JAMES L. COPELAND AND STEVENRADAK
4360
Effect of Inert Gas Pressure and Solubility on Fused-Salt Conductance. 111. Helium and Argon with Silver Nitrate’
by James L. Copeland and Steven Radak Department of Chemistry, Kansas State University, Manhattan, Kansas 66602 (Received M a y 17, 1967)
The solubilities of He and Ar in fused AgN03 at 250’ have been determined to pressures of 247 and 375 atm, respectively. Henry’s law constants are KAr = (3.35 ==! 0.55) X mole of Ar atm-’ and K H = ~ (3.57 f 0.48) X mole of He ~ m atm-’. - ~ Specific conductance, K, of the melt a t the same temperature has been determined under He pressures to a maximum of 350 atm, and under Ar pressures to a maximum of 343 atm. This conductance decreases linearly with increasing pressure of either gas above 1 atm. The pressure coefficients of K for two runs each with He and Ar are for He: -(7.01 f ohm-’ cm-* atm-’ and -(5.28 f 0.12) X 0.24) X ohm-’ cm-’ atm-I, and for ohm-’ cm-’ atm-’ and -(5.11 f 0.09) X ohm-‘ Ar: -(5.24 f 0.18) X cm-’ atm-’, from which data it is concluded that the nature of the gas is irrelevant. The results are compared to those of similar studies with KaNO3. Specific conductance appeared to fall in a rather abrupt manner between vacuum conditions and 1 atm saturating pressure of either gas. The results are interpreted in terms of a combination model for conductance in which both individual ionic jumps and cooperative rearrangements of groups of ions form the transport mechanism.
Introduction During the past few years interest has increased in studies of pressure effects on fused-salt systems, not the least intriguing of which are their transport properties. One of the more important objectives of using the pressure parameter is to attempt constant-volume measurements of transport properties with the idea of obtaining “true” activation e n e r g i e ~ . ~ -In ~ any such experiments there are only two feasible means of applying static high pressure : mechanical (piston) pressure or the use of an “inert” gas as a pressurizing medium. Employment of the former, especially in work requiring some type of transducing probe to be located within the fused-salt medium (e.g., conductance electrodes), is greatly limited a t present because of the concurrent high temperatures. Thus, most piston pressure research on fused-salt systems has been restricted to ascertaining their melting properties, compressibilities, and volume changes. Such work is well typified by the work of Owens.5 Otherwise it appears that only Angell, Pollard, and Strauss6 have been able to investigate mechanical pressure effects on the electrical conductiviThe Journal of Physical Chemistry
ties of such systems with reasonable success, but these systems were relatively low-temperature Ca(S03)z KN03 glass-forming melts in the region of 138 to 180”. Earlier, of course, Bockris and Richards’ succeeded in determining the compressibilities of several fused salts by a dynamic-sound-velocity technique. To date, it appears as if relatively little work has been done in the investigation of transport properties
+
(1) This paper was presented in part at the second Midwest Regional Meeting of the American Chemical Society, Lawrence, Kan., Oct 1966. (2) B. R. Sundheim, “Transport Properties of Liquid Electrolytes,” in “Fused Salt Chemistry,” B. R. Sundheim, Ed., McCraw-Hill Book Co., Inc., New York, N. Y . , 1964, p 209. (3) M. K. Nagarajan, L. Nanis, and J. O’M. Bockris, J . Phys. Chem., 68, 2726 (1964). (4) M. K. Nagarajan and J. O’M. Bockris, ibid., 70, 1854 (1966). (5) (a) B. B. Owens, J. Chem. Phys., 39, 1053 (1963); (b) B. B. Owens, ibid., 41, 2210 (1964); (c) B. B. Owens, ibid., 42, 2259 (1965); (d) B. B. Owens, ibid., 44, 3144 (1966); ( e ) B. B. Owens, ibid., 44, 3918 (1966). (6) C. A. Angell, L. J. Pollard, and W. Strauss, ibid., 43, 2899 (1965). (7) J. O’M. Bockris and N. E. Richards, Proc. Roy. SOC.(London), A241, 44 (1957).
