THERMAL DIFFUSIONIN DENSEGASES
April, 1958
42 1
TABLE I11 HEATOF FORMATION OF ALUMINUM CHLORIDE HEXAHYDRATE (Mol. wt. = 241.45) Reaction
+
(7) (8) (9) (10) (11)
Al(c)
+
Al(c) 3Hf(so1) = 3(HC1.12.731HzO)(l) = AlCla.GHzO( C) = 32.193H2(1) = 3(HC1.12.731H20)(1) A t 298.15”K., AH11 =
AH808.16,
+ + +
Al+++(sol) 3/2Hz(g) 3H+(sol) 3cl-(s01) 38.193Hzo(s01) A l + + + ( d ) 3C1-(~01) 6HzO(sol) 32.193HzO(SOl) AlC1~.6HzO(c) 32.193H20(1) 3/2Hz(g) -117,000 f 130 cal.
+
+
+
AlCL(0)
TABLE IV HEATOF SOLUTION OF HYDRATED ALUMINUM CHLORIDE HnO, %
AHaor.16, cal./g.
44.73 44.73 44.73 44.73 44.71 44.64 44.62 44.61
-31.63 -31.64 -31.59 -31.67 -31.77 -31.97 -31.74 -31.89
+
AHaor.16
- 2.5(%
AH303.16
HnO)
cal.
-127,050 f 120 O f 10 - 7 , 6 1 0 f 40 -2,570* 20 - 1 1 6 , 8 7 0 i 130
+ 6Hz0(1) = AlCls*6HzO(c) (15) = -65,380 f 80 cal.
LWZSS.IS = -65,130 f 80 cal.
-143.45 - 143.46 -143.41 - 143.49 - 143.55 - 143.57 - 143.29 -143.41
Discussion
Previously accept.ed values3 of the heats of reactions 6 and 15 (the heats of formation and hydration of anhydrous aluminum chloride) are - 166,200 and - 65,000 cal., respectively. The present work agrees with the value for the hydration reaction but differs on the heat of formation of the anhydrous compound by 2370 cal. From examination Mean -143.45=k0.07 of the bibliography of NBS Circular 500,3it appears Al(c) 3/2Clz(g) 6Hz0(1) AlC13.6HzO(c) (13) that the “best” values of the heats of solution of AH2g8.16 = - 233,700 f 200 cal., aluminum metal, the anhydrous chloride and the AKc) 3/2clz(g) 6Hz(g) 3oz(g) = hexahydrated chloride of necessity were taken from AlCla*6HzO(c) (14) the work of at least three different investigators. AHzs8.l~ = -643,600 i 210 cal. This involves possible errors due to variations in The heat of reaction 15 wasevaluated at 3 0 3 ~ 5 ° K . sample purity, solution concentration, temperature by combining the data for reactions 3, 4, 9 and 10. of measurement, and variation in systematic errors Correction to 298.15”K. was made, using an esti- in apparatus, all of which are avoided in the new mated AC, = -51 cal./deg. values presented here.
+
+
+
+
+
THERMAL DIFFUSION I N DENSE GASES BY J. E. WALTHER AND H. G. DRICKAMER Department of Chemistry and Chemical Engineering, University of Illinois, Urbana, Illinois Received November 4, 1067
Thermal diffusion measurements have been made on a series of binary mixtures of gases to 500 atm. (Several systems were studied to 1000 atm.). Mixtures far from the critical temperature showed only small ressure effects. For systems where one component is near its critical temperature, a large negative value of the thermardiffusion ratio 01 is obtained. Neither present kinetic theories, nor the thermodynamics of irreversible processes offer a satisfactory explanation, but i t is possible t o get some insight into the phenomenon from each theory.
