THERMODYNAMICS O F VAPORIZATION
OF
LIQUIDTHALLOUS BROMIDE
I n conclusion, it may be stated that none of the above three mechanisms is free froin objections, and only further experiments niay help to achieve a final decisive answer.
3835
Acknowledgmenk. Tire express thanks to Dr. E. J. Hart for many useful discussions and for advice in 1 he work. We also thank Miss P. Walsh, i\Ir, E. Baobstrom, and Ah. B. E. Clifft, who helped with the work.
Thermodynamics of Vaporization of Liquid Thallous Bromide and Its Gaseous Dimerization'
by Daniel Cubicciotti Stanford Research Institute, Menlo Park, California 940%
(Received Julv 16, IQS4)
The vapor pressure of liquid thallous bromide was measured by a quasi-static method from the melting point to the boiling point. The results can be represented by the equation: log p = -7324/T 22.874 - 4.38 log T . The species in the vapor were found to be mainly monomer (TlBr) and some dimer (T12Br2). The partial pressures of these species were established by combining transpiration measurements with the vapor pressure measurements. Extrapolation of the data indicated that the dimer would constitute about 25y0 of the vapor a t the nornial boiling point and about O.O5oj, a t the melting point. The heats of evaporation a t 1000°K. were 24.3 kcal. to imnonier and 50 to dimer. The corresponding entropies were 22.0 and 42 e.u.
+
Introduction Vapor saturated with liquid thallous chloride has been found2 to corltsin Some dimer in addition to the predominant nionomeric species. Conlparison of the behaviors of the thallous halides and the alkali halides should provide some understanding of the binding in such molecules; thus, our study was extended to thallous bromide. A qualitative exarnination of the vapors produced from liquid thellous bromide was made using a Bendix time-of-flight mass spectrometer. In this experiment the sample was contained in a graphite cell having a narrow slit orifice. With the sample above its melting point the shutter-dependent peaks observed were T1+ (relative intensity unknown because of interference by Hg+ peaks), TlBr+ (very strong), TIz+ (weak), TlzBr+ (strong), and T12Br2+ (medium). No higher molecular weight species were observed. These results
were interpreted a,s indicating that diniers existed in the VaPOrS, but higher P o b e r s ere not important. Also, it appeared that the dimer to monomer ratio W:B smaller for the brioinide than for the chloride. This was borne out by the more quantitative masurements reported below.
Experimental The composition of the saturated vapor was determined from measurements of the vapor pressuire and transpiration pressure. These data, together with the indication from the mass spectrometer results that higher polymers were unimportant, permitted a calculation of the partial pressures of niononier and
(1) Thls work was made possible by the support of the Research Division of the U. S. Atomic Energy Commission under Contract N ~AT(04-3)-106. . (2) D. Cubicciotti, J . Phys. Chem., 68, 1528 (1964).
Volume 68, Number 12 December IScig
DANIELCUBICCIOTTI
3836
dimer in the equilibrium vapor as a function of temperature. The vapor pressure was measured by the quasistatic method of Rodebush, et al. The details of our apparatus for this measurement have been described elsewhere.z For the present work the cell was made of fused quartz and required about 200 g. of TlBr. The inert gas used was high-purity, dry nitrogen. The transpiration apparatus has also been described in ref. 3 . I n the present work high-purity, dry nitrogen was again used as a carrier gas. Thallous bromide was made by dissolving pure thallium (99.95yo from American Smelting and Refining Co.) in dilute HNOa and adding sufficient dilute HBr to precipitate TlBr. The precipitate was collected on a sintered glass filter and air-dried. A sample of this inaterial was prepared for analysis by fuming in concentrated HzS04, diluting, and reducing with SOz. The resulting solution was analyzed for thallium by the chromate m e t h ~ d . It ~ was found necessary to perform the chromate precipitations at 0' because samples precipitated at room temperature gave values that were low by a few tenths of 1%. The analysis indicated 71,89y0 of T1 in the TlBr compared with 71.89Oj, theoretical for TlBr. The freezing point of this material was found to be 460.0 f 0.5'. Temperatures in both sets of measurenients were determined with a platinum-10% rhodium thermocouple that had been checked against a similar NBS-Calibrated theniocouple.
