COXDUCTANCE OF COPPERm-BENZENEDISULFONATE HEXAHYDRATE
zero concentration, give the following values for the liniiting diffusion coefficients: mesitylene, 2.85 X p-nitroaniline, 2.49 X and lj3,5-trinitrobenzene, 2.22 X As expected, the polar molecules diffuse more slowly than the nonpolar mesitylene.
3003
The differences in 105Dare 0.36 and 0.133, respectively, for p-nitroaniline and trinitrobenzerie compared to mesitylene. Thus both viscosity coefficients and diffusion constants show the effects of local iiiolecular interaction.
Conductance ad' Copper m.-BenzenedisnlfonateHexahydrate in N-Methylpropiconamide from 20 to 4OC'l
by Thomas B. Hoover National Bureau of Standards, Washington, D . C.
(Received M a y $6, 1964)
The conductance of copper in-benzenedisulfonate hexahydrate in N-methylpropionaniide was measured a t 5" intervals froin 20 to 40°, and in the concentration range of 3 X M . Viscosity, conductance, and solubility observations indicate that water to 1 X of crystalliza,tion does not remain associated with the electrolyte in solution. The FuossOnsager conductance equation represents the data satisfactorily, although there is a barely significant, temperature-dependent contribution froin higher order terms in concentration. The ion-size parameter, &, increases from 3.0 to 4.5 with increasing temperature, while the mean hydrodynamic (Stok.es) radius is 4.9 8. The limiting equivalent conductance is 25% larger than that of potassiuin chloride in the same solvent.
Introduction Despite the reniairkably high dielectric constant of N-methylpropionainkde (NMP) , previous conductance measurenients2 indicated that potassium chloride was appreciably associated in this solvenl,. That conclusioin was based primarily on the unrealistically small values of the ion-size parameter, d J , needed to fit the conductance data to the Fuoss-Onsager equation for strong electrolytes. Both the ion-pair association of potassium chloride and the large effect of salts on the viscosity of solutions in NBIP were indicative of pronounced ioiisolvent interactions. Such effects were expected to be enhanced by more highly charged ions; hence, the present conductance study of the 2-2 electrolyte, copper n~-benzenedisulfcinate (CuBDS) was undertaken. This salt is not only readily soluble in NRlP but previous
conductance measurements3 have shown that it is fully dissociated in aqueous solution, in contrast to most 2-2 salts. Dawson and co-workers4have measured conductances of a nuinber of multivalent electrolytes in the related solvent, K-metjhylacetaniide. Apart froin some anoinalies that were attributed to traces of acetate ion in the solvent, the salts all behaved as typical strong electrolytes. (1) Presented, in part, before the Division of Physical Chemistry a t the 145th National Meeting of the American Chemical Society, New Tork, N. T..September 9-13, 1963. (2) T. E. Hoover, J . P h y s . Chem., 6 8 , 876 (1964). (3) G. Atkinson, M . 1-okoi, and C. J. Hallada, J . A m . Chem. Soc., 8 3 , 1570 (1961). (4) L. R. Dawson, J. W. Vaughn, G. It. Lester, >I. E. Pruitt, and P. G. Sears, J . Ph:ys. Chem., 67, 2i8 (1963).
Volume 68, Sumber 10 October, 1864
THOMAS B. HOOVER
3004
Experimental The conductance bridge, cells, and techniques have been described.2 The solvent used in the present study had a specific conductance in the range 0.8 to 1.3 X ohm-’ c n r l at 25’. Analysis of the solvent by gas chromatography showed no more than 0.05yGby volume of water and less than 0.01% propionic acid The CuBDS, in the hexahydrate form, was very kindly supplied by Dr. Gordon Atkinson and was used without further purification. An attempt was made to prepare an anhydrous stock solution. A portion of the hydrate, when dried to constant weight a t 130’ and cooled over PZOb, showed a weight loss of 22.79%. A quantity of the dried salt, sufficient to give a 2.829y0 solution, was quiclcly transferred to ShIP. The copper content of this stock solution mas determined by electrodeposition to be 0.5720%. Thus, the copper content of the original salt, as received, was l5.6l%. The theoretical copper content of CuBDS .6H20is 15.5870. Because of the difficulty of making accurate dilutions of the stock solution and of weighing the dried material, nearly all the solutions used for conductance were prepared from the “as-received” sainple, and concentrations were calculated on the basis of the analytical, rather than the theoretical, composition. The density of the hexahydrate, needed for maliing vacuum corrections to the weighings, was found to be 1.74 by pycnometric displacement of hexane at rooin temperature. Densities of solutions were measured in a modified Sprengel pycnometer having a capacity of 20 ml. At all temperatures the densities mere represented by the equation p = po(1
+ 0.21na)
(1)
where po is the density of the solvent2 and 7n is the concentration in g.-atoms of copper lig. of total solvent including water introduced with the solute. Molarities (cj were calculated from m by the equation c
712.
