W. M. RUTHERFORD AND J. G. ROOF
1506
+
Vol. 63
HT - Hasm = 16.72' 7.8 X 10-8 TZ - 5642 cal. mole-' TABLE I1 ST Sm.15 = 38.5 log (T/298.15) 15.6 X lo-* (T - ENTHALPIES, ENTROPIES AND FREEENERGY FUNCTIONS FOR
-
+
298.15) e.u.
C,,= 16.7
+ 15.6 X 10-8) T,cal. mole-' degree-'
TABLE I EXPERIMENTAL VALUESOF ENTHALPIES, ENTROPIES AND FREEENERGY FUNCTIONS FOR Nas02 OK.
(HOT - HOngs), cal. mole-'
375.4 472.9 573.3 672.9 722.3 739.6 769.5 794.0 822.2 869.2
1712 4021 6525 9184 10527 10890 11733 13747 14640 15803
Temp,,
-
S029E), cal. mole-1 deg.-l
(SOT
5.01 10.46 15.27 19.52 21.43 21.91 23.04 25.62 26.70 28.07
-(F%
- H029a)
T Gal. mole-1 deg. -1
23.10 24.61 26.54 28.52 29.51 29.84 30.44 30.96 31.54 32.54
A discontinuity was observed in the heat content between 773 and 793OK. indicating some kind of transition. Rode and Gol'derQ suggested that sodium peroxide melts at 510" based on differential thermal analysis. The transition was observed to be reversible. The heat of transition (1280 cal./ mole) calculated from the experimental results seems too small to be the heat of fusion. The capsule was opened inside a dry box after it had been (9) T. V. Rode and G. A. Gol'der, Itvest. Akad. Nouk S.S.R.Otdel, Khim. Nouk, 3, 299 (1956).
NaaOr (COMPUTED FROM ENTHALPY EQUATION)
0 22.65 2286 29.16 4658 34.43 7186 39.05 9870 43.17 13990 48.63 16040 51.03 s0~~s.l~ = 22.65, taken from ref. 2.
298.15 400 500 600 700 800 869
22.65 23.44 25.11 27.07 29.07 31.14 32.57 c
heated to 869OK. and no apparent melting of the sample was found. A solid-solid transition has been reported by Foppl from X-ray studies of NazOz.l0 Recent high temperature X-ray studies by Tallman and Margravel' have established a crystal transition a t 510 i loo. Acknowledgment.-The authors wish to acknowledge the support of the Callery Chemical Company, the U. S. Air Force, and the Wisconsin Alumni Research Foundation for high temperature calorimetric studies. The Na202 was generously provided by Dr. A. S. Bjornson of the Niagara Falls Laboratory of E. I. du Pont de Nemours and Company. (IO) H. FGppl, 2. anor& alloem. Chem., 291, 12 (1957). .(11) R. L. Tallman and J. L. Margrave, unpublished work, University of Wisconsin, 1958.
THERMAL DIFFUSION IN METHANE-TZ-BUTANEMIXTURES IN THE CRITICAL REGION BY W. M. RUTHERFORD AND J. G. ROOF Shell Development Company, Exploration and Production Research Division, Houston, Texas Received April 10, 1969
Thermal diffusion measurements have been made on the methane+-butane system at two compositions, 0.40 and 0.49 mole fraction methane, in the pressure range from 1400 to 3000 lb./in.*. These measurements have been carried out in a single-stage apparatus at temperatures of 115, 160, 190,220 and 250'F. The experimental conditions fall in the liquid and critical regions of the mixture. The thermodynamics of irreversible processes predicts that, if the net heat of transport is essentially constant, the thermal diffusion factor 0: is inversely proportional to xI(b p l / d p I ) , where p1 is the chemical potential and x1is the mole fraction of component 1. In order to examine this relationship, values of xl(bpl/bz~)were calculated from the Benedict-Webb-Rubin equation of state. It was found that the experimentally determined values of a exhibited essentially the same dependence on temperature and pressure as the function 2000/21(bplbxl),where the factor 2000 has units of cal./mole.