Results Vapor pressures were obtained over the range from a few niilliineters to slightly inore than 1 atm. The results are shown in Fig. 1. The quasi-static results which represent the total vapor pressure of all thallous bromide species can be represented by log p (inin.) =
froin 500 to 850'. These results should be comparable with the boiling point data obtained by von Wartenberg and B o ~ s e . ~Their data have alinost the same slope as the present data, but their curve is displaced toward lower temperatures by a few degrees. A siiuilar difference, observed between our results and those of von Wartenberg and Bosse for TlC1, was presuiiied to be due to a correction they applied for superheating. The sanie presuniption holds for TlBr. The results of the transpiration iiieasurelnents were reduced to the pressure of TlBr using 284 for the T h e Journal of Physical Chemistry
3.0 I
-E
,g
3.0
2.5
2.5
2.0
2.0
I .5
1.5
I .o
I .o
0.5
n P cr,
2
0.5
0.9
I .o
1.2
1.1
I
x
1.3
3
IO
Figure 1. Vapor pressure of TlBr. Lower set of curves from quasi-static or boiling point method. Full line and points, present data; dashed line, data of von Wartenberg and Bosse. Upper set of curves from transpiration. Full line, present data; dashed line, data of Volmer.
molecular weight of the gaseous species. When calculated in this way, the transpiration pressures are greater than the vapor pressures by approximately the partial pressure of dimer. The results of the transpiration study are also shown in Fig. 1. Multiple points at a given temperature were obtained at different flow rates of carrier gas, usually over a five- or tenfold range. The results at different flow rates were within a 5% range, thus indicating that for our experimental arrangement the gas stream was salurated with thallium chloride. These data are compared in Fig. 1 with the transpiration results of Voliner.6 His data are higher than the present results and have a greater slope. The vapor pressures were combined with the transpiration results to calculate partial pressures of mono(3) F. J. Keneshea and D. Cubicciotti, J . Chem. Phys., 40, 191 (1964). (4) 0. L. Forchheimer and R. P. Epple. Anal. Chem., 23, 1445 (1951). (5) H. von Wartenberg and 0. Bosse, Z . Elektrochem., 28, 384 (1922); see also H. yon Wartenberg and P. Albrecht, ibid., 27, 162 (1921), for technique. (6) F. Volmer, Physik. Z., 30, 590 (1929).
THERMODYN AhIICS OF
VAPORIZATION
OF
LIQUIDTHALLOUS BROMIDE
partial pressure of monomer derived from the 2 plot is
2.7
log PM (min.)
26
7895
T 25 I-,
24
23
IO
111
1.2
1.4
1.3
I O~/T ) Figure 2. Part,ial pressures of monomer ( P M and dimer (PD)and 2 plot for monomer.
mer and dimer by thLe same method used for the analysis of the thallium chloride data since the mass spectrometer indicated only two important vapor speciesmonomer and dimer. The partial pressures of monomer and dimer calculated in this way are shown as the points i n Fig. 2. The monomer data showed a small curvature, which was presumed to be due to the effect of the difference in heat capacities of the i-nonomer and the liquid. Accordingly, a 2 plot treatment' of the data was applied. The heat capacity of gaseous TlBr was calculated from molecular constant data.8 I n the temperature range of interest it was found to be essentially constant and equal to 8.9 cal./mole/deg. The heat capacity of the liquid was remeasured flor t was found to have a value of 25.3 this ~ o r k .I ~ 9.04 X 10-3T OK. cal./mole/deg. The expression for 2 therefore becomes &I
=
-log P M (mrri.) - 8.27 log T
(OK.)
=
8.27 log T
+ 0.99 X IOW8T + 34.090 f
- ,L
09
3837
+ 0.99 X
10-377 (OK.)
The B plot for the monomer data is shown in Fig. 2. All the points except that at the highest temperature fall quite well on a straight line indicating that the curvature of the pressure data did arise from heat capacity effects. At the highest temperature the low value for P M probably arises from errors in the transpiration measurements. An equation for the
2%
The partial pressures of the dimer ( P D ) as calculated from the vapor pressure and transpiration nwasurements are given in Fig. 2. Those data also show some curvature; however, since the pressures, being relatively small differences of experimental quantities, are not known too well, it was felt they mere well enough represented by a straight line. The equation for that line is
The equation represents the dimer pressures to within 2075, except for the lowest pressure calculated. The vapor pressure over solid thallous bromide has been measured by Barrow, et aZ.I0 (from 220 to 340°), by Volmer6 (335 to 460°), and Xiwall (270 to 340'). Linear extrapolations of their data are represented in Fig. 3. The present data join quite well with those of Barrow, et al., and of Volmer. The partial pressure of dimer over solid thallous bromide mas calculated from the present values over the liquid. The heat of evaporation to dimer from the solid must be larger than that from the liquid by twice the heat OF fusion and, of course, the dimer pressure curves must join at the melting point. The partial pressure of dimer is less than 0.1 of 1% of that of the monomer over the solid. Therefore, pressure measurements over the solid can be assumed to be monomer pressures, within experimental accuracy.
