LIQUIDDIFFUSIVITIES IN THE GLYCOL-WATER SYSTEM
2499
us. the concentration of sodium sulfate.
The slope of this line at a concentration of sodium sulfate equal to zero is taken as K1 (Figure 3). Table I11 reports the values of the cryoscopic number, vo, at infinite dilution for the various systems studied. Table IV is a list of the values of K1 obtained from
the plots of the limiting slopes of the various systems studied. It should be noted that the cadmium fluoride does not appear to form any complexes at all in the concentration ranges investigated. Because of the error associated with K1 values obtained, it was decided the values of K 2 would be meaningless at the present time.
Table IV : Values of K , for Certain Salts
Conclusion
in Molten Lithium Nitrate Salt
Ki
CdSO4
5.3 f1.2 0.93 f 0 . 3 2.7 f 0 . 5 0.13 f ? 0.40 A 0 . 4
PbSOc cuso, COClZ cos04 CdFn
0.0 f ?
A variety of different salts have been added to lithium nitrate and lithium nitrate-sodium sulfate or chloride mixtures. It was found that all but copper sulfate, lead sulfate, cobalt sulfate, cadmium sulfate, and cobalt chloride were completely dissociated in lithium nitrate. For these five incompletely dissociated salts, K1, the thermodynamic stability constant was calculated, using the method of Braunstein, et al.
Liquid Diffusivities in the Glycol-Water System
by Charles H. Byers and C. Judson King Lawrence Radiation Laboratory and Departmnt of Chemical Engineering, University of California, Berkeley, California (Received January 26, 1966)
Mutual diffusion coefficients are reported for the system ethylene glycol-water over the entire range of compositions at temperatures ranging from 25 to 70". Differential coefficients were obtained by the use of diaphragm cells and a differential interferometer. It was found that the group Dv/T is temperature independent and varies linearly with the mole fraction of glycol present. The theoretical implications of these results are discussed briefly.
effect of concentration level upon diffusivity is limited to quite simple systems. Corrections for nonidealities have often been confined to instances where regular solution theory is postulated1 and the activity coeffi-
(1) R. J. Bearman, J . Phys. Chem., 6 5 , 1961 (1961). (2) D.L. Bidlack and D. K. Anderson, ibid., 68, 206, 3790 (1964). (3) D. K. Anderson, J. R. Hall, and A. L, Babb, ibid., 62, 404 (1958).
Volume 70, Number 8 August 1966
CHARLES H. BYERSAND C. JUDSON KING
2500
have endeavored to show that for associating solutions, one must consider clustered groupings rather than a true random binary in correlating diffusivity data. The ethylene glycol-water system presents an opportunity to study an associated solution where the molecules are of quite different sizes and where there is an order of magnitude change in viscosity across the concentration range. Vapor pressure data for this systems show that it follows Raoult's law closely throughout the temperature range of interest. A system of this type should provide a unique test of the existing theories. Two previous studies of the glycol-water system have been reported. One study reports a single value for ethylene glycol at high dilution in water at 15°.6 The other investigation covers a range of compositions a t 20" and provides high dilution values at 25, 30, and 40°.7 The present experiments were designed to complete and extend the previous data. I n correlating liquid diff usivity data, most workers have included the effect of temperature. However, most of the data which exist for various systems at the present time are for the temperature range 15 to 40". It was therefore of some interest to attempt to extend this rather narrow range in order to place the temperature effect upon a stronger foundation.
