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Measurement of the activity of sodium in sodium + lead alloys by use of β-alumina
J. Chem. Thermodynamics 1!375,7,485-491
Measurement of the activity of sodium in sodium + lead alloys by use of p-alumina D. J. FRAY and B. SAVORY a Department of Metallurgy and Materials Science, University of Cambridge, U.K. (Received 24 May 1974; in revised form 20 September 1974) An e.m.f. technique, incorporating the P-alumina electrolyte, was used to measure the thermodynamics of sodium+lead solutions in the range 623 to 773 K and in the mole fraction range xNa= 0.044 to xN.=0.78. The results obtained are in good agreement with many of the previous determinations.
1. Introduction P-Alumina has the formula Na,O*xAl,Os, where x can vary between 5 and 11, and a hexagonal layer-type structure of spine1 blocks containing 4 layers of cubic-closepacked oxygen ions with aluminium occupying all the sites normally occupied by the aluminium and magnesium ions in the spine1 MgAl,O,.(‘) Recent workC2) has shown that depending on the temperature two solid phases, p and i3”, are present in the composition range Na,O* llAl,O, to Na,0~5A120,. The p” structure, whose unit cell contains three blocks, exists at the highest mole fractions of sodium oxide and spontaneously decomposes to j3 above 1860 K. Due to the crystal structure of fi-alumina, diffusion of sodium ions in this material can occur in a direction perpendicular to the c axis whereas diffusion parallel to the c axis is likely to be difficult. For a polycrystalline sample, with crystals of random orientation, this effect is not apparent and dense compacts have low ionic resistance. This material has been used as a solid-electrolyte membrane in sodium + sulphur storage batteries.‘3-6) As p-alumina is a solid ionic conductor, it is ideal for determining sodium activities in metal alloys by the e.m.f. method. Previous work using p-alumina has been the determination of sodium activities in amalgams (‘) and a preliminary study by Smeltzer and co-workers of sodium activities in liquid tin.‘*’ Unfortunately, the method of sealing p-alumina pellets into a-alumina tubes, was not satisfactory as penetration of the sodium + tin alloy into the sodium reservoir was observed after 4 h. The thermodynamics of sodium -I- lead alloys have been investigated several times using the e.m.f. technique with a glass electrolyte as the ionic conductor of sodium a Now at Department of Chemistry, University of Leeds.
486
D. J. FRAY AND B. SAVORY
ions. Hauffe and Vierk(” determined the activities from xNa = 0.34 to x,, = 0.94 at 698 and 748 K and Alabyshev, Lantratov, and Morachevskii(‘“) measured the sodium activities in the range 648 to 748 K and from xNa = 0.13 to 0.90. There was agreement between the results over the regions of common composition. Further data given by Lantratov’“) are also in good agreement while the work of Morachevskii(r” shows some divergence from the other results. Hubberstey and Castleman(13) measured the thermodynamic properties of lead + sodium alloys at temperatures ranging from 518 to 773 K and compositions between xps = 0.0235 and xpb = 0.1679. The results were in general agreement with the earlier work. More recently, Bartlett, Neethling, and Crowther(r4’ examined mixtures of lead + sodium from x,, = 0.12 to XNa = 0.855 over a range of temperatures and the results agreed with most of the earlier work. Using a block of monofrax H, the commercial form of p-alumina which has application as a refractory brick, Porter and Feinleib”” determined sodium activities from x,, = 0.151 to x,, = 0.401 in the temperature range 875 to 1100 K but extrapolation of their results to a common temperature with the other determinations showed some scatter. This short introduction shows that previous thermodynamic determinations using the B-alumina electrolyte have not been totally successful and it was decided to examine sodium + lead alloys, for which data are well defined, using B-alumina tubes which should overcome the sealing problems experienced by Smeltzer and his co-workers.
