Communications to the IEditor
I 200
2 2'0
Figure 9 .
Raman spectra of
2307
13-
I
I80
I i , 160 140 Raman Shift, an-'
I
I 100
1
80
3
solutions.
References m a l Notes (1) M. E. Heyde, L. Rimai,
I
1 20
H. (3. Kilponen, and D. Gill, J. Amer. Chem. Soc.,
94,5222 (1972). (2)K. Kaya, N. Nlikami, Y . Ildagawa, and M. Ito, Chem. Phys. Lett., 16, 151 (1972). (3)W. Kiefer and H. J. Elernstein, Chem, Phys. Left., 16,5 (1972). (4)E. Fermi, Z.Phys., 71, 250 (1931). (5)E. E. Genser antl R. E. Connick. J. Chem. Phys., 58, 990 (1973). (6)D. A. French and J. A. Effenberger, Abstracts of Papers, 140th National Meeting of the Americm Chemical Society, Chicago, 111.. Sept 1961, Abstract 25T. (7)I?. W. Ramette wld R. VI/. Sanford, Jr., J. Amer. Chem. SOC., 87, 5001 (1965). (8)M. Dwvies and E. Gwynnc?,J. Amer. Chem. Soc., 74,2748 (1952). (9)R. C.L. Mooney Slater, Acta Crysta//ogr.,12, 187 (1959). (10)W. (;abes, D. d. Stufkens, and H. Gerding, J. Mol. Struct. 17, 329 (1973).
Shell Development Company P. 0.Box 48 I Houston, Texas 7700f
K. I?.LOOS* A. C. Jones
chemical composition of the radioactive solution in capillaries and the nonradioactive solution surrounding the capillaries was the same. Reagent grade chemicals (POCh, Poland) were purified by double distillation with metallic sodium. We used benzene-14C (CEA, France), toluene-14C (Isocomerz, G.D.R.), and c y ~ l o h e x a n e - ~(Amersham, ~C England) for the preparation of radioactive solutions. The radioactivity of the tracers was determined in a toluene solution of 2,5-diphenyloxazole (PPO), 4 g/I. and p - bis[2(5phenyloxazolyl)]benzene (POPOP), 0.3 gfl. with a liquid scintillation counter (USB, Poland) connected to a scaler (PEL-5, ZWN-25, Poland). The diffusion times, varying within the range 16-25 hr, were adjusted to result in diffusion of an amount corresponding to half of the initial radioactivity of the solution in capillaries. The tracer diffusion coefficients were calculated as mean values from more than nine experiments. We determined them from the equation
Received February I I , 1974; Revised Manuscript ReceivedAugust 12, 1974
Self-Diffusion in Liquid Binary Solutions
Sir: Investigations of the self-diffusion of binary organic solutions have furnished valuable information as to the inner structure solutions and molecular interactions. However, a description of the relationship between the structure of liquids antl the diffusion rate is hardly possible. We have determined the dependence of the tracer diffusion coefficient o f the components of a liquid mixture on the system composition, taking benzene-toluene as an example of an ideel system and benzene-cyclohexane as a nonideal one. We used the capillary-cell methodl and determined tracer diffusion coefficients for benzene-14C (DB), toluenel 4 C ( ( D ~ )and ., cy~lohexane-'~C ( D c ] at 25.00 f 0.05'. The
where A0 and A are the radioactivities of solutions in capillaries before and after diffusion, respectively; 1 is the capillary length, determined by the mercury method and verified by the self-diffusion coefficient of benzene-14C, D go = 2.18 cm2/sec.2 Figure 1 shows the dependence of diffusion eoei'fieients D B and D T for the benzene-toluene system on the mole fraction of toluene X T and Figure 2 shows the dependence of D B and D c on the mole fraction of cyclohexane X C . We ~ have found that the tracer diffusion coefficient of benzene14C is equal to the tracer diffusion coefficient of toluene14C for all solution compositions. The dependence on the mole fraction of toluene is described by the equation DB = DT = DBo - (DBo - DTo)xT
(2 )
ox
DB = DT =
DB'x,
+
DTOX,
The Journal of Physical Chemistry, Vol. 78, No. 22, 1974
Communications to the Editor
2305
us. mole fraction of cyclohexane shows maximum for I c = 0.4 but D c shows a minimum for x c = 0.6. In the range of x c = 0.4-0.6 this system reveals the largest deviation from ideality. We tested the product of the tracer diffusion coefficient and the viscosity of the solution, Div, and found that in the benzene-toluene system this product changes with the composition for both components of the solution. In benzene-cyclohexane solutions the product of the viscosity and benzene- 14C diffusion coefficient ( D~ 7 was ) constant for all mole fraction of cyclohexane, but the cyclohexane-14C diffusion coefficient fulfills the equation D,q/(d
t Q5
x,
f,O
Figure I. Benzene-'"C (0) and t~luene-'~C (A)diffusion coefficients as a function of mole fraction of toluene at 25.0'.
.a0
9.0
I
I
as
10 XC
Ben~ana-'~C (0)and ~yclohexane-'~C (A)diffusion coefficients as a. function 'of mole fraction of cyclohexane at 25.0'.
Figure 2.
where DBO and DTO are the self-diffusion coefficients of benzene and toluene, respectively, and X B = 1 - XT. The relationships between D B and D C and the composition of the benzene- cyclohexane system are parabolical, and D B
The Journal of Physical Chemistry, Voi. 78, No. 22, 1974
In a,/d
In x c ) = constant
(3 )
where (d In ac/d In I C ) is the thermodynamic factor representing the systems deviation from ideality. These experimental data show that the inner structure of the solution is very complex. The molecules probably form aggregates and the diffusion process is related to the transfer of these species rather than to single molecules. The size and structure of the aggregates vary with the composition of liquids. More accurate information about the inner structure of solution will probably be obtained by the examination of the temperature dependence of the tracer diffusion coefficient. Such studies are in progress in our laboratory. Supplementary Material Available. Tables I and 11, tabular listings of the data shown in Figures 1 and 2, will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the.supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number JPC-742307.
References and Notes (1) S. Anderson and J. K. Saddington, J. Chem. Sac., S 381 (1949). (2) R. R . lrani and A. W. Adamson, J. Phys. Chem., 62, 1517 (1958). (3) See paragraph at end of text regarding supplementary material.
lnsitute of Radiation Chemistry Lodz, Poland Received April 75, 797.4
~
Reimschussel' E. Hawlicka