There have been numerous studies of thermal diffusion in gases at or near atmospheric pressure2; the theory is well developed and gives good agreement with expCriment. There also have been rather frequent investigations of the phenomenon in liquids and it can be described with reasonable qualitative accuracya in terms of activated motion. There are only a very few investigations in the dense gas region, and these have been over a very limited pressure range,4 or have used the thermal (1) This work waa supported in part by the A.E.C. (2) J. 0. Hirsohfelder, C. F. Curtiss and R. B. Bird, “Molecular
diffusion column.b The theory of the column is at best only semi-quantitat.ive and, in dense gases, particularly near the critical point, its applicability is very doubtful. Therefore thermal diffusion measurements have been made, in a single stage cell, on a series of binary gas mixtures. In most cases the pressure range was to 500 atm.,’although a few data were obtained to 1000 atm. In all cases the gases were pure grade commercial products used as purchased. The defining equation for the thermal diffusion ratio in a binarg system is
Theory.of Liquids and Gases,” John Wiley and Sons, Ino., New York,
N. Y.,1954, p. 582 ff. (3) L. J. Tichrtcek, W. 8. Kmak and H. G. Driokamer, THISJOWR( 5 ) N . C. Pierce, R. B. Duffield and H. G. Driokamer, J. Chsm, NAL, 60, 660 (1956); E. L. Dougherty, Jr., and H. G. Driokamer, ibid., Phus., 18, 950 (1950); E. B. Giller, R. B. Duffield and H. G. Dricka59,443 (1955); J. Cham. Phus., 23, 295 (1955). mer, ibid.. 18, 1027 (1950); F. E. Caskey and H. G. Drickamer, (4) E. W, Becker, Naturforechung, Oa, 457 (1950). $bid., 88, 153 (1953),
J. E. WALTHER AND H. G. DRICKAMER
422
d - P- CONC.
1.0
Vol. 62
+1.0
c02-N~ T=3Z°C
0
0
- 1.0
- 1.0
6 -2.0
-2.0
6
c
-3.0
-4.0
-5.0
-3.0
20% co,
-..-4.0
-5.0
1 0
0
I>
400 600 800 1,000 Pressure, atm. Fig. 1.-a-P-concentration: COZ-Ns, T = 32". 200
I
'
I
I
I
I
I
100
200 300 400 Pressure, atm. Fig. 3.--or-P-T: SO% COr20% Ne.
500
0.2 0.4
I
4-P-T
6
0
-0.2
d -1.0
1
-0.4 I 0 Fig, 4.-a-P:
tI 0
I
I
I
I
200 300 400 Pressure, atm. Fig. 2.--or-P-T: 50% c 0 ~ - 5 0 %N1. 100
1 1
'
1
500
where 4
J1 p D
= flux of component 1 = density = diffusion coefficient
a
= = =
XI T
mole fraction component i absolute temperature thermal diffusion ratio
The steady state solution is from which a can be calculated if the temperature difference and concentration difference across an appropriate membrane are known for the steady state. Equipment and Procedure.-The gas mixtures were made up in a large U tube consisting of two high pressure cylinders
I
I
I
I
I
300 400 500 200 Pressure, atm. 40% C01-60% CZHI; T = 32", 60% C O r 40% CzHc. 100
connected by high pressure tubing. Oil transmitted pressure to mercury which transmitted pressure to the gases. Mixing was obtained by raising and lowering pressure for several cycles and by letting the mixture stand 24-72 hours. The thermal diffusion cell consisted of a large hot chamber and a much smaller cold chamber, separated by a layer of porous glass. Convection from the heater provided mixing and uniform temperature in the lower chamber. The upper chamber was filled with high porosity bronze which provided a uniform temperature. The chamber was designed so that diffusion provided mixing rapidly compared with the rate of transport across the porous glass. Thermocouples were inserted on each side of the porous glass. The lower couple was protected from radiation by a thin porous bronze disc. The temperature difference averaged 8". The upper chamber could be sampled by means of a valve built in the head. The lower chamber could be sampled through a line which also served as entry for the gas. The lines could be evacuated up to the bomb. In practice, however, the lower chamber never deviated significantly from the feed. The analysis was performed by use of a thermal conductivity bridge. For each mixture the bridge was calibrated from mixtures of known composition. The analysis could be performed either by measuring both lower and upper samples against a known standard, or by measuring the upper sample against the lower. Where both methods were employed, no difference in the measured separation was noted. It was possible to estimate relaxation times from measured or estimated diffusion coefficients. The duration of runs
THERMAL DIFFUSION IN DENSE GASES
April, 1958 I
I
I
I
I
I
423 (
1
I
I
I
I
I
d - P- CONC. C2 H,+- He T 32°C
8 4 0
-4 -8 ,100
0
Fig. 5.-a-P:
200 300 400 500 Pressure, atm. 60% CzH+IO% Nz; T = 32", 60% CzHs 40% A. I
I
I
I
d - fJ T=3Z°C
d -12
- 16
-20 -24 -28 -32 -36
0
-2
-4
-6
-8
5 0 % N,
\
-
-A
50%Nz-He
400 GOO 800 1,000 Pressure, atm. Fig. 7.-o~-P-concentration: CzHrHe, T = 32":
+'*
-0-
I
+*
I ' -
Fig. G.--a-P:
200 300 400 500 Pressure. atm. 70% C~H4-30% Ne; T = 32", 50% Nz50% A; 50% Nz-50% He. 100
was a t least 5-6 relaxation times. I n all cases in doubt runs were made a t several time lengths to ensure steady-state conditions.