Discussion The thermodynamic quantities for the evaporation processes were evaluated from the partial pressure (7) (a) K. K. Kelley, U. S. Bureau of Mines Bulletin 383 (193.5), reprinted in U.S.Bureau of Mines Bulletin 601, U.S. Govt. Printing Office, Washington, D. C., 1962; (b) G. N. Lewis and M.Randatll, "Thermodynamics," revised by K . S.Pitzer and L. Brewer, McGrawHill Book Co., Inc., New York, S . Y . , 1961, p. 175 ff. (8) Internuclear distance from M. Xandel and A. H. Barrett, Phys. Rev., 98, 1159 (1955); vibration frequencies from G. Hersberg, "Molecular Spectra and Molecular Structure," 5'01. I, 2nd E d . , D. Van Nostrand Co., Inc., S e w York, N. Y., 1950. (9) D. Cubicciotti and H. Eding, "Heat Contents of Thallous Halides," t,o be publkhed. (10) R. F. Barrow, E. A. N. S. Jeffries, and J. M.Swinstead, Trans. Faraday Soc., 51, 1650 (1955). (11) K . Kiwa, J . Fac. Sei., Hokkaido Imp. Cnizl., Ser. 111,3 , 17 (1940).
Volume 68, IYumber 19 December, l S S 4
DANIEL CUBICCIOTTI
3838
3 2
E E v
I
0.
0
0
-
0,
0
-I -2
-3
-4 1.0
1.2
1.6
1.4
Io3
1.8
2.0
/ ~
Figure 3. Pressures of species above and below melting point. PM = partial pressure of monomer; above melting point-present data; below melting point-dotted line from Volmer, full line from Barrow, et al., dashed line from Niwa. P D = partial pressure of dimer; above melting point-present data; below melting point-extrapolation of present data.
The standard thermodynamic quantities for vaporization of liquid thallous bromide are given in Table I. It is interesting to note that the thermodynamic quantities for evaporation to the monomer are essentially the same as those for the chloride as, in fact, they must be because the monomer partial pressure curves for these two substances are almost identical. The values for the dimer are much less precisely known because the dimer pressures were obtained as differences of large numbers. Both the entropy and heat of vaporization to the bromide dimer are substantially larger than the corresponding values for thallous chloride. At 1000’K. these quantities combine so that the resultant ratio of dimer to monomer pressures is smaller for the bromide than for the chloride; liowever, above about 1150’K. the situation is reversed and the bromide should have a larger dimer to monomer ratio. The behavior of the bromide compared to the chloride for thallium is different from that for potassium.12 With potassium, which may be considered as representative of the alkali halides, the thermodynamic quantities of vaporization of the bromide are almost the same as those for the chloride. The fact that the change from chloride to bromide has a significantly different effect in the thallium case from that in the potassium case indicates that the nature of the binding in the liquid, or the gas, or both is different in the two cases. -~
data. For the inonoiner the heat of evaporation derived from the I: plot is given by
AHT (kcal./mole of monomer) 10-ST
=
~
PD/
[36.13 - 16.4 X
4A.o
+ 4.52 X 10-6T2] fi 0.1
with T in OK. i2t 1000°K. AH of evaporation is 24.25 kcal./mole. For gaseous TlBr the quantity (Hlooo H2g8) was calculated from molecular constant data’ to be 6.25 kcal,/niole and (H,,,, - H298)for thallous bromide has been measured in our laboratory9 to be 14.49 kcal./mole. Therefore, the heat of sublimation to the monomer a t 298’K. is 32.50 f 0.1 kcal./inole. We have slightly revised the data of Barrow, et al., and their treatment of Volnier’s data in the light of our new measurements of the heat content of the solid and find their second-law values to be 32.40 f 0.05 and 32.33 f 0.4 kcal./mole, respectively. Thus, the heats of sublimation (as well as the pressure of monomer a t the melting point) are in good agreement. The absolute entropy of solid thallous bromide has not been measured calorimetrically, so a precise third-law treatment of the data is not possible. The Journal of Physical Chemistry
~~~~
Table I : Thermodynamic Data for Vaporization of Liquid TlBr Compared to Other Liquid Halides
T, OK.