2. Experimental The cell: stainless steel, Na(1) IO-alumina! {xNa + (1 - x)Pb}(l), stainless steel, was used to investigate the thermodynamic properties of sodium + lead alloys. The measured e.m.f. E is related to the difference in chemical potential of sodium at the two electrodes: h&a - Pii, = -z&F, where ,u&, and && are the chemical potentiaIs of pure sodium and sodium in the alloy, F is the Faraday constant, and z is the charge number of the cation. As pNNa = && + RTh aNa, where aNa is the activity of sodium in the alloy, -zEF = RT In a&. Therefore, from a knowledge of the e.m.f., the activity of sodium in the alloy can easily be calculated. The alloys, in general, were prepared before the experiments to give an approximately known composition. The sodium (Hopkins and Williams, Laboratory Reagent) was cut to remove the outer oxide layer, and transferred to a crucible under dry benzene, to reduce the chance of oxidation. The benzene was removed into a cold trap by evacuation and the alloy melted under argon which had been dried over magnesium perchlorate and from which the oxygen had been removed by passing the gas over heated titanium and calcium granules. The lead used was Hopkins and Williams Analar grade. The p-alumina tubes were kindly supplied by the Electricity Council Research Laboratories, Capenhurst, having been fabricated by the technique described by Wynn Jones and Miles.“@
SODIUM IN SODIUM + LEAD ALLOYS
487
In preliminary experiments various cell designs were used, the most successful being shown in figure 1 in which the alloy was contained in a p-alumina tube sealed at the top with an alumina crucible and “autostic” cement (Carlton, Brown, and Partners Ltd.). Contact was made with the alloy by a stainless-steel wire also sealed into the
Stainless steel wire
Argon Alumina crucible
@-alumina tube Alumina crucible
Calcium FIGURE 1. Diagrammatic layout of the cell.
tube. This then passed through a narrow-bore glass tube, which served both as an electrical insulator and a gas outlet, and was secured by a gas-tight seal. A crucible containing sodium metal was placed inside a wide bore glass tube. The tube of palumina was arranged so that it would slip into the crucible when the sodium was molten. The seaIed tube enabled reliabIe e.m.f. rest&s to be obtained as it is necessary that the mole fraction of sodium should remain constant throughout a run. This can be accomplished only in a sealed chamber in which the liquid sodium alloy is in equilibrium with sodium vapour with no escape of the vapour. For alloys containing only a small mole fraction of sodium, a titration technique was adopted to transfer sodium from the reservoir into the lead.
D. J. FRAY AND B. SAVORY
488
Usually, observations were made at 50 K intervals between 623 and 773 K. The low temperature limit was governed by the minimum temperature at which the liquid phase only was present in the alloy. The nichrome-wound furnace, used to heat the cell, was controlled to within + 1 K by a Eurotherm temperature controller, while the temperature of the cell itself was monitored with a Pye potentiometer using a chrome-to-alumel thermocouple. E.m.f. measurements were made with an accuracy of fl mV with a Keithley 610C electrometer and in the ranges where sufficient accuracy could not be attained directly on the electrometer, a portion of the potential was backed off so as to permit use of the high-accuracy ranges. Measurements were taken both on heating and cooling and provided the final e.m.f. agreed with the initial e.m.f. at the same temperature within + 1 mV the result was accepted. It was found that equilibrium was quickly attained so that each run could be completed within two days. If the cell was displaced from equilibrium by passing a minute current, it was found that the equilibrium e.m.f. returned in a matter of minutes. The whole cell was kept in the even temperature zone so that there was no possibility of the generation of a thermoelectric potential. After each experiment the alloy was analysed for both components by atomic absorption spectrometry. 3. Results The values of the e.m.f. together with their temperature dependence are shown in table 1. Activities of sodium in the alloy were calculated from the e.m.f.‘s, and by use TABLE 1. Results for the e.m.f. E of the cell containing xNaS(1 -x)Pb at 698 K and the temperature dependence (dE/dT). 10S(dE/dT) V K-l
EC698 K) V
X
0.78 0.696 0.594 0.490 0.402
0.032 0.094 0.148 0.203 0.294
X
0.339 0.266 0.196 0.097 0.044
-2.5 -6.8 -4.0 -6.4 -4.0
E(698 K) V
106(dE/dT) V K-’
0.325 -0.357 0.399 0.460 0.535
-1.9 -2.7 0 $8.5 +19.5
TABLE 2. Thermodynamic results for xNa+(l -x)Pb at 698 K X
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
aNa
8.81 x10-1 5.32x10-l 2.28 x10-l 9.28 x~O-~ 3.60~19-~ 9.70x10-3 3.34 x10-3 1.43 x10-3 4.39 x10-4
apb
J mol-1
J mol-l
AGm
AG Jmol-l
AH -. J mol-1
AS J moi-1
2.37 x 1O-5 7.08 x 1O-4 5.79 x10-3 3.14 x10-2 1.01 x10-1 2.95x10-l 5.31 x10-1 6.96 x10-l 8.55 x10-l
-735 -3655 -8580 -13800 -19295 -26905 -33095 -38015 -44870
-61820 -42100 -29900 -20090 -13310 -7085 -3675 -2105 -910
- 6840 -11350 -14980 -16315 -16305 -15015 -12500 -9285 -5310
-5730 -13640 -16445 -17175 -16300 -14205 -11250 -7720 -3890
+I.6 -3.3 -2.1 -1.2 to.007 +1.2 +1.8 +2.2 +2.0
AC&a
SODIUM IN SODIUM + LEAD ALLOYS
489
of the Gibbs-Duhem integration the activities of lead were obtained. From both sets of activities, the integral Gibbs free energies were derived at 698 K, and from the experimental enthalpies of mixing of the liquid alloys of Wittig and Kleinsteuber,(17’ the integral entropies were obtained. These are shown in table 2. The enthalpies of mixing were, in fact, determined at 703 K, but using them at 698K should not introduce a significant error.
