206
NOTE6
iodobenzenc with J r added (0.1 M ) resulted in a strong suppression of the iodoriium product. Prcvious studies of the radiation chemistry of chlorobenzene have shown that the primary chemical reaction upon irradiation is the formation of phenyl radicals and chlorine atoms.6 In the presence of iodoberizene the phenyl radical could then add to form the diphenyliodonium radicals. Proof t,hat, the phenyl rings do indeed come from both the chloro- and bromobenzene and the iodoberizcne was obtained by irradiation of pchlorotolurne and p-bromotoluene with 7% iodobenzene. Both these mixtures yielded the mixed iodonium compounds (4-met~hyldiphenyliodonium chloride and bromide diiodide), Conversion to the known 4-methyl diphenyliodonium bromide (m.p. 174- 177"") served to prove the struct,ures. The eflect of excess iodine would certainly hinder the phenyl radical attack on iodobenzcne. However, thc relative ineffectiveness of iodine scaverigirig indicates that plieriyl radical trappirig by iodobenecne is a fast reaction. The following scheme is consistent with the results obtained and reported in this study.
+ X*
AR-X +AR.
(11
fast
+ PhI +AR,PhI. fast ARPhI. + I +ARPhI+IAR.
1.
+ 1.
-
(3)
fat
PhI +Phi. (8)
(2)
12
+ 1.
(4) (5)
A. Xlxi:I,ac:hlan and It. I,. hfi:Cxrt,l~y,.I. A m . Chcm. Sor.. 84, 2519 (1962).
Mutual IJiLFusion in the Liquid System Hexane-llexadecune
Experimental Method and Mntericsbs. The diffusion data were obtaincd using a diffusiometer very similar to the one described by Caldwll, Hall, arid Habb,a That paper describes both the apparatus and method in great detail and will not be repeated here. The experimental diffusivities were obtained by measuring thc mutual diffusion of two solutions of very nearly equal concentrations. The measured value was taken to be that of a solution with a concentration q u a l to the average of the two solutions. To trst the accuracy of this diffusiomctcr, diffusion coefficients for aqwous sucrose sohitions with conccntratioiis of 0.3751, 0.5027, arid 0.7506 g./ml. were compared with diffusivitics reported by Gosting and Morris * Seven runs were made at these corwentrations and the values obtained deviated by less than 1% in all cases from t,hc Costing and Morris data and had an average deviation of 0.5%. Viscosities w r c obtained with an Ostwald-Fwiske type viscometer and dcnsitics u-ere determined with a 10-Inl. glass spccific gravity bottle. The results of this work are rccordcd in Tablc I. Thc mutual diffusion coefficients were measured a t a temperature of 25.1 * 0.05", viscosities a t 25.0 + 0.05", and densities a t 25 f 1'. The chemicals for the investigation were purchased from Mathcson Coleman and Hell. The hexane was chromatography or spectroquality grade and the hexadecane was SS+% (olefin-free). In order to test the purity of thc chemicals, the refractivc index and density were compared with values given by Timmermans6 (see Tablc 11). Activity Data. The choice of thc sy8ttm was based partially 011 the availability of activity data. AIcGlashan and Williamsona mcasiircd tho activities at wvcral difterent temperatures and showed that a t 25' In
by
L).
fA
-0.110AXR2
-
0.00736X~~( 3 4x13)(1)
L. Uidlack and 1). K. Anderson
Lhpartmont of Chemical Engineering, Michigan State Univcraity, Bast Lansing, Michigan (Received August 1P, 1.963)
RLuch work has been done recently to study mutual diffusion of binary systems of liquids. Searly all of the systems studied were either idcall or nonideal with the nonideality attributable to association.* The purposc of this paper is to cxpand the understanding of liquid diffusion by prcsentirig accurate data for a nonassociating, nonidcal systmi. The system chosen wlts hexane-hrxadecanc in which the rionideality is ciaused by thc. unequal size of the moleculcs of thc two species. The .Journal of Physical Chemistry
C. S. Coldwell ond A. L. Rabb, J . Phgn. C h m . . 6 0 , 51 (1956). Scc P. A. Johnson and A. L. Babb, Chem. Rev., 56, 387 (1956); A. P. Hardt, D. K. A n d e r s o n , R. Rathhiin, l3. W. Mar, srd A. L. Rahh, J . Phyn. Chem., 63, 2059 (1959);.'1 C. (hriiirtn arid I,. M i l l P r , Truna. FarcuiaU SOC.,55, 1838 (1959); 1). K. Andrmon, ,J. R.. Hall, arid A. 1,. Babb, .I. Phys. Chem., 62, 404 (1958); and footriotr rofrreriees 8-13 for discussion and further refercnws to associated systems. C . S. Crtldwell, J. It. Hall, and A. 1,. Babb. Reu. Sei. Inslr., 28, 816 (1957). L. J. Gosting and >S. I.Morris. J . Am. Chem. SOC.,71, 1998 (1949). J. Tiinmnrmans. "Physico-Chemical Constants of Pure Organic Compounds," Elscwirr I'uhlishing Co.. h c . , New York. N. Y., 1950. M. L. AfcGlsshan and A. G. Williamson, Trans. Faraday h e . , 57, 588 (1961).