p o ( l $-
0.21~1)(1
+ 0.3007?2)
(2)
Thus, all concentrations were calculated for anhydrous salt in slightly n-et solvent, although the solute was usually introduced as the hexahydrate. Viscosities were ineasured in two Cannon-Fenske, size 50, viscometers, which were calibrated with SBS Oil H, Lot 12. The same solution was run in each viscoineter and the measurements were repeated a t least once. Solutions were transferred to the auxiliary bulb by pressure of dried air and were allomed to drain in a closed system to minimize contamination from atmospheric moisture. Each viscometer was timed by its own stopwatch both during calibration and measurement. All flow times were longer than 15 iuin. The Journal of Phusical Chemistru
Since preliminary results indicated an effect of water on viscosity, 12 solutions were prepared according to an incomplete block design covering electrolyte concentrations of 0 to 0.020 M and water concentrations, including that added with the electrolyte, of 0 to 1.0 wt. %. The solutions were measured in a randomized order, each a t three or inore temperatures, also chosen in a randomized order. The variate used in the statistical analysis of the results was
Y
= (7 ’70) -
1 - S,c12 ’
(3)
where 7 is the viscosity of the solution and qo is that of the solvent at the same temperature; S , is the Fallienhagen coefficient, estimated from Aos and shown in Table I. The analysis revealed no significant teniperature or cross-product terms. Within experimental error, the data were represented by the equation
Y
=
4.2c
+ 0.020w
(41
where w is the weight per cent of water, including that of hydration. The standard deviation from eq. 4 was 0.5%. The standard deviation of the relative differences between the two viscometers was 0.2%. The viscosity ofathe solvent, shown in Table I, was about 1% lower at all temperatures than the previously reported values. The difference is tentatively ascribed to greater purity of the recently prepared solvent.
Table I : Viscosity Parameters for Solutions of CuBDS in NMP t,
oc. 20 25 30 35 40
?a,
poise
0.0602 ,0522 0456 ,0400 ,0352
SV
0.0265 ,0272 ,0277 0280 ,0285
Results and Discussion Values of the equivalent conductance, A, are presented in Table 11. 50correction has been made for hydrolysis or solvolysis. I n aqueous solution, hydrolysis was small but not negligible.3 The function A,,’ is defined by the equation A,’ =
(Y + l ) A
+ SC”’ - EC log c
(5)
+
where ( Y 1) is a viscosity correction based on eq. 4, S and E are theoretical constants of the Fuoss-Onsager equation, and c is the concentration, expressed in gram( 5 ) R. M . Fuoss and F. Accascina. “Electrolytir Conductance,’’ Interscience Publishers, Inc.. New ’I’ork. N. Y., 1959, p . 234.
CONDUCTANCE OF COPPER VI-BENZENEDISULFOKATE HEXAHYDRATE
3005
Table I1 : Equiva.lent Conductance of CulBDS.6H20 in N M P
3.60 9 16 9 . I6 19.17 30.32 G1,85 61 85 91,58
10.554 10.225 10.230 9.843 9.299 8,870 8,872 8.471
_--_-
3.57 13.62 19.01 23.96 45.59 45.59 48.88 61.32 65.45 65.45 90,80 106.08
-25 0
104~
A
12.159 11.783 11.788 11.338 10,700 10.203 9.741
3.59 9.12 9.12 19.09 39.15 61.59 91.19
13.912 13.181 12.960 12.744 12,044 12.021 11.982 11.649 11,592 11.577 11,116 10.825
3.56 9.04 9.04 13.57 18,92 23.86 38.81 45,40 48.67 61.06 65.17 105.62
15,779 15,291 15.318 14.973 14.710 14.465 13,862 13,637 13.575 13,204 13,129 12,264
3.54 13.51 18.84 18.84 23.78 38.65 45.20 48.46 60.79 64.89 90.02 105.17
17,818 16,903 16.593 16.593 16.318 15.624 15.373 15.300 14,875 14.788 14.194 13.804
atoms of copper per liter. The theory predicts that should be a linear function of c but plots of A,' us. c showed slight curvature. Accordingly, the data were fitted by the method of least squares to an equation of the forin 11,'
A,,' = bo
+ A C + Bca/'
(6)
All points were given equal weight. Table 111presents the values of S and E used in eq. 56and the values found for Aa, A , and B , together with their standard deviations. Figure 1, in which the broken curves correspond to the regression equation ( t ~ )portrays , the extent of curvature and the experimental scatter a t three temperatures.
