132
ROBERTD. EULER AND EDGAR F. WESTRUM,JR.
hydrogen content of the alloy is increased. Were hydrogen concentrating at the surface, the opposite effect would be expected at high dilution, i.e., that the heat vaporization would fall as the amount of hydrogen in the sample is increased. A similar conclusion can be arrived a t from our experimental data in the following way. Figure 2 shows that the total hydrogen being exchanged obeys Sievert's law over the range studied. Sievert's law itself holds for a gas dissolved in a metal under conditions of ideal behavior. If the process of dissolving gaseous hydrogen in the tantalum metal is described by the two steps of adsorption-desorption and surfacebulk equilibrium, it seems only reasonable to expect ideal behavior to be followed in both of these. For the step involving adsorption with dissociation, ideal behavior may be represented by a Langmuir isotherm K~ = e/(i - e)pi/2 (8) The surface-bulk equilibrium may be described by
Vol. 65
The data of Fig. 2 show that R
=
krPH,
(11)
Since the pressure was held constant as the temperature was varied, it is clear that Et a In R - = - d(ln kr) = (12) 6i d(l/T) b (l/T) P
1
1
where 6i represents the gas constant. If now, (11) is identified with (4),Le., if it is taken as the rate of the forward reaction, it can be seen that Er corresponds to the activation energy for the adsorption process. For desorption, therefore, it would be necessary to write R =
kbOe
=
kbKiZPm
(13)
corresponding to (5). From ( l l ) , (12) and (13) it is at once obvious that EO = Et = (EI,- 2X) = 14.9 kcal./mole (14) where h is the heat of adsorption and corresponds to the temperature coefficient of K1. Thus, if the K2 = S/O (9) activation energy for adsorption is 14.9 kcal./mole and Sievert's law for the over-all process as shown and if it is supposed that the heat of adsorption is 2 requires that of the same order of magnitude as the heat of soluK, = S/P'/a (10) tion (16 kcal./mole), i.e., that Kz is not a strong However, KIKz = KB, and inspection shows that the function of temperature, then it follows that the only way that this can come about is if 0 < < 1,indi- activation energy for the backward step is approxicating that the surface is sparsely covered. Thus, mately 31 kcal./mole, providing the estimate used since all of the available evidence points toward the in calculating the theoretical desorption rate. Acknowledgment.-This work was sponsored by sparsely covered surface, it is concluded that, in all probability, the rate-determining process involves the Gulf Research & Development Company as a the microscopically reversible act of adsorption with part of the research program of the Multiple Fellowship on Petroleum. dissociation and desorption with recombination.
HEAT CAPACITY AND THERMODYNAMIC PROPERTIES OF TITANIUIM TETRAFLUORIDE FROM 6 T O 304'K.l BYROBERTD. EULER AND EDGAR F. WESTRUM,JR. Department of Chemistry, University of Michigan, Ann Arbor, Michigan Received Julu 18, 1060
The low temperature heat capacity of titanium tetrafluoride has been determined by adiabatic calorimetry and found to be without thermal anomalies. The thermodynamic properties have been computed by numerical quadrature from these data. The values of the thermodynamic functions at 298.15"K. are: C, = 27.31 cal./(deg. mole), So = 32.02 cal./(deg. mole), HO - Ha@ = 4841 cal./mole, and (FO - HoO)/T = 15.78 cal./(deg. mole). Comparison of the heat capacity of TiFa with other tekafluorides supports the view that its crystal structure is intermediate between the molecular carbon tetrafluoride type and the coordinative zirconiuni tetrafluoride type.
-
Introduction From the endeavor to improve the resolution of the lattice arid magnetic contributions to the heat capacity of lJF42Jinterest developed in the heat capacity of the Group I V tetrafluorides. Because TiFl is the only member of this family that apparently is not xsostructural, it was considered desirable to study its low temperature heat capacity. ( 1 ) Submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in chemistry at the University of Miohigan. (2) H. R. Lohr, D. W. Osborne and E. F. Westrum, Jr., J . Am. Chem. Soe., 76,3837 (1954). (3) D. W. Osborne. E. F. "estrum, Jr.. and H. R. Lohr, ibad., 77, 2737 (195.5): J. II. Burns, D. W. Osborne and E. F. Weatrum, Jr., J . Chsm. Phye., 18, 387 (1960).