NOTES
207
Table I : Summary of Kxperimental Data Mutual diffueion coefficients 0.0953 0.1531 0.2504 0.0082 0.0096 0.0124
Av. mole fraction hexadecane IXfference in mole fraction between upper and lower level in cell D A H X 106, cm.2/sec.
0.00417 0.00833 2.193
1.933
Mole fraction, hexndecane
0 0.2958
7,centipoisea
Mole fraction, hexadecane
0 ,6550
Density, g./cm.3
0.3924 0.0108
0.6025 0.0153
0.7422 0,0320
0,9854 ,0293
1.665
1.492
1.254
1.108
. 8 668
Viscosities 0.1995 0.3978 ,6062 1.0166
0.5746 1,4530
0.8011 2.2091
1.O00 3.0306
1)emities ,0995 0.1995 ,6822 ,7017
0.3978 ,7277
0.6101 ,7480
0.7k32 ,7584
Table I1 : Comparison of Physical Constants with Previous Data
--Deneity This
work
Hexane Hexadecane
0.6550 0.7698
a t 25'-
Ref. 6
0,6549" 0.7699
Refractive index a t 25O (sodium lamp) Thia work Ref. 6
1.3720 1.4319
1 ,3723" 1.4325
Average of several recorded data.
where f A is the activity coefficient of hexane and XB is the mole fraction of hexadecane. From their experimental results and analysis of error, an estimation a t XB = 0.50 and 20' shows that In a A = -0.718 f 0.001, where aA is the activity of hexane. This is well within the accuracy required for our purposes.
Discussion Hartley and Crank' have shown that for nonideal systems the behavior of the mutual diffusion coefficient, DAB,is described by
RT ' X A+ x. 1 dhaA DAB= -- ___ f A -J d In XA Nq fB
1.
(2)
where X is mole fraction, a is the activity, 7 is the solution viscosity, f is a friction coefficient dependent on molccular size, and R, T , N have their usual definitions of gas constant, temperature, and Avogadro's number. The subscripts A and B refer to the two species of the system. Although there is some disagreement about Hartley and Crank's arguments,8-'o both the absolute rate theory" and the statistical mechanical approach8 agree with the Hartley-Crank theory that the quantity Dq/(d In a/d In X ) should be a straight line function with mole fraction a t constant temperature. The linearity of Dq forideal systems has been verified experimentally by Caldwell and Babb. However,
1.820
1.OOOO 0.7698
attempts to test for the linear behavior of Dn/(d In a/d In X) for nonideal systems have been unsuccessfula2 In all cases the activity correction overcorrects, sometimes by as much as several hundred per cent.I2 In one case, chloroform+ther,ll the activity correction was used with apparent success, but closer examination with more accurate data shows that the correction is also too large for this system.I3 The tendency to overcorrect is common for both negatively and positively deviating systems from Raoult's law. The overcorrection has been ascribed to association of the molecules in solution.l2~l8It is thought that the molecules, instead of acting as monomers during the diffusion process, form dimers and polymers or complexes with the other species in the system and are thus inhibited in their movement. Miller and CarmanI4 recently published a study of another nonideal, nonassociating system, heptanehexadecane, in which they compared self-diff usion with mutual diffusion. The activity correction term for this work is derived from eq. 1: d-1nfA _d In_ UA_ -- d_In ~a B - - 1 + = d In XA d 111XB d In XA 1 0.221oXAxB 0.0442XAXB(1 - 2xB)
+
+
(3)
(7) G . S. Hartley and J. Crank, Trans. Faruday Boc., 45,801 (1949). R. J. Bearman, J . Phy8. Chem., 65, 1961 (1961). (9) R. Mills, ibid., 67, 600 (1963). (10) J. G. Kirkwood, R. L. Baldwin, P. J. Dunlop, L. J. Costing, and G. Kegeles, J . Chem. Phys., 3 3 , 1505 (1960). (11) S.Glasstone, K. J. Laidler, and H. Eyring, "The Theory of Rate Processes," McGraw-Hill Book Co., Inc., New York, N. Y . , 1941, Chapter IX. (12) B. R. Hamrnond and R. 1%.Stokes, Trans. Faraday Soc., 5 2 , (8)
781 (1956). (13)
