556
J. H. STERNAND N. W. GR.EGORY
indicated that the quadratic term becomes important at colloid concentration about 1/10 as large as is the case in eq. 4. This also is in qualitative agreement with Klaarenbeek's results on gum arabicg The present results for Bz may be compared with earlier work based on a hard sphere model, where the surface of the sphere, replacing the colloid particle and its double layer, was defined as the surface on which the interaction energy W ( R ) equals kT.lS I n Table IV the results for ( N O M ) / & are given in the case of micelles of sodium lauryl sulfate in aqueous NaCl solutions at 2 5 O , N Obeing Avogadro's number and M the micellar weight. It will be observed in Table IV that the hard sphere values of Bz are consistently too low, showing that the hard sphere cut off should have been (13) D . Stigter, Rec. trau. ohim., 78, 693 (1954).
Vol. 63
chosen at some surface where W ( R )< 1cT. I n any case, the hard sphere model is rather poor since W ( R )decreases with R over a considerable range. TABLE IV COMPARISON OF DIFFBRENT CALCULATIONS OF B2FOR NaLS MICELLES CNaOl. mole/l.
(No/M)Bo, cc./g. Hard sphere Present work
0
.03 .1
80 24 12
143 34.8 15.6
Finally, it should be recalled. that the McMilIan-Mayer (virial expansion) approach fails a t very low ionic strength. I n the limit K --+ 0, the potentials of interaction W ( R ) and W'(r) fall off as 1/R and l / r , respectively and, as a consequence, the virial c0efficient.sbecome infinitely large.
VAPORIZATION CHARACTERISTICS OF p-DIBROMOBENZEKE BY J. H. STERNAND N. W. GREGORY Contributk from the Departmat of chemistry, University of Washington, Xeattle, Waahinghn Received August 19, 1968
Vapor pressures of p-dibromobenzene have been measured in the temperature range -45 to 74' using effusion?gas saturation and static techniques: log P.tm = -3850T-1 8.80. Condensation coefficients, estimated from effusion pressure dependence on cell geometry, range from near unity a t the lowest temperatures to ca. 0.025 at 13'.
+
Recently the use of the effusion method as a means of determining the condensation coefficient of iodine has been described.' A similar study of p dibromobenzene has been made to test further the applicability of the method. Its properties are well-suited for an effusion study. Only a limited study of its vapor pressure appears in the literature2 (there is a general paucity of low vapor pressure data for simple aromatic compounds). I n the present work effusion, gas saturation (transpiration), rate of vaporization and static vapor pressure measurements have been made in the temperature interval -45 to 74". Experimental Samples of p-dibromobeneene from two sources (Matheson, Coleman and Bell, Reagent Grade; Eastman Kodak, White Label) were used. Melting points of both samples, before and after recrystallization from 95% ethanol, were the same, 86-87'. The small quantities transported at low vapor pressures in the dynamic methods were determined by spectrophotometry, using solutions of p-dibromobenzene in 95% ethanol. Quantities of the order of a micromole were determined a t 2710 A. (Beckman D.U.); the more strongly absorbing region at 2400 8. was used for smaller amounts; as little as 5 X 10-8 mole easily could he determined within 5% uncertainty. Beer's law appeared valid at both wave lengths. Effusion.-Measurements were made with the same cells and techni ue described fully in the recent publication on iodine. C& numbers on Fig. 4 and cited in the discussion correspond to those listed in ref. 1. Gas Saturation.-The f i s t measurements using this technique were made in the very low vapor pressure rairge, 10-6 atmosphere or less; poor reproducibility and an apparent dependence on carrier gas was noted. These difficulties disappeared a t higher vapor pressures, but the carrier (1) J. H. Stern and N. W. Gregory, THIBJOURNAL, 61, 1226 (1957). ( 2 ) F. W. Kiister, 2.physik. Chem., 61, 222 (1905).
