June, 1963
SORETCOEFFICIEXTS FOR CuSOl ASD CoS04
observed for amorphous carbon and the lines, unlike t h e carbon lines of graphite, decrease steadily in intensity with increasing mass. Graphite, which may be thought to consist of layers of a practically infinite number of condensed benzene rings with weak van der Waal’s binding between layers, can be considered as the limiting case of an infinitely extended polynuclear aromatic hydrocarbon. An aliphatic carbon-carbon bond length is 1.54 8. while an olefinic carbon-carbon double bond is 1.34 8. in length. The hybrid bonds of benzene have the intermediate length of 1.39 8. One might expect that as the number of condensed benzene rings of a compound increases, the average carbon-carbon bond length approaches the value for the carbon-carbon distance of graphite] 1.42 8. If the lines of the coronene spark mass spectrum which are due solely to carbon, namely, the first line of each of the groups, are plotted in the same manner as the graphite data of Fig. 5a, the resulting plot, Fig. 5b, is quite similar to that of graphite. This fact doubtlessly derives from the structural similarity of coronene and graphite. For all compounds studied, the line a t mass number 12 was sufficiently intense to cause photographic reversal in exposures that were strong enough for a inolecular ion to be observed. Most of the low mass lines are quite intense, indicating that a large portion of the sample was reduced to atomic species. The remainder was preferentially fragmented and produced a mass spectrum characteristic of the structure. Ions of masses greater than the molecular weight have been observed for most of the compounds. The spectrum of coronene shows a group of lines greater than the molecular weight with the strongest line of the group falling at 311 m/e. A spectrum of anthracene
1253
c .
b
4
8
12
16
20
-Number Fig. 5.-Carbon
4
€3
12
16
20
of Carbons-
associations observed in the spark: (a) graphite; ( b ) coronene.
recorded a t coulomb exposure showed lines up to the molecular weight, but the spectrum of anthracene recorded a t a coulomb exposure 20-fold greater showed ions of masses up to the anthracene dimer. These additional lines are much less intense than the parent ion, however. Though photographic plate line blackening meagurements cannot be equated directly to ion abundance, they provide an arbitrary scale on which to measure ion beam intensities. Electrometer detection of the ions, which would yield ion abundances directly, would, of course, be more desirable. However, the erratic nature of the spark does not permit its use. Acknowledgment.-Gratitude is expressed to Dr. B. S. Wildi, Moiisanto Chemical Company, for providing the compounds triphenylene, chrysene, naphthacene, picene, benzoperylene, and coronene, and to Mr. A. G. Sharkey, U. S. Bureau of Mines, for providing the compound pyrene .
SORET COEFFICIENTS FOR CuS04,CoS04,AND MIXED SALT AQUEOUS SOLUTIONS USING AN IMPROVED DESIGN OF A SORET CELL BY DAKIEL HERS HEY^ AND JOHN W. PRADOS College of Engineering, University of Cincinnati, Cincinnati, Ohio Received November 86, 196.2 A Soret cell has been built, incorporating two cellophane DuPont PT-600 membranes. The membranes partitioned the cell so that the “differential” volumes contiguous to the hot and cold zones offered a 0.050-in. diffusion path with the remainder of the cell offering a 0.350-in. diffusion path. The entire “differential” volume could be removed as a sample without disrupting the rest of the cell. It was found for the CuSOrHzO system that the Soret coefficient increased monotonically from 9.0-10.3 X 10-soC.-’ over a 0.1-0.6 molarity range and 7.0-7.4 X lO-3”C.-1 for C:oS04 over the same molarity range. For the mixed salt system, CuSO4-CoSO4HaO, no significant change in Soret coefficient of each component was detected as a result of the mixing.