4. Discussion The values of the e.m.f. obtained using the p-alumina cell at 698 K are plotted, together with the data from other investigations at the same temperature, against mole fraction x of sodium in figure 2. There is good agreement between the results of our experiments and the results of Hauffe and Vierk,“) Hubberstey and Castleman,” ‘) and
0.5 -‘f DO I *aO 0 0.4- y 0 % > 0.3 -
I
I
I
6. 6%
9
0.2
B \
0.1 ’+ \ I 0
0
I.-I--I0.2
0.4
0.6
0 - 9y: . I I ’ 0.8
s NR
FIGURE 2. The e.m.f. E plotted against the mole fraction x of sodium in the sodium+lead alloy: , this work; +, reference 9; 0, reference 14; n reference 11; 0, reference 12; A, reference 10; 0, reference 15; X, reference 13.
l
Alabyshev, Lantratov, and Morachevskii.(“’ The data of Bartlett et aZ.(14) Morachevskii,(‘*) and Porter”‘) appear to diverge from the other results at low values of x. To check the data further, the temperature dependence of the e.m.f. is plotted against x in figure 3. Again there is reasonable agreement between the various sets of results. Further confirmation of our results is given by the agreement between the
490
D. J. FRAY AND B. SAVORY
calculated temperature dependence of p found in these experiments and the partial molar enthalpies of Wittig and Kleinsteuber.(l’) Recently, there have been two critical assessments (‘*,i9)of liquid sodium + lead alloys and as the results obtained in this work are in close agreement with the assessed values, there is no need to re-examine 18
. \
I
I
I
I
I 0.4
I 0.6
I 0.8
16
7 12 z\ 8 fi 9 2 p
4 o-
-4 -8 -121 ’ 0 0.2
I 1
.Y FI.1 FIGURE 3. The temperature dependence dE/dT of the e.m.f. plotted against the mole fraction x of sodium in the sodium+ lead alloy : 0, this work ; n , reference 11; 0, reference 14 ; A, calculated from data given in table 1 and reference 17.
all the data. The error limits quoted by Hultgren et al. are much smaller than those given by Spencer and, from our examination of the results, it is felt that Spencer’s assessed errors are more realistic. This work has shown that the p-alumina electrolyte can be used for the determination of sodium activities in liquid sodium + lead alloys and that it gives results which correlate closely with those determined using solid glass electrolytes. This is in contrast with previous published measurements using p-alumina in this type of system where either scatter in the results was obtained or the seal between the p-alumina electrolyte and the alumina tube failed after a few hours. The authors are grateful to the Science Research Council for the financial support of this project and to Dr I. Wynn Jones of the Electricity Council Research Laboratories for the p-alumina tubes. The authors wish to thank Professor R. W. K. Honeycombe for the provision of laboratory facilities. REFERENCES 1. Kummer, J. T. Progress in SolidState Chemistry 7. Reiss, Il.; McCaldin, J. 0. Editors. Pergamon. Oxford. 1972. 2. DeVries, R. C.; Roth, W. L. J. Amer. Ceram. Sot. 1969, 52, 364. 3. Weber, N.; Kummer, J. T. Intersoc. Energ. Conwrs. Engng Conf: 1967, 913. 4. Weber, N.; Kummer, J. T. U.S. Pat. 3,404,036.
