The Journal of Physical Chemistry, Vol. 82, No. 11, 1978
M. J. Rudolph, P. H. Mogul, and F. R. Longo
universal gas constant, N m mol-l K-l molecular radius of the solute, m time, s absolute temperature, K space coordinate in the transport direction, m osmotic pressure, N m-2 reflection coefficient (eq 31) tortuosity factor
(3) M. Hoffmann and M. Unbehend, J . folym. Scl. C , 16,977 (1967). (4) J. Crank, in "The Mathematics of Diffusion", 2nd ed, Clarendon Press, Oxford, 1975. (5) For convenience we have dropped the lower indices 2 for c and k , used in part 1, ref. 1. (6) C. W. Versluijs and J. A. M. Smit, to be published. (7) J. P. Meyer and M. D. Kostin, Bull. Math. Blol., 38, 527 (1976). (8) Parts of the treatment have been presented by J. A. M. Smit (1973), Forges-les-Eaux, "Advanced Study Institute on Charged and Reactive Poiymers 11" and by A. J. Staverman (1975), Rome, "Semaine d'Etude sur le Theme Membranes Biologlques et Artificlelles et la DBsalination de I'eau" (Rome, Pontificiae Academiae Scientiarium Scripta Varla). (9) G. Meyerhoff, Z . fhys. Chem., 4, 335 (1955). (io) H. S. Carslaw and J. C. Jaeger in "Conduction of Heat in Solids", Clarendon Press, Oxford, 1973. (1 1) A. J. Staverman, Trans. Faraday Soc., 48, 623 (1952). (12) F. 8. Rolfson and H. Coll, Anal. Chem., 36, 888 (1964). (13) C. J. P. Hoogervorst, J. A. M. Smit, and A. J. Staverman, J. folym. Sci., 16, 297 (1978). (14) H. Margenau and G. M. Murphy, "Mathematics of Physics and Chemistry", Van Nostrand, New York, N.Y., 1956, Chapter 13.
Supplementary Material Available: The deriviation of eq 13-29 (8 pages). Ordering information is available on any current masthead page. References and Notes (1) C. J. P. Hoogervorst, J. A. P. P. van Dijk, and J. A. M. Smit, J . fhys. Chem., preceding artlcle in this issue. (2) M. Hoffmann and M. Unbehend, Macromol. Chem., 38, 256 (1965).
The Conductances of Barium, Barium Perchlorate, and Potassium Perchlorate in Liquid Ammonia at -62.37 OC Marvln J.' Rudolph, General Foods Corporatlon, Technical Center, White Plains, New York 10602
Phlllp H. Mogul, North Bellmore, New York I1710
and Frederick R. Longo" Chemlstty Department, Drexel Universiyy, Philadelphia, fennsy' March 6, 1978)
C 19 104 (Received February 17, 1976;Revised Manuscrlpt Received
Publlcation costs assisted by Drexel University
We have measured the conductances of dilute solutions of Ba metal, Ba(C104)2,and KC104in liquid ammonia at -62.37 OC. The data show that Ba metal and Ba(C104)2behave like weak 1:l electrolytes under the conditions of our experiments. Values of A, and the ionization constants for all three solutes obtained by Shedlovsky 272 ku and 1.90 X and 249 ku and 7.13 analyses are 582 ku [l ku = 1 (ohm cm equiv)-l] and 2.14 X X respectively, for Ba, Ba(C104)2,and KC104solutions.
