Mar., 1956
HEATO F FORMATION OF T I T A N I U M
Skinner and Ruehrweid determined the heat of formation of TiC13(s) by a direct method, reporting the value of - 170.0 f 0.8 kcal./mole. In view of the agreement between the present results and those of Pfeffer and co-workers by two independent methods, the difference between the heat of formation of Tic14 and TiCla appears t o be fixed within f0.3 kcal./mole. Therefore, unless
DICHLORIDE
31 I
there were an error in the heat of formation of TiCh, which is rather improbable, the heat of formation of TiC13 a t 298.16 is -172.2 f 0.7 kcal./ mole. Acknowledgment.-D. G.C. would like to express his appreciation to the Eastman Kodak Company for a fellowship which he held during part of this investigation.
THERMODYNAMICS OF THE TITANIUM CHLORIDES. 11. HEAT OF FORMATION OF TITANIUM DICHLORIDE1 BYDAVID G. CLIFTON~ AND GEORGE E. MACWOOD Contribution from the McPherson Chemical Laboratory, The Ohio State University, Columbus 10, Ohio Received August 16, 1966
The heat of formation of titanium dichloride has been determined by two independent methods. In the first method the heats of solution of TiC14(1)and TiClz(s) in a.solvent of HCl-FeCla were measured. In the second method the heats of solution of TiCla(s) and TiC12(s)in an HCI solution were used. The two values obtained are -123.3 f 0.7 and - 123.7 i 1.0 kcal./mole, based on - 192.1 f 0.6 kcal./mole for the heat of formation of TiClr(l).
I. Introduction Brewer3 and Kubaschewski4 report estimated values for the heat of formation of titanium dichloride. Skinner and Ruehrweins recently have reported a value for the heat of formation of the dichloride, calculated from disproportionation data. This research gives the differences between the heats of formation of Tic14 and TiClz and between TiC13 and Tic&. This information and that reported for TiC136can then be used t o give consistency t o the heats of formation of the titanium chlorides. 11. Apparatus and Materials The apparatus and some of the materials used for the measurements are described in the previous paper on Ticla.& The titanium dichloride was prepared by disproportionation of sublimed titanium trichloride.' The trichloride was placed in a nickel boat which was put in a Vycor tube in a furnace. The heating chamber was evacuated using a mercury diffusion pump backed by a mechanical pump. The trichloride was held at 485" for 8 hours and then at 470" for 10.5 hours. The titanium tetrachloride formed during the reaction was condensed out in a liquid air trap. Chloride analysis of the product gave an empirical formula of TiClz.oor. Total titanium analysis of the sample gave an empirical formula of TiC11.g9g. The sample dissolved completely in distilled water with slow evolution of hydrogen. This indicates that there was no appreciable metallic titanium impurity. Since the chloride analysis afforded the greater precision, the empirical formula used in all calculations was TiClz.oor. (1) Work performed under the Office of Naval Research, Contract No. Nonr-495(06). (2) Taken in part from the dissertation submitted by David G. Clifton in partial fulfillment of the requirements for the Ph.D. degree a t The Ohio State University, March, 1955. (3) L. Brewer, Paper 6, "National Nuclear Energy SerieR." Vol. IV-19B, edited by L. L. Quill, McGraw-Hill Book Co., New York, N. Y., 1950. (4) 0. Kubaschewski, "Metallurgical Thermochemistry," Academic Press Inc., New York, N. Y., 1951. 59, 113 (5) 0 . B. Skinner and R. A. Ruehrwein, THISJOURNAL, (1955). ( 6 ) D. G. Clifton and G. E. MacWood, T H I SJOURNAL, 60, 309 (1956). (7) W. C. Schumb and R . F. Sundstrom, J . Am. Chcm. Soc.. 55, 596 (1933).
