NQV.,1959
TRACER DIFFUSION OF SODIUM AND RUBIDIUM IONS IN ALKALICHLORIDES
1873
TRACER DIFFUSION OF SODIUM AND RUBIDIUM IONS IN AQUEOUS ALKALI CHLORIDE SOLUTIONS AT 85’ BY REGINALD MILLS Contribution from the Department of Radiochemistry, Research School of Physical Sciences, Australian National University, Canberra, A.C.T., Australia Received April 87, I969
Diffusion coefficients for two cations, N a + and Rb+, have been measured over the concentration range 0.1-4 M in KC1, NaCl and LiCl solutions. The diffusion pattern in concentrated solutions shows similar viscosity relationships to those obtained with anions. At low concentrations, however, the separation between cation coefficients is much more marked, and this difference may be reconciled with the anion case by reference to the Onsager limiting law with an extension for ion size.
Introduction Diaphragm-cell measurements of trace-ion diffusion Coefficients can now be regarded as sufficiently accurate and precise to justify accumulation of data for various ions. The best evidence for this reliability is the agreement between two groups of workers’ for the tracer diffusion of I- ion in the three supporting electrolytes KC1, NaCl and LiC1. These studies were carried out in separate laboratories and with distinctly different analytical techniques, yet agreement to within an average precision of 0.40j, was obtained for all measurements. Data from this study and a parallel one,2 have allowed comparisons to be made between the trace-diffusion of the two anions, I- and C1in the above three supporting electrolytes. No comparable data exist for cation diffusion in these media beyond those for Naf in KC13 and Na+ in NaC14 solutions. Since cations might be expected to exhibit wider divergencies than anions in diffusional behavior, because of their stronger degrees of hydration, such a comparison seems warranted. In this study, Na+ ion diffusion in LiCl has been measured to complete the series for a hydrated ion and Rb+ ion diffusion in the three electrolytes, KC1, NaCl and LiC1, to afford comparison with an uiihydrated species. Experimental Diffusion Technique.-All diffusion measurements were made with magnetically-stirred diaphragm cells of the general pattern prescribed by Stokes.6 The cells were calibrated at regular intervals by diffusing 0.5 M KC1 into water and analyzing the compartment solutions by conductance measurements with a Leeds and Northrup Jones bridge. All diffusion measurements were made in water thermostats maintained at 25 =t0.01 Sodium and potassium chloride solutions were made by accurately weighing the dried A.R. grade salts and diluting to volume. Lithium chloride solutions were made by a niethod described by Stokes and Stokes6 and their concentrations determined by conductance measurements with the Jones bridge using the data of Shedlovsky.’ Radioactive Analyses.-The radiotracers Na22 and Rb*6 were obtained as their aqueous chlorides from the Radiochemical Centre, Amersham, England. One sample of Rba6 tracer as RbCl in HCl solution was obtained from the Isotopes Division, Oak Ridge National Laboratories, Oak Ridge, O.
(1) R. H. Stokes, L. A . Woolf and R. Milla, THISJOURNAL, 61, 1634 (1957). (2) R. Mille, ibid., 61, 1631 (1957). (3) R. Mills, ibid., 61, 1258 (1957). (4) R. Mills, J . Am. Chem. Soe., 7 7 , 6116 (1955). (5) R. H.Stokes, ibid., 73,763 (1950). ( 6 ) J. M.Stokes and R. H. Stokes, T H r s JOURNAL, 60, 217 (1956). (7) D.A. MacInnes, “ T h e Principles of Electrochemistry,” Reinhold Publ. Gorp., New York, N. Y.,1939, p. 339.