Results The results are shown in Figs. 1-9. The sign of CY as originally assigned is arbitrary, as long as one adheres to a consistent convention. Here a is considered positive when the species with the larger molecular weight concentrated in the cold chamber. For systems where the average temperature of operation was far above the critical temperature of either component (and presumably that of the mixture) the effect of pressure on CY is not large. For systems were T,, was reasonably near T c for one of the components, CY usually started at a small positive value, became large and negative, passed through a minimum (apparently near the critical density of the mixture) and then increased in value. It usually became positive again within the pressure range studied. For the mixture 80% COz-
I
I
I
I
X - P-CONC. A - He
1 .o 0.5
5
;
L
L,
O
6 -1.0:
0
200
-2.0
-
-3.0
0
\, 100
200 300 Pressure, atm. Fig. B.-a-P-concentration:
-
T=3ZDC
80%4 50% A
i tit
f = -55OC 80% A +-.*-s-
400
500
A-He.
20% Nz CY became negative again at the highest pressures. The minimum in CY was larger, the larger the difference in the critical temperatures of the two components. The results are qualitatively consistent, with previous column data6 on other systems. Discussion For dilute gases of simple molecules, the transport behavior can be characterized by two parameters, using the Lennard-Jones model, the maximum attractive energy of interaction E, and the collision diameter T O . These are listed for the pure components as obtained from viscosity and
424
J. E. WALTHER AND H. G. DRICKAMER
C0,-
He 80%C02
-
-
10
0
-20 d
-40 -60 -80 0
200
400 600 Pressure, atm. Fig. 9.-cu-P-concentration:
800
Vol. 62
1000
in this form of theory. The factor (C 1) appears also in the theory of dilute gases. The LennardJones model predicts negative values of CY below about 0.7Tc at low densities. This prediction is confirmed by experiment. If one ignores for the moment the fact that the dense gas theory was developed only for solid elastic spheres, it is of interest to note that one could predict a negative CY at higher densities if e12 were larger than el, or e2. More generally, an increase in W(l)(1) relative to W(1)(2) (Le., an increase in the importance of low relative kinetic energy collisions relative to high relative kinetic energy collisions, would give a negative CY). Since one approaches the phase envelope by increasing pressure as well as by lowering temperature it is qualitatively consistent with theory that CY would become negative particularly near the critical density. It is also reasonable that low relative kinetic energy collisions be emphasized near saturation. There appears at present to be no way to formulate these generalizations quantitatively and in particular, no hint in the available theory of the very large negative values of CY near the critical density. A second, quite different, approach to thermal diffusion is supplied by the thermodynamics of irreversible processes. From this theory one obtains for d2)
COa-He.
p-v-t data6 in Table I. It is usually assumed for unlike molecules that rot* = 1/2 (ro, rC2) where and €12 = (elez)'/a.