TlBr
TIC1 KBr KC1
PM
AH’
4so
dimer,
in
4H0
dimer,
cal./
eatu-
monomer, kcal./mole
koal./
monomer, cal./mole/ deg.
mole/ deg.
vapor
22.0 i 0 . 2 22.0 24.9 25.1
42 i 4 25.7 23 4 22.0
0.067 0.15 0.24 0.0
1000 2 4 . 3 k 0 . 1 1000 24.4 1100 41.1 4 2.5 1100
mole 50 & 5 31.8 42.6 41.0
rated
The standard thermodynamic functions for dissociation of the dimer, T12Br2(g) = 2TlBr(g), at 1000°K. are AHo = - 2 f 5 kcal. and A S o = 2 + 4 e.u. These values are smaller than the corresponding ones for the chloride (17 kcal. and 18 e.u., respectively). The absolute entropy of the dimer is equal to that of two monomers minus its dissociation entropy. At 1O0OoK. the absolute entropy of the gaseous mono(12) “JANAF Thermochemical Tables,” The Dow Chemical Co., Midland, Mich., revised as of December, 1963.
THERMODYNAMICB OF VAPORIZATION OF LIQUID THALLOUS BROMIDE
mer is 74.67 e.u.; thus, the absolute entropy of the dimer is 147 e.u. The translational entropy of the dimer was calculated to be 51 e.u. On the assumption of a square-plana: molecule (in analogy with LC2Clzls)of side 2.65 A. (slightly larger than the mononwr internuclear distance) the entropy of rotation is 35 e.u. Thus, on a square-planar model the vibrational entropy should be 61 e.u. a t IOOOOK. An estimate of the vibrational entropy of the square-planar molecule can be made as follows. Berkowitz14 has calculated the vibration frequencies expected for the alkali halide dimers on an ionic model. For the heavier alkadi chlorides one can roughly summarize the frequencies he obtained: four frequencies with values about twothirds that of monomer, and two frequencies about one-third that of monomer. Using this approximation, one calculates the vibrational entropy of the squareplanar TlzBrs a t 1000°K. to be 35 e.u., about 26 e.u. snialler than the experimental value deduced above. A linear model for the dimer molecule would have a larger absolute entropy than the square-planar. For instance, the linear molecule BrTlTlBr would have 51 e.u. translational and 25 e!. rotational entropy (assuming TlBr distance = 2.6 A. and TlTl distance = 2.4 A.), and the vibrational entropy, arising largely from the four very low-frequency bending inodes of such a flexible linear molecule, would be quite large. I n order to fit the experimental entropy, the vibrational entropy would have to be about 70 e.u. This is possible if the bending vibrations have frequencies of the order of a few wave numbers. The dissociation energy of the gaseous molecule
3839
TlBr was calculaited from the heat of formation of the solid and the heat of subliniabion as shown in Table 11. This thermochemical value is about 0.2 e.v. larger than the spectroscopic value (3.2 e . v . 9 .
Table I1 : Thermochemical Calculation of TlBr Dissociation Energy bH, Reaction
+
kcal.
Tl(s) lhBrz(l) = TlBr(s) [298'K.] TlBr(s) = TlBr(g) (298"K.I Tl(s) = Tl(g) [298"K.] l/zBrz(l) = Br(g) [I!98"K.] TlBr(g) [ O O ] = TlBr(g) [298"K.] Tl(g) [O"] = Tl(g) [298'K.] Br(g) LO0] = Br(g) r298'K.I TlBr(g) = Tl(g) Br(g) [O'K.]
+
Ref
a -41.9 32.5 This work b 43.6 0 26.8 C 2.4 a 1.5 a 1.5 79.2 ( = 3.43 e.v.)
a See ref. 7b, Appendix 7. * R. Hultgren, R. L. Orr, P. ID. Anderson, and K. K . Kelley, "Thermodynamic Properties of Metals and Alloys," John Wiley and Sons, New York, N. Y . , 1963, p. 290. Calculated from molecular constant data.
Acknowledgment. The author is indebted to Mr. W. E. Robbins, who carried out much of the experimental work. (13) See S. H. Bauer and R. F. Porter in "Molten Salt Chemistry,"
M. Blander, Ed., Interscience Publishers, Inc., New York, N. Y., 1964, p 652. (14) J. Berkowitz, J . Chem. Phys., 32, 1519 (1960). (15) See T. L. Cottrell, "The Strengths of Chemical Bonds," 2nd Ed., Butterworths, London, 1958, p. 233.
Volume 68, Number 1 2
December, 1964