Experimental Section Diffusion measurements were carried out in a group of glass diaphragm cells. The cells were of the horizontal type described by Holmes, et aL8sg The two solution compartments are horizontally opposed across a vertical fritted glass diaphragm. The temperature bath and other auxiliary equipment are also described by Holmes, et al. The cell constants (p) were obtained in the present work by calibration with 0.1 N KC1 solutions. It is interesting to note that the constants found by Holmes for some of the same cells several years earlier were almost identical with those found in this study, in spite of the fact that his calibration was carried out with 0.2 N HCl solutions. Temperatures in the surrounding bath were controlled to *0.05" in all cases. A Zeiss differential interferometer was used to analyze the difference in concentration between the solutions on either side of the diaphragm cells. The classical diaphragm Cell equationlo was used to analyze the data log caP,(l
- X/6)
. b i r
1
= @t(l
- X/6)
(1)
The term (1 - X/6) is a correction for finite holdup in the frit which was first proposed by Barnes." The two liquids used were distilled water and reagent The Journal of Physical Chemistry
grade ethylene glycol. Various tests showed that the glycol contained less than 0.5% water. It was found necessary to degas both of the liquids before mixing the solutions. The solutions on either side of a cell typically differed in concentration by 1.5 wt %. The use of the differential interferometer made it possible to measure concentration differences of this size to an accuracy of 0.15% of the total difference in concentration. It is necessary to employ small concentration differences when one is dealing with horizontal diaphragm cells and with a solution of markedly varying density. When the densities of the solutions on either side of the diaphragm differ greatly, bulk flow caused by pressure gradients across the vertical diaphragm tends to provide apparent values of diffusivity which are far higher than the molecular values. At the start of a run, the entire cell was filled with the water-rich solution and allowed to stand in the bath for several hours. This solution was then removed from one side of the cell, and after several washings with the glycol-rich solution this side of the cell was filled with the latter solution. A run normally lasted 2 to 3 days. Since refractive index is a linear function of concentration over small ranges in concentration, the ratio of the interferometer readings for the initial and final concentration differences between compartments could be used directly in the left-hand side of eq 1.
Results The results of this experimental program are presented in Table I. The reported diffusivities are based upon the currently prevalent Chapman-Cowling definition,12by which
D = - j /1 PVWl
(2)
At constant temperature and either at constant pressure or for incompressible fluids, this definition is equivalent to
D
=
- j P/V P1
(3)
(4) R. R. Irani and A. W. Adamson, J. Phys. Chem., 64, 199 (1960). (5) G. 0. Curme and F. Johnston, "Glycols," Reinhold Publishing co.,New York, N. y., 1952. (6) C. Rossi, E. Bianchi, and A. Rossi, J. Chim. Phys., 55,93 (1958). (7) F. H. Garner and P. J. M. Marchant, Trans. Inst. Chem. Enurs. (London), 39, 397 (1961). (8) J. T. Holmes, U. 5. Atomic Energy Commission Report UCRL9145 (1960). (9) J. T.Holmes, C. R. Wilke, and D. R. Olander, J. Phys. Chem., 67, 1469 (1963). (10) A. R. Gordon, Ann. N . Y.Acad. Sci., 46,285 (1945). (11) C. Barnes, Physics, 5 , 4 (1934). (12) E. N. Lightfoot and E. L. Cussler, Jr., Chem. Eng. Progr. Symp. Ser., 65, N ~5 . 8 , (1965). ~
LIQUIDDIFFUSIVITIES IN THE GLYCOL-WATER SYSTEM
2501
Since the diaphragm cell configuration corresponds closely to no net volume flux across the diaphragm, eq 3 leads directly to eq 1. 40
t
Table I: Experimental Diffusion Coefficients x l@(cmz/sec) Temp, "C
0.70
22.5
25 40 55 70
1.160 1.712 2.256 2.75
0.933 1.177 1.802 2.20
Wt % glycol 43.4 62.7
0.710 0.954 1.401
...
0.509 0.751 1.155
...
82.0
99.2
0.360 0.569 0.938
0.2% 0.500 0.706 1.13
...
A complete set of data is not presented at 70" since the data taken for the unreported compositions were reasonably scattered. At 70", cell handling and expansion and contraction become major problems. All of the values reported are an average of at least two values measured in different cells. The deviation from the average in all cases is less than 5% of the reported figure. This i s within the estimated experimental error. The concentrations are presented as average weight per cent.
