WISHVENDER K. BEHLAND JAMESJ. EGAN
1764
wrong sign. Although we still cannot rule out the possibility that integral variations are responsible for this discrepancy, the improved stability of the above calculations with respect to such variations suggests that this factor is not as significant as previously thought. Thus, the neglect of other factors, such as ionic terms and multiple exchange integrals, may be quite important. Ionic terms are not easily included in the usual formulation of the theory, but could be incorporated in a manner similar to that reported by Craig.*' It is very unlikely that this would be fruitful, however, in view of the relatively small changes in
couplings calculated by Hiroike28 and Ranft,2Qwhere ionic character was introduced in a more empirical way. Multiple-exchange interactions are almost always excluded] apparently in many cases for no better reason than that they are difficult to calculate. They probably are worthy of consideration, even if they could only bc dealt with in a very approximate way. ~~
~
~
(27) D. P. Craig, Proc. Roy. SOC.(London), A200, 272, 390, 401 (1950). (28) E. Hiroike, J . Phys. SOC.Japan, 15, 270 (1960); Progr. Theoret. Phys. (Kyoto), 26, 283 (1961). (29) J. Ranft, Ann. Phy8ik., 8, 322 (1961); 9, 124 (1962).
Transference Numbers and Ionic Mobilities from Electromotive Force Measurements on Molten Salt Mixtures'
by Wishvender K. Behl and James J. Egan Brookhaven National Laboratory, Upton, New York
(Received November 4, 1966)
Transference numbers and ionic mobilities of the cations relative to the chloride ion in the mixtures of molten chlorides LiC1-PbC12, KCl-PbClZ, KC1-CaCl2, KCI-MgC12, and KCI-NaC1 were determined over the entire composition range from electromotive force measurements. The experimental arrangement of the cell employs a special junction using alumina powder to join the two salt compartments. The relative ionic mobilities of the cations were equal in the system KC1-NaCl over the whole concentration range, while in other systems the alkali ion had a greater mobility than the divalent cation. The transference numbers and ionic mobilities obtained in the present measurements for the systems KC1-PbC12 and LiC1-PbC12 agree very well with literature values obtained by moving-boundary and Hittorf-type measurements. The systems KC1-CaC12, KC1-MgC12, and NaCl-KCl have not been previously studied.
Introduction Transference numbers in molten salt mixtures are in general determined by one of three methods-Hittorftype measurements, moving-boundary measurements, or studies of emf of cells with transference. Examples of Hittorf-type measurements may be found in the works of Azia and Wetmore, Duke, Laity, and coWorkers.2d The moving-boundav n ~ t h o dhas been The Journal of Physical Chemistry
used by Klemm and co-worker~.~JAlso, Berlin, et al.,* have studied trace amounts of cations in nitrate melts by countercurrent electromigration experiments. Emf (1) This work was performed under the auspices of the U. S. Atomic
(2) P. M. Aziz and F. E. W. Wetmore, Can. J . Chem., 30, 779 (1952). (3) F. R. Duke and G.Victor, J . Am. Chem. SOC.,83, 3337 (1961).
ELECTROMOT:-JE FORCEMEASUREMENTS ON MOLTEN SALTMIXTURES
cells with transference have been used by Schwarz,g Murgelescu and co-workers,'"12 Stern,18J4 Laity,'S and Bloom and Easteal.'6 In the present study, emf's of cells of the types
1765
HLOMNE GAS INLET
PLbTINUM ELECTRUE LEMS
and XED
were measured as a function of the concentration of the molten salt mixtures, where M was Na+, Pb2+, Caz+, or Mg2+. For the study of the system LiC1-PbCla, KCI in cell I was replaced by LiCl and MCl. by PbC12. From the results of these measurements and the thermodynamic properties of the mixtures, transference numbers of the cations relative to the chloride ion were determined. The relative ionic mobilities (internal mobilities) were calculated from the above transference numbers using known data on density and conductance of the molten salt mixtures. It was found that the usual quartz frit, used to connect the two salt compartments in the above cells, gave results in disagreement with previous reliable measurements so that a special junction was designed and is described in the experimental section. It was also found that the elimination of metal electrodes was very helpful. Experimental Section Purification of Materials. Reagent grade chemicals were used. Sodium and potassium chloride were melted under vacuum and stored in an argon atmosphere in storage tubes. Lithium chloride, lead chloride, and magnesium chloride (anhydrous) were heated at 100" under a flowing atmosphere of hydrogen chloride gas for 24 hr. The temperature was then slowly raised to the melting point and HCI gas bubbled through the molten chlorides for a period of 3-4 hr. The temperature was then lowered and the anhydrous salts so obtained were remelted and filtered in an inert atmosphere of argon gas, cooled, and stored. Calcium chloride dihydrate (CaCI2.2Hz0) was similarly heated under a flowing atmosphere of HCI gas at 100" for 24 hr and the temperature then raised to 280" when CaClz. Hz0 melted and HCI gas was allowed to bubble for another 8-10 hr. After all the water of hydration was removed, the temperature was gradually raised to the melting point of calcium chloride and HCI gas was bubbled for another 3-4 hr. Finally the anhydrous salt was allowed to solidify. It was then transferred to the filter tube, remelted, filtered in an inert atmosphere of argon, cooled, and stored.