SODIUM IN SODIUM + LEAD ALLOYS
491
5. Miles, L. J.; Wynn Jones, I. Power Sources 3. Collins, D. H., editor. Oriel: Newcastle upon Tyne. 1970. 6. Sudworth, J. L.; Hames, M. D. Power Sources 3. Collins, D. H ., editor. Oriel: Newcastle upon Tyne. 1970. 7. Hsueh, L.; Bennion, D. N. J. Electrochem Sot. 1971, 118, 1128. 8. Joglekar, B. U.; Nicholson, P. S.; Smeltzer, W. W. Can. Met. Quart. 1973, 12, 155. 9. Hauffe, K.; Vierk, A. L. Z. Elektrochem. 1949, 53, 151. 10. Alabyshev, A. F.; Lantratov, M. F.; Morachevskii, A. G. Usp. Khim. 1%8,27, 921. 11. Lantratov, M. F. Russ. J. Znorg. Chem. 1959, 4, 2043. 12. Morachevskii, A. G. Zhur. Prikl. Khim. 1958, 31, 1266. 13. Hubberstey, P. ; Castleman, A. W. J. Electrochem. Sot. 1972, 119, 963. 14. Bartlett, H. E.; Neethling, A. J.; Crowther, P. J. Chem. Thermodynamics 1970.2, 583. 15. Porter, B.; Feinleib, M. J. Electrochem. Sot. 1956, 103, 300. 16. Wynn Jones, I.; Miles, L. J. Proc. Brit. Cerum. Sot. 1%9, 19, 161. 17. Wittig, F. E.; Kleinsteuber, T. XVZZZth International Congress of Pure and Applied Chemistry, Montreal, August l%l. 18. Spencer, P. J.; DCS Report 10, 1971, National Physical Laboratory. 19. Hultgren, R. et al. Selected Values of Thermodynamic Properties of Bbtary Alloys. Amer. Sot. Metals: Metals Park, Ohio. 1973.
Measurement of the activity of sodium in sodium + lead alloys by use of p-alumina D. J. FRAY and B. SAVORY a Department of Metallurgy and Materials Science, University of Cambridge, U.K. (Received 24 May 1974; in revised form 20 September 1974) An e.m.f. technique, incorporating the P-alumina electrolyte, was used to measure the thermodynamics of sodium+lead solutions in the range 623 to 773 K and in the mole fraction range xNa= 0.044 to xN.=0.78. The results obtained are in good agreement with many of the previous determinations.
1. Introduction P-Alumina has the formula Na,O*xAl,Os, where x can vary between 5 and 11, and a hexagonal layer-type structure of spine1 blocks containing 4 layers of cubic-closepacked oxygen ions with aluminium occupying all the sites normally occupied by the aluminium and magnesium ions in the spine1 MgAl,O,.(‘) Recent workC2) has shown that depending on the temperature two solid phases, p and i3”, are present in the composition range Na,O* llAl,O, to Na,0~5A120,. The p” structure, whose unit cell contains three blocks, exists at the highest mole fractions of sodium oxide and spontaneously decomposes to j3 above 1860 K. Due to the crystal structure of fi-alumina, diffusion of sodium ions in this material can occur in a direction perpendicular to the c axis whereas diffusion parallel to the c axis is likely to be difficult. For a polycrystalline sample, with crystals of random orientation, this effect is not apparent and dense compacts have low ionic resistance. This material has been used as a solid-electrolyte membrane in sodium + sulphur storage batteries.‘3-6) As p-alumina is a solid ionic conductor, it is ideal for determining sodium activities in metal alloys by the e.m.f. method. Previous work using p-alumina has been the determination of sodium activities in amalgams (‘) and a preliminary study by Smeltzer and co-workers of sodium activities in liquid tin.‘*’ Unfortunately, the method of sealing p-alumina pellets into a-alumina tubes, was not satisfactory as penetration of the sodium + tin alloy into the sodium reservoir was observed after 4 h. The thermodynamics of sodium -I- lead alloys have been investigated several times using the e.m.f. technique with a glass electrolyte as the ionic conductor of sodium a Now at Department of Chemistry, University of Leeds.
