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at ionic strength 0.05 would have fallen on the dashed line if the solubility had been observed as 9.14 instead 9.17 mmoles/l. Thus, the deviations cannot be taken as significant. According to these results, a one-tenth molar solution of silver nitrate is 94% dissociated, while a one molar solution would be about 75% dissociated. These values of Q may be compared 17-ith the calculations by Monk,ll based on conductivity data, which indicate a formation constant of 0.58 =t0.01. Acknowledgment.-This work was supported by a Xationnl Science Foundation grant for scientific research. (11) C. B. Monk, “Electrolytic Dissociation,” Academic Press, New York, N. Y., 1861, p. 140.
THEItJlAL DIFFUSION OF POLYSTYRENE IN SOLUTION1 BY B. RACCHAND G. RfEYERHOFF Instztute o f Physzcal Chemzstry, Unznersity of Mainz, Germany Recezeed October 5 , 1988
Introduction and Basic Equations.-Tith a convection-free thermodiffusion cell, applying continuous optical observation of the concentration gradient, it is possible to measure simultaneously the Ludwig-Soret coefficient D’/D and the regular (isothermal) diffusion coefficient D of polymers in solution.2a From the knowledge of these coefficients the thermal diffusion coefficient D’ results. I n a one-dimensional two-component system with concentrations cl and cz and movement of the particles in the %-direction there are mean relative velocities v1 of material flux, due to the concentration difference alone
due to the thermal gradient alone
and for combined effects as observed during therino diffusion.
Former Experimental Work.-Determinations of the thermal diffusion coefficient were performed by Debye-Bueche,Zb who used a diffusion cell with convection, by Hoffman-Zimm,B Whitmore,4 Nachtigall-Meyerhoffj and Herren-Ham,e working under convection-free conditions, but applying different experimental techniques. Since all the authars tested polystyrene in toluene a comparison of tharesults is possible. This is done in Fig. 3 for the experiments with non-convectional diffusion. The data of Whitmore,4 which were discussed recently, see Fig. 11 of ref. Za, are omitted to avoid a too complicated drawing. The indirect determination of D‘ from D’/D and D delivered a thermal diffusion (1) Presented on September 13, 1862, before the Polymer Division a t the fall meeting of the American Chemical Society, Atlantic City, N. J. (2) (a) G. Meyerhoff and K. Nachtigall, J . Polymer Sci., 57,227 (1962); (h) P. Debye a n d A. M. Bueche in H. A. Robinson, Ed., “High Polymer Physics.” (3) J. D. Hoffman a n d B . H. Zimm, J . Polymer Sci., 15, 405 (1955). (4) F. C. Whitmore, J . A p p l . Phys., 31, 1858 (1960). ( 5 ) K. Nachtigall a n d G. Meyerhoff, Z. physik. Chem. (Frankfurt), 30, 35
(1961).
(6) C. L. Herren and J. S. Ham, J . Chem. Phys., 36, 1479 (1961).
Vol. 6’7
coefficient D‘ which is nearly independent of both the concentration, c > g./ml., and the molecular weight ranging from 44,000 to 2,850,000. Hoffman-Zimm3 and Herren-Ham8 measured the migration velocity of a solution-solvent boundary formed in a thermal gradient (70”/cm. with the former authors). The observation was performed by a cathetometer telescope or by a triangle path interferometer, which could only beused after taking off the temperature gradient, which produced too high a refraction. An observation of the boundary was not possible. Hoffman-Zimm3 observed a pronounced concentration dependence, but nearly no effect of the molecular weight. HerrenHame operating at one concentration only measured from M but for M 82,000, D’ = 0.6 267,000-1000,000 a D‘ -1.5 lo-’, a value appreciably lower than found by the other authors.
Experimental Details and Results,-Since the behavior of D’ = f(M, e) was rather unclear, on the other hand D’ being a very important factor in the understanding of the thermofractionation of polymers, it seemed interesting to determine D’ as done by Hoffman-Zimni3 but using a refined optical technique. This technique, recently7described, is able to reproduce by the Philipot-Svensson-Schlieren method the shape of the moving boundary continuously. The optical observation also a t very high temperature gradients, e . g . , 70°/cm., was possible by placing two cells, one filled with the solution-solvent, the other with pure solvent on the optical path. The thermal refraction gradient of the solvent was eliminated by a reversal prism, which resulted in an optical inversion of one of the cells, such that a t the image the cold side was up and the hot side down. Further details on the cells applied are reported elsewhere.’ We tested two good fractions of polystyrene, M , = 70,000 and 950,000, a t a mean temperature of 20’. Figure 1 shows a typical photograph of the concentration gradient at increasing times after putting 011 the temperature difference. The curves shorn a pronounced skewness with a steep descent at the side of the boundary, with the higher temperature and the lower concentration. Therefore the skewness is probably a result of the temperature and concentration dependence of D and (for small e) of D’. Observation of such a curve by a cathetometer telescope means practically measuring the maximum. It is rather unlikely that the migration of this maximum is a good representation of the mean relative velocity VI’ demanded by eq. 2 . Being aware of this hitherto unknown skewness me calculated for each curve the center of gravity abscissa. The migration of this point away from the hot plate of the cell is demonstrated for the experiment of Fig. 1 in Fig. 2 . There is a good straight line to be found during this 5-hr. test. For comparison we applied also the cathetometer telescope technique and received for X = 9.5 X lo5and c = 2 X 10-2 g./ml. a D’ = 0.6 X IO-’ which is practically the same as reported by Hoffman-Zimm3 for the similar molecular weight sample r\Tith M = 1.1 X 105. [Also for the low concentration c =5 X g./ml. me observed with D’ = 1.5 X lo-’ nearly the same result as Hoff man-Zimm. I The application of the more reliable center of gravity migration resulted in D’ values which were nearIy independent of both the concentration and the 1110lecular weight, as shown in Fig. 3. The behavior is iiearly the same as measured indirectly by NachtigallilTeyerhoff . 5 The indirect D’ obtained by a technique which means a homogeneous concentratio11 throughout (7) G. hIe>erhoff, H. Lutle, and B Rnuch, Xakromol. Chern., 44-46, 489 (1961).