INERT GAS PRESSURE AND SOLUBILITY EFFECTS ON FUSED-SALT CONDUCTANCE
of molten salts under high gas pressures. Nagarajan, Nanis, and Bock+ and Nagarajan and Bockris4 have investigated self-duffusion coefficients, D, of NaZ2and C S ' ions ~ ~ in their nitrates over a range of 1 to 1200 atm using nitrogen as the pressurizing medium.s These workers concluded that the activation volumes for diffusion, AV *, obtained from the relationship A V * = -RT(b In D/bP)T
(1)
(based on the quasi-thermodynamic formula of Evans and PolanyiQ)are approximately equal to the most probable volumes of "holes" in the liquids. Also, they found the activation energies a t constant volunie, E,, to be about one-fifth the value of the activation enthalpies a t constant pressure, E,. Their major conclusions were that the primary contribution to E , is the heat of formation of holes in the liquid, and that the formation of holes is the rate-determining step in the diffusion process at constant p r e ~ s u r e . ~ However, whenever one attempts high-pressure measurements of liquid properties by utilizing gases as the pressure-transmitting media, there is always the uncertainty as to whether or not gas solubility, however small, may affect the desired measurernentss6 This laboratory has been involved in trying to ascertain such effects, if any.'* Thus, we have been able to demonstrate that both He and Nz depress the isothermal specific conductance of NaN03 essentially in a linear manner with gas pressure to very nearly the same extent.locFe However, Ar pressure depresses this specific conductance to a noticeably greater extent than does either that of He or K2.10c These observations have been attributed primarily to dilution eff ects.loc*e The solubility of NS in NaiY03 a t 369" is intermediate between those of He and Ar in the system.lod Furthermore, the Nzsolubility exhibited a distinctly exothermic heat of solution together with a fairly large negative entropy of solution (-16.6 eu).Iod In summary, of the gas solubilities in NaN03 compared at, e.g., 400 atm and 369", we found Henry's law reasonably obeyed, and mole fractions of He, Ar, and Nzin the melt of about 0.039,0.030, and 0.034, respectively. The present work continues our investigabions in this area with the reporting of the effects of high-pressure He and Ar in fused AgN03 at 250". The results are basically similar to those of the NaN03 work, but some striking features not hitherto observed are also apparent.
Experimental Section The equipment and techniques were essentially the same as those described in ref 10b and c with a few exceptions. The conductivity bridge employed in this
4361
work was an Industrial Instruments Co. Model RC-18 instrument operated at a frequency of 3000 cps. It was necessary to equip this bridge with an external decadecapacitance box (Industrial Instruments Co. Model DK 2A, as recommended) to allow complete capacitivereactance balance. Pyrex conductance cells were identical with the construction described in ref 1Oc. Two such cells were employed: one with a cell constant of about 300 cm-I for run no. 1with He and for run no. 1 with Ar, and the second with a cell constant of about 384 cm-' for run no. 2 with He and for run no. 2 with Ar. Reagent grade AgN03 samples from ;\lallinckrodt, Fisher Scientific, and Baker were used. Prior to each solubility or conductance run, about 400 g or more of AgN03 was fused, allowed to cool and to solidify in a porcelain casserole contained in a desiccator, and then finely pulverized. The He and Ar gases were obtained from the National Cylinder Gas Co. and each had a stated purity of more than 99.98%. New samples of AgN03 from unopened containers were used for each of the four conductance runs. Although no extensive decomposition of the salt beyond a slight yellowing seemed to occur at the prevailing temperature of 250" employed in this work, it was deemed desirable not to reuse old samples in the conductivity experiments. Each such experiment lasted from 1.5 to 3 weeks with the same sample, and the reproducibility of conductance data for that sample during such time intervals would seem to rule out any noticeable complications due to salt decomposition. However, used salt samples were employed for the gassolubility determinations. In the conductance experiments, about 400 g of finely pulverized AgN03 (previously treated as described above) was placed in the conductance cell, and the assembly was sealed in the Parr A243HC5 Inconel autoclave as before.'OcVd The system was then evacuated at room temperature by constant pumping with a mechanical vacuum pump for a t least 24 hr. The bomb valve was closed with the salt still under vacuum. The unit was heated in a Parr A404HC2 autoclave furnace, and the mechanical vacuum pump was reapplied until a temperature of about 150-175" was attained. At this point the autoclave valve was again closed, and the salt (8) S. B. Tricklebank, L. Nanis, and J. O'M. Bockris, Rea. Sci. Instr., 35, 807 (1964). (9) M. G. Evans and M. Polanyi, Trans. Faraday SOC.,31, 885 (1935). (10) (a) J. L. Copeland and W. C. Zybko, J. Am. Chem. SOC.,86, 4734 (1964); (b) J. L. Copeland and W. C. Zybko, J . Phys. Chem., 69, 3631 (1965); (c) J. L. Copeland and W. C. Zybko, ibid., 70, 181 (1966); (d) J. L.Copeland and L. Seibles, ibid., 70, 1811 (1966); (e) J. L.Copeland and S. Radak, ibid., 70,3356 (1966).