486
D. J. FRAY AND B. SAVORY
ions. Hauffe and Vierk(” determined the activities from xNa = 0.34 to x,, = 0.94 at 698 and 748 K and Alabyshev, Lantratov, and Morachevskii(‘“) measured the sodium activities in the range 648 to 748 K and from xNa = 0.13 to 0.90. There was agreement between the results over the regions of common composition. Further data given by Lantratov’“) are also in good agreement while the work of Morachevskii(r” shows some divergence from the other results. Hubberstey and Castleman(13) measured the thermodynamic properties of lead + sodium alloys at temperatures ranging from 518 to 773 K and compositions between xps = 0.0235 and xpb = 0.1679. The results were in general agreement with the earlier work. More recently, Bartlett, Neethling, and Crowther(r4’ examined mixtures of lead + sodium from x,, = 0.12 to XNa = 0.855 over a range of temperatures and the results agreed with most of the earlier work. Using a block of monofrax H, the commercial form of p-alumina which has application as a refractory brick, Porter and Feinleib”” determined sodium activities from x,, = 0.151 to x,, = 0.401 in the temperature range 875 to 1100 K but extrapolation of their results to a common temperature with the other determinations showed some scatter. This short introduction shows that previous thermodynamic determinations using the B-alumina electrolyte have not been totally successful and it was decided to examine sodium + lead alloys, for which data are well defined, using B-alumina tubes which should overcome the sealing problems experienced by Smeltzer and his co-workers.
2. Experimental The cell: stainless steel, Na(1) IO-alumina! {xNa + (1 - x)Pb}(l), stainless steel, was used to investigate the thermodynamic properties of sodium + lead alloys. The measured e.m.f. E is related to the difference in chemical potential of sodium at the two electrodes: h&a - Pii, = -z&F, where ,u&, and && are the chemical potentiaIs of pure sodium and sodium in the alloy, F is the Faraday constant, and z is the charge number of the cation. As pNNa = && + RTh aNa, where aNa is the activity of sodium in the alloy, -zEF = RT In a&. Therefore, from a knowledge of the e.m.f., the activity of sodium in the alloy can easily be calculated. The alloys, in general, were prepared before the experiments to give an approximately known composition. The sodium (Hopkins and Williams, Laboratory Reagent) was cut to remove the outer oxide layer, and transferred to a crucible under dry benzene, to reduce the chance of oxidation. The benzene was removed into a cold trap by evacuation and the alloy melted under argon which had been dried over magnesium perchlorate and from which the oxygen had been removed by passing the gas over heated titanium and calcium granules. The lead used was Hopkins and Williams Analar grade. The p-alumina tubes were kindly supplied by the Electricity Council Research Laboratories, Capenhurst, having been fabricated by the technique described by Wynn Jones and Miles.“@
SODIUM IN SODIUM + LEAD ALLOYS
487
In preliminary experiments various cell designs were used, the most successful being shown in figure 1 in which the alloy was contained in a p-alumina tube sealed at the top with an alumina crucible and “autostic” cement (Carlton, Brown, and Partners Ltd.). Contact was made with the alloy by a stainless-steel wire also sealed into the
Stainless steel wire
Argon Alumina crucible
@-alumina tube Alumina crucible
Calcium FIGURE 1. Diagrammatic layout of the cell.
tube. This then passed through a narrow-bore glass tube, which served both as an electrical insulator and a gas outlet, and was secured by a gas-tight seal. A crucible containing sodium metal was placed inside a wide bore glass tube. The tube of palumina was arranged so that it would slip into the crucible when the sodium was molten. The seaIed tube enabled reliabIe e.m.f. rest&s to be obtained as it is necessary that the mole fraction of sodium should remain constant throughout a run. This can be accomplished only in a sealed chamber in which the liquid sodium alloy is in equilibrium with sodium vapour with no escape of the vapour. For alloys containing only a small mole fraction of sodium, a titration technique was adopted to transfer sodium from the reservoir into the lead.