Experimental Preparation and Purity of the TiF,Sample.-The titanium tetrafluoride sample waa obtained from the General Chemical Division of Allied Chemical and Dye Corporation. It was prepared by reaction of elemental fluorine on pure titanium dioxide and purified further by sublimation in nickel reactors. Analysis for fluorine by the method of Saylor and Larkin' (utilizing titration of aqueous fluonde ion with AlC1, solution and Eriochromcyanine R as an internal indicator), together with determination of titanium by dissolution in concentrated sulfuric acid, followed by subsequent precipitation and ignition, indicated that the material assayed approximately 99.9% TiF,. Because the sample was very hvgroscopic and finely divided i t was handled and loaded entirely within a nitrogen-filled dry box. The sublimate (52.494 grams ( i n vacuo)) waa sealed into the calorimeter. Correc(4) J.
H. Saylor and M. E. Larkin, A n d . Chem., 20,194 (1948).
Jan., 1961
THERMODYNAMIC PROPERTIES OF TITANIUM TETRAFLUORIDE
tions for buoyancy were made on a densit of 2.798 for TiF4. Calorimetric Technique.-The Mark I Hquid helium cryostat and circuits employed in these measurements were quite similar to those described by Westrum, Hatcher and OSborne.’ Temperatures were measured with a platinum resistance thermometer (laboratory designation A-3) calibrated by the National Bureau of Standards above IO’K., and against a provisional scale at lower temperatures. Accuracy of the adiabatic calorimetric technique was tested with a Calorimetry Conference sample of benzoic acid.@ The copper calorimeter (laboratory designation W-5) was goldplated on the exterioi. surface and had an internal volume of approximately 90 cc. Eight radial vanes of thin copper foil aided rapid achievement of thermal equilibrium. Helium gas (3 cm. pressure) was added to the sample space t o facilitate thermal conduction. Lubriseal N stopcock grease was used to establish thermal contact between the calorimeter, thermometer and heater, as well as with the differential thermocouple for adiabatic shield control. The heat capacity of the empty calorimeter assembly with identical amounts of Lubriseal and solder was determined in a separate series of determinations and represented about 20% of the total heat capacity at lO’K., gradually increased, and averaged about 44% above 40°K.
133
TABLEI HEATCAPACITY OF TITANIUM TETRAFLUORIDE [TiFd, mol. weight = 123.90 g.; in cal./(deg. mole)] T,OK.
Cp
Series I 59.43 7.364 64.57 8.157 70.02 8.951 76.58 9.905 84.02 10.97 91.68 12.02 99.40 12.95 107.44 13.91 116.12 14.91 125.04 15.90 133.96 16.80 142.87 17.64 151.90 18.43 161.26 19.24 170.85 20.01 180.15 20.71 189.34 21.35 198.31 21.97 207.09 22.53 215.89 23.07 224.78 23.62
T,OK.
Cp
233.81 243.02 252.21 261.69 271.80 282.34 292.74 301.54
24.12 24.64 25.06 25.56 26.06 26.59 27.06 27.56
Series I1 6.32 0.075 7.06 .lo6 7.68 .120 8.35 .189 9.26 .266 10.21 ,348 11.35 .461 12.68 .583 13.94 .713 15.28 .866 16.76 1.037 18.42 1.239
T,OK.
