March, 1057
S U D I U M ~ ~ L U ~ R I l ) ~ - ~ I l ~ C O FLUORIDE NIUM SYSTEM
337
VAPOlt PRESSURE ANI) DERIVED INFORMATION OF THE SODIUAI FLUORIDE-ZIRCONIUM FLUORIDE SYSTEM. DESCRIPTION OF it METHOD FOH THE DETERMINATION OF MOLECULAR COMPLEXES PRESENT IN THE VAPOR PHASE1 BY KARLA. SENSE, C. A. ALEXANDER, R. E. BOWMAN AND R. B. FILBERT, JR. Batlelle Memorial Institute, Columbus, Ohio Received SeptembeT 17, 1866
By use of the transpiration method, the vapor pressures of the NaF-ZrF4 system were measured over the range 599-1075”. On the basis of the Duhem-Margules equation and the thermodynamic stability of a system, it was deduced that, in addition to NaF and ZrF4, a compound composed of NaF and ZrF4 must exist in the vapor hase. The molar composition ratio of this compound must be NaF/ZrF4 < 1.38. The assumption is made that the comprex has the simple structure NaZrFb. On the basis of this assumption, partial pressures of NaF, ZrF4 and NaZrFBare calculated. As a first approximation, the dissociation constant for the reaction, NaZrFs = NaF ZrF4, was determined as a function of the temperature. A partial phase diagram of the NaF-ZrF4 system derived from the vapor pressure data shows a constant boiling oint to exist a t 25 mole % ZrF4. The composition at this constant b o i l i 3 point does not seem to change with pressure. %his behavior, considered together with an activity lot of the system a -NaZrFs, suggests the existence of Na3ZrF~in the liquid state. The extent of dissociation of NarZr$r in the vapor phase could not be determined. Plots showing vapor-liquid-solid equilibria are presented. A d o t is given showing the change - of the total vapor pressure of the NaF-ZrF4 system with composition for various temperatuies.
+
1
This work was undertaken as part of a program to irivestigate the physical properties of fused-balt systems.
the NaF-ZrF, system. The curves behave as expected, since for a given temperature pNaF decreases as the NaF-ZrFd system becomes poorer in NaF. Figure 4 also shows plots of pNaF as a Experimental function of the reciprocal temperature for NaFThe method and apparatus have been described in sufficient detail in previoue papers.Bt8 A slight change from ZrF4 compositions poorer in NaF than those shown previous procedure consisted in the use of argon rather than in Fig. 3. In spite of the rather considerable scatnitrogen as a carrier gas. The results obtained when argon ter, it is quite evident, and interesting, that pNaF was used were fully comparable with those when nitrogen was used. The use of another vapor pressure a paratus increases as the composition of the liquid becomes similar to the one built ori$inally permtted the letection poorer in NaF. This behavior is brought out mort! of systematic errors peculiar to either set. A revised clearly by Fig. 5 which shows how the partial pressrheniatic diagram is given in Fig. 1 . The low melting mixtures of NaF and ZrF4, as well as sures of NaF and ZrF4 vary with composition for R ZrFd, werc provided by the Oak Ridge National given temperature. It is noted that for composirtboratory. The NaF was J. T. Baker highest grade. tions greater than about 34 mole % ZrF,, the parExcept for a few prehsed salt mixtures, the desired com- tial pressure of NaF is greater than the vapor prcfipositions were obtained by adding the proper amounts sure of pure NaF. In terms of activities, this mcans of NaF or ZrF4 to a prefused NaF-ZrFc mixture. The components necessary to make up a desired composition that the apparent activity of NaF is greater than 1.
E“‘“
wrre first ground to a fine powder. The necessary quantities of thc powdered components were then intimately mixed to ensure liomogcneity . The results obtained using charges preprtred in this manner were checked against results obtained with rt prefused salt having the samc composition. Although thc manually preparcd charges produced morc scatter ahout the vapor pressure curve obtained, the results were romparable with those from prefused salts. All results were corrected for composition changes which orcurred whilc the runs were being made.
Results and Discussion Molecular Species in the Vapor Phase.-Initially, in the absence of any information regarding complex molecules in the vapor phase, the partial pressures of NaF and ZrR were calculated on the assumption that only NaF and ZrFl exist in the vapor phase. The results are presented graphically in Figs. 2, 3 and 4, and in terms of the constants A and B defined by the vapor pressure equation in Table I logp = A
103 - BT(xOK.) ~
Figure 3 shows plots of pNaF as a function of the reciprocal temperature for the NaF-rich region of (1) Work performed under AEC Contract W-7405-eng-92. (2) K. A. Sense, M. J. Snyder and J. W. Clcgg, THISJOURNAL, 68, 223 (1954). (3) K . A. Sense, M. J. Snyder and R. B. Filbert. Jr., ibid., 68, 095 (1954).
