OSMOTICAND ACTIVITYCOEFFICIENTS OF DIVALENT METALPERCHLORATES
3229
Coordination and Association Equilibria in Aqueous Electrolyte Solutions. I.
Osmotic and Activity Coefficients
of Divalent Metal Perchlorates by Zofia Libus and Teresa Sadowska Department of Physical Chemistry, Technical University of Gdahsk, Gdahsk, Poland
(Received February 6 , 1969)
Osmotic coefficients have been determined by the isopiestic method for aqueous solutions of Mn(C104)2,CO(C104)2,Ni(C104)2, and Cu(C104)2 at 25’. Activity coefficientsfor cO(c104)~and Ni(C104)2are calculated. The results are compared with the data for Mg(C104)~and Zn(ClO4)z of Robinson and Stokes. The osmotic coefficients of equally concentrated solutions of Mn(C104)2, cO(c104)~, Ni(C104)~,and Zn(CIOd)zare found to be the same, within the experimental error, up to approximately 3.0 rn, while they are slightly lower for Mg(C101)2 and Cu(C104)2at concentrationsexceeding 1.0 m. Absorption spectra of cO(c104)~ and Ni(C104)2solutionsare found to be independent of concentration, while the spectrum of Cu(C104)~shows small changes which may be ascribed to the formation of an outer-spherecomplex. Taking into account both osmotic and absorption spectra results, the conclusion is drawn that octahedral hexaaquo complexes, probably with second layers of hydrogen-bonded water molecules, are maintained unchanged in the whole concentration range investigated in solutions of %h(C104)2, C0(c104)~,Ni(C10&, and Zn(ClO4)z. On the other hand, an interaction with the perchlorate anion, probably consisting in its penetration into the second hydration sphere of the cation, takes place on increasing concentrationin solutions of Cu(ClO4)2and Mg(C104)z.
Introduction Several observations made in this laboratory suggested that the interactions with the medium of coordination clusters containing specified ligands and having a specified structure may, in some cases, be essentially independent of the nature of the central metal atom.’-4 I n the field of thermodynamic properties of solutions this results in essentially the same variation of the activity coefficients of analogous coordination forms of different metals with the composition of the s o l ~ t i o n . ~The ! ~ above generalization seems to be a good one for systems involving monofunctional organic ligands such as pyridine, acetonitrile, or dimethyl sulfoxide. It proves to be useful in the interpretation of thermodynamic properties of nonaqueous inorganic salt solutions in terms of coordination equilibria. However, it is not clear whether it will be equally satisfactory for systems involving water as a ligand. It was often suggested, and also shown experimentally, that coordinated water molecules may form strong hydrogen bonds with water molecules or other species present outside the coordination sphere^.^ These hydrogen bonds may be expected to be the stronger, the greater the coordinating power of the central metal atom. I n this way the specific properties of metal ions may become of importance in determining the interactions outside the first coordination spheres of coordination clusters containing water molecules as ligands. I n the present investigation we intended to study to what an extent the concentration dependences of the
chemical potentials of both components of an aqueous electrolyte solution are governed by the nature of coordination clusters formed by the cations. Perchlorates of manganese(II), cobalt(II), nickel(II), and copper(I1) have been chosen for the study, since they were expected to exist in a broad range of concentrations exclusively in one coordination form, namely that consisting of six-coordinate octahedral cations with the anions outside the coordination spheres. As it is customary to discuss the chemical potentials of the solvent and solute in terms of the osmotic and activity coefficients, respectively, these quantities were determined in our work using the isopjestic method. Existing literature data on the osmotic and activity coefficients of Zn(C104)zand Mg(C104)t solutionse enabled us to include these two salts in the discussion. Evidence for the existence of six-coordinate octahedral aquo complexes of &!fn(II), Co(II), Ni(II), and Cu(I1) in dilute water solutions in the absence of complexing anions has been provided mainly by the ligand field theoretical analysis of the visible absorption spectra of corresponding solutions.’ Zinc(I1) and mag(1) W. Libus and I. Uruska, Inorg. Chem., 5,256 (1966). (2) W. Libub, D. Puchalska, and T. Szuchnicka, J . Phys. Chem., 72, 2075 (1968). (3) W. Libus and H. Strzelecki, Electrochim. Acta, in press. (4) W. Libub, M. Kluczkowski, and I. Uruska, in preparation for publication in J . Phys. Chem. ( 5 ) T. G. Baliczewa and S. N. Andriejew, Zh. Strukt. Khim., 5, 29 (1964). (6) R.A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth and Co. Ltd., London, 1955.