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April, 1963
947
averaging of both techniques may cause a slight difference though our polymers were of good uniformity. Discussion Our results on polystyrene in toluene demonstrate that the thermal diffusion coefficient D',nearly independent of M and e, cannot be responsible for the thermofractionation effect on polymers, except perhaps for very low concentrations, So the regular diffusion coefficient 23, the pronounced molecular weight and concentration dependence of which is well known, seems to be the governing factor with this fractionation, proven to be effective, e.g., by Debye-Bueche,2b Langhammerj8and Kossler-Kresj asg (8) G. Langhammer, H. Pfenning, a n d K. Quitzsch, 2. Elektio ci,em., 62, 458 (1958). (9) 1. Kossler and J. Rresia, J . Polymer Sci., 67,509 (1962).
Fig. 1.-Concentration gradient of the migratirg boundary a t 60, 120, 180 min.: M = 9.5 x 105; c = 2 x 10-2 g./ml. 0,48
I
4 "
I
I
I
I
EFFECT OF AlLKALI Ah-D ALKSLINE EARTH PRONOTERS ON IRON OXIDE CATALYSTS FOR DEHYDROGENATIOh- OF ETHYLBENZENE IN THE PRESENCE OF STEAM BY EMERSON H. LEE AND LAWRENCE H. HOLMES, JR.
0,44
Hydrocarbons Dzvision, Monsanto Chemical C o m p a n y , Texas Czty, Texas
042
Received October 6, 1969
0,40
0,38
0,36
0
6000
3000
12000
9000
15000
18000
Fig. 2.--Migration of the center of gravity of the boundary due t o a thermal gradient of 40°/cm. of polystyrene in toluene. 2.0 ',
\
'\ '\
D'.1o7
1 \
\ '
X
'.' \xx
1.5
\
\
\
330000 1000000 267000
\
1.0
0.5
0
1
0
3
2
c Fig. 3.-Thermal
4
102g/rnl
diffusion coefficients of polystyrene in toluene
us. concentration; the numbers are the molecular weights of the
samples : - - -, Hoffman and Zimm3; X X X , Herren and Ham6; -- , Nachtigall and Meyerhoff28,6 44,000-2,850,000; this work: 0 , 70,000; C), 950,000. ~
the cell are a few per cent smaller. This little difference can easily be explained by the different thermal difference, which were AT = 1-2"/cm. as compared with AT = 40-70°/cm. here. Also the different
The literature1 describes the use of alkali (group I) and alkaline earth (group 11) promoters on iron oxide catalysts for dehydrogenation of ethylbenzene to styrene, but this literature does not clarify the functions of these additives, except that they are known water gas and structural promoters. We have measured the intrinsic activities of promoted iron oxide catalysts for dehydrogenation of ethylbenzene, using a differential reactor. The group I and group I1 promoters increased the intrinsic activity of iron oxide in a regular trend for each group; an apparent relation between electronic and catalytic properties was observed and investigated. Experimental A. Catalyst Preparation and Activity Measurements.Catalysts were prepared from reagent grade materials. A paste of iron oxide powder and distilled water was mixed with the proper concentration of nitrates of the group I or I1 metals. The paste was oven dried and broken into granules, then calcined a t 800-900" in an electric furnace for two hours. 20 X 30 mesh granules of this material were used for activity measurements. For contact potential measurements, a finely ground paste was packed into each sample hole (described below), smoothed, dried, and calcined a t 800-900°. The specific surface areas of all of these catalysts were about 2 m.Z/g. as determined by nitrogen absorption isotherms and the B.E.T. equation, utilizing a flow system previously described.2 The catalyst activities were measured with a differential reactor, keeping conversions of ethylbenzene to styrene below 10%. The water used for the feed was distilled and de-ionized; the ethylbenzene was of 99.77" purity. Ethylbenzene and a 13/1 mole ratio of steam were metered and fed in the gas phase into a 20 mm. 0.d. horizontal Vycor reactor a t 1 atm.; 20 X 30 mesh (TJ.S. series) catalyst pellets were supported on a stainless steel screen in an open-ended quartz boat. Temperatures were measured by three thermocouples in a 8 mm. Vycor tube just above the catalyst bed. The temperature was 600 rt 2' alcove the 4 X 0.5 in. catalyst bed; temperature control was better than k0.5'. Tests were made for mass (1) K. K.Kearby, from P. H. Emmett, Ed., "Catalysis," Vol. 111, Reinhold Publ. Gorp., New York, N.Y.,1955,p. 453. (2) K. V. Wise and E. H. Lee, A n d . Chem., 34,301 (1962).
