3001
HEATOF FORMATION OF AlCl(g)
The Heat of Formation of Aluminum(1) Chloride(g) and the Entropy of Aluminum(II1) Chloride@)
by Margaret A. Frisch, Michael A. Greenbaum, and Milton Farber
A second-law value for the A H f ’ 2 9 8 of AlCl(g) of - 13.3 10.4 kcal./mole has been obtained from a molecular flow effusionstudy of the reaction 2AlO) AlCls(g) + 3AlCl(g) over the temperature range 930-1034’K. The first one-step determination of the Soa2of AlC13(g) has also been derived from this study. This value was found to be 104.6 f 2.1 cal./deg. mole.
+
Introduction Various values ranging from -11 to -20 kcal./ mole have been reported in the literature for the aHfo298of AlCl(g). Gross, et uZ.,I compared the equilibrium vapor pressure of mixtures of molten aluminum with solid KCl and both liquid and solid NaCl with the vapor pressures of the pure salts. From these measurements they derived an average thirdlaw value for the A H f ’ 2 9 8 of -11.58 kcal./mole. They also studied the equilibrium 2A10)
+ &cls(g)
=
3AlCl(g)
(1)
at a temperature of 1250’K. and reported a value for A H t 0 2 9 8 of AlCl(g) of -10.92 kcal./mole. Russell, et aZ.,2measured the equilibrium constant for reaction (eq. 1) at 1400°K. and obtained a third-law value for AHto298 of -12.18 kcal./mole. Semenkovich’s3 measurements on the reaction from 950 to 1200” gave a second-law heat of reaction at 298°K. of 77.98 kcal./mole which led to a AHfo2% for AlCl(g) of -19.20 kcal./mole. Gaydon4 selected for Do of AlCl(g) the value of 5.1 =t0.2 e.v. which resulted in a heat of formation of - 11.62 kcal./mole. The AHf0298 of Ac&(g) was measured by Several in~estigators~-~ based on studies of the dimerization reaction Of Mc13(g), and their second-1aw values Obtained for the heat of reaction agree with each other within 1 0 . 5 kcal./mole. The corresponding 8’268 MCl3(g) was deriveds using one experimental vibrafrequency Of Klemperep and three estimated frequencies so that the second- and third-law values
for the heat of reaction were in agreement. This resulting entropy for NC13(g) (74.6 cal./deg. mole) should be considered somewhat unreliable since its value is based on the estimated entropy of A12Cle(g).5 The 8’2% Al2Cl~(g)was calculated using eleven observed vibrational frequencies and seven estimated ones such that the experimental5Ag-l1heat of sublimation of &Cla(C) was in reasonable agreement with the third-law calculation. In view of the uncertainty in the reported thermodynamic values for AlCl(g) and AICla(g), the present study was undertaken to obtain a value for both AHfo2s of AlCl(g) and S O 2 9 8 of MCls(g) by a secondlaw measurement. (1) P. Gross, C. S. Campbell, P. J. C. Kent, and D. L. Levi, Di8cuseiona Fararaday SOC.,4, 206 (1948). (2) A. 9.R w U , E. E. Martin, and C. N. Cochran, J. Am. Chem. Soc., 7 3 , 1466 (1951). (3) S. A. Semenkovich, Zh. PrikE. Khim., 33, 1281 (1960); Chem. Abstr., 54, 1926% (1960). (4) A. G. Gaydon, “Dissociation Energies and Spectra of Diatomic Molecules,” Chapman and Hall Ltd., London, 1953. (5) “Janaf Thermochemical Tables,” USAF Contract No. AF 33(616)-6149, Advanced Research Projects Agency, Washington, D. C. AICl(&, June 30, 1961; AICls(g), March 31, 1965; AI@) Dec. 31, 1980; Al&ls(g), March 31, 1964. (6) A. Smits and J. L. Meijering, 2. physik. C h . ,~ 4 1 98 , (1938). (7) W. Fischer, 0. Rahlfs, and B. Benze, Z . anorg. allgem. Chem., 205, 1 (1932). (8) W. memperer, J . C h . Phys., 24, 353 (1956). (9) c. G. MGer, u. s. Bureau of Mines, Technicd Paper 360, U.8. Government Printing Office, Washington,D. C., 1929. (10) W. D. Treadwell and L. Terebesi, HeZu. Chim. Acta, 15, 1053 (1932). (11) T.G. Dunne and N. W. Gregory, J. Am. chsm. SOC.,80, 1526 (1968).