Volume 73, Number 10 October 1969
3230 nesium(I1) are also believed to form six-coordinate aquo complexes. Direct evidence for the hydration number of 6 for Mg2+has recently been obtained from nmr measurements.* Although six-coordination of zinc(I1) in the aquo complex has not, so far, been shown directly, it may be assumed as very probable in view of the fact that octahedral aquo complexes, [Zn(OH2)6]2+, were detected as structural units in crystals of hydrated zinc(I1) salts.@
ZOFIA LIBUSAND TERESA SADOWSKA
down to approximately -45" and then evacuated for 30 min, while its temperature slowly increased approaching the room temperature. For dilute solutions, a procedure consisting of a very slow evacuation of unfrozen solutions placed in the slowly rotating isopiestic unit proved to be better, in the sense that fewer experiments were spoiled as a result of splattering. After evacuation the apparatus was immersed in the thermostated water bath, where it remained for 2-7 days. I n order to diminish time necessary for equilibration, slow Experimental Section rocking of the isopiestic apparatus was applied. The temperature of equilibration was 25.00 + 0.01". After Materials. Perchlorates of magnesium(II), manequilibrium had been reached, the isopiestic unit was reganese(II), cobalt(II), nickel(II), and copper(I1) were moved from the bath, air was slowly admitted, and the obtained by dissolving analytical grade carbonates in lids were placed on the dishes as soon as possible. The analytical grade perchloric acid. I n each case the reequilibrium concentrations of the investigated and the sulting solution was filtered off from the undissolved exstandard solutions were calculated from the final cess of the solid phase and evaporated to crystallization, weights of the dishes. Depending on the concentration The materials were further purified by repeated crystalrange of the investigated solutions, solutions of potaslizations-at least three-using conductivity water in sium chloride, sodium perchlorate, or magnesium perthe last operation. Analytical grade sodium perchlochlorate were used as standards. The whole procedure rate and potassium chloride were recrystallized thrice was checked by determining water activities of the from conductivity water. and Mg(C104)2solutions at several concentraProcedures. The concentration of the C O ( C ~ O ~ ) ~NaC104 , tions using KC1 solutions as standards. The results Ni(C104)2,and Cu(ClO& stock solutions were deterwere found to be consistent with the interpolated values mined by standard electrogravimetric methods. At of Robinson and Stokese with the mean deviation of least five determinations were performed in each case. 0.0007 in terms of water activity, when its value was beNickel(I1) was, in addition, determined gravimetrically tween 0.846 and 0.967. using dimethylglyoxime. The concentration found in Spectrophotometric measurements were carried out this way was 1.911 X lo-* mol g-' of the solution, while + 0.1" by means of a Unicam SP-500 spectroat 25.0 that found electrogravimetrically was 1.913 X photometer using 1,0.5,0.2, and 0.1-cm cells. The latter value was used in further calculations. Equilibrium isopiestic molalities of the investigated Manganese(I1) in the Mn(C104)2 stock solution was I. Osmotic coefficients solutions are collected in Table determined gravimetrically in the form of MnS04. The of the divalent metal perchlorate solutions were evalconcentration of this solution was confirmed by EDTA uated from the equation titration, but only the gravimetric result was used in the calculations of the osmotic coefficients. The con+=--v