gas dependence was examined fully, using helium, argon, chlorotrifluoromethane (F-13). hydrogen and air. All gases (except air) were taken directly from commercial reagent grade tanks. Air was dis laced from a five liter flask, driven at a constant rate by aBding water from a constant level column above the flask. The carrier gases were dried, passed through a flow meter for qualitative indication of rate, into a thermal equilibration tube and then through the saturator. The latter two were immersed in a thermostat; the saturator column consisted of a sim le Pyrex trap, about 20 mm. 0.d. and 20 cm. in length, wit{ the inner surface of the outer walls coated with p-dibromobenzene, reviously sublimed in under high vacuum. The saturatefgas mixture then left the thermostat region Via a heated tube leading to a U tube where the vapor was condensed (U tube cooled with liquid oxygen, or with a diethyl malonate slush bath (-55') when F-13 was used as the carrier gas). The carrier gas then passed through an additional dryin tube, to prevent back diffusion of water, and into a dariotte flask where it displaced a measured volume of water. The latter was used to determine the flow rate. The sample collected from a given run was dissolved in ethanol and removzd from the U tube for analysis. The saturation column was evacuated before changing flow gas and flushed each time with gas flowing in reverse to the normal direction before initiating a run. Carrier gas pressures were kept near atmospheric pressure. Flow rates were varied between 4 and 84 ml./minute without noticeable variation in the calculated vapor pressures. Most runs were for periods less than one hour.8 Static Pressure Measurements.-p-Dibromobenzene was not observed to react with mercury a t temperatures below its melting point. A modification of a mercury gauge suggested by P e a r ~ o n Fig. , ~ 1, was used to make direct measurements of the vapor pressure in the range around one millimeter. Tube A , containing the sample, was connected by a multiple bore stopcock, lubricated with Apiezon T, to B, the null-point reference tube of the gauge. B is also connected to C, a precision bore tube of diameter 25.42 mm., (3) Details of these and other experiments may be found in the Doctoral Thesis of John Hanus Stern, University of Washington, Seattle, 1958. (4) T. G. Pearson. ibid., 8166, 86 (1931).
. .
VAPORIZATION CHARACTERISTICS OF ~DIBROMOBENZENE
April, 1959
557
a uniform capillary tube D, 2.68 mm. diameter, and a mercury reservoir E. The entire gauge was initially evacuated and the level of the mercury adjusted by a stainless steel valve F so as to just close an electrical circuit between vertical and horizontal tungsten electrodes in the nullpoint tube. The electrodes were attached to an electronic indicating device. The entire apparatus was immersed in a water thermostat. To measure the vapor pressure, the sample vapor was allowed t o enter B, depressing the level of mercury. Air was then admitted to D to displace sufficient mercur to restore the initial level in B. The volume of mercury &placed from D is equal to that added to C; from the known ratio of cross-sectional areas of the two tubes (giving a multiplication factor of 90) the small pressure may be calculated from the relatively large change in height observed in D. The mercury and glass must be cleaned carefully to minimize abnormal- capillary displacement effects. Rates of Free Vaporization.-A limited number of measurements of the rate of vaporization into vacuum of powder and pressed tablets was made in the same manner as described for iodine.] The irregular surface changes on single crystals undergoing free evaporation were recorded at various intervals by macrophotography.8
Results and Discussion P , values, calculated from the equation' P,(atm) = n(MT)'/1(44.38AolK)-'
(1)
where n is the number of moles of molecular weight M collected in time t a t To (Kelvin), AOthe orifice area and K the cell geometry factor, from effusion cells 3,4,5 and G are shown in Fig. 2. Between ca. -13 and -45" results from all cells were indistinguishable, indicating that the condensation coefficient is near unity in this low temperature range. At higher temperatures a dependence of steadystate pressures on cell geometry becomes apparent; data from the various cells may be correlated with the equation' P. = P, - jP,/ff (2) where f is the ratio of cell orifice area to cross-sectional area, P, the apparent equilibrium pressure and a the condensation coefficient. P, values selected to give the most consistent set of LY values for all cells were only a few per cent. larger than steady-state pressures observed in cell 6. Condensation coefficients so determined are summarized in the table Cell
3 4 5 5 t
47
30
13
16 16
23 21 19 18
28 25 32 29
a X 101
0
50 60 90
-0
110 180
Fig. l.--Static pressure gauge.