Volume 69,Number 9 September 1966
M. A. FRISCH,M. A. GREENBAUM, AND M. FARBER
3002
Experimental Method. The heat of formation of AlCl(g) was determined by a molecular flow effusion12study of the reaction as given by eq. 1 over the temperature range 930-1034°K. This procedure consists of passing gaseous AlCl3 at temperature T and pressure P over the surface of molten A1 at the same temperature and allowing the resulting vapor species to escape through an effusion orifice into a high vacuum. The fraction of molecules which leaves the surface of Al as gaseous AlCl is determined by the equilibrium constant Kp. Kp = P A ~ c ~ ~ / P A ~ c I ~
(2)
For molecular flow conditions to exist, the mean free path of the vapor must be of the order of the inside diameter of the Knudsen cell (0.6 em. for the present system, which is equivalent to a pressure of 2 X lo-‘ atm.). The pressures of AlCl and AlCL were calculated from the weight losses of Al and NcI3using the Knudsen equation.
P, = Zx(M,T)’”/(44.33AW~)
ZAicis
= =
- AWtube)/26.98
3/2(AW~1
AW~ici,/133.34- Z A I C ~ / ~
Thermocouple WEll
To AICls(g) generator
Graphite cylinder
Knudsen cell
Flow tube
Figure 1. Knudsen cell in a tungsten resistance furnace.
To Knudsen Flow cell tube
AlCls(c) aample well
Lead-through for hinhtempirature Immersion furnace heater wells thermocouple
(4) (5)
The flow of AlCl was corrected for back diffusion by subtracting the weight increase of the flow tube from the mass of Al lost from the cell, &s indicated in eq. 4. Procedure. A 0.25-g. sample of 99.5% Al wire was placed in a cell constructed of 99+% aluminum oxide (0.38 in. 0.d. X 0.25 in. i.d. X 0.75 in. long) which was closed at one end. An effusion hole was drilled 1.64 mm. in diameter, approximately 0.13 in. off center in the closed end of the tube. The cell was press-fitted into a graphite cylinder (2 in. long x 0.94 in. 0.d.) The Journal of Physical Chemistry
Alumina furnace core with tungaten 003
(3)
where P, is the pressure in atmospheres; 2, is the effusion rate of the species in moles see.-’; M, is the molecular weight of the species; T is the temperature of reaction in degrees Kelvin; A is the orifice area in and Wois the Clausing factor. The cell used in these investigations had an orifice area of 2.20 X and a Clausing factor Woof 0.52. A blank run was made during which AlC13(g) waa passed through the apparatus at 1034°K. at a high flow rate in the absence of any AI. No weight changes occurred in either the flow tube or effusion cell, thus indicating no reaction between AlC4 and the materials of construction. The moles of AlCl formed and the unreacted moles of AlCls were calculated according to eq. 4 and 5, respectively. ZAlCl
so that the front of the cell was! recessed by 0.5 in. A hole (0.25 in. diameter X 0.75 in. long) was drilled in the other end of the graphite cylinder into which an alumina flow tube (9 in. long X 0.13 in. i.d.) was inserted. The cell assembly was brought to the desired temperature using a tungsten resistance furnace with a heating zone of 3.25 in. which has been described in detail previously.18 In Figures 1 and 2 diagrams of the furnace and AlCls generator are shown. The temperature of the graphite cylinder was monitored by a calibrated chromel-alumel thermocouple. The thermocouple voltage was measured on a Rubicori potentiometer which was preset to the desired po-
Thermocouple Immersion well heater well
Figure 2. AICls(g) generator: cross section and rear view.
(12) M. Farber and J. Blauer, Trans. Faraday Soc., 58, 2090 (1962). (13) M. A. Greenbeum, R. E. Yates, M. L. k i n , M, Arshadi, J. Weiher, and M. Farber, J. Phys. C h m . , 67, 703 (1963).