Introduction Although the phenomenon of thermal diffusion has been known for many years, experimental data on compressed systems are meager. Precise thermal diffusion measurements for compressed hydrocarbon systems are of considerable theoretical interest, particularly near the critical state. Previous investigators have studied thermal diffusion in the critical region by means of the thermal diffusion ~ o l u m n l - ~ ;however, no binary hydro(1) N. C. Pierce, R. B. Duffield and H. G . Drickamer, J . Chem. Phys., 18, 950 (1950). (2) E.B.Giller, R. B. DuReld and H. G . Dricksmer, ibid., 18, 1027 (1950).
carbon pairs have been studied. This paper presents the results of thermal diffusion measurements on the methane%-butane system in the critical region. We have used steadystate thermodynamics t o interpret the thermal diffusion behavior of this system, and we shall demonstrate the strong dependence of the thermal diffusion factor on the composition derivative of the chemical potential. Phenomenological Theory I n this paper, we shall use the thermal diffusion (3) W. L. Robb and H. G.Drickamer, ibid., 18, 1380 (1950). (4) F. E. Caskey and H. G . Drickamer, ibid., 21, 153 (1953).
t
Sept,., 1959
THERMAL DIFFUSION IN METHANE%-BUTANE MIXTURES IN
factor a as defined by the following equation for the mass flux of one component of a binary mixture subjected to a temperature gradient J1 =
- 0 1 2 Mip --- (gradtl M
- -ax122 grad T ) T
(1)
where DI2 is the ordinary diffusion coefficient, is the mass flux, p is the density, 21 and x2 are the mole fractions of components 1 and 2, and T is the absolute temperature. Ml is the molecular weight of 1, and M is xlMl xzMz. At the steady state (J1 = 0), the above expression can be integrated to give JI
+
where the subscripts h and c refer to the hot and cold boundaries, respectively, and qm is the steadystate separation. In the strictest sense, the above integration is valid only if a is independelit of temperature and composition. It is easy to show, however, that extremely large temperature and composition coefficients are necessary to cause a significant error in values of the thermal diffusion factor calculated by means of equation 2.
Thermodynamic Theory Ordinary thermodynamic methods are inadequate for the treatment of steady-state, non-equilibrium processes such as thermal diffusion. It is possible, however, to treat such phenomena by means of the thermodynamics of the steady state, the methods of which have been described by De Groot6 and 0thers.68~ In steady-state thermodynamics, the assumption is made that fluxes of beat and matter are linearly related to thermodynamic forces. For instance, we may write the following flux equations for a n n-component system subjected to a temperature gradient
THE
CRITICAL REGION 1507 (5)
where u is the rate of entropy generation in the process, and T is the absolute temperature. For the case under discussion, these forces are Xk
=
- (grad pk)T
(6)
1
Xu = - (7) T grad T where fik is the chemical potential of component k. Equations 3, 4, 6 and 7 can be used in the manner outlined by De Groot6 to arrive at the following expression for the thermal diffusion factor in a binary system
&I**, the net heat of transport, is the heat transported a t uniform temperature per mole of moving molecules of type 1 less the enthalpy transport. If different conventions are used for such quantities as the flux of matter or the flux of heat, somewhat different expressions for a result. Such expressions are equivalent and can be readily transformed to equation 8.