D. K. Anderson and A. L. Babb. J . Phys. Chem., 65, 1281 (1961).
(14)
L. Miller and P. C. Carman, Trans. Faradau Soc., 58, 1529 ( 1962).
Volume 68, Number 1
January, 1964
NOTER
208
3.0
On the System Niobium Pentoxide-Tantalum Pentoxide by G. 1'. Mohanty, L. J. Fiegel, and J.
W. Healy
A. 0. Smith Corpordion, Milwaukee 1. Wisconsin (Received August 16, 1963)
Investigations of phase equilibria in the system NbzOb-Taz06 have been reported by Shafer, Durkop, and Jori, l Goldschmidt,2 arid Holteberg and Reisman3 within the past ten years. Because of the variation of the results reported by these workers, it appeared worthwhile to re-examine this system in an attempt to resolve the discrepancies. This paper briefly reports the results of this investigation.
Experimental
0
0.2
0.4
0.6
0.8
1.0
Mole fraction hexadecane.
Ftgure l.-Dv and Dv/(d In a / d In X) a8 a function of mole fractton for the systeni hexane-hexadec~sne: 6, Dv; 0, &/(d In a / d In X ) ; - - -, linear or ideal behavior.
- -
In Fig. 1, Dq and Dq/(d In a/d In X ) are shown as functions of mole fraction along with the predicted linear behavior of Dq/(d ln a/d In X ) . The activity corrected product of the diffusivity and viscosity agrees quite closely with theory. At X R = 0.5, Dq/(d In a/d In X ) = 1.616 X lo-' dyne, which is 0.2% different from linearity. The maximum deviation of Dq/(d In a/d In X ) from linearity is 1.7% where the uncorrected Dq deviates 5.5%. The authors feel that 1.7% is within experimental error since Dn/(d In a/d In X ) is a result of four different sets of measured data. In any case, the tendency to overcorrect is not found in this system. Acknowledgment. This work was supported by a grant from the Petroleum Research Fund, administered by thc American Chemical Society. Grateful acknowledgment is hereby made to the donors of the fund. The .Journal of Physical Chemistry
Materials. Nb& and Taz05 obtained from A. D. Mackay and Co. were used for preparing all the samples. The purities wcre given as 99.9% for both the Nb206and Ta206. Sample Preparation. Before preparing the binary oxide samples, batches of pure IVbzOband Taz06 were pressed and fired in atmospheres of oxygen, argon, and 80% a~gon-20% oxygen to determine the effects of such treatments on the stoichiometry and structure of the base materials. Changes in the stoichiometry were followed by electrical resistivity measurements. A room temperature value of approximately 1O1O ohmcm. was obtained for the Nbz06sample fired in air a t 1400' while approximately 10" ohm-cm. was obtained for Taz06 fired a t 1520'. Attempts were also made a t melting the base materials both in an argon arc and in an oxygen acetylene flame. The resistivities of the solid Nbz06 samples prepared in this manner were in the range 10-100 ohm-cm. I n comparing these results with those of Greener and H i ~ t h e these ,~ low values indicated that the materials deviated greatly from stoichiometry, possibly from contaminations during melting. Consequently, the melting procedure was abandoned in favor of the sintering treatment in all subsequent sample preparations. Determinations of structural changes in Nbz06 confirmed the results reported by Holtzberg, Reisman, Berry, and BerkenbliL6 Once NbzO6 undergoes the (1) H. Shafer, A. Durkop, and M. Jori, 2.anorg. allgem. Chem., 275,
289 (1964). H. J. Goldschmidt, Metdurgia, 6 2 , 211, 241 (1960). F. Holtaberg and A. Reisman, J . Phys. Chem., 65, 1192 (1961). (4) E. H. Greener and W. M. Hirthe, J . Electrochem. Soc., 109, 600 (1962).
(2) (3)