+
Substance
A
r / k ("K.P
B
A
TO
10.2 2.576 10.22 34.9 2.789 35.7 124.0 122.0 3.418 95.0 3.681 91.5 3.897 13.0 205.0 coz 199.2 4.232 CzH' 205.0 243.0 4.418 CzHa 230.0 QA-from viscosity data; B-from efficients. He Ne Ar Nz
(k.).
B
Mol.
wt.
2.56 4.003 2.78 20.18 3.40 39.94 3.698 28.02 44.01 4.07 4.52 28.05 3.95 30.07 second virial co-
Thorne' has applied Enskog's dense gas theory to thermal diffusion, obtaining a complex result which can be written I2
= (C
- 1)s
= partial molar volume of component i = chemical potential of component i Xi = mole fraction of component i &i* = net heat of transport of component i. This quantity is discussed in detail in the references on liquid thermal diffusion6 Vi pi
TABLE I MOLECULAR PROPERTIES
(3)
S is a complex function which contains parameters depending on density. It changes very slowly with density (only about 10% from one atmosphere to the critical density). (C.- 1) can be expressed in terms of collision cross section integrals averaged so as to weight more or less heavily collisions a t high relative kinetic energy8
(C - 1) is a function of rand T but not of density (6) Ref. 2, pp. 1110-1111. (7) 5. Chapman and T. G. Cowling,"Mathematical Theory of Non-
Uniform Gases," Cambridge University Press, 1939, pp. 292-294. ( 8 ) Ref. 2, p. 541.
The lack of p-v-t data for mixtures and the complex nature of the net heat of transport make it difficult to extract quantitative results from equation 5 , but some interesting qualitative conb I ) = RT for siderations are available. X l ( b p ~ / X an ideal gas mixture. From a few data for mixtures XI (bp1/bX1)= 0.3RT near the critical density and some 2030" above Tc. One would need a value of 0.005RT to account for the minimum value of CY for COzHe by this means alone. Available data indicate that the factor V,V,/V cannot contribute significantly to the change of CY with pressure. The subscript 2 refers to the component with the larger value of E , hereafter called the "heavier" component, although it need not always have the higher molecular weight. It seems then, that the heavier component must have a large negative net heat of transport Q2*. Q2" is the total energy transported isothermally with one mole of component two, above the average (thermodynamic) value of the partial molar enthalpy of component two. It is generally assumed, based on a variety of evidence, that molecules tend to form clusters, on nuclei of the condensed phase, near saturation. The clustering process is greatly intensified in the critical region. The clusters presumably have less energy per molecule than single molecules.
April, 1958
INTENSITY OF THE S-H
If the average entity of component two moving from the cold to the hot chamber were a cluster of a size larger than the average cluster in the cold chamber, and if this cluster disintegrated at the hot wall and returned (in the steady state) as individual molecules, this would result in a negative net heat of transport. There is certainly no a priori reason for assuming that the moving entity is a cluster of larger than average size, and it seems inconsistent with a simple kinetic picture. One could assume that there is significant clustering in each chamber but that the entities leaving the hot chamber were smaller relative to the average size at that temperature than those leaving the cold chamber. Again, there is no independent supporting evidence, nor is it intuitively reasonable.
STRETCHING FUNDAMENTAL
425
The possibility that the “lighter” component (one) might have a large positive heat of transport seems rather unlikely, particularly for helium. Neither the present kinetic theory nor the thermodynamics of irreversible processes gives a satisfactory explanation of thermal diffusion in dense gases where motion is neither completely “collisional” nor completely “activated.” These data provide a significant and important test of any more refined theory of molecular motion in this region. The authors wish to acknowledge most gratefully the work of R. E. Harder who developed and erected the equipment as his M.S. thesis. J. E. Walther wishes t o acknowledge assistance from the Standard Oil Company (Ohio) Fellowship.