Volume 71. Number 13
December 1967
JAMESL. COPELAND AND STEVEN RADAR
4362
was permitted to fuse in vacuo and to attain a final temperature of 250". Conductance (resistance) measurements were made on the AgN03 at 250" under vacuum and a t several increments of increasing He or Ar pressure. Additional readings were taken with descending pressures occasionally to check reproducibility. Prolonged agitation and long periods of time (sometimes 1-2 days) were necessary for the system to attain equilibrium at each of the several pressures. The approach to such an equilibrium took place more slowly than it did for the NaSOa work. This conductance procedure represents a slight departure from the NaN03 work, where initial measurements were for high pressures rather than for vacuum. Gas solubilities at 250" and a t various pressures were determined by exactly the same procedure as described in ref lob, using the same literature sources for finding molar volumes of Ar" and He.12 The solubility determinations were accomplished between the first set of conductance runs with He and Ar (with the first cell) and the second set of conductance runs with these gases (with the second cell). Volumes of liquid AgNOa a t 250" at the various pressures were calculated using the density-piston-pressure data of Owens.6e
Results The solubility data for He and Ar in AgN03 at 250" are summarized in Tables I and I1 and are plotted in Figure 1. It is seen from this graph that the Ar point at 306 atm is rather high; however, Chauvenet's principle would not allow it to be excluded. Again, as in the NaXOs work, the solubilities follow Henry's law within experimental error with average Henry's law constants
K H =~ (3.57
f
0.48) X
mole
C M - ~atm-'
(2)
and
K A =~ (3.35 f 0.55) X
mole ~ m atm-' - ~
(3)
for H e and Ar, respectively. The errors are probable errors for a single observation. It is to be noted that these constants are greater than the corresponding ones and for He and Ar in NaNOa a t 369" (2.27 X 1.72 X lod6 mole C M - ~atm-l, respectively)lob~D and that they are essentially equal, within error. The specific conductance data are summarized for two runs each for H e and Ar in Tables I11 and IV and are plotted in Figure 2. One unusual feature of these data can be seen in runs 1 and 2 for He, and in run 1 for Ar. This feature is that the specific conductance, K , resulting when the melt was saturated with gas at only 1 atm pressure, was lower than it was for vacuum conditions. Although this sudden drop in K in the range The Journal of Physieal Chemistry
100
-0
300
900
400
P (ATMI Figure 1. Solubility of helium (top) and argon (bottom) in molten AgN08 at 250°, Caeand C A ~respectively, , us. saturating pressures of the gases, P.
Table I : Saturation Concentration of He, Cae, at 250' in Molten AgNOs at He Pressures, Pae, and Henry's Law Constants, Kae
--
PHel
atm
-
51
73
79
96
216
C H ~X, lo4 mole
2.20
2.52
2.70
2.90
7.30
9.37
om-8 K H ~X, 108 mole cm-a atm-1"
4.32
3.46
3.42
3.02
3.39
3.79
a
247
Av Kae = (3.57 & 0.48) X 10" mole cm-a atm-1.
from 0 to 1 atm was not reproducible in its extent (from 0.8370 to 0.8312 ohm-' cni-l in H e run 1, from 0.8370 to 0.8350 ohm-' cm-l in He run 2, from 0.8370 to 0.8342 ohm-' cm-l in Ar run 1, and not a t all in Ar run 2), it. occurred not only in these runs (except Ar run (11) F. Din, "Thermodynamic Functions of Gases,'' Vol. 11, Butterworth and Co. Ltd., London, 1962, pp 192, 193. (12) C. E. Holley, Jr., W. J. Worlton, and R. K. Zeigler, "Compressibility Factors and Fugacity Coefficients Calculated from the Beattie-Bridgeman Equation of State for Hydrogen, Nitrogen, Oxygen, Carbon Dioxide, Ammonia, Methane, and Helium," Project LA-2271, Los Alamos Scientific Laboratory of the University of California, Los Alamos, N . M., 1969.