Apparatus and Procedure
Two types of single-stage apparatus are commonly used for experimental study of thermal diffusion in fluids. These are the open cell and the two-chamber cell. The open cell is the simpler type in principle. I n such a cell, fluid is confined between two parallel surfaces, one hot and one cold, thereby achieving an essentially uniform temperature gradient. The resulting steady-state concentration gradient can be determined by removing successive layers of fluid for analysis or by optical means. Absolute values of the thermal diffusion factor can be determined for most systems from measurements with such a cell. The two-chamber cell consists of two well-mixed reservoirs maintained a t different temperatures and connected by a porous diaphragm or by a capillary tube. I n this configuration, the diffusional processes take place in microscopic pores where ronvection is easily inhibited; in addition, the presence of the reservoirs permits easy removal of samples n for analysis. A two-chamber cell is convenient for highpressure operation; however, uncertainty as to the effective (3) temperature difference in such a cell makes calibration necessary for best results. In this investigation, thermal diffusion measurements Jq = LukXk L u J u were made in a two-chamber, magnetically stirred, thermal k=l diffusion cell suitable for pressures to 8000 lb./in.s and temto 300’F. The cell was a small pressure vessel Ji/’Mi is the molecular flux of component i; Jq peratures into two chambers by means of a porous diaphragm. is the reduced heat flow, which is defined as the divided The vessel, machined from type 302 stainless steel, was 3.75 total heat flow less the enthalpy transported with inches in outside diameter. The interior of the cell was 1.5 the molecular flux. The x k are the thermody- inches in length and had a diameter of 1.5 inches. The cold chamber of the cell was attached to one of the namic forces related to flow of matter in isothermal heads (Fig. 1). This chamber was formed by a Teflon diffusion, and Xu is the force involved in heat con- vessel cup with a stainless steel liner for internal support. A porceduction. lain filter disk (Selas microporous porcelain No. 02) which Lik, hi,, L,k and L,, are phenomenological co- served as the diaphragm was held against the open end of the cup by a stainless steel sleeve screwed onto the vessel head. efficients which are related by the Oii~agerS~~ The remainder of the vessel was the hot chamber. reciprocal relations Each chamber contained a’ small, magnetically operated, iron stirrer for the purpose of maintaining uniform temperaLik Lkij L i u = Lui (4) ture and composition. A sample tube and a mercury inlet The forces must be chosen to satisfy the rehtion- were provided on each side. These were made from stainless steel hypodermic tubing, 0.032-inch 0.d. by 0.020-inch i.d., ship introduced through the heads of the cell and sealed with steel (5) S. R. de Groot, “Thermodynamics of Irreversible Processes,” ferrules. Interscience Publishers, New York, N. Y.,1951. The thermocouple wells were hypodermic tubing welded (6) K. G. Denbigh, “The Thermodynamics of the Steady State,” shut a t one end and sealed into the head in the same manner John Wiley and Sona, New York, N. Y.,1951. as the other tubes. The iron-constantan thermocouples (7) I. Prigogine, Thesis, L‘Universite Libre de Bruxelles, 1947. were made of No. 36 B & S gauge wire with soldered junc(8) L. Onsager, Phys. Rev., 37,405 (1931). tions. Testing of these thermocouples indicated that the (9) L. Onaager, ibid., 38, 2266 (1931). temperature-sensitive area was confined to a region extendn
E
Sept., 1959
00
120
THERMAL DIFFUSIONIN METHANE- BUTANE MIXTURESIN
140
160
I80
200
220
240
260
280
T E M P L R A T U R E . 'F.
Fig. 4.-Lines of constant a in the methane-n-butane system at 0.40 mole fract.ion methane.
TABLE I THERMAL DIFFUSION FACTORS IN THE METHANE-n-BUTANE SYSTEMAT 0.40 MOLEFRACTION METHANE Mean temp.,
115.3 114.9 115.2 114.7 114.3
115.5 115.7 160.5 160.7 100.9 160.5 160.6 160.7 161.1 220.3
220,5 220. 6 219.8 220.2 220.3 220.5 220.7 220.0 249.7
250.0 240. !I 250.6 250.4 250, (i
O F .
Pressure, IbJin.2
1385 1-180 1659 1855 221 8 2890
2925 1503
1575 1700 2010 2253 2558 2855 1560 1657 176i liO9 1820 2002 22 15 2,500 :!XU
1485 15!)2 I -I -Id r 3M17 ZJLKj 2872
Thermal diffusion factor, a
3.56 3.06 2.92 2.4i
2.24 2.24
2.06 5.70 4.96
3.95 3.38 2.82
2.60 2.30 12.19 9.43 6.95 7.26 7.07 5,78 4.49 3.67 2.76 1 ti. 33 1;3. 1 1 9,45 ti. (i:! .I. 45
: I . I:!