HEATOF FORMATION OF AlCl(g)
tential and the imbalance plotted on a Leeds and Northrup 5-0-5 mv. recorder. The temperature was maintained constant to rtO.3" by a Leeds and Northrup Series 60 control unit regulating the output of a Fincor saturable core reactor. The AICla generator was constructed of high density graphite (1.22 in. 0.d. X 2.56 in. long with a cavity 0.25 in. i.d. X 2 in. long). A 1-g. sample of 99+% punty AlC13 was placed in the cell and the other end of the alumina flow tube press fitted in the 0.25-in. opening, effecting a gas-tight seal. The NC13(c) was handled entirely in a drybox which was maintained under a constant pressure of dry nitrogen. Weighing of the A1C13 in the closed cell was the only operation not carried out in the drybox. Opportunity of moisture pickup must be considered negligible. The graphite cell was heated directly using two General Electric G2 immersion heaters (0.38 in. 0.d. X 2.38 in. long, resistance 13.5 ohms each) in intimate contact with the graphite. The temperature of the AlC1, generator was measured by a chromel-alumel thermocouple and continuously plotted on a 0-5-mv. recorder. A Lee& and Northrup Series 60 control unit, operating a Fincor SCR power supply, automatically controlled the temperature to *0.2'. Both the high-temperature furnace and the AlCI, generator were mounted in a high vacuum system (3 X mm.). The AlC13 generator protruded from the vacuum system through a brass tube (1.25 in. diameter X 3 in. long). The reaction furnace was brought to temperature and allowed to equilibrate for 1hr. during which time the outgassing of the furnace diminished to give a constant pressure of approximately 2 X KIM. The experimental run was commenced by rapidly heating the 4 c 1 3 generator to 90" and maintaining it at that temperature for a time sufficient to lose at least 10 mg. of Al. Termination of the run was effected by cooling the brass tube with ice and in this manner the on-off time was accurate to within 2 min. The mass loss of Al was determined from the mass difference of the Knudsen cell before and after the run and the AlCla maw transfer was determined in a similar manner. The flow tube was also weighed to determine the extent of possible back diffusion of the AlCl. These weighings were repeated until a reproducibility of 0.1 mg. was obtained.
Results and Discussion The reaction was studied at nine different temperatures and the data are presented in Tables IA and IB. A plot of log K , us. 1/T is shown in Figure 3. The
3003
-9.0 0.950
1.000
1.050
1.100
10*/T.
Figure 3. Equilibrium constants for reaction 1 plotted aa a function of temperature.
least-squares line based on these data is given by the equation log K , = -19,742/T
+ 12.036
(6) The present work and all previous experimental data for eq. 1are plotted in Figure 4. An extrapolation of eq. 6 as indicated in Figure 4 yields an equilibrium constant which agrees with the one obtained by Gross,
1.0
1
- 3.0 6
3
-4.0
4
-6.0 - 7.0
\
-8.0
0.60
0.70
0.80 10*/T.
0.90
1.00
1.10
Figure 4. Summary of equilibrium data for reaction 1 plotted as a function of temperature: 1, this work; 2, Semenkovichs; 0, Gross, et uL1; n, Russell, et uZ.2
Volume 69,Number 9 SeptembeT 1966
3004
M. A. FRISCH, M. A. GREENBAUM, AND M. FARBER
Table IA: Experimental Data for the Reaction 2Al(l) AlCla(g) = 3AlCl(g)
-+
930.8 933.3 953.7 974.0 976.0 984.1 994.8 1014.4 1034.0
210 240 120 100 120 160 60 60 60
0.1599 0.2801 0.0934 0.1302 0.0529 0.1379 0.0513 0.0523 0.0670
0.01685 0.02295 0.0138 0.0186 0.0134 0.0279 0.0115 0.0143 0.01835
Table IB: Thermodynamic Properties for the Reaction 2Al(l) AlC&(g) = 3AlCl(g)
+
T, OK.