I
// 30'0
A', A
,
P '
/
/" I
Table 111: Conductance Parameters and Constants for Eq. 6 200
s E ho
25'
30'
350
40'
29.223 12.45i 11.126
34,452 16.456 12,835
40.434 21.572 14 676
47.190 28.790 16.698
54.612 37.142 18.872
0.008
0.012 85
0 018 136
0.015 176
0.029 224
Std. dev. of A"
A
61
Std. dev. of
A B Std. dev. of
B ?Obi,
7 171 76 0.6696
12 133 122 0.6701
12
- 140 110 0 6685
12 -- 249
116 0.6673
18 .362 166 0 6643
Effect of Water. If C U +is~solvated by mater in preference to NfiIP, differences in viscosity and conductance would be expected depending on whether or not the solution contained sufficient water to satisfy the coordination number of the ion. As a test, solutions
IOOOC
Figure 1. Conductance of CuBDS.GHz0 in NMP a t 20, 30, and 40". The solid curge was calculated according to eq. 9 with a = 4.0.
were prepared, containing 0.02, 0.007, and 0.005 mole/ 1. of the oven-dried CuBDS, the analysis of which corresponded to 0.8 mole of water/atom of copper. Thus, these solutions certainly held less than 4 moles of water/copper ion. The viscosity ineasureinents failed (6) S. J. Bass, W. I. Nathan, R. M. Meighan, and R. H. Cole, J . P h w Chem., 68, 509 (1964), give values for the dielectric constant of NMP 7% lower than those of ref. 2 . Pending a resolution of the discrepancy, the higher set of values is adopted here. While this paper was in press, Prof. Cole informed the author t h a t his latest results agree with those of ref. 2 within 0.5%, the estimated error of the lat,ter.
Volume 68, ,Vumbsr IO
October, I964
T ~ o h i a sB. HOOVER
3006
to establish any specific interaction between water and electrolyte concentrations, but the equivalent coiiductances of these solutions were uniformly 27& higher than for those of the corresponding concentrations of hydrated salt. Since solvation by water rather than S M P should result in smaller ions with greater mobility, the latter result niay be indicative of partial hydrolysis of the salt during drying. These conductance results are not included in Table 11. Water was added to a solution 0.006128 J I in CuBDS to give a concentration of 0.76% water (11 times that introduced with the salt). The equivalent conductance of the resulting solution was 3y0lower than that for the same concentration of CuBDS . GH,O in dry solvent. Application of a viscosity correction according to eq. 4 removed about two-thirds of the discrepancy. When allowance was made for the effect of the water on the dielectric constant2 and viscosity of the solvent in computing the parameters S and E , this measurement was brought into good agreement with the data far solutions containing no added water beyond the water of crystallization. This represented the extreme example of alteration of the solvent properties, and in all other cases the parameters listed in Table TIT were used without regard for the negligible effects due to differences in water content. Although the dat,a and analysis given here apply to solutions of CuBDS.6H20, it appears that the results for anhydrous solutions would not differ appreciably. The foregoing viscosity and conductance measurements are consistent with the vievi that the hydrate water does not remain intinlately associated with the P solution. This conclusion was reached by Dawson, et al.,4 with regard to hydrated salts in N-methylacetaniide and is supported by qualitative observations of solubility. The sulfates of copper, potassium, and lithium are very insoluble in KhIP. The addition of five volumes of P to a concentrated aqueous solution of CuS04 produced an immediate, blue flocculent precipitate in a colorless liquid. The addition of a solution of H,S04 in 1P to solutions of KXO, or LiCl in the same solvent produced inmediate precipitation but a similar addition to solutions of CUBDS, C U ( ~ \ - O or ~)~ CuClz , (all added as hydrates) had no apparent effect and the mixtures remained blue and clear indefinitely a t room temperature. When these solutions were heated nearly to the boiling point, or better, mere refluxed with a little toluene, the speciiiiens of copper nitrate, and sonietinies of CuBDS, mere decolorized with the forination of a finc, pale precipitate. At room temperature CuS04 apparently precipitates froni SR1P only if the copper ion is hydrated. The addition of an S S I P solution of H2SOIto a small voluine The Journal of Physical Chemistry