Results The thermal diffusion cell was calibrated with an equimolar mixture of n-propyl iodide and q-heptane; this mixture has been run on an absolute basis in an open cell by Drickainer and co-workers.lo The (10) E. L. Doiigherty and H. G. Drickamer. THISJOURNAL, 69, 443 (1956).
100
20
140
60
THE
CRITICALREGION 1509
180 2oa I E M P E R I T U R E . F ,,
220
240
280
280
Fig. 5.-Lines of constant 2O0O/m(dpL1/bz1) in the methanen-butane system a t 0.40 mole fraction methane.
thermal diffusion factor a for this system, as measured in our apparatus, was 2.0 f 0.1 a t 150 lb./ in.2 and 112"F.l' This is to be compared to the value of 2.3 f 0.1 a t atmospheric pressure and 80°F. reported by Drickamer., Since the effect of temperature is small and the effect of pressure is negligible for this system, it appears that the results obtained with this cell are about 15% low. This is very satisfactory agreement for comparison between measurements made with a two-chamber cell and nieasurements made with an open cell. After calibration, measurenients of the thermal diffusion factor were made on the methane-nbutane system a t two compositions, 0.40 and 0.49 mole fraction methane, in the pressure range from 1400 to 3000 I b . / h 2 These measurements were carried out a t temperatures of 115, 160, 220 and 250°F. An additional isotherm at 190°F. wa.s included in the measurements a t 0.49 mole fraction methane. The results12 of these experiments are presented in Tables I and I1 and are plotted in Fig. 2 and 3. The values of a reported here are the experimental values calculated according to equation 2 and multiplied by 1.15 to account for thc instrument error indicated by the calibration. Because of the necessity of avoiding conditions which could create two phases a t any point in the cell, a mininiuni experimental pressure existed for giveii values of teniperature and compositioii. The presence of temperature and conce1itr:Ltion grttdients hi thc ii.pparatiis recluired that this pressure be solnewhat above the sntur:ition pressurc at average cell conditions. Tieproducibility of the experinieiital values of a is very good, coilsidering the small separations illvolved in a single-stage apparatus. An uncertainty (11) \\.all. (12) \r.a11.
Q
is defined
Q
is defined as ~iositireivhen Inethanc concentrates a t the hot
a6
1)ositive when n-heptane concentrates a t the hot
W. M. RUTHERFORD AND J. G. ROOF
1510 3000
I
I
I
I
3000
I
z800
I
I
Vol. 63 I
1
I
1
I
I
t
i
,400-
Fig. G.-Lines of constant 01 in the methane+-butane system at. 0.49 mole fraction methane.
Fig. 7.-Lines of constant 2000/sl( afi,/az,) in the methanen-butane system at 0.49 mole fraction methane.
TABLE I1 THERMAL DIFFUSION FACTORS IN THE METHANE%-BUTANE SYSTEM AT
Mean temp., OF.