Investigation of the thermal diffusion phenomenon has transcended the merely academic phase. It is recognized that in some cases thermal diffusion can represent an effective means of separating components, such as isotopes in gases, close boiling components, and isotopes in the liquid phase and electrolytes in aqueous solution. Thermal diffusion is a transport process, whereby a temperature gradient imposed upon the system usually causes a migration of molecules with a concomitant concentration gradient. The concentra(1) h s t . Prof. Chemical EnEineering, Univ. of Cincinnati, Cincinnati,
Ohio.
tion gradient then gives rise to an ordinary diffusive flux in the opposite direction. A steady state is attained when both fluxes are equal. Phenomenologically, this is represented as
Ji
=
p[Di’[i(l
- Si) Grad T - D i Grad pi].;
(1) The initial recorded observation of a concentration gradient across a system resulting from a temperature gradient is attributed to Ludwig.2 Subsequently, Soret3investigated this effect more extensively with the (2) C. Ludwig, Sitzber. Akad. IVisiss.
(3) C. Soret, Arch. Sei. (Geneva),
Wien., 20, 539 (1956).
a, 48 (1879).
DSKIELHERSHEY ASD JOHN W. PRADOS
1254
result that thermal diffusion is sometimes referred to as the Ludwig-Soret or Soret effect, Separation data are generally obtained in a Soret cell. A Soret or “equilibrium” cell consists essentially of a hot surface, the interstitial liquid, and a cold surface, arranged contiguously. The hot surface is on top to avoid convective currents. There is no flow of material into or out of the cell, only a migration of molecules within the system. A measure of the separations obtained in a thermal diffusion cell is the Soret coefficient, u, generally calculated from the relation
1 u=-lnAT
xp XI
Equation 2 can be obtained from eq. 1 a t steady d a t e when the net flux, J,, is set equal to zero. It is implicitly assumed that D’jD is independent of temperature and concentration, and that (1 - Xs)/(l - X,)is approximately equal to unity. Soret coefFcients vary, depending on the component, its concentration, and temperature. Reports of Soret coefhients in the literature are sparse and subject to disagreement. Two of the major experimental difficulties involved in obtaining separation data from a Soret cell are sampling techniques and the determination of the point of attainment of a steady-state condition. Sampling difficulties hinge upon the requirement that there must be no disruptive convection currents caused by the technique. Some designs circumvent both of the above difficulties by not removing a sample from the cell. For example, a cell described by Tanner4 utilized a transparent glass Soret cell and an optical system which measured the deflection of a beam of light passed through the cell. Chipman; had two electrodes in the solution. Both of the schemes could monitor the concentration changes and note simultaneously the arrival at steady state and the concentration at that point. There have been many variations of these methods reported in the literature. These methods, however, are not easily applied to the two-salt aqueous solutions since the property measured would now also be a function of the amount of each salt present. Since one of the aims of this investigation was to determine the change in individual Soret coefficients as a result of mixing two or more salt species in aqueous solution, it was decided to forego the conductivity or optical methods of analysis. Experimental Cell Design.-The cell used in this investigation allows the removal of 7-ml. samples from the hot and cold ends without disrupting the remainder of the cell. This is acconiplished by cellophane membranes close to each end. Longafound that these porous membranes, though resistant t o rapid macroscopic flow of solution, apparently did not affect the distribution of the components under conditions of no net transfer. With a Beckman spectrophotameter available for analysis of samples as small as 1 ml., the cell design incorporated: (1) a minimal diffusion path and (2) solution samples that were representative of end conditions. The systems chosen were CuS04-Hz0, CoS04-H20, and the mixed salt system, CuSO~-CoSOd-H,O. The concentration, mean temperature, and temperature gradient were varied for the systems. The cell consisted essentially of three circular sections, two of copper and a plexiglass spacer betareen the copper sections. Each (4) C . C . Tanner, Trans. Faradau Soe., 49, 611 (1953). ( 5 ) J. Chipman, J . Am. Chem. Soc., 48, 2577 (1926). (6) G. W. Long, M.S. Thesis, The UniTersity of Tennessee, 1958.