The contaminant was assumed to be TiCls, and the necessary corrections on the measured heats were made. The same HCl-FeCls solvent as previously reported6 was used. The same weight-ratio of solvent to Ti-ion was maintained as in the previous experiments (123.19 g. of solvent per g. Ti). The water-to-HC1 ratio in this solvent was 9.69. The HC1 solution used in the heat of dilution measurements of the solvent analyzed as HCL9.60HzO. The waterto-HCI ratio in the solution is not exactly the same as that in the solvent. However, this slight difference between the two ratios does not result in an appreciable difference in the heats calculated. This same HCI solution was used to determine the heats of solution of TiCl3 and Tic12 in hydrochloric acid. The density of this solution was measured to be 1.0843 g./ml. at 27". The weight-ratio of solution to Ti-ion used for the trichloride and dichloride heats of solution in hydrochloric acid was 104.32 g. of solution per g. Ti.
111. Theory The heat of formation of titanium dichloride can be obtained by using the following set of reactions
+
TiCZ(1) solvent = end soln. 1 TiClz(s) solvent = end soln. 2 Ti(s) 2Clz(g) = TiCb(1) FeClz(end soln. 2) l/zClz(g) = FeC13(endsoln. 1 )
+
+ +
(1) (2) (3) (4)
Adding together the heat for (1) and (3) and subtracting those for (2) and (4), the heat of reaction ( 5 ) is obtained Ti@)
+ CL(g) = TiClz(s)
(5)
ie., the heat of formation of TiC12. Practically, complications arise in the above scheme. Reaction (2) involves the evolution of hydrogen. I n order t o use the above series of reactions, a correction must be made for the hydrogen evolution so that the end-solution after correction corresponds to the end solution 2. This required knowing quantitatively the amount of hydrogen evolved. If no hydrogen were evolved, one equivalent of ferrous ion would be formed for every equivalent of divalent Ti-ion introduced into the solvent. Hence, the difference between the number of equivalents of ferrous-ion in the end solution actually found by titration, and that calculated from the
DAVIDG. CLIFTON AND GEORGE E. MACWOOD
3 12
amount of divalent Ti added, gives a measure of the anmulit of hydrogen evolved. A small correction to the ferrous-ion coilcontration must be made to compensate for that which resulted from the trichloride contamination. The heat of the following reaction is necessary for the hydrogen correction FcC13(soln.)
TARLE 111 HEATOF SOIJJTION OF TiCls I N TIC1 SOJJJTION 1 2 3
+
(7) (8)
The heat of reaction (7) is the negative of the heat of reaction (4). The heat of reaction (8) is equal t o the partial molal enthalpy of HC1 at the applicable concentration. Rather than assume that the partial molal enthalpy of HC1 in an aqueous solution is the same as in an HCl-solution containing FeCls, it was established experimentally. The following series of reactions was used to determine the heat of reaction (8) ‘/pH&)
+ ‘/zClz(gl + 9.69HzO = RCl(9.69 HaO) HCI(9.6YHZO) + solvent = end soln. 3 solvent + 0.69H20 = end soln. 3-HCI
(9) (10) (11)
Reaction (8) is obtained by adding (9) and (10) and subtracting (11). A second method of establishing the heat of formation of titanium dichloride involves measuring the heats of the following reactions:
+
HEATOF SOLUTION OF TiC12 IN HCI SOLUTION Run
1 2 3
TiC1z.m
TiCla, wt.,
g.
g.
+ 1/2C12(g)= TiC13(s)
-AH,
kcal./’ mole
46.4 47.0 45.7
I n Table I, the weight of Tic12 is that in the particular sample of TiCIP.oorused for the measurement. This is calculated from the analysis. The third column lists the heat assigned t o the dichloride sample after the corrections have been made t o the measured heat. Table I1 lists the measured heats, the corrections for the TiCI3 contamination, and the corrections for hydrogen evolution, which were used t o get the quantity “Heat evolved” in Table I. The various other heats of reaction required for reduction of the present data are given in Table V. TABLEV Heat,kcal.