r m A centration of the YIg(ClO4)2 stock solution was deter3m mined by EDTA titration in a pH 10 buffer using murexide indicator. Sodium perchlorate and potassium where m and 4 are molality and the osmotic coefficient, chloride in their stock solutions were determined by respectively, of the investigated solution, while vr, m,, drying weighed amounts of the solutions at 180". and $r are the number of ions, molality, and the osmotic Osmotic coefficients were determined isopiestically coefficient, respectively, of the reference solution. For following the method described by Robinson and Sinsolutions which contained perchloric acid in addition to clair1° taking into acount the modifications introduced a divalent perchlorate the following equation was used by Scatchard, et uZ.ll The massive, vacuum-tight brass vessel contained six depressions in which goldplated silver dishes with lids were placed. Weighed amounts, approximately 1 g of the investigated solution where m' denotes the molality of the acid. The of known initial concentration, were placed in three of (7) C. K. Jgirgensen, "Inorganic Complexes," Academic Press, them, while the other three contained the standard soLondon and New York, N. Y.1963. lution. In some experiments two of the investigated (8) N. A. Matwiyoff and H. Taube, J. Amer. Chem. Soc., 90, 2796 solutions of approximately equal osmotic coefficients (1968). were placed in duplicates in four dishes, while the re(9) A. F.Wells, "Structural Inorganic Chemistry," Clarendon Press, Oxford, 1962,p 582. maining two contained the standard solution. Two (10) R.A. Robinson and D. A. Sinolair, J. Amer. Chem. SOC., 5 6 , 1830 methods were used to remove air from the apparatus. (1934). In one, used for concentrated solutions, the isopiestic (11) G. Soatchard, W. J. Hamer, and S. E. Wood, ibid., 60, 3061 apparatus containing the solutions was initially cooled (1938). The Journal of Physical Chemistry
OSMOTIC AND ACTIVITY COEFFICIENTS OF DIVALENT METALPERCHLORATES
323 1
Table I: Molalities of Isopiestic Solutions m ~ ~ ( c i o ~ ) ~
mKc 1
0.0972 0.1104 0.1820 0.1951 0,4241 0.5664 0.5828 0.7364 0.7653 0.9104 0.9570 0.9811 1.0758 1.2178 1,2939 1.3212 1.4760
0.1430 0.1633 0.2791 0.3034 0.7326 1.0404 1.0796 1.4556 1.5373 1.9347 2.0641 2.1445 2.4299 2.8885 3.1317 3.2409 3.7999
mKcl
mNi(0104)z
WKCl
0.1430 0.1525 0.2791 0.3034 0.5969 0.7326 0.9745 1.0404 1.0796 1.4556 1.5373 1.8753 2.0641 2,1445 2.8885 2,9324 3 1317 3.2409 3.6870 4.0686
0 0981 0.1036 0.1818 0.1959 0.3578 0.4255 0.5382 0.5683 0.5855 0.7390 0.7685 0.8930 0.9607 0.9855 1.2221 1.2353 1.2974 1.3253 1.4497 1.5562
0.1622 0.6263 1.2391 1.6185 2.2394 3.3720 4.4722
I
I
mNaClO4
mivacio4
4.4884 5.2573
1.6963 1.8915
4.4844 5.2573 m~ll~(cio~)~
2.4010 2.8464 3.2085 3.5809
0.1111 0.3744 0.6579 0.8088 1.0328 1.3875 1.6901
mNsclo4
1.7015 1.8952
mi~~(cio~)~
2.1877 2.4104 2.7967 3.0572 3.5145
2.2216 2.4500 2.8464 3.1093 3.5809
m ~ ~ ( c i o ~ ) ~
5.0430 8.2392
1.8792 2.6229
2.8471 3.1903 3.5569
~
0.898 0.936 0.975 1.018 1.064 1,111 1.164 1.220 1 276 1.337 1.456 1.583 1.712 1,845 1,990 2.373 2.762 3.163 I
4.4338 5.0430 8.2392
1.6734 1.8299 2.5511
2.8147 3.1494 3.5059
2 7694 3.1012 3.4562 I
Cu(C104)2and Mn( C104)2 cu(c104)2----~ m
0.579 0.564 0.577 0,602 0.637 0.681 0.734 0.795 0 866 0.949 1.155 1.422 1.762 2.196 2.81 5.33 10.39 20.6
0.1091 0.3641 0.6440 0.7908 1.0079 1.3505
~%11g(Cl04)z
2.8147 3.1494 3.5059
e -
0.900 0.938 0.978 1.021 1.069 1.118 1.170 1.225 1.282 1.340 1.465 1.592 1.718 1.848 1.996 2.373 2.755 3.140
0.1622 0.6263 1.2391 1.6185 2.2394 3.3720
Table I11 : Osmotic Coefficients at 25' of