Tennessee, U.S.A. The radioactive solutions were counted in the liquid phase in a well-type scintillation counter using a sodium iodide crystal as detector. Integral bias curves were obtained for each isotope to select suitable voltage and bias settings for good counting stability. No trouble was experienced using the Na*Z tracer but anomalous results were obtained using Rba8tracer from both sources. These anomalies varied from batch to batch of tracer but had the common feature that low coefficients were obtained after several half-lives of the tracer had elapsed. Rb86 has a half-life of 19 days and it was suspected that there was a radioactive impurity with a much longer half-life present in the tracer solutions. Tracer solutions from each of the above sources of supply, were therefore examined with a scintillation spectrometer which was coupled to a multichannel analyzer. I n well-decayed specimens, the y spectrum of 2.3 year Cs1a4 was plainly exhibited with energy peaks at 0.605, 0.80 and 1.37 Mev. The probable presence of cesium impurity in rubidium salts plus the comparatively high slow neutron capture cross-section of Cs133 reinforce these conclusions. Further, the anomalous diffusion coefficients were ca. 1% lower than the measurements made with fresh tracer and this is consistent with recent data obtained by Mills and Woolfa which shows that the Cs+ diffusion rate is on the average 1yolower than Rb + values in the same system. Provided measurements were made before the elapse of three to four half-lives of the tracer, however, reproducibility to within 0.3% could be obtained with all tracer solutions and only data recorded in this period has been given. It is recommended that future diffusion measurements with Rbs6 be made within this period or alternatively, spectroscopically pure rubidium salts be sent for neutron irradiation.
Results The diffusion coefficients for Na+ in LiCl and for Rb+ in KC1, NaCl and LiCl are reported in Tables I and 11. Values of a)./a>o are also given since this ratio allows direct comparison of the diffusional behavior of the two ions. The limiting diffusion coefficients Dohave been calculated by the Neriist equation using Xo Na+ = 50.10 and Xo Rb+ = 77.81 from Robinson and stoke^.^ The rootmean-square error in the Na+ measurements averages 0.3% but because of the factors outlined in the experimental section, the error for the Rbf measurements has been arbitrarily doubled t o 0.6%.
Discussion The results are plotted in Fig. 1, together with data for Na+ in KC1 and NaCl which have been reported in previous papers in this ~eries.30~ Comparison with the anion diffusion curves2 shows no real divergencies in moderate to high concentrations, in that viscosity-related effects again appear to have the predominating influence and the ( 8 ) R. Milla and L. A. Woolf, THISJOURNAL, 6S, in press (1959). (9) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions.“ Butterworth Scientific Publications, London, England, 1955.p. 452.
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REGINALD MILLS
Vol. 63
TABLEI1 TRACER-DIFFUSION COEFFICIENTS OF Rb + IN AQUEOUS ALKALI CHLORIDE SOLUTIONS AT 25'
1.0
0.9
C,
a,
moles/l.
cm.Z/sec.
0.1 0.5 1.0 2.0 2.56 3.0 4.0
.0.8 R \ G2
0.7
0.6
0.5
1.o
1.5
2.0
Ire.
Fig. 1.-Cation diffusion curves in KCI, NaCl and LiCI:
(1) Na+' in KCP; (2) Rb+ in KC1; (3) Na+ in NaC14;
(4) Rb in NaCl; (5) Na+ in LiCl; (6) Rb+in LiCI.
TABLE I TRACER-DIFFUSION COEFFICIENTS OF Na+ IN LiCl (AQ.)AT 25' rnolesh.