D. J. FRAY AND B. SAVORY
488
Usually, observations were made at 50 K intervals between 623 and 773 K. The low temperature limit was governed by the minimum temperature at which the liquid phase only was present in the alloy. The nichrome-wound furnace, used to heat the cell, was controlled to within + 1 K by a Eurotherm temperature controller, while the temperature of the cell itself was monitored with a Pye potentiometer using a chrome-to-alumel thermocouple. E.m.f. measurements were made with an accuracy of fl mV with a Keithley 610C electrometer and in the ranges where sufficient accuracy could not be attained directly on the electrometer, a portion of the potential was backed off so as to permit use of the high-accuracy ranges. Measurements were taken both on heating and cooling and provided the final e.m.f. agreed with the initial e.m.f. at the same temperature within + 1 mV the result was accepted. It was found that equilibrium was quickly attained so that each run could be completed within two days. If the cell was displaced from equilibrium by passing a minute current, it was found that the equilibrium e.m.f. returned in a matter of minutes. The whole cell was kept in the even temperature zone so that there was no possibility of the generation of a thermoelectric potential. After each experiment the alloy was analysed for both components by atomic absorption spectrometry. 3. Results The values of the e.m.f. together with their temperature dependence are shown in table 1. Activities of sodium in the alloy were calculated from the e.m.f.‘s, and by use TABLE 1. Results for the e.m.f. E of the cell containing xNaS(1 -x)Pb at 698 K and the temperature dependence (dE/dT). 10S(dE/dT) V K-l
EC698 K) V
X
0.78 0.696 0.594 0.490 0.402
0.032 0.094 0.148 0.203 0.294
X
0.339 0.266 0.196 0.097 0.044
-2.5 -6.8 -4.0 -6.4 -4.0
E(698 K) V
106(dE/dT) V K-’
0.325 -0.357 0.399 0.460 0.535
-1.9 -2.7 0 $8.5 +19.5
TABLE 2. Thermodynamic results for xNa+(l -x)Pb at 698 K X
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
aNa
8.81 x10-1 5.32x10-l 2.28 x10-l 9.28 x~O-~ 3.60~19-~ 9.70x10-3 3.34 x10-3 1.43 x10-3 4.39 x10-4
apb
J mol-1
J mol-l
AGm
AG Jmol-l
AH -. J mol-1
AS J moi-1
2.37 x 1O-5 7.08 x 1O-4 5.79 x10-3 3.14 x10-2 1.01 x10-1 2.95x10-l 5.31 x10-1 6.96 x10-l 8.55 x10-l
-735 -3655 -8580 -13800 -19295 -26905 -33095 -38015 -44870
-61820 -42100 -29900 -20090 -13310 -7085 -3675 -2105 -910
- 6840 -11350 -14980 -16315 -16305 -15015 -12500 -9285 -5310
-5730 -13640 -16445 -17175 -16300 -14205 -11250 -7720 -3890
+I.6 -3.3 -2.1 -1.2 to.007 +1.2 +1.8 +2.2 +2.0
AC&a
SODIUM IN SODIUM + LEAD ALLOYS
489
of the Gibbs-Duhem integration the activities of lead were obtained. From both sets of activities, the integral Gibbs free energies were derived at 698 K, and from the experimental enthalpies of mixing of the liquid alloys of Wittig and Kleinsteuber,(17’ the integral entropies were obtained. These are shown in table 2. The enthalpies of mixing were, in fact, determined at 703 K, but using them at 698K should not introduce a significant error.
4. Discussion The values of the e.m.f. obtained using the p-alumina cell at 698 K are plotted, together with the data from other investigations at the same temperature, against mole fraction x of sodium in figure 2. There is good agreement between the results of our experiments and the results of Hauffe and Vierk,“) Hubberstey and Castleman,” ‘) and
0.5 -‘f DO I *aO 0 0.4- y 0 % > 0.3 -
I
I
I
6. 6%
9
0.2
B \
0.1 ’+ \ I 0
0
I.-I--I0.2
0.4
0.6
0 - 9y: . I I ’ 0.8
s NR
FIGURE 2. The e.m.f. E plotted against the mole fraction x of sodium in the sodium+lead alloy: , this work; +, reference 9; 0, reference 14; n reference 11; 0, reference 12; A, reference 10; 0, reference 15; X, reference 13.