Source
-40.4 -192.1 -21.4 -37.8
f 0.2 f 0.6 f 0.1 f 0.01 0.0 -1 .o st 0.04 -36.7 f 0.04 -39.2 f 0.12
Adding reactions (13) and (14) and subtracting reaction (12) gives TiClz(s)
Measured heat. TiCla cor., cal. cal.
-0.5 0.2534 0.2512 98.8 .1736 .1722 68.5 - .4 .2189 84.0 - .5 ,2170 Av. AHls = -46.4 f 0.65 kcal./mole
+
+
kcal./nrole
34.2 0.4764 105.5 .3466 78.3 34.9 .5415 121.9 34.7 Av. AHl2 = -34.6 i 0.4 kcd./mole
TiCl,(s) HCl(sH20) = end soln. 4 (12) TiClz(s) HCl(sHzO) = end soln. 5 l/*H2(g) (13) 1/zH2(g) l / ~ C l ~ ( g=) HCKsoln.) (14)
+
--Ha,
Measured Ireat, cal.
g.
TABLE IV
which can be obtained from the heats of the following reactions
+
TiCla wt.,
Run no.
+ l/2€1z(g) = HCl(soln.) + FcCl2(soln.) (6)
FeC13(soln.) = l / ~ C l ~ ( g ) FeCla(soln.) l/A(g) l/zClz(g) = HCKsoln.)
Vol. 60
(15)
6 10
8 9 Measured Measured 9 6
Hence, knowing the heat of formation of Tic18 permits the calculation of the heat of formation of I n order to evaluate the hydrogen-correction, titanium dichloride. the heat of reaction (6) was determined using the IV. Results scheme outlined in Section 111. The heat of solution measurements are listed in AH6 = AH, + AH9 + AH10 - AH11 Tables I, 11,111and IV. =
TABLE I HEATOF SOLUTION OF Ticla I N SOLVENT TiClz wt.,
Run no.
1 2
3 4 5
Heat evolved, cal.
!4.
0,2463 .1816 .2166 .2157 .2207 Av. AHz = -66.7
&
138.1 102.6 120.7 120.8 124.7 0.4 kcal./mole
- AHa,
kcal./mole
66.6 67.1 66.2 66.5 67.1
TABLE I1 CORRECTIONS FOR THE HEATOF SOLUTION OF TiCh TiCh.oor wt., Run
g.
Measured heat, cal.
1
0.2484 .1831 .2185 .2177 ,2227
124.2 194.4 110.1 113.2 111.8
2
3 4 5
TiCl cor., cal.
-0.5
-
.4 .5 .5 .5
Hydrogen cor., cal.
14.4 8.6 11.1 8.1
13.4
-15.4 f 0.11 kcal./mole
The correction t o the TiClz heats of solution for the TiCl3-impurity was made using the heat of the reaction TiCl,(s)
+ solvent = end solvent 1
(16)
given in Table V.
V. Discussion The difference between the heats of formation of TiCh(s) and TiClz(s) at 0” is obtained by using the heats of reactions (l), (2), (3) and (4)
-
+
-
AHfTiC,,(,) AHfTiClr(.) = AH2 2AH4 AH1 = -69.1 f 0.5 kcal./mole ( 8 ) W. Bilta and C. Fendius. 2. anorg. Chcm., 176, 49 (1928). (9) F. D. Rossini. J . Research Natl. Bur. Standards, 9, 679 (1932); S. 313 (1930). (10) W. H. Johnson, R. A. Nelson and E. J. Prosen, unpublished
resulta, Reported to the Office of Naval Research in National Bureau of Standards Report No. 3663 revised (1055).