SEAL
CHLORlM W E T -
X T bDDlTloN TUBE GRAPHITE ELECTRbDa
WAR72 TUBE RAPHllE COYER
THERMOCOUPLE IN OUbRTZ PROTECTW TUBE
SPIRbL TUBE MNTAWING
4% FUSED SALT UlXTURE
NNER OUPRTZ CUP
Figure 1. Cell assembly.
Apparatus. The cell assembly used is shown in Figure 1. A 5-in. long quartz tube (25-mm diameter) closed at the bottom was used as one compartment of the cell. This was placed in an outer Vycor container (57-mm diameter), which was used as the second (4) (a) F. R. Duke, R. W. Laity, and B. Owens. J . Eleclrockem. Soc.. 104,299 (1957); (b) F. R. Duke and K. A. Fleming, ibid.. 106, 130 (1959). (5) C. T. Moynihan and R. W. Laity. J . Phya. Chem.. 68, 3312 (1964). (6) A. Klemm in "Molten Salt Chemistry." Milton Blender. Ed.. Interscience Publishers. Inc.. New York. N. Y . . 1964. (7) A. Klemm and E. U. Monse. Z. Noturfwsch., 121).319 (1957). (8)A. Berlin. F. MBnBs. S. Forcheri. and C. Monfrini. J . Phya. Chem., 67, 2505 (1963). (9) K. E. Schwarz, Z. Elektrochem.. 47, 144 (1941). (10) I. G. Murgelesm and D. I. Marehidan. Rusa. J . Phys. Chem.. 34, 1196 (1960). (11) I. G. Murgelescu and 8. Sternberg. Discussions Faradav Soc.. 32. 107 (1961). (12) I. G. Murgelescu and D. I. Marohidan. Acad. Rep. Populare Rmnine. Slvdii Cercefari Ckim.. 8, 383 (1960). (13) K. H.Stern. J . Phya. Chem., 63, 741 (1959). (14) K. H.Stern, J . Electrochem. Soe., 112, 1049 (1965). (15) R. W.Laity, J . Am. Chem. Soc.. 79, 1849 (1957). (16) H. Bloom and A. J. Eaateal, Australian J . Ckem.. IS, 2039 (1965).
Volume 71, Number 6
May 1967
WISHVENDER K. BEHLAND JAMESJ. EGAN
1766
compartment. The small compartment contained the pure chloride while the other compartment contained the mixture. The mole fraction of the mixture was varied from 0.1 to 0.9. The liquid junction between the two solutions was established through a 5-in. length of 6-mm diameter tubing, formed in a spiral and opening to the second compartment as shown. The spiral was filled with powdered alumina T-61 (120 mesh, Aluminum Co. of America). The powdered alumina was found ideal for these experiments as it prevented any gravitational flow from one side to the other due to any difference in levels. It generally took 24 hr for the molten salt to flow through the alumina column and establish contact with the solution in the outside container. However, this process was hastened by evacuating the cell for 1-2 min after the salts were molten in the two compartments and when the pressure was brought back to atmospheric pressure with argon, the alumina column was filled with the molten salt. The contact was then confirmed by measuring the resistance across the two carbon electrodes; it was usually about 100-200 ohms, if proper contact was established. In earlier experiments the liquid junction was established by using a fine-porosity quartz disk between the two compartments. However, while working on the system LiC1-PbC12, it was observed that the emf increased steadily with time. This was interpreted as an indication that Li+ from the melt was exchanging with the quartz disk. The alumina was found to be inert. Spectroscopic carbon rods were used as the electrodes and platinum wires were used as leads. The whole cell assembly was heated at 825” under vacuum for 3-4 hr and under chlorine atmosphere for a period of 24 hr before loading the cell with salts. The chlorine gas was used from the cylinder. A wirewound cylindrical furnace was used to heat the cell assembly and the temperature of the cell was controlled within * 2 O with a Honeywell Brown Pyr-o-vane temperature controller.