3.00
4.00
d
5.00
M
'
e
6.00
7.00
-15OC.
>ZOO >200
Effusion measurements were made up to the millimeter pressure range (1.5 X atm.). At pressures above atmosphere (ca. loo), however, P, for cells 3 and G calculated from equation l lie above those indicated by gas saturation and static measurements as equilibrium pressures, shown as the datted line on Fig. 2. This appears to be a manifsstation of the breakdown of molecular flow conditions; i t is concluded that P , values based on (2) are too high at temperatures above 13' leaving doubt as to the validity of a values tabulated a t 30 and 47". Results of the gas saturation and static pressure measurements are shown in Fig. 3. Ideal gas behavior was assumed. The various carrier gases all gave vapor pressures in good mutual accord
i
\
1 t I
8.00
dI . . .
3.10
I-.I 3.30
3.50
i-I 3.70
3.90
4.10
4.30
1000/ T.
Fig. 2.-Vapor pressures measured by effusion: 6, 0 ;3, C>; 4, -0; 5, 0 ; Ptrana, atatiot ---.
above 20" (v.P. ca. 5 X low6atm. and higher) and are seen to be in excellent agreement with the static pressure measurements. An extrapolation of the line shown in Fig. 3 correlates very well with effusion data between - 13 and -45") the range in which a is near unity; the combined data lead to the equation log P(atm) = -3850T-I
+ 8.80
(3)
giving a mean standard heat and entropy of sublimation of 17,650 cal. mole-' and 40.3 cal. deg.-l mole-', respectively. P, from cell 6 is shown at two temperatures on Fig. 3 to indicate its relationshir, to the-equilibrium line in the high pressure regon.
J. H. STERNAND N. W. GREGORY
558
Vol. 63
effusion data at temperatures higher than 13' appear to correlate well with equation 2, the breakdown of the Knudsen equation at the higher pressures makes the significance of the a values questionable (the deviation from molecular flow conditions would be different in each cell). A plot of the apparent a values vs. 1/T shows considerable curvature and does not give a suitable basis for estimation of activation energy and entropy. The EFFUSION DATA
3.00
j
4
24.00
7
Cell 3 (A0 24.2 X lo+*cm.*;f25.0 X 5.00 I I I I I I I I 1 2.90 3.10 3.30
j
I
/ I 1 3.50
1
%
1000/T. Fig. 3.-Vapor
pressures measured by gas saturation and static methods.
Pressures reported by Kuster are considerably lower than those predicted by equation 3 . The continuous rise of the effusion apparent equilibrium vapor pressure curve above the correct line (at higher temperatures), 30y0 higher for cell 6 a t 55" (p = 1.1mm.) is in contrast to the behavior observed with iodine. Iodine cell 6 pressures agreed closely with transpiration data of Baxter, Hickey and Holmes6 in the pressure region near one millimeter. At higher temperatures a rather sudden fall-off, or flattening, of the In P vs. 1/T curve was observed; the pressure a t which this occurred was a function of cell geometry, 1.2 mm. for cell 6 , 0.1 mm. for cell 5. The fall-off in the case of iodine is thought to be due principally to the self-cooling of the sample at the relatively large net rates of vaporization from the effusion cells at the highest pressures; however, a similar phenomenon was not observed with p-dibromobenzene. Molecular diameters, mean free paths and heats of vaporization are quite similar for the two substances; hence the fall-off in the case of iodine seems to be determined by solid characteristics rather than a molecular flow problem. It is concluded that the breakdown of the Knudsen equation a t pressures above mm. may result in a rise of apparent pressures above the actual values as viscous flow becomes more important, as predicted by Dushman,6 or, depending on the heat conduction properties of the solid, a fall-off due to lowered surface temperatures produced by self-cooling. A fortuitous combination of these effects may result in close correspondence of effusion pressures with correct values at pressures up to the millimeter range. The condensation coefficient of p-dibromobenzene, like that of iodine, appears to decrease as the temperature is increased. Equation 2 is of little value for its estimation below temperatures of O", where a becomes materially larger than 0.1, because of the small difference between Pe and P,. While ( 5 ) G. P. Baxter, C. H. Hickey and W. C. Holmes. J . A m . Chem. Soc., 29, 127 (1907). (0) e. Dushman, "Vscuiiiii Technique," Cliapt. 2 , J o h n W l e y and
Sons, Inc., New York, N. Y . , 1949.