Vol. 67
of the copper sections had an outside diameter of 6.75 in. and an inside diameter of 4 in., with a 0.050-in. diffusion path. Cellophane membranes separated the copper sections from the plastic spacer. The plastic spacer provided the bulk of the diffusion path, 0.330 in., and measured 5.75 in. in outside diameter and 4 in. in inside diameter. The three sections were clamped together. All of the “differential” liquid between the membrane and the end of the cell constituted a sample which was removed from the cell by tipping the cell, opening the sample ports, and drawing the liquid into a hypodermic syringe. The upper Copper section housed a 375-watt “pancake” electric heater. Two copper-constantan thermocouples in the volume between the membrane and the hot well monitored the temperature for a Leeds and Northrup hlicromax controller, Provisions \T-ere also made for the simultaneous check of the thermocouple signal to the controller, using a Leeds and Northrup portable potentiometer. The lower copper section incorporated a hollowed porticn through which flowed the refrigerant, Freon-12. The refrigeration system was of a standard 0.5 h.p., 6000 BTU/hr. type. Two copper-constantan thermocouples were installed in the space between the membrane and the cold wall, with the e.m.f. signals read on the portable potentiometer. Experimental Procedure.-A run consisted in tipping the clamped cell vertically, filling the cell by inserting a hypodermic needle filled with solution into the lower sample port of each section, and injecting solution until it overflowed out of the upper sample port of each section. After the sample ports were closed, the cell was returned t o a horizontal condition and heating and cooling begun. At the conclusion of the run, the copper sections’ sample ports were opened, the empty hypodermic needle inserted, the cell tipped, and the sample drawn out. A steady state was achieved in about 24 hr. The cellophane membrane was DuPont PT-600 which had been soaked in distilled water to remove the plasticizer. The membrane life was about one month under constant operation, so that a cell had to be dismantled only once a month. IT%-e mesh screens provided support for the membrane in the cell. The analysis for the CuSOrHsO, CoSOd-HgO, and C u S O r CoS04-H20 system was made with a Beckman Model DU spectrophotometer.
Discussion of Results The experimental results for CuSO4, Cos04 aqueous solutions are summarized in Fig. 1 and 2 . It is noted
“ r :
107;
*-
u
o
0.1
0.2
0.3
04
Molarity
Fig. l.-Soret
0.5
.
0.6
0.7
a8
o
01
0.2
0.3
0.4
0.5
06
0.7
M ~ l ~ i i t ~ .
coefficients GS. concentration for Cui304 and CoSOg in aqueous solution.
from Fig. 1 that the Soret coeficient increases with increasing concentration and there did not seem to be a measurable difference in the value of the coefficient for mixed salt and single salt aqueous solutions. For the 100°F. gradient, the experimental results were about 10% higher than the corresponding data of B ~ s a n q u e t . ~ He used a cell partitioned in two equal halves, separated by a cellophane membrane. Arithmetic average values of concentration and temperature mere assumed for each half. Figure 2 is a plot of the temperature dependence of the experimental CuS04Soret coefficients. (7) L. P. Bosanguet, n1.S. Thesis, The Umverslty of Tennessee, 19150.
EQUATIONS FOR PREDICTING SEPARATIOS IX GASESAND LIQUIDS
June, 1963
T, TC E T L g . e Experimental : Arithmetic
d
Average Temper a ture
x103.
2 01
I
1.00
1.20
1.10 I
lo5
T:q
Fig. 2.-Soret
coefficient us. the reciprocal of the square of the average temperature for CuSOn.
At the higher average cell temperatures, the Soret
[email protected] a small temperature dependence. However for decreasing average cell temperatures the Soret coefficient decreases.
1255
Temperature control on the hot and cold sides was maintained at approximately flo. The two thermocouples in each sample zone mere always within two degrees of each other. There was no measurement that introduced an unwarrantable degree of uncertainty. In summary, a soret cell has been designed which allows the removal of a sample from the hot and cold ends of the cell without disrupting the rest of the comtents. Soret coefficients increased monotonically from 9.0-10.3 X 10-30C.-1 over a 0.1-0.6 molarity range for CuSO4 and 7.0-7.4 X 10-30C.-1 for CoS04 over the same molarity range. For the mixed salt system, no significant change m Soret coefficient of each component was detected as a result of the mixing. At higher average temperatures the Soret coefficient for CuS04 was essentially constant if the concentration was fixed. Lower average temperatures yielded decreasing values in the coefficient. List of Symbols D,‘ Coefficient of thermal diffusion of the ith component, eq. 1 D, Coefficient of ordinary diffusion of the i t h component, eq. 1 J,
T AT n X
--.