of aqueous solution of C U ( X ' O ~or) ~of CuBDS foriiied an iiiitially clear mixture. I n 5 to 30 niin., however, a flocculent or finely crystalline blue precipitate slowly formed. On the other hand, when the copper ion was first dissolved in XXP, there was no apparent reaction with H2S0,. Thus, copper evidently loses its water of hydratioii in N i P solution. Conductance Results and the Ion-Size Paitameter. The liniiting equivalent conductance, Ao, shown in Table 111is appreciably larger than that found for KC1 in the same solvent,2 in contrast to the results for aqueous solutions. The Walden product, presented in the same table, shows a slight change with temperature, which is practically identical in magnitude and direction with that of KC1. The hydrodynamic radii, RH, corresponding to values of the 'VValden product are shown in Table IY. Zwanzig' has calculated a correction of the Stokes hydrodynamic radius due to the dielectric friction on an ion moving through a medium of dipoles that are much smaller than the ion. The recently measured dielectric relaxation times for SMP8 are inconsisteiit with Zwanzig's equation, Evidently the relaxation process in hydrogen-bonded NSIP is more complicated than a simile rotational orientation of the dipoles.
Table IV: Ion-Size Parameters for CuBDS in NiLIP t , "C.
20 25 30 35 40
RE, i,
4.90 4.90 4.91 4.92 4.94
dJ
2.3-3.1 2.6-3.6 3.9-4.7 4.2-4.9 4.4-5.2
3.5
2 .9--3.3 3,0-3.6 3.7-4.3 4,0--4,4 4.1-4.6
The three-parameter Fuoss-Onsager equationgmay be m i t t e n A?' =
62
dl
(4.0)
conductance
+ Gc + ( 0 )' ~ ~
(7) where terms in c' ' or higher powers of c were shown to be negligible for K a < 0.2. The coefficient G is made up of several terms that depend only on the ion-size parameter, is, and a term containing an empirical ion-pair association constant, K , multiplied by the square of the mean ionic activity coefficient, f*. I n the recently completed two-parameter version,1° K -10
W.Zwanig, J . Chem. Phys., 38, 1606 (1963). (8) R. H. Cole, private communication. Values given for the relaxation times of N M P and NMA in Table I11 of ref. 6 should he multiplied by 10. ( 7 ) R.
(9) See ref. 5 , p. 239. (10) R. >I. Fuoss and L. Onsager, J . Phys. Chom., 6 8 , 1 (1964).
3007
COXDUCTANCE O F COPPER V2-BENZENEDISULFONBTE HEXAHYDRATE
-
is developed autoinatically and G is a function only of d and j,, while ca terms are still neglected. The enipirical need for higher order t e r m in e in representing the data of the present study is shown by the regression analysis according to eq. 6. The coefficients, B , shown in Table 111, are more than twice as large as their standard deviations a t the extreme temperatures and show a inonotonic variation with temperature. Except for the point at 25’, the values form a remarkably si nooth plot with respect to teniperature. This does not prove, of course, that ca” is necessarily the proper representation of the higher order contribution to conductance. Atkinson and co-worl;ers3 found evidence for the same effect in aqueous solutions. Although barely significant for CuBDS, the c3 * contribution mas apprcciable for the unsyinnietric and 3-3 electrolytes. The data may be fitted to the theoretical equations in three ways, giving different empirical evaluations of the parameter 8. I n choosing among these estimates we shall adopt as a criterion that d should be independent of teniperature if it has the physical significance given it in the theory. For the first trial, we use thl. three-parameter theoretical eq. 7 and assume complete ionization, thus reducing it to two parameters, *io and 8. Further, we negJect the higher order term in the enipirical eq. 6. Thlen A of eq. 6 may be equated to G of eq. 7. With the oniission of the ion-pair association constant , the G ~ ~ f f i c i e corresponds nt to the conventional J term for strong electrolytes” and the resulting ion-size parameters have been labeled d J in Table IV. These values show an appreciable variation with temperature. The range of values at each temperature in Table IT corresponds to twice the standard deviation of A . A second estiniate is obtained by applying the new again two-parameter equation in the following neglecting the ea’* term in the empirical eq. 6. A’
D, =
UI’IN’
+ (Di& + D ~ ) +C (0)~”’ + l l ( 2 - 2T1) + 1.1515 log (3
=
(8)
do
0-1’)
3J**Kl
D,
=
2u,’{F
-