20.52 22.80 25.01 27.60 30.53 33.59 36.93 40.63 44.75 49.43 54.70 60.38
Cp
1.500 1.805 2.106 2.467 2.897 3.361 3.877 4.442 5.075 5.810 6.629 7.505
Series I11 246.39 24.75
Results 255.26 25.23 264.83 25.74 Heat Capacity Data.-Experimental determina274.54 26.14 tions of the heat capacity are presented in chrono284.09 26.67 logical order in Table 1. The approximate tem292.34 27.05 perature increment of each measurement can 300.45 27.42 usually be inferred from the adjacent mean temperature values. Heat capacities are reported on a basis of a mole weight equal to 123.90g., the defined ments on TiF, an estimated ACp of vaporization, thermochemical calorie equal to 4.1840 absolute and a calculated entropy of gaseous TiF4using an joules, and an ice point of 273.15OK. Corrections estimated Ti-F distance. The resulting value, have been applied to the heat capacity values for 31.3 f 0.40 e.u., agrees as well as can be expected curvature (ie.? for the finite temperature incre- with the present determination although it is ments employed in the measurements). While the definitely outside the assigned precision indices of finely divided samplel essentially a white powder, both measurements. Free Energy of Formation.-Utilizing the endoes not represent the most desirable thermodyof formation of TiF4 reported by Gross, thalpy namic reference state, theheat capacity data are conHayman and Levis of -392.5 f 0.3 kcal./mole a t sidered to have a probable error of about 5% a t 298.15”K. and entropies of t8he elementsg yield a 6°K. decreasing l,o 1% at 1O0K. and decreasing further to 0.1% above 30°K. Thermodynamic free energy of formation for TiF4 of -360 3 kcal./ functions, So and HO HOo,were computed by mole at 298.15’ K. Discussion numerical quadrature of the heat capacity us. log T and T,respectively; but all values were obtained Since low temperature thermal data are available from a single large scale plot. These functions, the for three other tetrafluorides of the Group IV elederived free energy function, and values of the molal ments, it is interesting to compare the heat capacity heat capacity read from the smooth curve through of TiF4 with those of ZrF4,’0ThF2 and UF4.a The the experimental points are shown at selected tem- result of this comparison may be seen readily in peratures in Table 11. The thermodynamic func- Fig. 1 which shows the experimental values of the tions are considered to have a probable error of less heat capacity of TiF; and those of the three other than 0.1% at temperatures above 100’K. Extrap- substances. As might be expected, the heat caolation below 6O:K. was done by means of the pacities of isostructural ZrFr, ThF, and UFI increase Debye T alaw. 1st is assumed to be zero. No with increasing molecular weight. If TiF4 were contribution from isotope mixing or from nuclear to follow this pattern, it should have a heat caspin has been included in the entropy and free en- pacity lower than any of them. Instead, TiF, has a ergy functions. Hence, these values are practical higher value than does ZrF4 over the entire range. entropies suitable for use in chemical calculations. Indeed, from 10 to 30°K. TiF4has the highest heat In order to make Table I1 internally consistent and capacity of the four. t o permit interpolation, one more digit is given in A comparison of the known physical properties some of the thermodynamic functions than is of the various tetrafluorides illustrates the interjustified by the experimental accuracy. mediate behavior of TiF4. Tetrafluorides of lower A calculation of the entropy of TiFJ has been molecular weight than TiFl (such as CF4 and SiF4) reported’ on the basis of vapor pressure measure- have a cubic structure, tend to be plastic crystals
-
(5) E. F. Weatrum, Jr , J. B. Hatcher and D. W. Oaborne, J . Chsm. Plus., 81, 419 (1953). (6) G . T. Furukawa, 13. E. McCoskey and G. J. King, J . Research
N d .Bur. Stan&&,
47, 256 (1951).
(7) E. H. Hall, J. M. Blocher, Jr., and I. E. Campbell, J . 1Fbctro*a. Sw.,106, 276 (1968).
(8) P. Groaa, C . Haymann and D. L. Levi, Transaction6 XVIIth International Congress of Pure and Applied Chemistry. Munich, September, 1959, p. 90. (9) “Selected Values of Chemical Thermodynsmio Properties,” Circular 600, National Bureau of Standards, Waahington, D.C.,1952. (10) E. F. Westrum, Jr., and D. H.Terwilliger, unpublthed dab.
ROBERTD. EULERBND EDGAR F. WESTRUM, JR.
134
TABLE I1 FUNCTIONS O F TITANIUM TETRAFLUORIDE (TiF4, mol. weight = 123.90 g.)
T,OK.