Furme.
lhllld
Fig. 1.-Cross-section
of vapor pressure appa,ratus.
Such a condition is not admissible for a thermodynamically stable ~ y s t e m . ~ Furthermore, begin’ ZrFd, both pNaF and ning with about 25 mole % pZrF4 increase as the salt composition becomes richer in ZrF4. This behavior is contrary to the Duhem-Margules equation 21
d In p1 = x* dIn p2 d XI d $a
where x is the mole fraction of either component 1 or 2, and p is the partial pressure of the corresponding component. According to this equation, for a two-component system, the partial pressure of one component must decrease as the other one increases, when the (4) J. H. Hildebrand and R. L. Scott, “Solubility of Non-Electrolytea,” 3rd Ed., Reinbold Publ. Corp., New York, N. Y.. 1950, p. 41.
338
I(. A. SENSE,C. A. ALEXANDER, R. E. BOWMAN AND R. B. FILBERT, JR.
I I050
1
I
1000
900
Recipocal Temperature, I 800
Vol. 61
I
I
roo
600
Temperature,%.
F i g . 2:.-Partial
VAPOR
pressure of ZrF4 based on assumption that only NaF and ZrF4 exist in vapor phase. note mole per cent. ZrF,.
Figures on plot de-
TABLE I PRESSURE CONSTANTS FOR THE N A F - Z ~ ? SYSTEM ~ BASED ON T H I ASSUMPTION THAT ONLY NAF AND ZRF4 EXIST IN THE VAPOR PHASE B X 108 logp A - -
T(OK.)
Cotnpoaition, mole % ZrFi
100 74.50" 67.79" 59.33" 53.16 53.16 50.00 46.50 41.88 38.00 33.50 32.72 28.27 19.54 11.89 Pure NaF Pure NaF a The constants
A
pZrFi
B
Temp. range, OC.
616-881 13.3995 12.3760 (solid) (liquid) 9.869 8.528 817-878 8.745 760-870 (liquid) 9.887 9.227 664-862 10.040 (liquid) (liquid) 9.939 9.448 621-887 12.95 599-621 (solid) 13.86 9.0432 682-884 9.3510 (liquid) 771-969 9,263 9.267 (liquid) 9.338 729-985 8.862 (liquid) 9.511 811-1039 8.441 (liquid) 948-1037 9.498 11.950 (liquid) 12.303 822-1049 9.643 (liquid) 9.675 13.33 984-1051 (liquid) 13.3 994-1059 (liquid) 8.8 976-1053 8.7 14.0 (liquid) (liquid ) ... ... ... (solid) ... ... ... for the solidus region are the same as those for ZrF4.
A
pNaF
E
Temp. range, "C
... ... ...
... ... ... ... 9.10 9.10 9.42 9.33 8.990 9.087 9.190 9.4188 11.3315
...
..
... ...
..
...
... ...
11.45 11.67 12.5 12.6 12.569 12.396 12.276 12.4283 14.8557
825-985 811-1039 948-1037 873-1049 978-1067 994-1059 976-1058 996-1075 034-996
...
March, 1957
SODIUM FLUORIDE-ZIRCONIUM FLUORIDE SYSTEM
composition is changed. To resolve the problem presented in Fig. 5 whcre the partial pressures of both NaF and ZrF4 increase as the composition is shifted toward pure ZrF4, the assumption was made that a complex molecule composed of NaF and ZrFd exists in the vapor phase. In accordance with the Duhem-Margules equation, the exact molecular composition of this complex is given by the peak of the partial pressure curve of NaF. From Fig. 5, it is noted that the peak of the partial pressure curve has obviously not yet been reached over the 0-42 mole % ZrF4 composition range, Hence, the peak of the apparent activity curve of NaF must occur in the 42-100 mole % ZrF4 composition region which mcans that in the complex, the molc ratio of NaF to ZrF4 must be smaller than 1.38. Unfortunately, the li~nitations of the chemical analysis for NaF in the condensates in that region were such that pNaF was known only as having less than a certain maximum value. This maximum was too high to be of any use in locating the maximum in the partial pressure curve. A plot of the activity of ZrF46of the NaF-ZrFc s stem at 918" (Fig. 0) suggests the possibility t at the complex has a NaF to ZrF4 ratio of 1:1, Le., that the simpIe complex NaZrF6 exists in the vapor phase. Such a complex would satisfy the requirement that it occur in the 42-100 mole yo ZrFc region. On the basis that NaZrFb exists in the vapor phase, a plot of the activity of ZrFr at 918" was constructed for the NaZrF5 system (Fig. 7).6 The fact that the deviations from Raoult's law in Fig. 7 are not nearly as great as those in Pig. 6 makes the assumption that the complex is NaZrF6 seem reasonable. The fact that the activity of ZrF4 does not go to zero at zero mole fraction ZrF4 implies partial dissociation of NaZrF6. Derived Partial Pressures of NaF, ZrF4 and NaZrF6.