Table I1 : Osmotic and Activity Coefficients at 25' for Interpolated Molalities
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5
mMn(cio4)n
mNsc104
mliig(c104)s
2.3638 2.7947 3.1453 3.5013
mKCl
0.578 0.561 0.572 0.597 0.630 0.672 0.723 0.784 0.853 0.937 1,134 1.395 1.728 2.165 2.76 5.26 10.29 20.8
necessary values of were found by interpolation from the tables of Robinson and StokesaG For Co(C104)2and Ni(C10& solutions, for which a great number of iso-
0,1111 0.3744 0.6579 0.8088 1.0328 1.3875 1.6901 1,8792 2.6229 2.8471 3.1903 3.5569
__-
Mn(C104)F---
4
m
-$
0.893 1.001 1.129 1.208 1.327 1.534 1.727 1.837 2.332 2.503 2.741 2.996
0.1091 0.3641 0.6440 0.7908 1.0079 1.3505 1.6734 1.8299 2.5511 2.7694 3.1012 3.4562
0,909 1.029 1,153 1.236 1.359 1.576 1.776 1,886 2.397 2.573 2 820 3.084 I
piestic experiments at closely spaced concentrations were performed, values of the osmotic coefficient a t rounded concentrations, found by interpolation from large scale graphs, are given in Table I1 along with the activity coefficients. For Mn(C104)~and CU(CIO~)~, for which fewer experiments were performed, we restricted ourselves to the calculation of the osmotic coefficients at the isopiestic molalities. They are given in Volume 73, Number 10 October 1969
ZOFIA LIBUSAND TERESA SADOWSKA
3232
Table IV : Isopiestic Molalities and Osmotic Coefficients for Acidified Solutions of Ni(Cl0a)z and Cu(C104)2
----
Reference solution
__---
Ni (Clodz solutions---
mNaC104
mN i(C 1 0 4 ) ~
rnHCl04
5.3416 6.8229 8.3040
1.9093 2.2442 2 * 5579
0.0164 0,0199 0.0227
d
Cu(C104)a solutions---
m~~(c104)~
1.9513 2.2955 2.6309
1.922 2.173 2.399
m~cio4
0.0145 0,0199 0.0227
d
1.882 2.124 2.333
3.5
3.0
28
cet 2.0
1.5
1.0
0.5
1.0
1.5
2.5
2.0
3.0
3.5
4.0
Concn, m. Figure 1. Concentration dependence of the osmotic coefficients for aqueous solutions of: A, Mn (Cl04)~;0, cO(c104)~;f, Ni(ClO4)z; A, Cu(ClO&; -, Zn(C10dZ; - - - -, Mg(C104)2;0 , Ni(C10& and HC104; W, C U ( C ~ Oand ~ ) ~HC104, a t 25'. Data for Zn(C104)zand Mg(ClO4)s from ref 6. For concentrations of HClO, see Table IV.
Table 111. Only a few experiments were performed with acidified C U ( C I O ~ )and ~ Ni(C104)2 solutions. Their results are collected in Table IV. Mean molal ionic coefficients, y, for cobalt(I1) and nickel(I1) perchlorates were calculated from the following form of the Gibbs-Duhem equation In Y
=
In
+ cp - 40.1+ L zy dm
70.1
where y0.1and cp0.1 are the activity and osmotic coefficients, respectively, at the molality of 0.1. The values of yo.1 were found following the procedure proposed by Guggenheim and Stokes. l 2 The following values of the The Journal of Physical Chemistry
parameters P and 4% of the Debye-Hiickel equation, using the notation of Guggenheim and Stokes, were assumed cO(c104)z
Ni(Clod)2
6
3.30
3.28
P
0.410
0.405
They give the best fit of the calculated osmotic coeficients to the experimental values, when the concentration range 0-0.4 m is taken into account, the maximum (12) E. A. Guggenheim and R. H. Stokes, Trans. Faraday Soc., 54, 1646 (1958).
3233
OSMOTIC AND ACTIVITY COEFFICIENTS OF DIVALENT METALPERCHLORATES 25
20
15 $:
10
5
Concn, m.
~ ; Ni(C104)2; Figure 2. Concentration dependences of the mean ionic activity coefficients for aqueous solutions of: 0, C O ( C I O ~ )x, -, Zn(C104)z;and - - - -, Mg(C104)Z,a t 25'. Data for Zn(CIOr)zand R/lg(ClO& were taken from ref 6 and corrected according t o ref 12.
deviations being 0.002. As a result of some uncertainty inherent in this method, the activity coefficients reported in Table I1 may involve a small systematic error, most probably the same for both cobalt(I1) and nickel(11) perchlorates.