Results and Discussion The transport number, t i , of the ion i is given by
where z I is charge, c, the concentration in moles per cubic centimeter of the ions i, 5 is the Faraday constant, b, the mobility of ion i, and K the specific conductance. Following Klemma we can define two sets of transport numbers by choosing two different references to measThe Journal of Physical ChemiStTy
ure the mobilities of the ions. Thus, if we choose walls of the cell as the references, we have
The transference number so defined is called the “external transport number” and is identical with the transport numbers obtained by several workers by Hittorftype measurements. However, if we choose one of the ions as a reference, then we have
The transport number so defined is called the “internal transport number’’ and is identical with the quantity 4 used by Aziz and Wetmore.2 The relation between the internal and external transport numbers in the case of a binary mixture of molten salts with the common ion as the reference can be easily shown to be t13
=
tlw
t23
=
tzw
+ +
E13f3w
(4)
E23t3w
(5)
where t13 and tz3 are the internal transport numbers of the cations, tlw and hWare the corresponding external transport numbers, and E13 and ET3are the equivalent fractions of the salts 13 and 23. t3w is the external transport number of the anion. Thus, according to the definition t13
+
t23
+ + + +
= tlw
=
tlW
tZw
(E13
tzw
t3w
+
=
EZ3)t3w
1
(6)
Now consider the cell
A
B
The emf of the above cell may be expressed by the equation E ~ i i=
l
-5
B A
1
ti3dp~ci- 25
B A
h3dppbci2 (7)
where t13 and t23 are the internal transport numbers of the ions K+ and Pb2+, respectively, and C(KC1 and PpbCl2 are the chemical potentials of the respective chlorides. The derivation of this equation is discussed in detail by Wagner.” Now, using the Gibbs-Duhem equation, we have
(17) C. Wagner, Advan. Electroehem. Electrochem. Eng., 4 , 1 (1966).
ELECTROMOTIVE FORCEMEASUREMENTS ON MOLTEN SALTMIXTURES
1767
and from the definition of internal transport numbers t23
=
1-
(9)
t13
Substituting eq 8 and 9 into eq 7
I '
d
I
YI
N
Since
therefore
h
M
Differentiating eq 12
v N
6
...
-2.303RT 2t13 - tlflKC1 - XKCl 1 - XKCl 25
(
h
)
B
M
W
(13)
Thus, if the measurements of the cell potential are made over the whole composition range, the transport number t13 can be calculated by use of eq 13 using graphical differentiation. The transport number 48 will then be given by eq 9. Similar equations can be derived for cells of type 11. The internal mobilities of the cations relative to the chloride ion can then be calculated by use of eq 3. Thus
h
M v N
6 El
t13K
b13
8."
=-
n
ZlC15
M
v n
and
I ' where K is the specific conductance of the mixture, z1 and z2 are the charges on cations 1 and 2, and c1 and c2 are their concentrations in moles per cubic centimeter. Since the equivalent conductance A is related to the specific conductance K and equivalent volume v by the equation
h
M v N
6 4 H
K
X = K V =
ZlCl
+ zzcz
(15)
F
I
d Lt
Volunte 71, Number 6 M a y 1967
WISHVENDER K. BEHLAND JAMESJ. EGAN
1768
Table I1 -KCl-PbClz tlS,
Zalksli chloride
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
present measurements
0.076 0.142 0,211 0.302 0.414 0.559
at 525O113, from the data of Duke, et al.rb
0.075 0.150 0.235 0.325 0.430 0.560
-KCI-PbCIz ha,
present measurements
at 825O-11, at 85O0, from the data of Duke, el a2.db
0.338 0.452 0.564 0.677 0.780 0.882
we now have the equations
0.670 0.780 0.885
KCI-CaClz at 825O
KCl-MgCh at 8 2 5 O
KCI-NaCI at 825"
LiC1-PbClr at 650°
tl8
tia
tis
tia
0.060 0.150 0.260 0.375 0.490 0.615 0,740 0.845 0.930
0.05 0.16 0.36 0.58 0.76 0.83 0.87 0.91 0.95
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
0.064 0.163 0.257 0.366 0.458 0.559 0.655 0.751 0.897
I
I
I
I
I
I
-
LiCl PbC12 SYSTEM
and
or
4
4c
and 0.2