cm.*/sec. (f0.3%)
9,
WDO, (Do= 1.334)
0,1023 .4817 .9G21 1.902 2.813 3.648
1.280 1.244 1.180 1.070 0.983 0.886
0.9GO .933 .889 .802 .737 .664
c,
1.961 1.952 1.865 1.842
D/PO (Do= 2.071)
0.963 .947 .943 .916 .go1 .889 .849
0.1 0.5 1 .o 2.0 3.0 4.0
1.845 1.721
0.947 .930 .89l .831 .745 .651
0.0805 ,4931 .9812 1.962 2.813 3.648 4.011
1.921 ' 1.844 1.740 1.582 &0.6% 1.395 1.260 1.208,
0.928 .890 .845 .7G4 .674 .608 .583
where i refers to the trace ion and d(uJ is a function depending on the valencies and mobilities of all the ions present. At zero concentration, this law reduces to the Nernst expression D0i
RThoi/ l ~ i F* l
(2)
where R is the gas constant in joule/mole/deg., Xoi and xi, the limiting conductance and valency, respectively, of ion i, and F the faraday. It will be realized that diaphragm-cells cannot be used below concentrations of 0.1 M owing to surface diffusion effects. However, data for the simplest viscosity correction in which (a)/Do) diffusion of Na+ in very dilute NaCl solution is being accumulated in this Laboratory by the con(q/qo) is plotted against 4.5,exhibits the overcorrection effect previously observed. The cation tinual monitoring capillary technique.I2 These curves are roughly parallel along their entire length results indicate that the limiting law as given by and do not progressively converge in going from equation 1 is valid to a concentration of 0.005 M KCI, through NaCl to LiC1. This is in part, due in this system. Further, by substituting the factor to the rather large differences in the values of the .\/Z/l+Ka for 4.5in the above equation, the data coefficients for the two ions in each electrolyte a t can be represented up to at least 0.05 M . Inca. 0.1 M concentrations. This separation be- troduction of the dZ/l+Ka term is a device which tween coefficients for the various ions in the same makes allowance for ion size through the parameter electrolyte can be examined by dilute solution "a" and has been used in an analogous manner to theory which is sometimes applicable to concentra- extend the applicability of the limiting law in conductivity studies. I n view of the above tions of this order. The two important equations, formulated for experimental evidence, the comparison of cation and tracer of self-diff usion a t very low concentrations, anion data in 0.1 M solution in terms of the exare the Onsager limiting lawlo and the Nernst tended equation seems justified. Examination of the data for diffusion of Na+, expression." The Onsager law based on the relaxation effect as derived from interionic attraction Rb+, C1- and I- in the three electrolytes shows that theory takes the form for aqueous 1:l electrolytes whereas D/D0 (Na+) is considerably higher than a)/Do(Rb+), D/Do(cl=) is only slightly more than a t 25" D/a>O(I-) at 0.1 M. These differences can be atDi = Poi 11 - 0.7816 (1 - z/m).\/c] (1) tributed to two factors. The first is the fact that the value of the Onsager limiting slope, for a)/D0. (10) L. Onssger, Ann. N. Y. Acad. Sei., 46, 209 (1945). (11) W. Nernst, 2. p h y s i k . Chem.. 2, 613 (1888).
(12) R. Mills and E. W. Godbole, Ausb. J . Chem., 11, 1 (1858).
,
I I
Nov., 1959
THESTRUCTURE OF LIQUID BORON TRIOXIDE
(Na+) is much higher than that for D/Do(Rb+). The actual calculated values are -0.193 and -0.261, respectively. In the anion case, however, the slopes for I- and C1- are practically identical and so there is no differentiation at this stage. The second factor is involved in the use of the v%/l+xa term. Use of this term will clearly reduce D/Do(Rb+) relative to D/Do(Na+) since “a” for NaCl is greater than for RbC1. The “a” values have been obtained from Harned and Owen.Ia It will be noted that “a” has been given the value corresponding to the distance of closest approach between the tracer ion and the solution ion of opposite charge. This would seem the more appropriate figure since it can be assumed that the potential immediately surrounding the trace ion will be the main influence on its diffusion rate. Similarly, D/Do(Cl-) will be reduced relative to D/Do(I-) by the operation of this factor, but the lowering is much less proportionately than that effected by the slope values. Comparison of the observed and calculated differences between anions and cations are shown in
1875
Table 111. It will be observed that, within the error of measurement, the differences are consistent and the figures indicate that their comparative separation can be correlated with dilute solution theory a t this concentration. In the anion case, good agreement is obtained between theory and experiment but in the cation case the observed differences whilst comparable are greater than the calculated values. TABI.E I11 AD/Do (Na +-Rb
Electrolyte (0.1 M )
Calcd.