Results and Discussion Plots of the osmotic coefficient vs. concentration for aqueous solutions of Mn(C104)2, CO(c104)2, Ni(C104)2, CU(CIO~)~, Mg(C104)2, and Zn(ClO4)z are shown in Figure 1. Figure 2, on the other hand, shows the concentration dependences of the mean ionic activity co)~, Zn(C104)z, and efficient for C O ( C ~ O ~ Ni(C104)2, Mg(C104)2. The data for both the osmotic and activity coefficients of hIg(C104)2and Zn(ClO4)z were taken from the work of Robinson and Stokes,G as they are essential for the present discussion. It is seen from Figure 1 that the osmotic coefficient a t any specified concentration is the same, within experimental error, for Mn(ClO4)2, Co (Clod)2, Ni (Clod)Z, and Zn(ClO& in the whole concentration range investigated, while it is slightly lower for Cu(C104)z and Mg(C104)z at concentrations exceeding 1.0 m. It may be assumed that the concentration dependences of the osmotic coefficient are the same within experimental
error for all the six metal perchlorates at concentrations not exceeding 1.0 m, and they remain the same up to approximately 3.0 m for the first four. It is noteworthy that, as inspection of Table IV and Figure 1 shows, addition of a small quantity of perchloric acid has no detectable effect on the difference in the value of the osmotic coefficient between Ni(C104)z, on one, and CU(CIO~)~, on the other hand, when solutions having equal concentrations are compared Thus, hydrolysis effects as a possible source of the difference in behavior between solutions of Cu(ClO&, on one hand, and those of co(c104)2, Ni(C10J2, and Zn(c104)z, on the other, observed in the region of higher concentrations, seem to be excluded. We may add that the osmotic and activity coefficients of zinc(I1) and copper(I1) p-toluenosulfonates, recently reported by Bonner, et al., l 3 for concentrations up to 0.3 m, also show a very close coincidence. Similarities and differences in concentration dependences of the osmotic coefficients should be reflected in concentration dependences of the activity coefficients. However, there are greater uncertainties in the I
(13) 0. D. Bonner, W. H. Breazeale, and C. Rushing, J.Phys. Chem., 69, 4345 (1965).
Volume 79, Number 10 October 1069
ZOFIA LIBUSAND TERESA SADOWSKA
3234
12
9
li 6
0
0.5
1.0
1.5
2.0
2.5
chl (C10412, Figure 3. Concentration dependences of the molar extinction mixtures coefficient for ( I ) Cu(C104)zin Cu(C1O4)&Ig(C1O4)~ a t 805 mp; (2) Co(C104)2at 510 m r ; (3) Ni(C10& at 395 mp; (4)Ni(C101)*at 675 mp.
latter, as a result of the integration process involved in their calculation. I n view of this fact, the small differences in the activity coefficients between CO(c104)z and Ni(C104)2,on one hand, and Zn(C104)2,on the other, which may be seen from Figure 2, should not be considered as serious and contradicting the apparent similarity of their osmotic coefficient curves. Further discussion will center on the osmotic coefficients since, being calculated directly from the experimental results a t any specified concentration, they are better suited for comparison purposes. It was essential, for the interpretation of the osmotic and activity coefficient data, to know whether or not the visible and ultraviolet absorption bands of the transition metal perchlorates involved in the present investigation are affected by changes in concentration. Solutions of c0(c104)2, Ni(C10&, and C U ( C ~ Owere ~ ) ~studied from this point of view. Their spectra corresponding to low concentrations are well known. I n the present work it was found that the molar extinction coefficients of Co(ClO.J2, measured a t 510 mp, and Ni(C104)2,measured at 395 and 675 mp, solutions are, within the experimental error, independent of concentration, at least up to 2.7 rn. Corresponding curves are shown in , other hand, Figure 3. Solutions of C U ( C ~ O ~on) ~the showed small but measurable changes in the spectrum with increasing concentration. It was found difficult, however, to perform sufficiently precise molar extinction coefficient determinations on concentrated Cu(C104)z solutions because of their strong light absorption. The Journal of Physical Chemistry
Three-component solutions Cu(C104)~-IVig(C104)2-HzO were studied instead. It might be expected that substitution of a part of Cu(C104)2 in a two-component solution by an equivalent amount of R/lg(C104)2,leading to the formation of a three-component system, will not change the state of the remaining part of C U ( C ~ O ~ ) ~ , since these two salts are very similar in their thermodynamic properties. Some of the determined spectra of the mixed Cu(C104)~-i\4g(Cl04)~ solutions, containing a small quantity of HC104 to prevent hydrolysis, are shown in Figure 4,while curve 1 in Figure 3 shows the dependence of the molar extinction coefficient of Cu(I1) at 805 mp on the total concentration of the solution, As is seen, the absorption maximum of the cupric ion originally at 805 mp undergoes a small shift to higher frequencies and a simultaneous increase in intensity when the concentration of the solution increases. A well-defined