2756
COMMUNICATIONB TO THE EDITOR
Relations between Mutual and Intradiffusion Coefficients in Aqueous Sucrose Solutions
0.8
0.6 0.4
(" 0.2
I .o
1.5
N
2 .o
2.5
Figure 1. A plot of the AT product u8. normality for concentrated solutions of tetra-n-pentylamrnonium thiocyanate in nitrobenzene at 52".
assumption that Aq/(Aq), is the high-concentration analog of the Arrhenius fraction of dissociation because we would have values of a greater than unity. Also, this observation weakens the hypothesis that the molten salt is completely free of ion aggregates; however, the latter condition may yet prevail. The fact that Aq goes through a maximum may only indicate that the mobility of the ions is enhanced to such an extent by the rapid drop in viscosity that there results an equivalent conductance increase which completely predominates in the Aq product. Microscopically, it is possible that the nitrobenzene molecule does not distort the symmetrical field about the ions as KEK suggest to account for association of ions upon addition of solvent to the fused salt. Nitrobenzene has a dipole moment of 4.23 D.6 and is a large molecule; it may very easily fit into the molten salt structure as an electrical and volume substitute for the cation plus the anion of the electrolyte. There may be only a small change in the electrical forces which operate in the fused salt when relatively few large polar molecules are present. A complete report of the conductance-viscosity behavior of this system will be submitted as soon as we have completed measurements in the more dilute region. (6) S. Glasstone, "Textbook of Physical Chemistry," 2nd ed, D. Van Nostrand C o . , Inc., Princeton, N. J., 1946, p 551.
Sir: We have been measuring by the diaphragm-cell method the intradiffusion' coefficients of a series of organic molecules in aqueous s o l u t i ~ n with ~ * ~ a view to calculating and comparing friction coefficients for the solutes. The sucrose-water system is of some interest in this respect. Irani and Adamson4 had previously measured intradiff usion coefficients for sucrose in this system. The curve so obtained when their coefficients were graphed against concentration first came below the corresponding curve for the mutualdiffusion coefficient D, and then at about 0.6 M crossed the latter curve and remained appreciably above it. Irani and Adamson realized that this behavior would not be expected since the intradiffusion coefficients depend on both sucrose-water and sucrose-sucrose interactions, whereas mutual coefficients depend only on the former. From size considerations, one would assume that the sucrose-sucrose interaction would be the greater so that the intradiffusion coefficient would be correspondingly smaller for a given concentration, and further that the divergence would increase with concentration. To explain their data, Irani and Adamson therefore suggested that at higher concentrations sucrose molecules can slide past one another by a special process such as mutual rotation. Another consequence resulting from the nature of Irani and Adamson's data is related to the dependence of the friction coefficients on concentration. The equation normally used for calculating friction coefficients is
RIZ= RT[
V&,(d In a,/d C,) lOOOD,
-
-I
1 (Dt>,CS
where Rlz is the friction coefficient for the isotopic forms of sucrose, Vo is the partial molal volume of solvent in milliliters/mole, Coand C, are the total concentration of solvent and sucrose, respectively, in moles/liter, d In a,/d C, is an activity term, and (Dt), the intradiffusion coefficient for sucrose. It is apparent that since the right-hand side of eq 1 involves essentially the difference between D, and (Dt),, then the cross-over of the curves would mean that the friction coefficients Rlz would change sign with concentration. No other set of friction coefficients so far calculated exhibits this type of behavior.
DEPARTMENT OF CHEMISTRY FREDERICK R. LONQO OF TECHNOLOGY H. DAUM (1) For a definition of intradiffusion, see ref 2. DREXEL INSTITGTE PETER PHILADELPHIA, PENNSYLVANIA 19104 RICHARD CHAPMAN (2) J. G. Albright and R. Mills, J. Phys. Chem., 69, 3120 (1965). WILLIAMG. THOMAS (3) J. G. Albright, ibid., 70, 2299 (1966). RECEIVEDAPRIL14, 1967 (4) R. R. Irani and A. W. Adamson, ibid., 62, 1517 (1958).
The Journal of Physic& Chemistry
(1)
COMMUNICATIONS TO THE EDITOR
2757
As the liquid scintillation counting technique has greatly improved the accuracy of C14 ana.lysis in the past decade, we decided to check a few sucrose intradiffusion coefficients to see if the above effect was real. The difFusion and counting techniques used have been adequately described e l s e ~ h e r e . ~The , ~ intradiffusion coefficients 60 measured are given in Table I. For comparison with other diffusion data, these (Dt)v values are graphed in Figure 1. The Gouy data from which the D , curve has been derived have been reported in separate concentration regions by Gosting and Morris,6 Gladden and Dole,Band E1lerton.l Table I : Intradiffusion Coefficients of Sucrose in Aqueous Solution a t 25" C, mole/l.
( D t h x 106 cma/sec
mole/l.
cmg/sec
0.00002 0.00285 0.1518
0.524 0.525 0.468
0.4086 0.7717 0.9272
0.398 0.299 0.267
C,
(Dt),X
5.0
7'
105
Clearly, the values of the intradiff usion coefficients measured in this work differ considerably from those of Irani and Adamson14 the discrepancy a t 1 M being -20%. Further, our intradiffusion data all lie below the mutual diffusion data in a manner consistent with the other systems so far studied. No special diffusive process a t high concentration needs now to be postulated. For the present, we have not extended our experiments beyond a concentration of 1 M because the normal stirring techniques are becoming inadequate here because of the rapidly increasing viscosity. Tests using colored liquid have been carried out to show that a stirring rate of 75 rpm gives barely adequate mixing at 1 M (comparable to 54 rpm for 0.5 M KC1 solution). In the 2 M region, the former speed was quite inadequate; complete mixing required about 10 min. We intend to extend these measurements when a new type of diaphragm cell, in which the compartment solutions are circulated by pumping, has been developed and tested. As these further measurements may not be completed for a year or more, we are reporting the present data now, as they serve to remove the anomalies discussed above. The trace sucrose intradiff usion values agree with the corresponding extrapolated Gouy value to within *0.2%, indicating the general accuracy of our method. We would estimate our overall precision a t this stage to be about f 1%. (5) L. J. Gosting and M. 9. Morris, J. Am. Chem. Soc., 71, 1998 (1949). (6) J. K.Gladden and M. Dole, ibid., 75, 3900 (1953). (7) H.D. Ellerton, Ph.D. Thesis, University of Adelaide, Australia, 1966.
4.0
P
3
DIFFUSIONRESEARCH UNIT RESEARCH SCHOOL OF PHYSICAL SCIENCES AUSTRALIAN NATIONAL UNIVERSITY CANBERRA, AUSTRALIA
.o-
2
X 4
J. F. TILLEY R. MILLS
RECEIVED APRIL20, 1967 3.0
Hydrophobic Hypercoiling i n Copolymers of Maleic Acid and Alkyl Vinyl Ethers 2.0 0
0.5 C, mole 1. -1.
1.0
Figure 1. Comparison of diffusion data in aqueous sucrose solutions a t 25': 0, intradiffusion (Dt), data, this work; , intradiffusion (Dt),data, Irani and Adamson; - - - _, mutual-diffusion D , Gouy data.
-
Sir: Potentiometric titrations of a hydrolyzed alternating copolymer of maleic anhydride and n-butyl vinyl ether indicate that there occurs a conformational transition which is not exhibited by a copolymer of maleic anhydride and ethyl vinyl ether. These results are presented in Figure 1, where pK,, defined by the relation listed as eq 1 Volume 71, Number 8 July 1967