Guntz' and Mentre12i3both reported the formation of blue viscous oil at -50 "C in a 0.16 M Ba in liquid ammonia solution but no quantitative measurements were reported. We have obtained extensive conductance data at -62.37 "C for three systems: Ba-NH3, KC104-NH3,and Ba(C104)2-NH3. The latter two were studied to provide a basis for interpreting the conductance behavior of dilute Ba-NH, solutions. The decomposition rate of Ba-NH, solutions is negligible a t this temperature. R
Experimental Section A cryostat, the description of which is presented elsewhere,4 maintained the temperature to within kO.01 "C. The resistance controller and heating elements of the cryostat were connected to a solid state temperature regulator (Hallikainen Instrumenh, Model 1053, sensitivity f0.001 OC). The temperature was measured with a copper-constantan thermocouple calibrated with a Leeds and Northrup platinum resistance thermometer. Used with the thermocouple was a Leeds-Northrup K-3 Universal potentiometer and a Honeywell null detector, Model 2GH-IP. 0022-3654/78/2082-1324$0 1.OO/O
Conductance measurements for barium-ammonia and Ba(C104)2-ammonia solutions were made in a cell fashioned from a 125-mL round-bottom flask with the bottom slightly flattened to accomodate a magnetic stirring bar. Two opposing 1.0-mm tungsten rods encapsulated in uranium glass sealed to Pyrex served as electrodes. The measurement ends were ground flat and smooth, and were separated by 2-3 mm. Tungsten was chosen over platinum as the electrode material because of the superior thermal shock resistance of tungsten-uranium glass seals (over platinum-uranium glass seals) and its weaker catalytic effect on metal-ammonia solution decomp~sition.~A thermocouple well near the electrode assembly provided a means of measuring solution temperatures. A large?: cell with a smaller cell constant was used for dilute solutions of KCIOl in ammonia. This cell was constructred from a 500-mL conical flask. The electrodes consisted of two 1-cm2heavy platinum foils separated by about 1 mm. All cell constants were determined by the method of Lind, Zwolenik, and F u o s ~ . ~ Conductance measurements were obtained with a Leeds and Northrup Jones bridge in conjunction with a tuned 0 1978 American Chemical Society
The Journal of Physical Chemistry. Vol. 82,No. 11, 1978 1325
Conductance of Ba, Ba(CI04)z, and KC104 in NH,
*I
1300
250
2004
0.5
I O
15
mx
20
25
I02
Figure 1. The conductance of KC104 (0)and Ba(CI04), (0)in liquid ammonia at -62.37 "C.
amplifier-null detector unit (General Radio, Type 1232-A), oscilloscope (Tektronix, Type 502A), and oscillator (Hewlett Packard, Model 201C). The measuring system was housed in a Faraday cage. Anhydrous ammonia (Matheson Chemical Co.) was purified by refluxing over successive portions of lithium under vacuum. The purified ammonia was stored in a 1500-mL stainless steel cylinder. Transfer of the liquid ammonia to the conductance cell was accomplished by a method described by Evers and Longoa7 Barium perchlorate was obtained as a hydrate, Ba(C104)z.3H20(Alfa Inorganics, Analytical Grade), and dehydrated under vacuum (lo-, Torr) at 200 "C; a dehydration transition occurs a t 174 oC.8 The mass of the dehydrated Ba(C104)2was determined to fO.O1 mg and rapidly transferred into a conductance cell. Barium (Alfa Inorganics, 99.99% Ba) samples were prepared, weighed (fO.O1 mg), and transferred into the conductance cell by the method developed by Evers and Longo7 for lithium. The potassium perchlorate (Fisher, 99.992%) was weighed (fO.OO1 mg) into the cell which was then sealed to the vacuum system. In all measurements, the cells were evacuated to W5Torr, the temperature was adjusted to -62.37 "C, and liquid ammonia was condensed over the sample.
Results Conductance data were obtained for Ba(C104)zsolutions and 1.0473 X M; for KCIOl between 2.210 X solutions between 2.7761 X and 9.3194 X M; and for Ba metal solutions between 3.1315 X and 0.32433 M. Here M does not represent the conventional molarity but is defined as the number of moles of solute per liter of solvent. The volume of the liquid ammonia solvent was determined from the mass of the solvent and the density function reported by Cragoe and Harperag(The dielectric constant, 24.0, and the viscosity coefficient, 0.00405 P , of the solvent a t -62.37 "C were obtained by interpolation from literature data.lOJ1)The data are plotted as AM vs. MI2in Figures 1-3. In the Ba-NH, solutions a second liquid phase appeared above a concentration of 0.014 M. This phase was in the form of a deep blue oil which adhered to the walls of the vessel. Vigorous shaking did not cause the system to become homogeneous. Upon warming the solution to -34 "C the oil appeared to dissolve, but the system was still inhomogeneous. A resistance measurement was performed on a rapidly stirred oil-solution mixture a t -62.37 "C at an overall metal concentration of 0.2830 M. The resistance was approximately 2000 ohm. After warming the solution
I50 1
10
2 0
-
I
40
3.3
Pi- x
50
13)-
Figure 2. The conductance of Ba(ClO,)* in liquid ammonia at -62.37 "C.