-As a first approximation, the vapor phase of the NaF-ZrFr system was treated as consisting only of NaF, ZrF4 and NaZrF6. Furthermore, NaZrF6 was considered to dissociate partially into NaF and ZrF4, the extent of dissociation being a function of the temperature. The partial pressures of the various vapor phase components were calculated by the following procedure. (Refer t o Fig. 5.) For compositions containing more than about 30 mole % ZrF4, the vapor phasc was assumed to consist almost entirely of pZrFa and pNaZrF5 with pNaF being considered negligible. Hence, the apparent' pNaF in this re-
339
g
( 5 ) Dcfincd as nZrFa/@ZrFa. The standard state, pOZrF4, is the vaiior prcssure of liquid ZrF4. Since ZrF4 sublimes at a pressure of 1 atni., thr vapor pressure at the melting point (918') had to be calciilatcd from thc P - T oquation for ZrF4, narncly, pZrF4 = 13.3995 12376.O/T("Ii.). From this equation, poZrB4 = 1020 mm. mercury at
-
0180. (6) The mole fraction. N'o, of ZrBa in the NaZrFs-ZrB4 syatetn is given by N'o = ( N o - , % ' ) / N o . wheio No and N are t l ~ cinolo fractions
of ZrFi and NaF, rcalicctivrly, iri tho NaI"-ZrF4 systent. (7) Throughout thc following disclission the "apparcnt" partial pressures arc thoac which werc calculatrd for a vapor phasc assuincd to consist simply of NaF and ZrF1. Sinco tho vapor pliasc is itiore accurately described as consisting of NaZrFs, NaF and ZrF4. the psrtis1 pressures of NaF and ZrF4 whcre NaZrFb is taken into account will be referred to as tho "triie" pertiat pressures.
hciprocol Temperolurr, I
I
I
1075
IOSO
loo0
gI
ma
Ternper0ture:C.
Fig. 3.7Partial pressures of NaF for the 0 to 28.3 mob o/n ZrFd re ion. Values based on assumption that only NaF and Zr#r exist in vapor phase. Figures denote mole % ZrF4.
gion became pNaZrF6.s The ZrF4tied up as NaZrF6 was then subtracted from that given by the ZrF4 curve to yield the true pZrF4. I n the composition region of 0 to about 20 mole % ZrS, the vapor phase was assumed to consist almost entirely of NaF and NaZrFo, with ZrF4 making only a negligible contribution to the total vapor pressure. Hence, the apparent pZrFl in this region became the pNaZrFo. The NaF tied up as NaZrF6 was then subtracted from that given by the NaF curve to give the true pNaF. The pNaZrF6 for the 28.3 mole % ZrF4 composition could not be determined in this manner since all the components exert comparable vapor pressures. However, from a plot of pNaZrF6 values already calculated for the other compositions, an interpolated value for the 28.3 mole per cent. composition could be obtained. This pNa%rF6was then subtracted, respectively, from the apparent pNaF and pZrF4 to give the true pNaF and pZrF4. Figure 8 shows the resulting curves of pNaF, pZrF4 and pNaZrF5 at 1026'. The vertical lines through the pNaZrF6 curve qualitatively reflect the degree of uncertainty of the partial pressures of NaF and ZrFc (see Figs. 2 and (8) This is so since for thc transpiration method
parM prcssure of component = (moles of coinponent) (total pressure of system) moles carrier gas 2(moles of components)
+
Froin the standpoint of ZrF4. the nuniber of niolee is the mme whether ZrFi is present 8 8 such or whcthcr it is part of the NaZrFl complex.
340
I>xmi
and therefore (4 For the extreme case discussed previously,'o the sum of the partial pressures of the components was less than 1 mm. for the 25 mole % region (Fig. 13). Therefore, inequality (c) is satisfied and equation (d) is applicable. Hence, two moles of NaF and one mole of NaZrFI, in the vapor phase exert a vapor pressure of three arbitrary units. If the two moles of NaF combined with one. mole of NaZrFo to form one mole of Na3ZrF7in the vapor phase, a vapor pressure of one arbitrary unit would result. The summation value in the denominator of (b) would change but the total value of the denominator would remain essentially the same because of (c). pi
where pi = partial pressure of the ith component P = total prcmrrre of system
moles of ith component in condenser (corrected for quant