INERT GASPRESSURE AND SOLUBILITY EFFECTS ON FUSED-SALT CONDUCTANCE
(certainty K a t 1 atm was never above its value for vacuum) has forced us to the conclusion that the effect is probably real, even though not yet quantitatively reproducible.
Table I1 : Saturation Concentrations of Ar, C A ~ , at 250' in Molten AgNOa a t Ar Pressures, PA^, and Henry's Law Constants, K A ~
--
Par, atm-254 306
47
138
C A ~X, lO'm01e
1.04
6.01
8.31
cm-8 K A ~X, 10s mole cm-a atm-1 a
2.21
4.35
3.27
337
375
12.1
9.82
12.6
3.95
2.92
3.38
Av K A = ~ (3.35 f: 0.55) X 10" mole cm-3 atm-1.
Table I11 : Summary of Specific Conductance of AgNOa a t 250' under He Pressure" ---Run 1 (3 weeks)SP Saturating pressure, conductance, P H ~atm , K H ~ohm-1 , cm-*
0 1 37 67 134 225 274 266 350
--
0.81
4363
--
Run 2 (18 days)-SP pressure, conductance P H ~atm , K H ~ ohm-I , om-1
Sat uratina
0 1 32 63 59 123 156 150 264
0.8370' 0.8312 0.8255 0.8262 0.8207 0.8158 0.8109 0.8118 0.8050
0 .8370' 0.8350 0.8322 0.8313 0.8317 0.8274 0.8261 0.8269 0.8208
e Data are recorded in the experimental order in which they were obtained. * This value, interpolated from published data of Sundheim and Berlin [B. R. Sundheim and A. Berlin, J. Phys. Chem., 68, 1266 (1964)] gave the cell constants 298.5 cm-l for run 1 and 383.0 cm-1 for run 2.
I
I
I
I
I
I
I
Table IV : Summary of Specific Conductance of AgNOa at 250' under Ar Pressure" -Run 1 (16 days)-Saturating SP conductance, pressure, PA^, atrn K A ~ ohm-' . cm-1
e
0.80
0 1 38 72 140 203 240 315 168 167 1
0 .8370' 0.8342 0.8323 0.8298 0.8282 0.8237 0.8221 0,8172 0.8241 0.8241 0,8335
-Run 2 (9 days)Saturating SP pressure, conductance, PA^? atm K A ~ ohm-' , cm-1
0 56 55 124 120 180 286 343 315 1 63 61
0 . 8370' 0.8326 0.8341 0.8294 0.8296 0.8273 0.8218 0.8188 0.8207 0.8370 0.8332 0.8337
o*8'8 oao
0
100
200
300
400
P (ATM) Figure 2. Specific conductance of molten AgNO, a t 250' saturated with helium (He-1 and He-2) or argon (Ar-1 and Ar-2) a t pressures P.
2) but also consistently in many other runs that were forced to be terminated before completion for various reasons. For example, Table V gives 0 to 1 atm Ar data for K at various times in a partial Ar run that failed to go to completion because of later mechanical difficulties. The fact that this happened nearly every time
a Data are recorded in the experimental order in which they were obtained. * This value, interpolated from published data of Sundheim and Berlin (see footnote b, Table 111) gave the cell constants 300.8 cm-1 for run 1 and 384.1 cm-l for run 2.