log Kp
930.8 933.3 953.7 974.0 976.0 984.1 994.8 1014.4 1034.0
-9.215 -9.086 -8.658 -8.212 -8.171 -8.018 -7.826 -7.426 -7.060
AF, AS, d./ A&d, 10*/T, OK. koal./mole deg. mole kosl./mole
1.0743 1.0715 1.0485 1.0267 1.0246 1.0162 1.0052 0.9858 0.9671
39.25 38.80 37.78 36.60 36.49 36.10 35.62 34.47 33.4'0
63.28 63.27 63.14 63.01 63.00 62.95 62.88 62.75 62.64
98.15 97.85 98.00 97.97 97.98 98.05 98.18 98.13 98.16
0.0019 0.0009 0.0013 0.0013 0.00075 0.0020 0.0007 0.0009 0.0000
0.314 0.406 0.465 0.781 0.476 0.734 0.820 1.028 1.421
0.508 0.816 0.457 0.776 0.160 0.412 0.369 0.290 0.329
6.09 X 8.20 x 2.20 x 6.14 X 6.74 X 9.60 x 1.49 X 3.75 x 8.72 x
10-10 10-9 10-0 10-0 10-9 10-8 10-8
kcal./mole for the heat of reaction and 55.1 f 1.1 caI./deg. mole for the corresponding entropy change at the average temperature of 982°K. (The uncertainities assigned to these numbers are the normal statistical standard deviations of the slope and intercept, respectively.) Heat of Formation of AZCZ(g). Using this second-law heat of reaction at 982°K. and AHf0sc12 for AlC13(g) of -142.9 h 0.5 kcal./mole6 (A.Htosclz for A10) = 0 by definition), -17.5 f 0.4 kcal./mole is obtained for A H f " g B for AlCl(g). The uncertainty assigned to this quantity is the square root of the sum of the squares of the weighted uncertainties of AHf"w AlCla(g) and AHfoss2. Employing the available heat content data for AlCl(g), AI0) and AlCla(g),5 the A H f " 2 9 8 for AlCl(g) is found to be -13.3 f 0.4 kcal./ mole. This heat of formation is in good agreement with -11.6 h 1.0 kcal./mole, the average of several previous third-law e~periments.~-~ The experimental and derived thermodynamic data can be found in Table 11. Entropy of AZCZ3(g). Since the entropies of Al(1) and AlCl(g) are known to a high degree of accuracy, the entropy of AICla(g) at 982°K. can be calculated
et u Z . , ~ at 1250°K. within the experimental uncertainty of the data. Furthermore, the reaction investigated was checked for any significant variation from unity of the accommodation coefficient by reducing the hole size area by a factor of 10 and observing no change in the K , within the experimental error. Since the plot of the data is linear to a high degree of precision, the presence of a competing reaction is extremely improbable, In addition, a greater than fivefold varirt. tion in pressure of MCh(g) at 975°K. (cf. Table IA) produces a negligible effect on the K , further indicating that only AlCl(g) is being produced in the reaction of Table II : Experimental and Derived Thermodynamic AICI3(g) with AI@). It is realized that a variation of Data for AlCl(g) and AlC&(g) even 10 in orifice area is probably not sufficient to AHrow 90.3 f 1.1kcal./mole eliminate the possibility of an accommodation coef55.1 f 1.1 cal./deg. mole A&' wz ficient in the range of 0.1 to 1.0. However, assuming AHf'OS2 MCl(g) -17.5 f 0.4 kcal./mole the accommodation coefficient as small as 0.1, it would s o w A1ClsW 104.6 I 2.1 cal./deg. mole flf0288 MC1k) -13.3 h 0.4 kcal./mole not alter significantly the reported value (within exS02w AlC&(g) 76-78 cal./deg. mole perimental error). It is felt, however, that the accommodation coescient in the present case is essentially unity. A detailed discussion of the validity of (14) M. A. Greenbaum, R. E. Yaks, and M. Farber, J . Phy8. Chem., such an assumption has been presented previou~ly.1~~1~ 67, 1802 (1963). Employing the second law of thermodynamics, the (16) H. C. KO,M. A. Greenbaum, and M. Farber, ibid., 69, constants from eq. 6 lead to a value of 90.3 f 1.1 2311 (1966). The Journal of Phymcal Chemistry
3005
HEATOF FORMATION OF AlCl(g)
Table 111: Equilibrium Data for the Reaction 2AlCl*(c) = Al&ls(g) Temp. range, AH,", koal./mole
osl./deg. mole
ASr',' cal./deg. mole
27.45 27.34 f 0.18 26.99 f 0.46 27.57 f 0.19 29.91
60.55 60.36 i 0.43 59.48 f 1.12 60.97 f 0.44 68.13
58.40 58.74 58.96 58.67 60.69
ASr O 3
Ref.
OK.
Taw OK.
6 7 7 10 11
420.8-464.6 395.0-450.2 392.6-428.1 388.6-466.4 294.2-322.2
442.7 422.6 410.1 427.3 308.0
'Authors did not report line.
log P (AlrCls), atm.