THE INTENSITY OF THE S-H STRETCHING FUNDAMENTAL; DIMERIZATION O F MERCAPTANS1 BY ROBERTA. S P U R RAND ~ H. FRANKLIN BYERS Contribution from the Department of Chemistry, University of Maryland, College Park, Md. Received November 4, 1967
Integrated absorption coefficients were determined for the 3.8-3.9 p band (the S-H stretching fundamental) of six mercaptans a t concentrations ranging from 0.1 to 7.5 M in carbon tetrachloride. This band is formed by two com onents at about 2580 and 2560 cm.-l, which are attributed to monomer and dimer forms of the mercaptans, respectively. !he variation with concentration of the total integrated absorption coefficient can be accounted for on the basis of a monomer-dimer equilibrium. For all compounds studied, the integrated absorption coefficient for the monomer is about 0.03 intensity unit; that of the dimer is about 0.3 unit for the aliphatic mercaptans and 0.7 unit for thiophenol. The equilibrium constant at 24” for the reaction (.RSH)zF? 2RSH is about 50.
Introduction The intensity of the S-H stretching fundamental apparently has not been measured previously. Bell” pointed out that the 3.8-3.9 E.c band is peculiar to mercaptans, and Ellis and others4-7 established it as the S-H stretching vibration. Hydrogen bonding of the S-H . S type has generally been considered unlikely. Paulings concluded on the basis of physical properties that hydrogen sulfide does not associate. Molecular weights determined by the freezing point method9 do not reveal any tendency t o polymerization. Gordy and Stanford10 scanned the S-H band using a 0.1 M solution of thiophenol and of pure thiophenol, failed to observe a shift of the peak to a lower frequency at the higher concentration, and concluded that thiophenol is not associated. Copley, Marvel and Ginsberg” found that thio-
. .
(1) Presented a t the Pittsburgh Conference on Analytical and Applied Spectroscopy, March 3, 1955. (2) Research Laboratories. Hughes Aircraft CO., Culver City, Calif. (3) F. K. Bell, Chem. Be?., 60B,1749 (1927); 61B,1918 (1928). (4) J. W. Ellis, J . Am. Chem. Soc., 50, 2113 (1928). (5) D. Williams, Phys. Rev., 64, 504 (1938). . soc., 81, si (e) H. w. Thompsonand N. P. Skerrett. ~ r a n a Faraday (1941).
(7) I. F. Trotter and H. w. Thompson, J . Chem. SOC., 481 (1946). (8) L. Pauling, “The Nature of the Chemical Bond,” Cornell Univ. Press, Ithaca, N. Y., 1940, p. 290. (9) E. N. Lassettre, Chem. Revs., 20, 259 (1939). (10) W. Gordy and S. C. Stanford, J . A m . Chem. SOL, 6 2 , 497 (1940). (11) M. J. Copley, C. 9. Marvel and E. H. Ginsberg. ibid., 61, 3161
(1939).
phenol associates with nitrogen- and oxygen-containing solvents forming 8-H . . N and S-H . . .o hydrogen bonds. They measured heats of mixing of thiophenol with the various solvents. Gordy and Stanford” confirmed the S-H N hydrogen bond spectroscopically by noticing that the S-H peak of thiophenol shifts to slightly lower frequencies when the thiophenol is dissolved in solvents of the amine type. On the basis of boiling point and melting point data of thioamides and other compounds containing sulfur and nitrogen, Hopkins, Burrows and Hunter12 claimed to have evidence for the N-H . . S hydrogen bond. This claim may be doubted, for, although their compounds are undoubtedly associated, the association more probably takes place through the Tu’-H . N hydrogen bond, the possibility of which the authors apparently overlooked.
.
. ..
.
. .
Experimental The model 12-c Perkin-Elmer infrared spectrophotometer was equipped with double-pass optics and a Iithium fluoride prism. Slits were set a t 0.2 mm., corresponding to a spectral slit width of 3.6 cm.-’ at 2580 crn.-l. Sodium chloride absorption cells varied in length from 0.01 to 1.5 cm. “Spectral-grade’’ carbon tetrachloride was the solvent. The mercaptans were obtained commercially and were purified by fractiyal distillation. Temperature was maintained at 24 f 1 Integrated absorption coefficients A are defined by the equation
.
(12) G. Hopkins and L. Hunter, J . Chem. SOC.,638 (1942): A. A. Burrowa and L, Hunter, ibid., 4118 (1952).
