CONDUCTAKCE OF CESIUMCHLORIDE IN DIOXANE-WATER
August, 1963
1707
CONDUCTANCE OF THE ALKALI HALIDES. VII. CESIUM CHLORIDE IN DIOXANE-WATER MIXTURES A'T 25' BY JEAN-CLAUDE JUSTICE' AND RAYMOND M. Fuoss Contribution N o . 1734 from the SterEing Chemistry Laboratory of YaEe Uniuersitg, New Haven, Connecticut Received March $0,1965' The conductance of cesium chloride at 25' was measured in dioxane-water mixtures covering the range of dielectric constant 12.73 6 D 6 78.54. As a function of concentration, the data can be reproduced by the Fuoss three-parameter conductance equation. As in the case of the other alkali halides studied in dioxane-water mixtures, the contact distance a varies with composition of solvent and according to the method of computation. The corrected value for Ao(CsC1, H20, 25") was found to be 152.81. From this value and data in the literature, Xo(Cs+) = 76.44, which is about 1% lower than the value 77.16 obtained by Lind3 from cesium iodide conductance and literature data.
We present in this paper conductance data for cesium chloride in a series of dioxane-water mixtures which cover the range 12.73 6 D 6 78.54 in dielectric constant. Symbols are defined in earlier papers of this series.2ea Experimefital Cesium chloride m-as used as received (except for drying) from A. D. MacKay, Inc., New York, N. Y. Analysis by the flame photometer showed the presence of the following trace impurities: RbCl, 0.013%; KCl, 0.017%; NaCl, 0.021%; LiC1, 0.059%. Correction to A0 in water for these impurities amounts to -0.258. The salt samples were dried in a small platinum boat for 24 hr. a t 141' and pressure lees than 0.1 p. No loss of weight ( A 3 p g ) . was observed. Conductances were measured at 25 =k 0.003', using previously described cells and electrical equipment.%v3 All solutions n-ere made up by weight; normality was calculated from molality by the equation c/m = PO km where k = -0.051. Purification of dioxane has already been described.2 The properties of the solvents are given in Table I and the conductance data are summarized in Table 11, where AA is the difference between observed conductance and that calculated from the Fuoss conductance equation with the Ja-term omitted. Activity coefficients are calculated by the equation
+
-In1 f = r/(1
+
TABLE I1 CONDUCTANCE OF CESIC'M CHLORIDEIN MIXTURESAT 25' 104~
93.817 72.530 58.244 36.076 19.355
D 45 ,026 27.453 18.927 8.277
D 33.919 28.120 21.232 14.078 7.179
lOsAA
A
D
10%
A
D
78.54 144.121 145.092 145.887 147.340 148.854
13 -17 2 -10 11
38.60 59,191 60.784 61.795 63.542
- 1 5 - 5 1
23.68 38.536 39 ,403 40.682 42.371 44.736
4 - 3 15 - 13 4
l0aAA~
23.189 17.928 13.271 9.109 4.763
18.73 31.403 32.797 34.325 36.130 38.830
-13 29 -3 -18 8
18.318 13.606 11.098 6.879 3.781
D = 15.01 23.693 25.312 26.440 29.047 32.148
- 5 12 16 - 23 9
=
=
=
DIOXANE-WATER
=
D = 12.73 15.729 12.267 9.366 6.395 3.172
17.574 18.830 23.233 22.290 26.163
- 16 32 12 - 28 9
(1)
7)
tem, as already mentioned, KA was set equal to zero and y equal to unity. The value A, = 153.066 -k r = /3~/2= e 2 ~ / 2 D k T (2) 0.016 was obtained; applying the correction for imis the dimensionless variable introduced by Fuoss and O n ~ a g e r . ~ purities, the corrected value for Ac(CsC1) is 152.81. UsFor the data obtained from aqueous solutions, the equation was ing Xo(Cl-) = 73.52 from Lind's value2 Ao(KCl) =: of course simplified by sebting the association constant K A equal 149.89 and Longsworth's value5 n- for chloride in to zero. potassium chloride, we find Xo(Cs+) = 76.44, which is about 1% lower than the value 77.16 obtained from TABLE I Lind's value3 Ao(Cs1) = 154.16 and the value Xo(I-) PROPEJtTIES O F SOLVEhTb = 77.00 derived from Voisinet's data6 for potassium NO. W P D 1001 106KG iodide which give' AO(K1) = 150.52, and the value 1 0 0 0 99707 78.54 0 890 1 46 2 47.5 Xo(K+) = 73.52 from the Lind2-Longsworth5 datst. 1.03193 38.60 1862 0.32 3 64.4 1.03666 23.68 The discrepancy is greater than the estimated probable 1980 ,109 4 70.5 1.03681 18.73 1921 063 errors in the various contributing measurements; fur5 75 5 1 03626 15 01 1 827 .042 ther work on cesium is therefore planned. 6 78.8 1.03573 12 73 1756 .035 For the dioxane-water mixtures, four variations of eq. 3 were examined, with the results summarized in Discussion Table 111. The constants labeled (1) in the table werle Several modifications of the equation obtained using eq. 3 as given and computing activities A = AQ - SC'ipy1'2 E c log ~ c y JCY by the Debye-Huckel equation In eq. 1
+
+
+
J z ( c ~ ) ~--' * KACyf2h (3) mere used to analyze the data.
For the aqueous sys-
(1) On leave of absence from the University of Paris. Grateful acknowledgment is made for a stipend from the Higgins Fund and for a travel grant from the University of Pans. ( 2 ) J. E. Lind, Jr., and R. M. Fuoss, J . Phys. Chem., 65, 999 (1961). (3) J. E. Lind, Jr., and R. M. Fuoss, zbzd., 65, 1414 (1961). (4) R. M. I'uoss and L. Onsager, Proc. N a t . Aead. Sea. U. S.,47, 818 (1961).