Discussion The data were first of all compared with those previously reported. A comparison can be made with some of the data of Garner and Marchant.' While comparable values at 25" agreed to better than 5%, their data at 40" are considerably lower than the present values. A graph of Dq/T as a function of temperature (Figure 3) casts some doubt upon the 40" data of Garner and Marchant. Several theories have been proposed to predict the effect of concentration level upon diffusivity. These have been summarized by Bearman, who has concluded that for regular solutions (as defined by Bearman) most of the prevalent theories are equivalent to the form
The glycol-water system clearly represents a case where the assumptions leading to eq 4 are not well obeyed; however, it is still interesting to assess the capability of this equation to describe the data. For example, in the present case the factor containing the activity is unity; hence, the product of the diffusivity and viscosity should be a linear function of mole fraction. Figure 1. shows the data for 40" plotted in this way. The viscosity data are taken from the book by Curme and J o h n ~ t o n . ~For comparison with eq 4,
-
80
0.2
0.6
0.4
1.0
0.8
Mole fraction glycol
Figure 1. Plot of Ds as a function of mole fraction of ethylene glycol a t 40": -, best fit of data; -I eq 4.
---
D1" is taken to be the experimental value a t 0.7 wt % glycol. A least-squares analysis indicates that a straight line fits the data well. The standard deviation in the slope is less than 5%; however, the slope is about 30% higher than predicted by eq 4. The results obtained at 25 and 55" are quite similar in nature. The data of Figure 1 and for the other temperatures appear to be best correlated by an equation originally suggested by Roseveare, Powell, and Eyring13 on a semiempirical basis
Two experimental values of diffusivity are required for eq 5 rather than the single value required for eq 4; thus an improved agreement is not surprising. The degree of agreement of the present data with eq 5 is nonetheless remarkable in view of the fact that the viscosity varies by a factor of 12 to 17 and the diffusivity varies by a factor of 3 to 5 across the range of compositions at a given temperature. Equation 5 may also be obtained from eq 12b given by Bearman,' using Bearman's prediction that D1q and D2v (his nomenclature) should be independent of concentration. ~~~~~
~
~
(13) W. E. Roseveare, R. E. Powell, and H. Eyring, J. AppE. Phys., 12, 669 (1941).
Volume 70,Number 8 August 1966
CHARLESH. BYERSAND C. JUDSON KING
2502
r
313
0.2
0.4
0.6
0.8
1.0
Weight fraction glycol Activation energy as a function of Figure 2. weight fraction of ethylene glycol.
99.2 '?/e c
2
.
0
I
.20
30
40
50
60
70
t ("C) Figure 3. Plot of Dq/T as a function of temperature: A, present study; 0, Garner and Marchant; H, Rossi, et al. Arrow indicates 40' data of Garner and Marchant.
glycol-water. For the hexane-carbon tetrachloride system, eq 4 predicts a substantial decrease in Dv with increasing mole fraction of carbon tetrachloride, while the opposite is found experimentally. Hence, the use of the condition Dlmq2/D2mql = s/a (or Dl/DZ = U ~ / U I ) to bring about the transformation from eq 5 to eq 4 appears not to be experimentally justified in most cases. As pointed out in the Introduction, eq 4 also can fail seriously in cases where the two components of a solution differ markedly in p ~ l a r i t y . ~ An activation energy for diffusion may be found by plotting the natural logarithm of diffusivity as a function of the reciprocal of absolute temperature. The best least-squares fit of the data produced a standard error in the resulting activation energy of less than 10%. Figure 2 shows the variation of activation energy with mole fraction. When this curve is compared with the one presented in the work of Garner and Marchant' for water-propane 1-2 diol, a similarity of shape is evident. As expected, the larger molecule presents a higher diffusion barrier. A good discussion of the interpretation of such a plot is given by Garner and Marchant. Most of the classical theories for diffusivity a t infinite dilution postulate that the group Dq/T is a constant. Recently, OlanderI5has shown, from a generalization of the Eyring theory, that this may not generally be the case. Only identical molecules can be expected to have similar free energies of activation for both diffusion and viscosity; hence, one could expect the grouping Dq/T to be a function of temperature. Figure 3 shows the correlation of Dq/T and temperature. While there is a certain amount of scatter in the data, the conclusion must be that no trend with respect to temperature is discernible.
Acknowledgments. This work was performed under the auspices of the U. S. Atomic Energy Commission. Thanks are due D. L. Osterholt for his patient laboratory assistance.