HEATOF FORMATION OF TITANIUM DICHLORIDE
Mar., 1956
The difference between the heat of formation of TiC13(1) and TiC12(s)at 0" is obtained by using the heats of reactions (12), (13) and (14). AHfTiClr(s)
- AHfTiCl,(s)= AHia =
+ AHir - AHiz
-48.5 f 0.85 kcal./mole
T o obtain the above differences in the heats of formation at 298 OK., the following heat capacities were used
CmicI,(I)= 37.0 cal./deg. mole 0.06 X 7' - 0.68 X 106 T-l cal./dep;. mole CPriCl,(si= 23.0 4.0 X 10-3 T - 1.7 X 106 T-l cal./deg. mole CPriC,r(B) = 17.0 2.7 X 10-8 T - 0.7 X lo5 T-l cal./deg. mole
Cpc18(g) = 8.82
+ + +
The heat capacity of liquid titanium tetrachloride is the average of the values reported by Gmelin" and by the National Bureau of Standards.12 The heat capacity of gaseous chlorine is that given by Kelley.I3 There are no reported heat capacities for titanium tri- and dichloride. The estimates used above are the rounded-off values of those reported for vanadium trichloride and vanadium dichloride, as given by Kelley.I3 The differences corrected to 298°K. are AHfTiCl,(l, - AHfTiClt(a) = -68.8 f 0.5 kcal./mole AHfTiCI - AHfTic = -48.5 f 0.85 kcal./mole
Combining the first difference with the heat of formation of TiCh(l), -192.1 f 0.6 kcal./mole, and the second difference with the heat of formation of TiClds), - 172.2 f 0.7 kcal./mole, one gets AHfTiCI,(m) = -123.3 i 0.8 kcal./moie = -123.7 f 1.0 kcal./mole AHfTiC,,(s)
Even though t.he present determinations of the heat of formation of titanium dichloride and that previously reported for titanium trichlorides both (11) Gmelin, "Kandbuch der Anorganisohen Chemie. Titan," Weinheim. 1951. (12) NBS, "Selected Values of Chemical Thermodynamic Properties," Circular No. 500. National Bureau of Standards, 1952. (13) K. K. Kelley, United States Bureau of Mines. Bulletin 476.
313
involve the heat of formation of TiCL(1) one can obtain the heat of the disproportionation reaction 2TiC13(s)= TiClz(s)
+ TiCL(1)
(17)
from the heat of solution measurements, independently of the heat of formation of TiCL(I), giving AH%*' = 29.0 f 0.8 kcal./mole
This agrees well with the heat of this reaction determined from disproportionation-pressure studies made by Sanderson and MacWood (29.2),"Skinner and Ruehrwein (29),5 and Farber and Darnell (28.3).15 In making the comparison 9.7 ked./ mole was used for the heat of vaporization of TiCh(1). I n view of the agreement, between the various investigators, with respect to the heat of disproportionation, it must be concluded that the reported values of the heats of formation of Skinner and Ruehrwein are in error due to a discrepancy of approximately 2 kcal./mole in the heat of formation of Ticla. If the heat of formation of TiC13is taken as -172.2 kcal./mole,s then, using their heat of disproportionation, the heat of formation of TiCls becomes -123.3 in excellent agreement with the value reported here. I n conclusion the following features are emphasized: (1) the difference between the heats of formation of titanium tetrachloride and titanium trichloride measured by three independent methods is about 20.0 kcal./mole a t 298°K.; (2) the heat of the disproportionation reaction has been found to be about 29.0 kcal./mole at 298°K. in four different investigations; and (3) the difference between the heats of formation of titanium trichloride and titanium dichloride measured in two independent ways was found to be about 48.9 kcal./mole. Taking -192.1 f 0.6 kcal./mole as the best value of the heat of formation for TiC14(1),10the recommended heats of formation for the lower titanium chlorides are AHfTiCll(s) = -172.2 f 0.7 kcal./mole AHRiCltcr, = -123.3 i 0.8 kcal./mole (14) B. 9. Sanderson and G. E. MacWood, THISJOURNAL,60, 316 (1956). (15) M. Farber and A. J. Darnell, ibad., 69, 156 (1955).