It appeared to us that the electrical resistances measured under vacuum conditions should be more common to all four runs in Tables I11 and I V than were the values at 1 atm. Several literature values are reported for the specific conductance of AgN03 a t various temVolume 71, Number 13 December 1967
JAMES L. COPELAND AND STEVEN RADAK
4364
Table V : Partial Run of Specific Conductance of AgNOs a t 250' under .4r Pressure a t Various Times r--
0
Saturating pressure, PA^, atm Specific conductance, K A ~ ohm-' , em-'
Time, h r - -
22
185
4Za
1
0
1
1
0.8350
0,8370
0.8350
0.8350
a Between 42 and 185 hr, there were several higher pressure excursions.
peratures, and it is assumed that all these measurements were made under atmospheric conditions. Duke and Fleming13 have pointed out the variance of literature values for this quantity and thereby felt obliged to redetermine this and similar properties. Thus, for examples, one observes for the K of pure AgN03 at 250" values such as 0.85 ohm-' cm-l,I4 0.840 ohm-' cm-',15 0.836 ohm-' cm-',l3 and 0.8370 ohm-' cm-l (reference in Table 111). It is assumed that all these values were found for atmospheric pressure conditions. Some inconsistencies of these literature values may be related to the previously undetected effect just reported here. To calculate the appropriate cell constants, therefore, we used an interpolated value for K a t 250" of 0.8370 ohm-' cm-' (reference given in Table 111) in conjunction with the common zero pressure-resistance value for each run. The published data of Sundheim and Berlin, from which this K value was derived, seemed to us to be the most reliable, if for no other reason than that they include four significant figures as compared to three or less for other works. Even here there may well be a slight error, since the cited data were no doubt compiled for atmospheric pressure conditions rather than for vacuum conditions.With K values calculated using the cell constants so obtained, least-squares analyses of the four runs (excluding the vacuum point in each case) gave the following empirical straight-line equations for K us. gas pressure, P, in atm H e run 1 : He run 2:
K H = ~
0.0005)
-
f
0.24) X 10-5PHeohm-' cm-l
KIfe
=
(0.8345
f
0.12) X 10-5PH, ohm-' cm-'
K A ~=
(5.24 Ar run 2:
f
(7.01 (5.28 Ar run 1:
(0.8302
f
K A ~=
(5.11
f
(0.8340
f
f
0.0002) 0.0003)
-
f
0.0002)
The Journal of Physicai Chemistry
The main features of this work are (a) the practical equality of the pressure coefficients of the specific conductance for He and Ar in AgN03, and their comparison with the NaNOa work; (b) the equality, within error, of the solubilities of He and Ar in AgN03, and their greater values than were observed for NaN03; and (c) the apparent tendency for the specific conductance of AgN03to decrease unusually from vacuum conditions to saturation with He or Ar at 1 atm. Scrutiny of eq 4a, b, 5a, b, and Figure 2 forces us to the conclusion that there is no noticeable difference in the effects of He and Ar pressure and solubility on the specific conductance of AgT\;03at 250" within the pressure range employed. This is indicated by the closeness of the pressure coefficients of K . The corresponding coefficients for He and Ar with N a S 0 3 a t 369" are, loc for He -(9.19
f
0.25) X
ohm-' cm-l atm-'
(6)
ohm-' cm-' atm-'
(7)
and for Ar -(1.94
* 0.06)
f
Certainly in comparison with these, t,he coefficients in the present work are nearer to, but still less in magnitude than that of H e in the NaN03. Similarly we must conclude from eq 2 and 3 that the solubilities of He and Ar in AgN03 are the same, within error, in the pressure ranges employed. The corresponding Henry's law constants for these gases in NaN03 a t 369" are,lob,cfor He (13) F. R. Duke and R. A. Fleming, J . Electrochem. Soc., 105, 412
(5a)
-
0.09) X 10-5PA,ohm-' cm-'
Discussion
(4b)
-
0.18) X 10-5PA, ohm-' cm-l (0.8364
(4a)
The errors are the least-squares probable errors. It is seen that the least-squares intercepts are below the vacuum value for K of 0.8370 ohm-' cm-l in eq 4a, b, and 5a, and just slightly below in eq 5b. In the first three cases the differences between 0.8370 ohm-' cm-' and the intercepts are outside many probable errors. This is seen in Figure 2 as well. This lends credibility of a statistical nature to our belief that the abrupt drop in K in the range from 0 to 1 atm may be a real effect. It is also apparent that the pressure coefficients of K in eq 4b, 5a, and 5b distinctly overlap with their probable error brackets, while the coefficient in eq 4a lies a bit outside the other three values and their ranges, although not greatly so.
