BENJAMIN S. SANDERSON AND GEORGE E. MACWOOD
316
The following thermodynamic constants for Tic13 obtained from the present results, heat of formation’ and disproportionation datas are considered as the most reliable values at present available AH&&) = -130.2 i 1.4 kcal./mole AHrop98(s)= -172.2 & 0.8 kcal./mole SoZas(g) = 73.8 i 2 cal./deg. mole S0ta8(s)= 33.3 2 cal./deg. mole
*
VI. Discussion Recently Farber and Darnell12 have reported values for the sublimation pressure of Tic13 determined by the Knudsen ‘method. Their values are considerably lower than those reported here. On the basis of work done in this Laboratory on the disproportionation equilibrium of TiCla6,it appears (11) D. G. Clifton and G. E. MacWood, THISJOURNAL,60, 309 (1956). (12) M. Farber and A.
G. Damell, ibid.,
probable that these low values are due to a low accommodation coefficient for gaseous TiC13. The agreement between the values of the heat of sublimation obtained by the two methods may imply that the temperature coefficient of the accommodation coefficient is very small as has been observed for gaseous TiCL in study of the disproportionation of Tic13 by the Knudsen method.12 Skinner and Ruehrwein,I3 have reported measurements using the transpiration method. Their experimental values, although admittedly low, are of the same order of magnitude as those reported here. Their pressures, obtained by estimating the degree of saturation of the carrier gas, appear to be high. This results in a slightly higher entropy of sublimation at 29SoK., 43.3 compared with 41.6, since the heats of sublimation at 298°K. agree within the precision of measurements. (13)
69, 156 (1955).
Vol. 60
G.B. Skinner and R. A. Ruehrwein, ibid..
69, 113 (1955).
THERMODYNAMICS OF THE TITANIUM CHLORIDES. IV. THE DISPROPORTIONATION OF TITANIUM TRICHLORIDES1*2 BY BENJAMIN S. SANDERSON AND GEORGE E. MACWOOD Contribution from the McPherson Chemical Laboratory, The Ohio Stale University, Columbus, Ohio Raceivsd Awust 16, 1866
The disproportionation equilibrium of TiC13 was studied in the temperature range 593-821°K. by an effusion and static method. The two sets of measurements do not agree and indicate that the vaporization coefficient of TiCl,(g) is of the order of 10-4. On th.e basis of the static measurements and previous work, a consistent set of thermodynamic properties of TiClp and TiCl, are given.
I. Introduction This is the fourth paper on the thermodynamic properties of titanium chlorides being investigated in this L a b o r a t ~ r y ~and - ~ gives the results of the investigation of the disproportionation equilibrium of TiC13 2TiCla(s) = TiClz(s)
+ TiCL(g)
(1)
The course of the equilibrium as a function of temperature was studied by following the pressure of the titanium tetrachloride. The usual methods for measuring vapor pressures may be employed and, in this investigation, an effusion and static method were used. 11. Experimental 1. Materials.-The TiClr and TiCh were prepared as previously described.’-6 2. Apparatus. (a) Knudsen Method.-The apparatus is shown in Fig. 1. The body of the cell, shown in Fig. 2, was machined from stainless steel. The diaphragm, which contained the orifice, was made of 3-mil nickel sheet. It was held firmly in place by a screw-collar, a stainless steel washer being used to prevent tearing of the thin diaphragm. The weight loss of the cell was determined by following the (1) This paper presents the results of one phase of a program wonaored by the Department of Navy, Office of Naval Research, under Contract No. Nonr-495(06). (2) Taken in part from the dissertation submitted b y B. S. S. in partial fulfillment of the requirements for the Ph.D. degree a t The Ohio State University, Marcb, 1955. (3) I. D. G. Clifton and G. E. MacWood, THIB JOURNAL. 60, 309 (1956). (4) 11, D. C. Clifton and 0. E. MaoWood, ibid., 60. 311 (1956). (5) 111, B. S. Sanderaon and G . E. MacWood, ibid., 80, 314 (1956).