Notations a
D
Equation 5 also agrees well in general with the data of Caldwell and Babb14 for the systems benzenecarbon tetrachloride, chlorobenzene-bromobenzene,and toluene-chlorobenzene and with the data of Bidlack and Anderson2 for hexane-carbon tetrachloride, hexane-dodecane, hexane-hexadecane, and heptane-hexadecane. Equation 4 agrees reasonably well with the Caldwell and Babb data where the molal volumes are nearly equal, but the Bidlack and Anderson data show a lack of agreement with eq 4 similar to that found for The J O U Tof~Physical Chemistry
Esct
j
P P T t V
W
5
Solute activity Diffusion coefficient, cmZ/sec Activation energy for diffusion, kcal/mole Mass flux relative to mass average velocity, g/cm2 sec Mass flux relative to volume average velocity, g/cm2 sec Pressure, atm Temperature, O K Temperature, "C Molar volume of pure component, cms/mole Weight fraction Mole fraction
(14) C. S. Caldwell and A. L. Babb, J . Phya. Chem., 60,51 (1956). (15) D.R. Olander, A. I. Ch. E . J., 9, 207 (1963).
EXCITED STATES IN PHOTOLYSIS OF CARBON SUBOXIDE
6
e 7
Ap p
Cell constant Total time, sec Volume of frit/volume of one cell chamber Viscosity, cp Difference in concentration across the diaphragm in the diaphragm cell, g/cma Concentration, g/cm;a with no subscript, p = density
2503
Subscripts i Initial f Final 1 , 2 Chemical component number
Superscripts m
At infinite dilution
The Role of Excited States in the Photolysis of Carbon Suboxide
by R. B. Cundall, A. S. Davies, and T. F. Palmer Department of Chemistry, The University, Nottingham, England
(Received January 86, 1966)
The photolysis of carbon suboxide in the presence of cis-butene-2 has been examined, and the yields of carbon monoxide and trans-butene-2 have been measured. At 2537 A, the decomposition occurs largely from the triplet state. At 3130 A, decomposition is not quenched by butene-2, but isomerization occurs showing that a triplet state is formed but does not decompose. The nature of the C20 radicals is briefly discussed.
the effect of olefins, a brief investigation of the photoStudies on the photolysis of carbon suboxide have chemistry of cis-butene-2-carbon suboxide mixtures indicated that dissociation, leading to the production of was carried out. carbon monoxide and polymerization, occurs by comThe product analysis, which was performed by gas plex mechanisms.' The introduction of ethylene has been shown to yield allene2 and methyla~etylene.~-~chromatography and mass spectrometry, was directed I n the presence of an excess of ethylene, 1 mole of C3H4 toward (a) an examination of the effect of added olefin upon carbon monoxide yields, (b) the production of is formed for every 2 moles of carbon monoxide. Fortrans-butene-2, the formation of which from the cismation of a colored polymer was suppressed by the presence of olefin. isomer may occur by a triplet-triplet transfer process,' I n the published work there is little discussion of the and (c) formation of higher molecular weight products role of excited states of the suboxide, and no quantum such as l13-dimethylallene by addition of a carbon atom from the C20 radical into the carbon-carbon yield measurements are reported, considerably limiting any speculations on the nature of the primary process(es). Bayes6 concludes that, since his CO/CaH4 product ratios are unaffected by nitric oxide and (1) H. W. Thompson and N. Healey, Proc. Rog. Soc. (London), A157, 331 (1936). oxygen at short wavelengths, singlet state CzO radicals (2) K. D.Bayes, J . Am. C h m . SOC.,8 3 , 3712 (1961). are involved, and, on the basis of the spin conserva(3) R.T.Mullen and A. P. Wolf, ibid., 84, 3214 (1962). tion rule, it would appear that dissociation of the sub(4) K. D. Bayes, ibid., 84, 4077 (1962). oxide occurs from the singlet manifold. Fluorescence (5) R. T. K. Baker, J. A. Kerr, and A. F. Trotman-Diokenson, or phosphorescence has not been observed with carbon Chem. Commun., 358 (1965). suboxide.' I n order to inquire further into the exist( 6 ) K. D.Bayes, J. Am. Chem. SOC.,8 5 , 1730 (1963). ence and nature of suspected transients and to elucidate (7) R. B. Cundall and D. G. Milne, ibid.,83, 3902 (1961). Volume 70, Number 8 August 1966