-
13.234 6 . 0 0 X 10a/T 13.192 - 5.976 X 103/Ta 13.002 - 5.898 X 10a/T" 13.324 - 6.025 X 10S/T" 14.89 - 6.536 X 108/T
Their data were fitted with a straight line by method of least squares.
Table IV: Equilibrium Data for the Reaction AlnCle(g) = ZAlCb(g) AS,',
ASr','
log Kp, atm.
AHro, koal./mole
cal./deg. mole
cal./deg. mole
7.15 - 61.5 X 10*/T 7.692 - 6.541 X 10S/T'
28.14 29.93 f 0 . 8 2
32.72 35.20 f 1.12
31.85 31.67
Temp. range, Ref
OK.
6 7
669-816 605-944
Tan
OK.
742 775
Authors did not report line. Their data were fitted with a straight h e by method of least squares.
from the entropy of reaction obtained in this study. The Sos2AlCl(g) of 64.84 f 0.5 cal./deg. mole was derived from statistical mechanics using measured molecular constants,lGwhile the Sog~2Al(1)of 17.42 f 0.5 cal./deg. mole is based on measurements on the The. un~ ~ s0lid1'-~ and the heat of f ~ ~ i o n certainties assigned to these entropies were estimated by the present authors. Thus, 104.6 f 2.1 cal./deg. mole is obtained for the entropy of AlCl(g) at 982°K. The entropy at 982OK. for AlC&(g)of 96.8 cal./deg. mole,5 computed from statistical mechanics, is 7.8 entropy units smaller than the experimental value reported here. Four entropy units of this difference can be attributed to the two assigned uncertainties. The tabulated entropy at 298°K. (74.6 cal./deg. mole)6 is uncertain by at least 2 cal./deg. mole, since this quantity is based entirely on estimated molecular parameters except for one experimental vibrational frequency using a rigid harmonic oscillator as the model. Since these frequencies [150(2), 245(1), 400(1) and 610(2) l5 are small, a sizable anharmonicity correction to the calculated entropy is certain to exist at 982 OK. Furthermore, the vibrational contribution to the entropy was approximated using the equation
8,
Rx
= __
e' - 1
- R In (1 -
e-'')
where x = hcwi/kT = 1.438wi/T. This approximation is valid only when x is small, which is hardly satisfied
for AlCla(g) even at 298OK. On this basis, it is reasonable that these statistical calculations may have an accumulated error of 3 to 4 cal./deg. mole at 982OK. Some experimental evidence supporting the higher value is indicated by the equilibrium data presented in Tables 11and ~ ~ 1~ ~ IV. ~ ~ In~each ~ of~these studies the experimental entropy of reaction is greater by 2 or more entropy units than that predicted from statistical entropies.6 Reduction of So at 982°K. to 298°K. is diEcult because of the aforementioned corrections. The most probable value for the entropy of AlC13 from these experiments is in the range 76-78 cal./deg. mole, ~
~~
(16) G. Hersberg, "Molecular Spectra and Molecular Structure. I. Spectra, of Diatomic Molecules," D. Van Nostrand Co., Inc., New York, N. Y.,1950. (17) N. E. Philips, Phys. Em., 114, 676 (1959). (18) J. A. Kok and W. H. Keesom, Physics, 4, 835 (1937). (19) W. F. Giauque and P. F. Meads, J . Am. Chem. SOC.,63, 1897 (1941). (20) K. K. Kelley, U. 8. Bureau of Minea Bulletin 476, U. 8. Government Printing Office, Washington, D. C., 1949. (21) 0.Kubaschewski, Z . EZektrochem., 54, 275 (1950). (22) J. H. Awberry and E. GrifEths, Proc. Phys. SOC.(London), 38, 378 (1926). (23) E. D.Eaatman, A. M. Williams, and T. F. Young, J . Am. Chem. Soc., 46, 1178 (1924). (24) H.Seekamp, 2.anorg. albem. Chem., 195, 345 (1931). (25) P.Schubel, ibid., 87, 81 (1914). (26) W. Oelsen, 0.Oelsen, and D. Thiel,2.Metallk., 46, 555 (1955). (27) F. E. Wittig, ibd., 43, 158 (1952).
V o l u m 69, Numbsr B
September 1966