114.6 114.3 112.9 114.1 116.1 116.4 115.1 114.8 114.8 115. I 115.5 158.0 160.9 160.6 1'20.7 158.7 lGO.1 160.9 161.3 159.7 161.3 160.5 190.2 190.4 190,4 100.4 190.5 219.3 218.B 221. 6 220.7 221.5 220.5 249.1 249.1 249 8 I
0.49
hfOLE FRACTION METHANE Pressure, Thermal diffusion 1bJin.s factor, a
1640 1653 1670 1G77 1725 1728 1754 2007 2198 2495 2880 1754 1767 1775 1780 1805 1845 1925 1940 2010 2390 2855 1780 2005 2200 2410 2820 1795
1810 2005 2225 2552 2865 1380 1588 1725
5.60 5.70 5.41 5.35 5.06 5.06 5.03 4.05 3.60 2.83 2.31 8.23 8.19 7.79 7.49 7.07 6.63 5.57 5.32 5.06 3.08 2.06 10.97 7.12 5.37 4.44 3.22 11.91 11.64 8.14 5.96 4.16 3.47 12 79 12.10 10.25 I
250.4 250.2 249.4 250.2 250.6 249.0 248.8 248.8 249.0
1780 1785 1862 2060 2075 2238 2486 2731 2955
9.45 9.83 8.88 7.21 7.05 5.92 4.86 3.88 3.42
in t,he absolute values of o is present because of iiihereiit limitations in the calibration method. Discussion When the experimental data of the preceding section are presented as lines of constant a on a pressure-temperature plot (Fig. 4 and G ) , it is quite evident that the most significant feature of the data is the rapid increase of a in the neighborhood of the critical point. This behavior is easily analyzed by means of equation 8. At the critical point (or at the critical solution temperature of a liquid mixture), the factor x1(dpl/dxl) goes to zero. Since the net heat of transport Q** can be expected to retain a non-zero value, it is evident that the thermal diffusion factor becomes infinitely large as the critical point is approached. Such behavior for liquid mixtures near the critical sohtion temperature has been described by Thomaes13 and by Tichacek and Drickamer.14 The Benedict-Webb-Rubin empirical equat'1011 for the fugacity of one component in a binary system caii be differentiated to give ai1 int-ernnlly selfconsistent set of values of bpl/bxl for the methanebutane system.15-16 (Partial volumetric data (13) G. Thomaes, J . Chsm. Phys., 26, 32 (1956). (14) L. J. Tichacek and H. G. Driokanier, TKISJOURNAL, 60,820 (1956). (15) A I . Benedict, G.B. Webb and L. C. Rubin, J . Chem. Phys., 10, 747 (1942). (16) M. Benediet, 0.5. Webb and L. C. Rubin, ibid., 8, 334 (1940).
Sept., 1959
SALTING-OUT CHROMATOGRAPHY OF SPECIAL RESINS
1511
exist for this system,17 from which bpllbx1 can the experimental values of a. Neither the acbe calculated; however, the precision proved not curacy of the calculated xl(bpl/bxl) values nor the good enough to give consistent values.) Such assumption of constancy of Q1**was sufficiently values have been calculated with the assistance good to justify intensive efforts to arrive a t the of an electronic digital computer. Figures 5 and best possible value of that quantity. 7 show lines of constant 2000/xl(bpl/bxl) on presFrom examination of Fig. 2 through 7, however, sure-temperature plots for the two mixtures. it is readily apparent that the function 2000/rl. (The factor 2000 has units of cal./mole.) Choice (bpl/btl) duplicates every qualitative feature of the thermal diffusion data a t both compositions. of the factor 2000, which corresponds to -QI** in equation 8, is rather arbitrary. This number The quantitative differences between this function was chosen to give reasonable correspondence with and the experimental values of the thermal diffusion factor could easily be the result of variations (17) B. H. Sage and W. N. Lacey, “Thermodynamic Properties of in &I**, the net heat of transport, and of inaccuthe Lighter Paraffin Hydrocarbons and Nitrogen,” Amer. Petroleum racies in the calculated values of xl(bp1/bx1). Inst., New York, N. Y., 1950.
SALTING-OUT CHROMATOGRAPHY. V. SPECIAL RESINS BY GLORIAD. MANALO, A. BREYER, JOSEPH SHERMA AND WM. RIEMAN I11 Ralph G. Wright Chemical Laboratory, Rutgers, The State University, New Brunswick, NEWJersey Received ApriI 14, 1969
Partly sulfonated, crosslinked polymers of styrene absorb organic non-electrolytes from aqueous solutions more tenaciously than do the fully sulfonated cation-exchange resins. Similarly, anion-exchange resins with less than the usual amount of quaternary ammonium groups generally absorb organic non-electrolytes more tenaciously than the usual anion exchangers. Resins with quaternary ammonium groups containing ethyl, propyl and butyl groups in place of the usual N-methyl groups were also studied.