430
1
0
0
0.5
0.25 V'Ti:
Figure 3. The conductance of Ba metal in liquid ammonia at -62.37 "C.
to -34 "C and rechilling to -62.37 "C, the resistance was less than 1 ohm, indicating that the system had become more homogeneous. However, the separate oil phase was still apparent. This oil phase has been previously observed a t -50 "C at a concentration of 0.16 M by Guntz' and by MentreL2J
Discussion Before comparing the conductance data obtained for Ba-NH, (and Ba(C104)z)solutions with other systems we had considered several different processes which might govern solution properties at low concentrations. It occurred to us that BaO might behave as a weak 1:l electrolyte: BaO = Ba'
+ e-
(1)
In this case one might obtain A,, and the ionization constant, k', by the method of Shedlovsky. Alternatively, the Ba might ionize to give two electrons per atom and the process described by eq 1 would be followed by: Ba' = Ba"
+ e-
(2)
Then it would be possible for the first ionization to be complete or incomplete. If the first ionization, eq 1, is complete the system would be formally similar to aqueous sulfuric acid and one could apply the Sherrill-N~yes'~ method to obtain A. and kz. In the event that both processes (eq 1 and 2) come to equilibrium one would be obliged to attempt to obtain Ao, k,, and kz. Sacks and Fuoss14have found that ethanolic MgClz is involved in a two-step ionization process in which both steps are incomplete. They have developed an analysis of the conductance data from which they obtained k,, k2,and Ao.
1326
The Journal of Physical Chemistry, Vol. 82, No. 11, 1978
TABLE I: Constants Derived from Conductance Data for Ammonia Solutions I _
System
Temp,"C
-62.37 -62.37 -62.37 -65.0 -65.0
Ba-NH, Ba(ClO,),-NH, RClO,-NH, Na-NH a
CS-NH) a Reference
15.
A,
A,r)
582 272 249 645 672
2.36 1.10 1.01 2.79 2.80
k, 2.14 X 1.90 X lo-, 7.13 X 1.88 X 2.17 X l o - ,
Reference 16.
It is also conceivable that aggregation of barium species might occur: Bao + Ba+= Ba,+ Bao t Ba2* = BazZ+
(3)
+ Bat = Ba,'+
(5)
Bat
(4)
(We rule out the diatomic species, Ba;, on the basis of simple molecular orbital considerations.) However, we feel that these processes are less likely at lower concentrations. Prom a more pragmatic point of view, it would probably be impossible to obtain good values of equilibrium constants for the aggregation processes from conductancedata alone. The comparison of the Baa or Ba(C104)2data with the KC104 data limits the possibilities considered above. Since the data for Ba(C104)2and KC104 are so similar we feel that Ba(C104)2cannot resemble aqueous H$04 in which the first ionization is complete; otherwise, the conductances for Ba(C104)2would be much higher than for KC104 at comparable molar concentrations. Hence, we are left with the possibilities that the Ba(C104)2ionizes in two incomplete steps or that it behaves like a 1:l electrolyte. Assuming the former possibility we applied the Sacks181 ku, hl Fuoss14analysis to our data and obtained A, N IO", and hz N 10-lo. A value of 181 ku for A, is lower than half of our measured A values and the very low value for kz suggests that the second ionization does not occur or is negligible. Finally, a Shedlovsky12analysis of the Ba(C10J2 data based on the assumption of a single dissociative equilibrium, eq 1,gives values of kl and A similar to the values we obtained for KC104which is unambigously a 1:l electrolyte. See Table I. In addition, the coefficient of the determination for the fit of the data in the Shedlovsky analysis of the Ba(C104)2data is 0.9998. We must conclude that the best guess from our work is that Ba(C104)2is a 1:l electrolyte in liquid ammonia at -62.37 "C, at concentrations above 2 X M. Perhaps at lower concentrations it may be possible to detect a second ionization. For reasons similar to those given above in the discussion of Ba(C104)2we have also concluded that BaO behaves as a 1:l electrolyte in dilute liquid ammonia solutions at -62.37 "C at concentrations above 3 X M. The equivalent conductance for BaO are unexpectedly low. The Sacks-Fuoss analysis of the data results in a A, of approximately 1200 ku, kl N lo*, and k 2 = 10-l'. At -62.37 "@ we expect a & value of approximately 600-700 ku; the low value kz again indicates that a second ionization (eq 2) is negligible. By a Shedlovsky analysis of the data assuming that Baois formally a 1:l electrolyte we obtained A, = 582 ku and hl = 2.14 X lo-*. Both these values are lower than anticipated, however, they are more reasonable than the Sacks-Fuoss results. Using the KC104data we guessed the A. for BaO: A, for KC104 is 249 ku. If we assume that the ionic conductances of K+ and C104 are equal since these ions are approximately the same size, the A o ~ is + approximately 150 ku. Assuming that Xo~,+ equals