Temp., OC.
Time (min.)
35.1 25.3 11.2 0 0 -12.9 -37.5 -37.4 -45.2
15.49 19.82 13.33 33.65 22.77 47,25 91.03 49.19 124.78
K 0.97) P X 106 (atm.
22.4 8.57 1.88 0.473 .476 .0927 .00349 .00328 ,000777
Cell 4 ( A o 13.3 X l o d 3crne2;f51.8 X loe4; K 0.98) 38.3 14.65 26.8 26.2 19.01 8.82 21.0 '21.88 4.93 11.5 34.07 1.72 0 48.88 0.445 0 55.12 .458 -12.6 58.01 .lo1 -37.3 77.74 ,00269 Cell 5 ( A o 16.7 X loea crn.I; f 135 X 48 21.37 42 13,86 28.5 30.76 21.5 33.55 17 21.60 13.1 17.38 7.2 36.18 0 26.89 -12.8 35.52 -21 91.30 -45 156.64 Cell 6 (A0 4.23 X cm.2; f 5.97 X 55 28.68 51 19.28 40 12.80 36.7 29.79 33 33.60 31 16.78 26 28.45 23 31.39 20 35.38 20 24.92 5 33.00 0 35.10 0 39.14 -13.1 62 37 -13.1
-38
e2.93 86. 80
K 0.96) 41.4 27.2 8.91 4.29 2.65 1.84 0,946 ,443 ,0821 .0263 ,000868 K 0.97) 147 106 42 28.9 20.4 16.9 10.5 8.15 5.04 4.94 0.832 .504 .502 .os00
,0800 .00222
)
April, 1959
ION-EXCHANGE SEPARATION OF TECHNETIUM AND RHENIUM
general behavior is comparable to that found for iodine, however, with a somewhat more rapid change of cy with temperature. As with iodine, it does not seem possible to attribute the deviation of P, values in the various effusion cells to surface cooling effects. For example the net rate of vaporization from cell 3 is larger than cell 5; yet the former yields P, values larger than the latter. Furthermore even in cell 3, which has the highest rate of effusion (moles set.-'), radiation transfer alone is sufficient to keep surface temperatures within less than a degree of the walls at temperatures as high as 0”. Hence the P, to P e relationship has been interpreted’ as an cy effect. It should be emphasized that the absolute value of a depends on the value selected for the sample area, A,; the latter has been taken as the cross-sectional area of the cell; if in reality it is only proportional t o this, possibly much larger, then cy may have a
559
much smaller value, as averaged over the total surface area. Photographs of freely vaporizing crystals show vaporization occurs more rapidly a t crystal edges than on the faces.a The condensation coefficient may well be different on the various crystal surfaces. The surfaces of freely vaporizing crystals were seen t o undergo irregular and chaotic disintegration; a reliable area of vaporization cannot be estimated under these extreme non-equilibrium conditions. This area must be known if quantitative interpretation of free vaporization data is to be attempted for evaluation of vapor pressures or condensation coefficients by the free evaporation method. Acknowledgment.-Financial support of this work by the Research Corporation and the Office of Ordnance Research, U. S. Army, is acknowledged with thanks.