Obsd.
IiCl NaCl LiCl
0.017 .021 .020
0.030 .027 .032
+)
Calod.
(cl--I-)
0.000 .001 .005
-
Obsd.
-
0.003 .OOl .004
Two further points of interest, arise from comparison of the diffusion of Rbf with ions of similar type such as Cs+ and I- ions. As would be expected, the D/D0curves for Csf ion in the three electrolytes,s are indistinguishable from the Rb + ones over this concentration range. However, the I- data exhibit a different dependence and the (13) H. S. Harned and B. B. Owen, “Physical Chemistry of Electrolytic Solutions,” 2nd Ed., Reinhold Publ. Corp., New York, N. Y., coefficients fall off more rapidly with concentration than do the Rb+ values. 1950, P. 380.
STRUCTURE O F LlQUID BORON TRIOXIDE” BY J. D. MACKENZIE General Electric Research Laboratory, Schenectady, New York Received April 88, 1969
The viscosity, electric conductivity and density of liquid B~OIhave been measured over the temperature range 800-1350’ and the effects of small amounts of residual H20 examined. The structure of the liquid is temperature dependent. Viscous flow data indicate that the degree of association decreases with increasing temperature. However, the molar volume exhibits negative departure from linearity with rising temperature. The very low specific conductance of 7 X 10-6 ohm-’ cm.-l at 900’ above the melting point is not corn atibIe with a structural variation which involves ionic dissociation. A tentative model is postulated to explain these resufts.
Introduction The structure of liquid and vitreous B203has been a subject of much controversy. Earlier concepts range from that of a molecular liquid consisting of B406 molecules,1an ionic melt involving complex boron-oxygen ions,2 to that of a highly associated network of interlinking BOa of viscosity, electric triangles. R e ~ e n t l ystudies ,~ conductivity and density suggested that the structure of the liquid is temperature dependent but that ionic dissociation is negligible, even at temperatures up to 1000° (m.p. 450’). However, in a concurrent X-ray diffraction study,6 extensive dissociation of the melt to give free oxygen ions was postulated t o occur at 1200-1600”. Electric
* This research waa supported by the U. S. Air Force under Contract No. AF33 (616)-5099,monitored by the Aeronautical Research Laboratory, Wright Air Development Center. (1) K.Fajans and S. W.Barber, J. Am. Chem. 8 0 c . ~74,2761 (1952). (2) S. Anderson, R. L. Bohon and D. D. Iiimpton, J. Am. Ceram. Soc.. 3 8 , 370 (195.5). (3) B. E. Warren, H. Krutter and 0. Morningstar, ibid., 19, 202 (1936). (4) J. D. Mackenzie, Trann. Faraday Soc., 52, 1504 (195G). (5) J. Zarzycki, Proc. I V Intern. Cong. on Glass, Paris, V I , 323 (1956).
conductivity data are not available at these elevated temperatures. Further, the specific conductances reported by various workers up to 1000° differ widely. The effects and the concentration of residual HzO have not been determined. The present work was therefore undertaken with liquid B203 containing varying amounts of H2O. Viscosity, conductivity and density have been redetermined and extended to 1350” to ascertain the validity of the interpretations from both the X-ray and the author’s previous measurements.
Experimental Mallinckrodt A. R. grade HsBOa was first dehydrated by gradual heating of the charge in a Pt-20% Rh crucible to about 1000° until a bubble-free melt was obtained. The crucible cpntaining 50 cc. of liquid B2O3was then transferred to a vertical Pt resistance furnace for subsequent measurements. The apparatus was essentially the same as that used in a previous study of liquid germanium dioxide.6 Viscosity was measured by the counterbalance technique employing two Pt-20% Rh bobs of different dimensions. Electric conductivity was determined over the frequency range 100010,000 c./sec., the central suspension being adopted as one electrode and the crucible containing the melt as the other. (6) J. D. Mackenzie, J . Chem. Phys., 2B, 605 (1958).