where E13and E 2 3 are the equivalent fractions of the salts 13 and 23, respectively. The emf measurements on the various molten salt mixtures are summarized in Table I. The activities of KC1 in the systems KC1-PbC12, KC1-MgC12, KC1CaC12,and KC1-NaC1 and of LiCl in the system LiC1PbC12 were taken from the unpublished results of Egan.ls The emf's of the cells in all the cases except for the system KCl-NaCl were nonzero and varied with concentration. In the case of the system KClNaCl, the emf was 0 within + 2 mv over the whole concentration range. The transference number of the potassium ion (t13) relative to the chloride ion in the system KC1-PbCh was calculated by use of eq 13 a t various concentrations of the mixture. These values are shown in Table I1 as a function of the potassium chloride mole fraction. The system KCl-PbClz was also investigated by Duke and Fleming4bby Hittorf-type measurements. The values of 4 for the potassium ion, which The Journal of Physical Chemistry
0.4
0.6 XLicl
0.e
1.0
Figure 2. Internal mobilities of Li+ and Pb2+ ions relative to the chloride ions as a function of composition: 0,mobilities obtained from the present measurements; A, mobilities taken from the data of Klemm, et a1.l
are the same as the internal transport numbers ( t I 3 ) obtained in the present measurements, are also shown in Table I1 and there is an excellent agreement between the two sets of data. The internal transport numbers of the potassium ion relative to the chloride ion in the systems KC1CaC12 and KC1-MgCls and that of the lithium ion in the system LiC1-PbC12 were similarly calculated by use of eq 13 and are given as a function of the alkali chloride mole fraction in Table 11. Since the emf for the cell
(18) J. J. Egan, unpublished results; see Abstracts of the Electrochemical Society Meeting, San Francisco, Calif., May 1965, and also BNL 954 (8-68).
ELECTROMOTIVE FORCE MEASUREMENTS ON MOLTENSALT MIXTURES
12
I
I
I
I
1769
I
I
I
I
KCI-MgCI2 SYSTEM
KCI-CoC12 SYSTEM 1.4
‘ I
1.2
m
2 x
0.8
c)
+
n P
6
0.6
nE
0.2
0.4
0.6
0.8
XKCl
Firmre - 3. Internal mobilities of K + and Ca%+ions relative to the chloride ion as a function of composition. 0 0
was zero over the whole concentration range, it can be easily shown that the internal transport number for the potassium ion at any concentration is equal to the mole fraction of potassium chloride in the mixture. Internal Mobilities. The internal mobilities of the cations Li+ and Pb2+ in the system LiC1-PbC12 were calculated by use of eq 17. The internal transport numbers determined in the present measurements were used. The specific conductance values were taken from the data of Klemm and Monsd and the equivalent conductance was calculated by use of eq 15. Since the density data for this system were not available, it was assumed that the relationship between the equivalent volume and mole fraction was linear. The values of the internal mobilities so obtained are plotted in Figure 2. Also plotted are the internal mobilities obtained by Klemm and Manse? from the moving-boundary experiments. There is a good agreement between the two sets of data except at concentrations below 0.4 mole fraction of lithium chloride. Klemm and Monse observed an increase in the internal mobility of lithium ion as the concentration of LiCl decreased below 0.4z~icl. This increase was not observed in the present measurements. The internal mobilities of the cations relative to
0.2
0.4
0.6
0.8
1.0
‘KCl
Figure 4. Internal mobilities of the K +and Mg9+ ions relative to the chloride ion aa E function of composition.
the chloride ions in the systems KC1-CaClP and KC1MgClt were similarly calculated by use of eq 17 and are plotted in Figures 3 and 4. The specific conductance and density data for these systems were taken from the literat~re.~9sW In each of the systems studied, the alkali ion was observed to have a relatively larger mobility than that of the alkaline earth ion. In the system NaC1-KC1, the cell potential was observed to be zero over the whole concentration range and hence it was concluded that the internal mobilities of the sodium and potassium ions are the same over the whole concentration range. Acknowledgments. The authors wish to acknowledge the help of Mr. John Bracker and Mr. R. J. Heus with the experiments and the helpful suggestions of Dr. R. H. Wiswall. (19) R. W. Huber, E. V. Potter, and H. W. St. Clair, Bureau of Mines Report of Investigation 4868, U. 8.Department of the Interior, Washington, D . C., March 1952. (20) C. Sandonnini, Oazz. Chim. Itol., 51,289 (1920).
Volume 71, Number 6 Mav IS87