isosbestic point, located at approximately 870 mp, is observed in the set of absorption curves, indicating an equilibrium between two discrete absorbing species. Since the hydrolysis effects have been excluded in the above described spectrophotometric experiments, the spectral changes observed may be explained only in terms of an interaction between the cupric cation, on one hand, and the perchlorate anion, on the other. It seems that this interaction may consist either in the formation of a true coordination complex or of an outer-sphere associate of the cupric and the perchlorate anion. It is difficult to make a definite choice between these two possibilities. However, the blue shift of the copper(I1) absorption band, which takes place on increasing perchlorate concentration, seems to be readily accountable in terms of an outer-sphere association, and not in terms of a direct coordination of the perchlorate anion. Being a very poor electron-pair donor the perchlorate anion may be expected to bring about a decrease of the ligand field strength within the complex upon coordination and, consequently, a red shift of the absorption band. On the other hand, a replacement of one or two strongly hydrogen-bonded water molecules in the second hydration sphere of the cupric ion in the process of outer-sphere association should result in an increase in the strength of the coordination bonds formed by the water molecules in the first coordination sphere and, consequently, in a blue shift of the absorption band under discussion. It is worth noting, also, that increasing concentration of the perchlorate anions results in a very small change of absorption within the charge-transfer band of the cupric ion located in the vicinity of 200 mp (see Figure 4),which is typical of outer-sphere association. The interpretation of the spectral changes observed for C U ( C I O ~solutions )~ as arising from the outer-sphere association of ions implies that this kind of interaction between ions does not occur in solutions of Co(c104)~. and Ni(C104)2,even at fairly high concentrations, as
OSMOTIC AND ACTIVITY COEFFICIENTS OF DIVALENT METALPERCHLORATES
3235
1500
1000 Id
500
200
250 600
760
800
900
1000
1, w . Cu(C104)2; (2) 4.985 X mixtures a t 25': (1) 1.004 X Figure 4. Absorption spectra of Cu(C104)2in Cu(C104)2--Mg(ClO~)~ lO-4M Cu(C104):!and 1.6869 M Mg(C104)2; (3) 0.0934 M Cu(C104)~;(4) 0.0966 M Cu(C104)~and 1.3892 M Mg(C104)2;(5) 0.0964 M Cu(C104)2 and 2.4061 M Mg(C104)~.
their absorption bands remain constant both in position and intensity. However, since this interpretation of the constancy of the ligand-field bands of hydrated transition metal cations is different from the generally accepted point of view,14J5 it may be subject to discussion. Similar problems arise in the interpretation of the results concerning the osmotic and activity coefficients. As is known, i t is only in the region of lowest concentrations that the activity and osmotic coefficients of electrolyte solutions show nonspecific concentration dependences determined solely by the Coulombic interactions between ions. Specific differences between salts of the same valency type, even if they have a common ion, usually become considerable a t higher concentrations. Since the activity coefficient, y, of a dissolved salt a t a specified concentration, m, is uniquely determined by the difference pi - pi', where pi is the chemical potential of the salt at concentration m and pi' is its standard chemical potential defined in the usual way, equal activity coefficients of analogous salts of different metals observed in the region of high concentrations seem to be possible only when the species in the form of which the corresponding cations exist a t infinite dilution remain unchanged when the concentration increases and
are to such an extent similar that their interactions with the medium are practically the same. I n the specific example of divalent metal perchlorates the coincidence of their osmotic and activity coefficient curves might be ascribed simply to the existence of the corresponding cations exclusively in the form of sixcoordinate, octahedral aquo complexes, [M(OHz>,]2+, There is little doubt that this explanation would account correctly for the main features of the results under discussion. However, it cannot satisfactorily account for the subtle differences in the osmotic and activity coefficients between Mn (C104)2, Co (ClO4) , Ni (C104)2, and Zn(ClO&, on one hand, and C U ( C ~ O ~and )~ Mg(Cl04)2, on the other, since it implies that the differences in the osmotic coefficients between these two groups of salts arise from the destruction of the aquo complexes in solutions of Cu(C104)2 and Mg(C104)2, consisting in the formation of perchlorato complexes, This was shown above to be rather unlikely in the case of Cu(C104)~,in view of our spectroscopic observations. It seems more likely that the difference between those (14) J. M. Smithson and R. J. P. Williams, J. Chem. Soc., 457 (1958). (15) D. A. L. Hope, R. J. Otter, and J. E. Prue, ibid.,5226 (1960).
