D. L. BIDLACK AND D. I 1) and positively deviating (d In a/ d In X ) < 1) systems from Raoult’s law. It has been suggested,8 since ideal solutions follow theory and associating systems do not, that association inhibits movement of the molecules and causes the deviation from theory. By investigating a group of nonideal solutions that do not associate, the effect of nonideality can be determined wheri the diffusion mechanism is not complicated by association.
Experimental Method and Materials. The diffusion data were obtained using a diffusiometer similar to the one described by Caldwell, Hall, and Babb.lo Although the (1) C. S.Caldwell and A. L. Babb, J . P h y s . Chem., 60, 51 (1956). (2) See P. A. Johnson and A. L. Babb, Chem. Rev., 56, 387 (1956); A. P. Hardt, D. K. Anderson, R. Rathbun, B. W. Mar, and A. L. Babb, J . P h y s . Chem., 6 3 , 2059 (1959); P. C. Carman and L. Miller, T r a n s . Faraday SOC.,55, 1838 (1959); D. K. Anderson. J. R. Hall, and A. 1,. Babb, J . P h y s . Chem., 62, 404 (1958); and ref. 8 and 9 for discussion and further references to associating systems (3) G. S. Hartley and J. Crank, T r a n s . Faraday SOC.,45, 801 (1949). (4) R. -Mills, J . Phgs. Chem., 67, 600 (1963). (5) R. J. Bearman, ibid., 65, 1961 (1961). (6) 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. (7) R. J. Bearman and P . F. Jones, J . Chem. Phys.. 3 3 , 1432 (1960). (8) B. R. Hammond and R. H. Stokes, Trans. Faraday Soc., 52, 781 (1956). ,9) D. K. Anderson and A. L. Babb, J . P h y s . Chem., 65, 1281 (l? , . (1( S.Caldwell, J. R. Hall, and A. L. Babb, Rev. Sci. Instr., 28, 8 1 ~,1957). % .:
MUTUAL DIFFUSION IN NOXIDEAL, KOKASSOCIATIPG LIQUIDSYSTEMS
3791
Table I : Summary of Experimental D a t a
Av. mole fraction of hexadecane Difference in mole fraction between upper and lower level in cell D . ~ BX cIn.2/sec. Av. mole fraction of dodecane Difference in mole fracbion between upper and lower level! in cell DABX cm.2/sec. Av. mole fraction of CC1, Difference in mole fraction between upper and lower level in cell DAB X 10-5, cm.2/sec.
Mole fraction of hexadecane CP. Density, g./cm.3
7,
Mole fraction of dodecane CP. Density, g./cm.3
7,
Mole fraction of CC4 CP. Density, g./cm.3
7,
lvIutual diffusion coefficients Heptane-hexadecane 0 0056 0 1064 0 2024 0 0112 0 0124 0 0172
0 3934 0 0161
0.5821 0,0362
0.7920 0.0343
0.9761 0.0478
1.775
1.238
1.065
0.895
0.760
0.3623 0.0253
0.5981 0.0317
0 7909 0,0336
0 9755 0 0491
2 . 066
1.799
1.618
1,450
0 . 5454 0 . 0097
0.7497 0,0098
0,9893 0.0215
2,368
1 ,943
1.487
0,5795 1 ,5520 0.7463
0.7867 2.2020 0,7596
1,000 3.0306 0.7698
0,6050 0.8243 0,7205
0.8064 1 ,0673 0.7340
1.000 1.3379 0,7450
0.5869 0.5067 1,1318
0,7906 0.6461 1,3385
1.000 0,8963 1,5842
0,0058 0.0116
1,586 1.451 Hexane-dodecane 0.1013 0,1989 0.0115 0.0160
2.533 2.327 Hexane-carbon tetrachloride 0.0042 0.1489 0,3234 0.0102 0,0084 0.0112 2,729
3,388 2.938 Solution viscosities and densities Heptane-hexadecane 0.4067 0 0.2110 0.7064 1,1020 0.3893 0.7315 0.6796 0.7117 Hexane-dodecane 0,4248 0 0,1924 0.6351 0.2958 0,4343 0.6550 0 6818 0.7059 Hexane-carbon tetrachloride 0.3869 0 0,1'729 0.3422 0.4102 0.2958 0.7803 0,9514 0 6550 3.858
exact details diff er !somewhat from their apparatus, the optical quality and experimental methods involved are essentially the same. That paper describes both the apparatus and method in great detail and will not be repeated here. The experimental diff usivities were obtained by measuring the interdiffusion of two solutions of slightly different concentration. The diffusion coefficient is taken as that of a solution with a concentration equal to the average of the two solutions. The accuracy of the diffusiometer was determined by comparing diff usivities of seven sucrose solutions with The values in all cases data of Gosting and deviated by less than 1% and had an average deviation of 0.5%. Viscosities were obtained with an Ostwald-Fenske type viscosimeter, and densities were obtained with a 10-cc. glass specific gravity bottle. The results of t h k work are recorded in Table I. The mutual diffusion coefficients were measured at a temperature of 25.1 f 0.05', viscosities at 25.0 f 0.05', and densities a t 25 i 1'. The hexane, heptane , dodecane, and hexadecane were purchased from Matheson Coleman and Bell Co. The hexane was Spectroquality grade, the heptane
Chromatoquality, and the dodecane and hexadecaiie were 99+% (olefin free) pure. Spectro grade carbon tetrachloride was purchased from Eastman Organic Chemical Co. The purity of the chemicals were further confirmed by comparing their densities and refractive indices with values given by Timmermans. 1 2 See Table 11. -
~~
Table I1 : Comparison of Physical Constants with Previous D a t a --Density This work
Hexane Heptane Dodecane Hexadecane Carbon tetrachloride a
0.6550 0,6796 0.7450 0.7698 1 ,5842
a t 25'--
Ref. 12
0.6549" 0.679P 0.7451 0.7699 1,5845"
--Refractive index, n%This Ref.
work
1.3720 1 3855 1 4193 1 4319 1.4570
12
1,3723" 1.3852