l
Alabyshev, Lantratov, and Morachevskii.(“’ The data of Bartlett et aZ.(14) Morachevskii,(‘*) and Porter”‘) appear to diverge from the other results at low values of x. To check the data further, the temperature dependence of the e.m.f. is plotted against x in figure 3. Again there is reasonable agreement between the various sets of results. Further confirmation of our results is given by the agreement between the
490
D. J. FRAY AND B. SAVORY
calculated temperature dependence of p found in these experiments and the partial molar enthalpies of Wittig and Kleinsteuber.(l’) Recently, there have been two critical assessments (‘*,i9)of liquid sodium + lead alloys and as the results obtained in this work are in close agreement with the assessed values, there is no need to re-examine 18
. \
I
I
I
I
I 0.4
I 0.6
I 0.8
16
7 12 z\ 8 fi 9 2 p
4 o-
-4 -8 -121 ’ 0 0.2
I 1
.Y FI.1 FIGURE 3. The temperature dependence dE/dT of the e.m.f. plotted against the mole fraction x of sodium in the sodium+ lead alloy : 0, this work ; n , reference 11; 0, reference 14 ; A, calculated from data given in table 1 and reference 17.
all the data. The error limits quoted by Hultgren et al. are much smaller than those given by Spencer and, from our examination of the results, it is felt that Spencer’s assessed errors are more realistic. This work has shown that the p-alumina electrolyte can be used for the determination of sodium activities in liquid sodium + lead alloys and that it gives results which correlate closely with those determined using solid glass electrolytes. This is in contrast with previous published measurements using p-alumina in this type of system where either scatter in the results was obtained or the seal between the p-alumina electrolyte and the alumina tube failed after a few hours. The authors are grateful to the Science Research Council for the financial support of this project and to Dr I. Wynn Jones of the Electricity Council Research Laboratories for the p-alumina tubes. The authors wish to thank Professor R. W. K. Honeycombe for the provision of laboratory facilities. REFERENCES 1. Kummer, J. T. Progress in SolidState Chemistry 7. Reiss, Il.; McCaldin, J. 0. Editors. Pergamon. Oxford. 1972. 2. DeVries, R. C.; Roth, W. L. J. Amer. Ceram. Sot. 1969, 52, 364. 3. Weber, N.; Kummer, J. T. Intersoc. Energ. Conwrs. Engng Conf: 1967, 913. 4. Weber, N.; Kummer, J. T. U.S. Pat. 3,404,036.
SODIUM IN SODIUM + LEAD ALLOYS
491
5. Miles, L. J.; Wynn Jones, I. Power Sources 3. Collins, D. H., editor. Oriel: Newcastle upon Tyne. 1970. 6. Sudworth, J. L.; Hames, M. D. Power Sources 3. Collins, D. H ., editor. Oriel: Newcastle upon Tyne. 1970. 7. Hsueh, L.; Bennion, D. N. J. Electrochem Sot. 1971, 118, 1128. 8. Joglekar, B. U.; Nicholson, P. S.; Smeltzer, W. W. Can. Met. Quart. 1973, 12, 155. 9. Hauffe, K.; Vierk, A. L. Z. Elektrochem. 1949, 53, 151. 10. Alabyshev, A. F.; Lantratov, M. F.; Morachevskii, A. G. Usp. Khim. 1%8,27, 921. 11. Lantratov, M. F. Russ. J. Znorg. Chem. 1959, 4, 2043. 12. Morachevskii, A. G. Zhur. Prikl. Khim. 1958, 31, 1266. 13. Hubberstey, P. ; Castleman, A. W. J. Electrochem. Sot. 1972, 119, 963. 14. Bartlett, H. E.; Neethling, A. J.; Crowther, P. J. Chem. Thermodynamics 1970.2, 583. 15. Porter, B.; Feinleib, M. J. Electrochem. Sot. 1956, 103, 300. 16. Wynn Jones, I.; Miles, L. J. Proc. Brit. Cerum. Sot. 1%9, 19, 161. 17. Wittig, F. E.; Kleinsteuber, T. XVZZZth International Congress of Pure and Applied Chemistry, Montreal, August l%l. 18. Spencer, P. J.; DCS Report 10, 1971, National Physical Laboratory. 19. Hultgren, R. et al. Selected Values of Thermodynamic Properties of Bbtary Alloys. Amer. Sot. Metals: Metals Park, Ohio. 1973.