Volume 73, Number 10 October 1969
D.C. DUBEAND R. PARSHAD
3236 divalent metal perchlorates, which show practically the same osmotic and activity coefficients, on one hand, and cupric perchlorate on the other, consists in the outer-sphere association of ions taking place in solutions of the latter. However, the absence of outer-sphere association in solutions of Mn(C104)2, Co(C104)2, Ni(C10J2, and Zn(C104)2would mean that the second hydration spheres of the corresponding cations remain unchanged in a broad range of concentrations. I n other words, this interpretation implies that there are greater units, formulated as { [M(OH&](OH2), j2+, which preserve their identity when changes in the concentration of the corresponding perchlorates occur, and which are independent in their interactions with other species present in the solution of the nature of the metal. The reason for a different behavior of the cupric cation, as compared with the divalent cations of manga-
nese, cobalt, nickel, and zinc, is readily accountable in terms of the known, strong tetragonal distortion of its aquo complex due to the Jahn-Teller effect. It may be expected that the two more distant water molecules in [CU(OH&]~+ are weaker proton donors than the other four and, consequently, form weaker hydrogen bonds with the second-sphere water molecules. As a result there are water molecules in the second hydration sphere of the cupric ion, which are relatively weakly bound to the aquo complex, and these may be expected to be squeezed out by the perchlorate anion. The magnesium ion is, in a sense, similar to the cupric ion, since having weaker coordination properties, i t may be expected to have less strongly hydrogen-bonded water molecules in the second hydration sphere.
Acknowledgment. The authors wish to thank Dr. W. Lib& for many helpful discussions and suggestions.
Application of Bottcher’s Formula to Dielectric Behavior of Liquid Mixtures and a New Method of Deducing Dipole Moments in Liquid and Vapor States by D. C. Dube and R. Parshad National Physical Laboratory, New Delhi-id, India
(Received February 7, 1969)
The paper describes attempts to apply Bottcher’s formula, originally derived for solid powders, to liquid mixtures. It has been shown that Bottcher’s formula, besides being applicable to mixtures of nonpolar liquids as found earlier by Scholte, can also be made to apply for polar-nonpolar systems. The dielectric behavior of these mixtures has been discussed and a new method of deducing dipole moments at infinite dilution has been introduced. An empirical relation has also been formulated which enables the real (vapor) values of the dipole moments to be obtained from the solution values (determined by use of Bottcher’s formula), in the general case of those substances which give the negative solvent effect.
Introduction Bottcher’s formula’ is widely used for correlating the dielectric constant of powders with the material in bulk form. I n the case of a powder dispersed in a binding medium, Bottcher’s formula is €12
-
3 €12
€1
= 6
€2 €2
-
+
€1
2€12
(1)
where el2 is the dielectric constant of the mixture, €1 is the dielectric constant of the binding material, €2 is the dielectric constant of the dispersed component, and 6 is the volume fraction of the component in the mixture The Journal of Physical Chemistry
having the dielectric constant €2. It was thought to be of interest to determine whether the formula above can be used for various kinds of liquid mixtures. Liquid mixtures of nonpolar and polar solutes in nonpolar solvents have been investigated. The former case has been studied earlier by Scholte.2 For the case of liquid mixtures, €1 in formula 1 may be taken as the true dielectric constant of the nonpolar liquid, €2 (1) C.J. F. Bottcher, Rec. Trav. Chim., 64,47 (1945).
(2) T.G.Scholte, Thesis, Leiden (1950), as quoted by H. Looyenga, Mol. Phys., 9,501 (1965).