change in length of a quartz helical spring, by comparison with a standard meter bar and cathetometer. The cathetometer has a Filar-micrometer eyepiece which could be read to 0.008 mm. The spring, obtained from the Houston Technical Laboratories, had a sensitivity of 5.092 cm./g. It had a maximum load capacity of ten grams. The cell was suspended from the spring by a I-mil molybdenum mire. The portion of the apparatus housing the helix was protected on three sides to minimize random temperature fluctuations. The cell was heated in a vertical resistance furnace, controlled by means of a Thyratron regulator. The sensing element for the regulator was B and S No. 30 platinum wire wound around the central portion of a nichrome tube which fitted between the glass tube containing the cell and the inside wall of the furnace. The wire was wound non-inductively and had a resistance of 35 ohms at room temperature. The resulting temperature regulation was within r t O . 5 O . The cell temperature was determined by means of a chromel-alumel thermocouple, placed about 1 cm. below the cell. From this measurement and preliminary calibration of the furnace temperature gradient as a function of position and temperature, a corrected value of the cell temperature was obtained. The system was connected to a conventional high-vacuum system for maintaining low pressures during measurement. (b) Static Method.-The Pyrex apparatus used for the static pressure determinations is shown in Fig. 3. The stopcocks were lubricated with a special fluorinated hydrocarbon grease. The tube for measuring the liquid T i c & was calibrated against water with the aid of a weight-buret. The gage used t o measure pressures inside the system was a “Spoon-gage.’’ I n order to increase its sensitivity, while still maintaining mechanical strength, three “spoons” in series were used. A number of these gages were used during the course of the invc tigations. Their average sensitivity was about 0.03 mm. The outside jacket of the gage was connected through a two-way stopcock to vacuum pump or a supply of dry argon. The balancing argon pressure was measured with a tipping McLeod gage in the range
317
DISPROPORTIONATION OF TITANIUM TRICHLORIDE
Mar., 1956
ifr
Boll and socket joint
Standard meter bar +
-
Cothetometer
I m i l molybdenum wire Thermocouple leads
tos heat shields
Nichrome furnace liner
/-Orifice
rJ "
Stainless steel ----a washer 3 m i l nickel
1
Resistance furnace
kI"+ Scale Fig. 1.-Knudsen
apparatus.
Fig. 2.-Knudsen
cell.
0.001 to 5 mm. and with a Zimmerli gage for the range above 5 mm.
111. Procedure (a) Knudsen Method.-A Lucite dry box was used in loading the cell with Ticla. A dry nitrogen atmosphere was used in the box. While the filled cell was being put into the effusion system dry argon was passed through the system. When the system had been assembled, it was evacuated, then the furnace temperature raised to about 200°, and maintained at this temperature for 12 hours. After the furnace had been at the desired temperature for some time, the length of the helix was measured. A temperature correction, which varied with the load, was applied to each extension-measurement. The corrected extension was plotted against the time and the run continued until enough points had been determined to calculate an accurate slope. (b) .Static Method.-Before loading the cell for the static runs, it was outgassad at 590'. Then the cell was filled with dry argon, weighed and loaded with either titanium trichloride or dichloride. As shown in Fig. 3, a plug of Pyrex wool was inserted into the entrance to the cell to cut down the rate of diffusion of Ticla vapor out of the constant temperature zone. After connecting the cell to the apparatus, the system was evacuated and the cell temperature raised to 200'. The cell and its charge were outgassed a t this temperature for 12 hours. The TiClr wa8 distilled into the reservoir at low pressure. After introduction into the system, it alternately was melted and frozen, followed by removal of gas by pumping until completely outgassed. In the course of making a run, the temperature was allowed to rcach a constant value and pressure readings were taken until a constant value obtained. In a few cases, it was nccessnry to plot the prewure against .the time and extrapolate to large times to obtain the equilibrium pressure. When the pressure was approached either from above or below, the time to reach equilibrium varied, but the final pressures were the same within the precision of measurements. The procedure for determining the pressurecomposition isotherms was similar to that given above, except that the temperature was kept constant and the composition was vafied by exchanging TiCl, between the system and reservoir. The amount of TiCl, which had been added to, or taken away from, the reservoir was followed with a catheto-
Copper
Dry Argon 4
vacuum t Manomet er
Fig. 3.-Static
II
-
YJI
Dewar
-~..
I vI
apparatus.
meter which measured the height of the meniscus to 0.1 mm., corresponding to 1.18 X mole of Tic],.