-
M. J. Rudolph, P. H. Mogul, and F. R. Longo
X o ~ and + that hoe-is 500 ku we estimate .lofor Baa, taken formally as a 1:l electrolyte, to be 650 ku. This is the value D e ~ a l dobtained l ~ ~ ~ ~for sodium and cesium solutions at -65 "C so that our .lo for barium appears to be about 70 ku lower than expected. (We had originally studied KC104 and Ba(C104)2 TI order to estimate the equivalent ionic conductance for Ba2+at infinite dilution. However our data indicate that the cation in Ba(C104), solutions is BaC104+not Ba2+and we must be satisfied with a less rigorous estimate of XaBa+.) We are surprised that BaO behaves like a 1:l electrolyte in dilute liquid ammonia solutions. From spectral studies of Ca-NH3 solutions Jolly et al.17 concluded that there appeared to be nothing abnormal about such solutions, implying that the dication, Ca2+,is present in dilute solutions. An examination of different properties of the Ba atom suggests that the relatively high second ionization potential for Ba (10 eV) may be the controlling factor in determining the nature of the cationic species in barium solutions. If this were true, calcium-":, solutions would also behave like 1:l electrolytes since the second ionization potential for Ca is about 11 eV. However, the fact that Ba(C10J2also appears to be a 1:l electrolyte argues against this idea and suggests that simple electrostatic forces may be operative. This would mean that the structure of the species we designate as Ba+ is a tightly bound ion pair composed of a Ba2+ion and a solvated electron, perhaps similar to the monomer species suggested by Evers and long^.^ The relatively low values of A, and hl are also difficult to explain. There must be processes occurring in dilute Ba-NH3 solutions which reduce the concentrations and/or mobilities of the charged species. Aggregative processes such as those indicated by eq 3-5 are suggested but a choice from among these processes cannot be guided by conductance data alone. Spectral and magnetic studies would probably be of great assistance in elucidating the processes which determine the state of affairs in Ba-NH3 solutions. 3
Acknowledgment. We shall always be grateful to the late Dr. E. Charles Evers, of the University of Pennsylvania, for his guidance, and, in particular, for suggesting the investigation reported in this paper. Supplementary Material Available: Three tables containing conductance vs. concentration data for BaO, Ba(C104)2,and KC104 (3 pages). Ordering information is available on any current masthead page. References and Notes (1) (2) (3) (4) (5) (6)
A. Guntz, Compt. Rend., 127, 874 (1901). R. C. Mentrel, Compt. Rend., 135, 740 (1902). R. C. Mentrel, Bull. Soc. Chem. Fr., 29, 493 (1903). M. J. Rudolph, Ph.D. Thesis, Drexel University, 1971. J. Varimbi, Ph.D. Thesis, University of Pennsylvania, 1953. J. E. Lind, J. J. Zwolenik, and R. M. Fuoss, J. Am. Chem. Soc., 81, 1557 (1958). (7) E. C. h e r s and F. R. Longo, J . Phys. Chem., 7 0 , 426 (1966). (8) A. A. Zinov'ev and L. I. Chudinova, Zh. Neorg. Khim., 1722 (1956). (9) C. S. Cragoe and D. R. Harper, Scientific Papers of the Bureau of Standards, No. 420, Oct 15, 1921. (IO) A. A. Maryott and E. R. Smith, "DielectricConstants of Pure Liquids", Natl. Bur. Stand. ( U . S . ) ,Clrc. (1951). (11) "Handbook of Chemistry and Physics", 39th ed, Chemical Rubber Publishing Co., Cleveland, Ohio, p 2037. (12) T. J. Shedlovsky, J . Franklh Inst., 225, 739 (1938). (13) M. S. Sherrill and A. A. Noyes, J. Am. Chem. Soc., 48, 1861 (1926). (14) F. M. Sacks and R. M. Fuoss, J. Electrochem. Soc., 99, 483 (1952). (15) R. R. Dewald and J. H. Roberts, J . Phys. Chem., 72, 4224 (1968). (16) R. R. Dewald, J . Phys. Chem., 73, 2615 (1969). (17) W. L. Jolly, C. J. Hallada, and M. Gold, "The Absorption Spectra of Metal-Ammonia Solutions", UCRL-10960 (1963).