(84
+ 0.3905 - jA’[O8669 + 1 6b2 + 0.5758 log (3u1’)
4-3K, 21) (8b)
The functions N ‘ , T L K , , and F of b have been defined and tabulatedI3; b = x2e2/aDlcI’is a function only of a for a given solveiit and temperature; u’] = K2a2b2~12c and u ’ ~ = KabP 8c‘ ’. The actiiity coefficient, SA, was evaluated for c == 0.005, about the middle of the experiniental range. As in the previous trial, the coefficient of e in eq. 8 was calculated for a series of values
of a and compared with the experimental A . The resulting values for the ion-size parameter, labeled d1 in Table IT‘, shoIv somewhat less variation with temperature than the former series. For the third approach, the nonlinearity of the experimental results was ascribed to the variation of and the two-parameter equation mas rearranged to the foriii
si2
A’ =
A0
+ Hc - Lfx2c
(9)
with
H
= Bl’[N’
+ 1/(2 - 2T1) + 1.1515 log (3u1’)]A0
+ 2u2’(F + 0.3905)
(sa)
and
L
=
+ 0.5758 log (3~1’)+ I / G b 2 ] - 3c~2’K
3~1’KAo-t 2~,’[0.8669
(9b)
At 20°, this form fits the data quite as well as eq. 6. The ion-size paraiiieter was evaluated by computing (.iv’ - ‘lo)’c and fA2 for each experimental point. Then, for an assumed value of L, H n a s calculated and found to approach a constant value at the higher concentrations. Repetition with a few values of L established an experimental function (N - L ) M. H , which m-as essentially linear. Then, for a series of assumed values of 0 , H and L were calculated by eq 9a and 9b. The resulting theoretical function ( H - 1,) L I S . H was also linear, but of opposite slope, intersecting the experimental line a t a point corresponding to d = 3.5 The method of evaluating 8 did not provide an e s t h a t e of the precision. At the higher temperatures, a difficulty immediately became apparent. Theoretically, L of eq. 9 is positive for reasonable values of 8 in this system, but experimentally, since fr2 is an inverse function of c, 1, has the opposite sign of the B coefficient in eq. G and, therefore, changes sign with increasing temperature. i l t 40°, eq. 9 predicts the wrong curvature, concave up. In Fig. I , the solid curve represents the theoretical function for a = 4.0 -I.,which was picked as the best coniproniise I n suiiiinary, no one value for the ion-size paraiiietei was found that could fit the data at all temperatures Estimates obtained from the new txyo-parametel equation vary lcss than thosc from the three-parameter
&I.
(11) See ref 5, p 197 (12) At the tlme of writing, the final installment of the theorb had not been published hut all the theoretical rontributions t o conductance had been corxputed and onlb a simple algebralc substitution and collection of t e m s v a s required to obtain eq 8 (13) 11 If Fuoss and L Onsager J Phys C h e m , 67, 621 628 (1963)
Volumc 68,A umber I O
October, io64
THOMAS B. HOOVER
3008
equation, ranging froin about 3 8. at 20' to 4.5 A. at 40'. The variation is comparable to that found for potassium chloride in the same solvent. At all teinperatures the conductance size parameters are sinaller than the hydrodynamic radii. As was found for potassium chloride, the a parameter for CuBDS was smaller in NMP than in aqueous solution. Atkinson, Yoltoi, and Hallada3 found d J = 5.02 8. a t 25' in water. When their data were treated according to the second procedure, above, a value of 4.6 was found for 8,. If C u f 2 is solvated by YRIP in the organic solvent, then one would expect the effective ionic size to be considerably greater than in water. The smaller values actually found may be in compensation for a greater extent of ion-pair formation than is predicted
K.
The Journal of Physical Chemistry
by the theory. Such an effect would be anticipated if the effective dielectric constant near an ion is reduced from that of the bulk solvent. The conductances of solutions of CuBDS in NhIP, like those of potassium chloride, yield estimates of the ion size that are temperature dependent and much smaller than expected. These results may be the consequence of short-range ion-solvent interactions, which do not seein to be appreciably greater for divalent than for univalent ions. Acknowledgments. The author is indebted to RIr. R. A. Paulson and Mr. E. L. Weise for the copper determination and gas chromatography, respectively, and to RIr. J. 11, Cameron for the statistical analysis of the conductance data.