-hf
= T/(1
f Ka)
(4)
Kay's program for the IBM computer8 was used to evaluate the constants. The computation was then re( 5 ) L. G. Longsworth, J. Am. Chem. Soc., 54, 2741 (1932). (6) 'A'. E. Voisinet, Thesis, Yale University, 1951.
(7) R. M. Fuoss and F. Accascina, "Electrolytic Conductance,'' Interscience Publishers, Inc., New York, N. Y., 1959, p. 203. (8) R. L. Kay, J . Am. Chem. Soc., 82, 2099 (1960).
1708
JEAN-CLL4UDE JUSTICE AND
peated, with J z set equal to zero; results are labeled (2) in the table. Omitting J 2 tends to give slightly larger values of ROas the dielectric constant decreases, but has no significant effect 011 association constant (the f spread for both constants is practically the same for varjat'ions 1 and 2). The values of UJ vary with D in both calculations; the spread is about the same, but the pattern of the dependence is different, as shown in the table. As mentioned in several earlier papers of this series, we are now inclined to consider UJ merely a numerical parameter for associated electrolytes, especially when the ions are small. The reason for this TABLE I11 DERIVED COSSTANTS No.
Ao(1)
1 2 3 4 5 6
..........
Adz)
66.66 f 0.02 50.07 f .06 45.26 f. .11 41.59 i .14 38.44 f .24
*b(4)
-4o(3)
...
153.12 66.65 50.08 45.27 41.65 38.54
66.65 50.10 45.27 41.62 38.38
153.07 66.64 50.06 45.26 41.63 38.59
KO.
K A (1)
KA (2)
KA (3)
KA (4)
2 3 4 5 6
17.1 f 1 . 4 83.2 f 4 . 7 222 f 14 818 f 27 2106 f 76
15 86 230 845 2165
16 95 250 885 2175
13 77 215 810 2130
No.
dJ (1)
1 2 3 4
. . . .. . . . . 6.49 f 0 . 5 3 5.00 f .28 4.61 f .31 5.78 f .25 6.10 f .30
5
6 NO.
s
1 2 3 4 5 6
95.6 85.4 118.8 146.5 181.6 211.5
dJ (2)
4.05 5.61 5.34 5.04 6.43 6.83 1.360 1.239 0.990 0.868 0.759 0.676
J (4)
J (3) , ,
.... .
835 f 50 2550 f 100 4870 i 220 9500 f 270 15000 f 500
154 f 3 685 =k 40 191Of 60 3 3 7 0 f 110 6 6 0 0 f 120 10300 f 180
E
108R-
lOBR+
60.3 254.6 862.6 1594 2875 4380
1.21 1.30 1.56 1.75 2.02 2.22
1.20 1.35 1.77 2.05 2.32 2.66
lack of confidence in the physical significance of UJ lies in some recent theoretical considerationsg which show that approximating the Boltzmann function by a truncated power series in the derivation of eq. 3 was too drastic for the case of IOU- dielectric constants or small ions (large b = e*/aDkT). We therefore used a simplified programlo in which J z was oniit'ted, and J (9) R. hi. Fuoss and L. Onsager, J . P h g s . Chew., 66, 1722 (1962); 67, 621, 628 (1968). (10) We are grateful t o Dr. J. E. Lind, Jr., and hir. J. F. Skinner, who wrote the program for us.
RAYMOND M. FUOSS
Vol. 67
was treated as an empirical constant with no (at present) pre-assigned physical significance. Two other methods of calculating activity coefficients were used; in method 3, eq. 1 was used, and in method 4, the limiting Debye-Huckel equation -1nf
= T
(3
was used. The values of Kt\ by the two variations were practically identical within their arithmetic uncertainty, but the spread in the J-values by method 4 is significantly less than by method 3. This verifies the results obtained in a similar study of data for cesium i ~ d i d ewhere , ~ the best fit was obtained by using eq. 5, the equation valid for point charges. As remarked earlier, this procedure can be justified on the argument that eq. 5 allows for Iong range interionic effects (which clearly are independent of the shape or size of the ions), while the short range effects are all subsumed in the Ka term which explicitly and sensitively depends on the contact distance a. We prefer this semi-empirical analysis, which dispenses with UJ values (pending completion of the theoretical re-investigation of the coefficient of the linear term) t o calculating UJ'S from the J's and then making (probably pointless) speculations about their variation with solvent composition. A plot of log Ka against reciprocal dielectric constant approximates linearity for D < 30, just as for the other alkali halides in dioxane-water mixtures, but the slope leads to &K = 6.2, which seems unreasonably large. The curve nearly coincides with that for rubidium chloride, and like it, becomes concave-down a t high dielectric constants. Finally, we consider briefly the limitiiig conductances. As seen in Table 111, the Walden product steadily decreases as the dielectric constant decreases; part of this is due to ion-dipole i n t e r a ~ t i o n , ' ~ -but '~ part is also due to unknown effects which always seem to appear when ordinary small ions and water are put together. A plot of the Stokes radii (R+ and R-) against reciprocal dielectric constant is linear for D < 30; the linear portions of the curves extrapolate to Rf = R- = 0.80 A,, giving tia = 1.6 or = 2.4, depending on whether the Sutherland correction of 3/2 for slipping is applied. The corrected value is, of course, more plausible. (11) R. (12) R (13) R (14) R
TV Kunze and R 11 Fuoss, 1. P h y s Chem , 67, 914 11963) M Fuoss, Proe X a t l Acad S c z , c' S I46, 807 (1959) H Boyd, J Chem P h y s , 36, 1281 (1961) Zuanzig, z b z d , 37, 1603 (1963).