p, p u
Diffusive flux of Lhe ith component, eq. 1 Temperature, eq. 1 Temperature gradient, eq. 2 Unit normal vector, eq. 1 Concentration, mole fraction Mole fraction of the ith compment, eq. 1. Molar density, eq. 1 Soret coefhient, eq. 2.
THERMAE DIFFUSION. A NOS-RIGOROUS SET OF EQUATIONS FOR PREDICTING SEPARATION3 IS GASES AND LIQUlDS
w.P R A 4 D 0 S
B Y DANIEL !dERSHEY1 AND JOHN
College of Engineerzng, Unaversity of Cincinnati,Czncznnatz, Ohio Received November 26, 1966 The derivation of a unified thermal diffusiontheory for predicting separations of both gases and liquids has not yet been successful. A non-rigorous set of equations has been derived here which allowed, within about 307,, the successful prediction of separations to be expected for helium-argon, neon-argon, non-polar organic liquid pairs, and electrolytes in aqueous solution. The over-all agreement between predicted and experimental results is encouraging and indicates the equations may be used with reasonable confidence for estimating separations where theoretical and experimental results are lacking.
Thermal diffusion is a transport process, as are heat transfer and ordinary diffusion. It is more complex than heat transfer and ordinary diffusion because the temperature gradient imposed upon the system usually causes a migration of molecules with a concomitant concentration gradient. The concentration gradient then gives rise to an ordinary diffusive flux in the opposite direction. A steady state is attained when both fluxes are equal. Attempts to present a unified, rigorous theory for thermal diffusion in gases and liquids have been unsuccessful due to a lack of knowledge concerning the liquid state. Though the rigorous mathematical treatment of this non-equilibrium phenomenon in non-uniform gases is complex, it has been treated extensively by Chapman and Cowling,zaChapman,2b E n ~ k o gClark , ~ Jones,4and
others with good results. The approach is from the kinetic theory point of view utilizing assumptions concerning intermolecular interactions. A comprehensive survey of thermal diffusion in gases is to be found in a text by Grew and I‘c~bs.~ Liquid thermal diffusion theories have been far less satisfactory since they are encumbered by the anomalous and abstruse behavior of liquids. Kinetic theories such as those proposed by Nernst,6Wirtz,’ and Denbighs conceived of liquid thermal diffusion as the transport of activated solute molecules from one equilibrium site to another in discrete jumps, requiring an “energy of activation.” Eastmang and Wagnerlo used a thermodynamic approach to liquid thermal diffusion, introducing a ‘(heat of transfer.” I n developing an irreversible
(1) Asst. Prof. Chemical Engineering, Univ. of Cincinnati, Cincinnati, Ohio. (2) (a) S. Chapman and T. G. Conling, “Mathematical Theory of Nonuniform Gases,“ Cambridge Univ. Press, Cambridge, England, 1939; (b) S. Chapman, Phil. Trans. Roy. Soc. (London), Ball, 433 (1912). (3) D. Enskog, P1i.D. Thesis, Upsala University, 1917. (4) R. Clark Jones, Phus. Rev., 68, 111 (1940).
( 5 ) K. E. Grew and T. L. Ibbs, “Thermal Diffusion in Gases,’’ Cambridge Univ. Press, Cambridge, England, 1962. (6) Nernst, Z, physilc. Chem., 2, 613 (1888). (7) K. Wirtz, 2. phvsik., 1a4, 482 (1948). ( 8 ) D. G. Denbigh, Trans. Faraday Soc., 48, 1 (1952). (9) E. D. Eastman, J . Am. Chen. Soc., 48, 1482 (1926). (10) C. Wagner, Ann. Physilo, 3, 629 (1928).