(5b)
(1958). (14) A. Klemm, "Transport Properties of Molten Salts," in "Molten
Salt Chemistry," M. Blander, Ed., Interscience Publishers, Inc., New York, N. Y.,1964,p 574. (15) R. C. Spooner and F. E. W. Wetmore, Can. J . Chem., 29, 777 (1951).
INERT GASPRESSURE AND SOLUBILITY EFFECTS ON FUSED-SALT CONDUCTANCE
K H e= (2.27
* 0.07) X
mole ~ m atm-' - ~
(8)
* 0.17) X
mole ~ m atm-' - ~
(9)
and for Ar
K A =~ (1.72
Comparison of the constants for the present work with these gases reveals He and Ar to be considerably more soluble in AgN03 a t 250" than they are in NaN03 at 369". At 400 atm, for example, He and Ar are present in AgX03 at 250" to the extent of 0.058 and 0.055 mole fraction, respectively, whereas we indicated earlier their mole fractions a t the same pressure in NaN03 a t 369" to be 0.039 and 0.030, respectively. This greater solubility in AgN03 is surprising if one accepts the approximate model of Blander, Grimes, Smith, and Watson.16 According to this model, a given noble gas should be less soluble in B fused salt of higher surface tension at a given temperature, and more soluble in a given salt a t higher temperatures. Thus, both He and Ar should be less soluble in molten AgN03 a t a lower temperature of 250" with a surface tension of 149.0 dynes crri-' than they would be in fused NaN03 at a higher temperature of 369" and with a surface tension of 113.5 dynes cm-'.17 We can advance no reason at this time why these solubility observations for He and Ar in AgNO, appear as they do. A possible hypothesis for this work conceives of the conductance process as being made up of a combination of (a) an ion-jumping mechanism utilizing liquid-free volume, similar to that suggested by Bockris and Richards' or Cohen and Turnbu1l,l8 and (b) the cooperative rearrangements of groups of ions, as suggested by the recent theory of Adam and G i b b P and amplified by Angell.20 This type of mechanism seems to be hinted at in the work of Lantelme and Chemla on transport properties of the NO3- ion in molten alkalinitrate mixtures.21 For this model applied to the present work, we conceive of some of the gas solubility as due to the occupancy of some liquid-free volume
4365
"cells," of favorable spatial extent, by the gas molecules with negligible expenditure of energy. This would remove some free volume from the conductance process. Additional gas solubility would be the result of the gas molecules e n d ~ t h e r m a l l y having ' ~ ~ ~ ~to ~ ~create ~ their own holes in the melt. This would give rise to a dilution effect on the cooperative mechanism, as hypothesized for the NaN03 work.locte If we wish to extend only the dilution hypothesis to cover this work, we must conclude that like solubilities of H e and Ar in the melt produce like partial molal volumes of these gases, with consequent similar effects on K at all pressures employed. The partial molal volumes of these gases would have to be smaller than they are at like pressures in the NahTO3 work, since the effects on K of AgN03 are less. And this would be in spite of higher gas solubilities in AgN03 than in NaN03. Evidently, AgN03 offers many intriguing opportunities for further studies of this nature.
Aclcnowledgments. The authors gratefully acknowledge support of this work by t,he National Science Foundation, Grants No. GP-4274 and GP-7012. This paper is based on the thesis of Steven Radak, which has been submitted to the Graduate School of Kansas State University in partial fulfillment of the requirements for the degree of Master of Science. (16) M. Blander, W. R. Grimes, N. V. Smith, and G. M. Watson, J . Phys. Chem., 63, 1164 (1959). (17) C. C. Addison and J. M.Coldrey, J . Chem. Soc., 468 (1961). (18) M.H.Cohen and D. Turnbull, J . Chem. Phvs., 29, 1049 (1958). (19) G. Adam and J. H. Gibbs, ibid., 43, 139 (1965). (20) C. A. Angell, J . Phgs. Chem., 70, 2793 (1966). (21) F. Lantelme and M. Chemla, Electrochim. Acta, 11, 1023 (1966). (22) W. R. Grimes, N. V. Smith, and G. M. Watson, J . Phys. Chem., 62, 862 (1958). (23) G. M. Watson, R. B. Evans, 111, W. R. Grimes, and N. V . Smith, J . Chem. Eng. Data, 7,285 (1962).
Volume 71,Number 13 December 1967