10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 273.15 298.15
CP,car./
So, cal./
HO - Hao, cal./mole
0.329 0.834 .t. 440 2.104 2.819 3.580 4.345 5.116 !j ,898 7.453 8.968 10.41 111.78 13.03 14,21 16.35 16. 41 17.37 18.28 19.14 19.95 20.70 211.40 22.08 22.72 23.32 23.90 24.44 24.96 25.47 25.97 26.47 26.94 27.39 26.13 27.31
0.110 ,335 ,656 1.048 1,494 1.985 2.513 3,069 3.649 4.862 6.126 7.418 8.725 10.031 11.328 12.614 13.885 15.137 16.366 17.574 18.757 19.921 21.058 22.173 23.266 24.337 25.388 26.416 27.424 28.413 29.384 30.337 31.274 32.195 29.69 32.02
0.82 3.68 9.33 18.16 30.44 46.43 66.24 89.89 117.43 184.20 266.39 363.30 474.36 598.5 734.7 882.5 1041.3 1210.3 1388.6 1578.7 1771.1 1974.4 2184.9 2402.3 2626.3 2856.5 3092.7 3334.4 3581.5 3833.6 4090.9 4353.1 4620.1 4891.4 4173. 4841.
(deg. mole) (deg. mole)
-(FO
- Hoe)/
T,cal./
25
(deg. mole)
0.028 ,090 ,189 ,321 .479 .658 ,857 1.071 1,300 1.792 2.320 2.877 3.454 4.046 4.649 5.260 5.875 6.492 7.109 7.726 8.341 8.952 9.558 10.161 10.760 11.353 11.942 12.523 13.098 13.668 14.233 14.790 15.343 15.889 14.41 15.78
with low heah of fusion, and tend to melt at very low temperalures, whereas those of higher molecular weight, including the monoclinic group IV tetrafluorides, tend to melt a t very high temperatures. With respect to the other titanium tetrahalides, TiF4 occupies a relatively unique position. The density of the solid TiF4and the persistence of the solid state and of the liquid state as well are out of line with the trend for the rest of the series. Crystal structure determinations1’ show SiFa, TiBr4 and Ti14 to be cubic and tetrahedrally symmetrical with molecular type structures. ZrF4, ThF4 and UF4, as well as HfF4and CeF4, are iso(11) R. W. G. Wyckoff, “Crystal Structures,” Val. I, Interscience Publishers Iw., New York, N. Y. 1961.
TE M P E R ATURE , “K. 100 200 300
0
THERMODYNAMIC
Vol. 65
i
-
wi 20 0 2
2
15
3 6 0 IO
4 5
0
IO
20
TEMPERATURE,
Fig. 1.-Heat
30
40
O K ,
capacities of Group IV tetrafluorides.
structural12 and have a monoclinic holohedral lattice in which the metal atom has a coordination number of 12. Presumably then, TiFd mill exhibit some structure intermediate between the molecular type lattice of SiF, and the coordinative type characteristic of ZrF4. HuckelI3 suggests the existence of a chain type structure in which TiFe octahedra are joined to each other along an edge, giving the titanium a coordination number of six except a t a chain terminus. This value lies between four for Si in SiF4 and twelve for Zr in the monoclinic structure and would be consistent with the intermediate density value. Four of the six fluorine atoms in each octahedron would be held jointly by two titanium atoms and two by one titanium atom. This would lead to two different TiF crystalline distances and resulting distorted octahedra. This hypothesis would explain the relatively high density and the moderately high boiling point characteristic of TiF4. The fact that the heat capacity of TiF4 exhibits a temperature dependence somewhat less than Tabelow 30°K. would also be consistent with the hypothesis of a chain type structure.l4 Acknowledgment.-The authors thank M r s. Emilia Martin for her assistance with the calculations, and the Division of Research of the United States Atomic Energy Commission for partial financial support. (12) W. H.Zaohariasen, Acta Cryst., 2, 288 (1949). (13) W. Hnokel, ”Structural Chemistry of Inorganio Compounds ’ Vol. 11, Elsevier Publishing Co.,Amsterdam, 1951, p. 470. (14) V. V. Tarassov, Zhur. Fiz. Khim., 24, 111 (1950).