IV. Results Knudsen Method.-The results of the measurement of the disproportionation pressure of Tic14 by this method are summarized in Table I. A plot of the logarithm of the TiClr pressure in 1.
BENJAMIN S. SANDERSON AND GEORGE E. MACWOOD
318
mm. against the reciprocal of the absolute temperature is given in Fig. 4. These data were fitted by least squares to the equation log p ( m m . ) =
-
7+
8.407
TABLEI SUMMARY O F Tic14 PRESSURES BY KNUDSEN METHOD Run no.
T,O K .
P (mm.)
-lop p (mm.)
28 5 33 23 29 25 34 30 43 7 26 8 44 35 31 6 32 45 24 27 46 21
593 596 600 613 617 627 628 639 643 651 658 661 664 665 665 673 683 687 690 706 714 720
0.000522 .000892 .00104 .00162 .00146 .00195 .00226 .00438 .a97 .00559 .00698 .00718 .0123 .0111 .0120 .0163 ,0220 .0257 .0229 .0304 .0548 .0815
3.282 3.050 2.984 2.791 2.837 2.710 2.646 2.359 2.304 2.253 2.156 2.144 1.910 1.955 1.921 1.788 1.658 1.590 1.640 1.517 1.261 1 ,089
with a standard deviation of the slope of A244 and of the intercept of A0.374. This equation gives an average heat of reaction of 32 1 kcal./ mole for the temperature range 593 to 730°K.
Vol. 60
The values listed in the table were calculated from the observed total weight-loss by correcting for the amount of T i c 4 effused using the reported TiC13pressures of Darnell and Farber.6 All of the pressures were corrected for the orifice thickness. The orifice used in runs 5 through 8 had a diameter of 0.1001 cm. The orifice used in runs 21 through 27 had a diameter of 0.0815 cm. Runs 28 through 46 were made with an orifice diameter of 0.1073 cm. No values of the pressure are reported for which the Cl/Ti mole ratio is below 2.50. 2. Static Method.-The results of the static measurements of the equilibrium Tic14 pressure are summarized in Table 11, Figs. 5 and 6. TABLE I1 SUMMARY OF TiC14 PRESSURES BY STATIC METHOD T ,OK.
P (mm.)
Cl/Ti
679.0 682.2 691.3 709.3 714.9 730.2 749.2 750.0 755.4 768.9 779.4 797.5 798.5 803.1 807.5 821.0
0.206 0.250 0.395 0.80 0.935 1.56 3.20 3.07 4.23 5.65 8.5 12.9 12.95 16.8 16.9 24.9
2.990 3.000 2.974 2.974 3.000 3.000 2.974 3.000 3.000 2.974 3.000 2.974 2.975 3.000 2.974 2.974
Using the static data, and the following heat capacitiesas4J
+
0.24 X lO-'T - 2.36 X lWT-' C p ~ i ~ ~ 4 ( 25.45 B) C,T~CI,(~)23 4 X 10-32' - 1.7 X 106!P2 C p ~ i ~ ~= r ( 17 s ) f 2.76 X 10-32' - 0.7 X 10V'-2
+
thermodynamic calculations were made. The results of the calculations for the disproportionation equilibrium of TiCls are AC, AH0
AFo
-3.55 40000 = 40000 = =
- 5 x 1 0 - 3 ~+ 0.34 x I W T - ~ - 3.552' - 2.5 X 10-3T2 - 0.34 X 106T-2 + 3.552' 1n T + 2.5 X IO-'T2 - 0.17 x
-
106T-1 67.75 T AHO~ss= 38.6 & 0.4 kcal./mole, AFOzgs = 25.9 f 0.8 kcal./ mole ASOzss = 42.5 & 1.5 cal./mole deg.
L
I
I
I40
150
+
1
I60
-
Discussion Clifton and MacWood have determined the heat of formation of TiClz(s)4and TiCla(s)a relative to TiCb(1). Using these measured differences and the heat of vaporization of TiCb(l), they obtained for the heat of disproportionation a t 298"K., 38.7 f 0.8 kcal./mole. This agrees quite well with the 38.6 kcal./mole determined in this investigation. Skinner and Ruehrweins have made measurements on the Tic13 disproportionation equilibrium.
1
I70
K 1030~rS.
Fig. 4,-Disproporti011at1on prcssures of TiCI, by Knudsen
method.