Salting-out chromatography is the separation of water-soluble organic non-electrolytes by elution through ion-exchange resins with aqueous salt solutions as the eluents. The best resins for this purpose are the sulfonated crosslinked polystyrene (a strong-acid cation exchanger) and the analogous polymer with the -CHzN(CH&+ group i? place of the sulfonate group (a strong-base anion exchanger). The use of an aqueous solution of an appropriate salt as eluent makes the separation much more efficient than when water is used as the eluent. This has been demonstrated in the separation of alcohols,1~2amine^,^ ethers4 and carbonyl compounds.6 This paper reports an investigation of the behavior of unusual ion-exchange resins as the stationary phase in the elutions of organic non-electrolytes with water and aqueous salt solutions as eluents. The resins were (1) partly sulfonated or partly quaternized crosslinked polystyrenes, Le., cation- and anion-exchange resins of less than the usual exchange capacity, and (2) anion-exchange resins containing three ethyl, n-propyl or n-butyl groups attached to the nitrogen atom instead of the usual methyl groups. Experimental Resins and Reagents .-The special resins were prepared for this study by The Dow Chemical Company. They were crosslinked with nominal 8% divinylbenzene. The sulfonate groups of the cation exchangers and the quaternary nitrogen groups of the anion exchangers were randomly distributed among the benzene rings of the resin. The mesh size, except where noted, was 200 to 400. Except for the (1) R. Sargent and W. Rieman, J . Orp. Chem., 21, 594 (1956). (2) R. Sargent and W. Rieman, THIS JOURNAL, 61, 354 (1957). (3) R. Sargent and W. Rieman, Anal. Chim. Acta, 17, 408 (1957). (4) R. Sargent and W. Rieman, ibid., 18, 197 (1958). (5) A. Breyer and W. Rieman, ibid., 18, 204 (1958).
low capacity and the change in the N-alkyl groups, these resins are analogous to Dowex 50-X8 and Dowex 1-X8. All common reagents were of the best grade available and did not require further purification. The exchange capacities of the resins were determined as follows: chromatographic tubes of internal cross-sectional area of 3.90 cm.3 were filled to de ths of 10 to 15 om. with the resin, either H R or RC1. Sochm chloride (for H R ) or nitrate (for RCl), about 1M , was passed through the column at a rate of about 0.8 cm. per minute until the hydrogen or chloride ions, respectively, were completely displaced. For resins of capacity of 2 meq. per g. or more, one liter or less sufficed; but larger volumes, sometimes up to 4 liters, were required for the resins of lower capacity because of the slow exchange rate. The hydrogen or chloride ion was determined in an aliquot of each effluent by titration with sodium hydroxide or silver nitrate to find the total exchange capacity of the column. Then the resins were converted, still in the column, to their original forms; and the determination was repeated. Finally, the resins were reconverted to the original forms, rinsed free of interstitial electrolytes, re; moved from the columns, dried to constant weight at 62 under vacuum (10 to 12 hours) and weighed. The interstitial volumes of the resin columns were determined with polyphosphate (for the cation exchangers) and polysoap (for the anion exchangers) as described elsewhere - 5 Elutions.-Samples of 0.05 to 0.1 mmole of alcohol or ketone were eluted through resin columns, about 20 cm. in length and 3.9 cm.* in cross-sectional area, with water or standard solutions of ammonium sulfate as eluents. The resins were in the ammonium or sulfate form. Small fractions of the eluate were collected; the organic compound in each was determined as previously described.s~7~*Elution graphs were plotted from these data. The distribution ratio C , defined as the quantity of organic solute in the resin of any plate divided by the quantity in the interstitial solution of the same plate at equilibrium, was calculated from the equation9 (6) G. D. Manalo, R. Turse and W. Rieman, ibid., in press. (7) R. Sargent and W. Rieman, ibid., 14, 381 (8) R. Sargent and Rieman, THIS JOURNAL, BO, 1370 (1956).
W.
(1956).
(9) W. Rieman and R. Sargent, “Ion Exchange” in “Physical Methods of Chemical Analysis,” Vol. IV, edited by W. G. Berl, Academic Press, New York, N. Y., 1959, in press.
