article.1° Experimental results are then presented and discussed. 0022-3654/79/2083-2603$0 1.OO/O
Theory Consider an aqueous solution containing a monodisperse polyelectrolyte and a low-molecular-weightmono-monovalent salt, at concenttations cp and c,, respectively. Ions present in the solution are the mutual counterions (l),the coions (2), and the polyions (3). The stoichiometric number of counterions per polyion is v,; it can differ from the effective number, v, because of counterion condensation. The stoichiometric fraction, x , of counterions belonging to the polyelectrolyte is then
and near the excess-of-salt limit, expressed by c, >> v,cp, we have x N 0. Let us call K“ and K the respective conductances (ratio of electrical current density to field strength) of the pure salt solution and of a polyelectrolyte-plus-salt solution. The following relation can be derived:
where the X;’s are the equivalent conductances of the ions. Superscript IJ refers to the property as observed in a pure salt solution at concentration c,, while subscript s refers to a stoichiometric property. Near the limit x N 0, we define the slope sK by 0 1979 American Chemical Society