(6) M. Farber and A. J. Darnell, THISJOURNAL, 69,156 (1955). (7) K. K. Kelley, United States Bureau of Mines, Bulletin 383 (1935). ( 8 ) G. B. Skinner and R. A. Ruehrwein, THISJOUBNAL, 59, 110 (1955).
DISPROPORTIONATION OF TITANIUM TRICHLORIDE
Mar. 1956
-I"'
1
30
1
29
1
28
I
27
I
26
I
I
25 "'TI
Fig. 6.-Isotherma
319
24
I
23
I
I
22
2.1
2 0
.
of Ticla disproportionation pressures.
indicate that in the TiClz-rich portion of the diagram there is solid solution of Tic13 in TiC4. 1 I I I Blitz and Juzal' in their investigation of the platI 20 I30 I40 I50 inum-sulfur system obtained similar isotherms, lo3 T which they attributed to the existence of solid Fig. 5.-Disproportionation pressures of Tic13 by static solution. method. Clifton12 in this Laboratory has determined the Using estimated free-energy functions they find, at heat of solution of a mechanical mixture of pure 298 OK. TiCL and TiCI2,as well as the heat of solution of a partially disproportionated solid phase of the same AHOzss = 38.7 kcal./mole, AFozo8= 26.0 kcal./mole average composition. He found a significant differASOzss = 42.6 ence which can be interpreted as a heat of solid in good agreement with the values reported here. solution of 2.5 kcal./mole for an equimolal soluAn examination of the Tic4 pressures determined tion at 0". by the effusion and static methods shows a large The observations suggest the existence of a miscidiscrepancy. On the other hand, the measure- bility gap. I n the TiC13-rich region, the solubility ments by either method are consistent and repro- of TiClz in Tic4 is very small, ie., the solubility ducible. This observation is supported, not only curve is very close to the TiCla-axis. While in the by the measurements reported here, but also by TiClz-rich region, the solubility of TiCla in Tic12 those of Farber and DarnelP and Skinner and is appreciable. I n the previous calculations, it has Ruehrwein.8 been assumed that the mole fraction of TiC12 in It is suggested that the explanation of the above the region of measurement, in the TiCLrich range, discrepancy is a low accommodation (vaporiza- is so small that, the vapor pressure lowering due to tion) coefficient for TiCh as recently suggested by it was insignificant and, furthermore, that the temIf this is true, the accommo- perature coefficient of the solubility of TiClz is Brewer and K a r ~ e . ~ dation coefficient can be calculated from Tic4 pres- small.13 sures determined by the two methods at the same In conclusion a consistent set of thermodynamic temperature and the known orifice to surface ratio, constants is given in Table 111. using the relation given by Speiser and Johnstonlo for the observed pressure in the Knudsen method TABLE I11 A CONSISTENT SET OF THERMODYNAMIC PROPERTIES OF pabs = p t r u e OK:',
(Y
~
a
+ h/s
where CY is the accommodation coefficient, h / s the is taken as the orifice to surface area ratio and ptrue pressure determined by the static method. On this basis, an accommodation coefficient of 2.4 X is found for the temperature range 680 to 720°K. It is evident from Fig. 6 that the isotherms observed do not correspond to those expected for a two-component, three-phase system, rather they (9) Leo Brewer and J. S. Kane, ibid., 59, 105 (1955). (10) R. Speiser and H. L. Johnston, Trans. A m . SOC.M e l d s , 12,283 (1956).
TITANIUM CHLORIDES
Substance
TiClM TiClr(l) TiCldg) TiCl,(s) TiCb(s)
AHfOma, kcal./mole
-182.4 -192.1 -130.2 -172.2 -123.7
f0.7 f0.6 f0.7 =I0 = .4 f0.4
SOWS.e a .
84.4 f 1 . 0 60.3 f 1.5 73.8 f 3 . 0 32.2 f 1 . 0 22.6 f 1 . 0
(11) W. Blitz and R. Juza, 2. anorg. Chen.. 190, 1G1 (1930). (12) D. G. Clifton, unpublished work. (13) NOTEADDED I N PROOF.-It appears that this system may be explained on the basis of a defect lattice as proposed by J. 9. Anderson, Proc. Roy. SOC.(London),A l a s , 69 (1946).