DEVIATIONS FROM PLATE THEORY IN THE ION-EXCHANGE SEPARATION OF TECHNETIUM AND RHENIUMZ BY R. N. SENS A R M AEDWARD ,~~ ANDER@AND J. M. MILLER^; Contributionfrom the Department of Chemistry and the Enrico Fermi Institute .for Nuclear Studies of the University of Chicago, Chicago, Ill., and the Department of Chemistry, Columbia University, New York, N . Y . Received August $1, 1968
Technetium and rhenium in their highest oxidation ststes can be separated by ion-exchange chromatography on the synthetic resin Dowex 1, using perchlorate ion as the elutriant. I n 0.1 and 0.2f HC104 solutions, the peak elution volumes (in units of free column volumes) are 43.0 f 0.8 and 23.6 f 0.4 for Reoa-, and 85.2 f 1.9 and 43.7 f 0.7 for Tc04-, respectively. The trailing edges of the elution curves deviate markedly from the predicted Gaussian shape, and the observed separation factors differ from those calculated from the late theory of Mayer and Tompkins, and Glueckauf, by factors of 10*to 10’8. Part of the discrepancy is due to a chemicaycause, presumably radiocolloid formation, and can be eliminated by appropriate chemical treatment. In addition, there appears to be a ‘‘residual” tailing-effect which can be reduced, but not eliminated, by changing the experimental variables. This effect, which appears to arise from the infrequent occurrence of a second, slow exchaiige process, limits the maximum separation factors attainable to 104-106, irrespective of the number of theoretical plates. The mechanism of this process could not be established with certainty, although its dependence on flow rate was consistent with the behavior expected if the chemical exchange reaction with the exchange site, rather than film or particle diffusion was the rate-determining step. It appears that the “residual” tailing-effect is not limited to the two elements studied, but occurs in other systems as well. At high acid concentrations, a broadening and distortion of the technetium peaks was observed, indicating oxidation of the resin by pertechnetate.
Introduction concentrations. For this reason, a new ionI n conjunction with a search3 for naturally oc- exchange procedure was developed3” using the curring Tcgs,a highly efficient method was needed synthetic resin Dowex-1 as the exchanger, and for the separation of trace quantities of Tc and Re. perchlorate ion as the elutriant. Upon application Separations of these elements had been described of this procedure, it was found, however, that the by Perrier and Segr&,* Sugarman and R i ~ h t e r , ~rhenium content of the technetium fractions, as determined by neutron activation analysis, was Rogers,6and Atteberry and Boyd.’ As shown previou~ly,~“ these methods suffered frequently about lo2-los times higher than prefrom one or more of the following shortcomings: dicted by the plate theory of Mayer and Tompkinss low separation factors, low yields and failure at trace and G l u e ~ k a u f . ~For example, in the experiment illustrated in Fig. 1, the technetium fraction cut a t ;i) Prrsented before the 130th National Meeting of the American 71.5 free column volumes would have contained C:iemicd Society, Atlantic City, September 19. 1956. This work >2.1 X of the initial amount of rhenium, comwas supported in part by the U. S. Atomic Energy Commission. 12) (a) Department of Chemical hngineering. Jadavpur University, and 3.0 X 10-7 pared to values of 1.1 X Calcutta, India: (b) Department of Chemistry and the Enrico Fermi calculated from the theories of Mayer and TompInstitute for Nuclear Studies of the University of Chicago, Chicago, kins, and Glueckauf, respectively. (An even more Illinois; (c) Department of Chemistry, Columbia University, New drastic case is shown in Fig. 4, where discrepancies York, N . Y. (3) (a) E. Alperovitch, Ph.D. Dissertation, Columbia University by factors of 2.4 X 10l8 and 1.3 X lo1*, respec(January 1954): U. S. Atomic Energy Commission Report NYO-6139. tively are found.) (b) E.Alperovitch and J. M. Miller. Nature, 176, 299 (1955). (4) C. Perrier and E. Segre. J . Chem. Phgs., 7 , 155 (1939). (5) N . Sugarman and H. Richter, Phys. Rev.. 73, 1411 (1048). (6) L. B. Rogers, J . A m . Chem. S o c . , 71, 1507 (1949). (7) R. W.Atteberry and G . E. Boyd, ibzd., 72, 4805 (1950).
( 8 ) 6 . W. Mayer and E. R. Tompkins, {bid.,89, 2866 (1947). (9) (a) E. Glueckauf, Trans. Faradag Soc., 61, 34 (1955): (b) IC. Glueckauf in “Ion Exchange and Its hp]iIications,” Society of Clieiiiical Industry, London, 1955,pp. 34-45.
