I. R. Shankland, P. S. Arora, and P. J. Dunlop
1518 CY
A, 6 €
A, us, v Vl
i2 Pi
degree of neutralization of polyelectrolyte acid defined in text algebraic electrical field strength ionic equivalent conductance of ions stoichiometric and effective number of counterions per polyelectrolyte molecule, respectively number of counterions per salt molecule number of coions per salt molecule dimensionless linear charge density parameter reduced self-diffusion coefficient of small ions
References and Notes (1) J. R. Huizenga, P. F. Grieger, and F. T. Wall, J. Am. Chem. Soc., 72, 2636, 4228 (1950). (2) G. S. Manning, J . Chem. Phys., 47, 2010 (1967). (3) A. Schmitt and R. Varoqui, J. Chem. Soc., Faraday Trans. 2 , 89, 1087 (1973). (4) D. I. Devore and G. S. Manning, J . Phys. Chem., 78, 1242 (1974). (5) G. S. Manning, J . Chem. Phys., 51, 923, 934 (1969). (6) A. Katchalsky and P. F. Curran, “Nonequilibrium Thermodynamics in Biophysics”, Harvard University Press, Cambridge, Mass., 1967.
(7) Laity’ was the first to show that this formulation Is an alternate way to write the usual linear force-flux relationships of irreversible thermodynamics. (8) R. W. Laity, J. Phys. Chem., 83, 80 (1959); J. Chem. Phys., 30, 682 (1959). (9) We consider here only frictional interactions with free counterions in order that the friction coefficients maintain their intrinsic significance. For a more detailed discussion, see ref 3. (10) Strictly speaking, the reduced selfdiffusion coefficient should include the f,, coefficient. However, it can be shown that, for an aqueous sodium chloride solution up to 1 M concentration, such a Coefficient is apparently negligible.” (1 1) A. Schmitt, ThBse, University Louis Pasteur, Strasbourg, 1972. (12) In these formulas, we neglecteda coefficient 6 = (f12uf21y/(flwufh~, which is always much less than one, as it can be seen from data in Appendix I1 or in ref 11. (13) R. Varoqui and A. Schmltt, Biopolymers, 11, 1119 (1972). (14) A. Schmitt and R. Varoqui, Eur. Polym. J., 11, 1, 9 (1974). (15) 0. S. Manning, Biopolymers, 14, 1991 (1975). (16) W. P. J. T. van der Drift, Thesis, Rijksuniversiteit, Utrecht, 1975. (17) R. A. Robinson and R. H. Stokes, “Electrolytes”, Academic Press, New York, N.Y., 1955. (18) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electroiytlc Solutions”, 3rd ed, Rheinhold, New York, N.Y., 1958. (19) T. W. Chapman, FhD. Thesis, University of California, Berkeley, 1967.
Isotope Effect in Diffusion of Perdeuteriobenzene and Benzene in a Series of Normal Hydrocarbons at 25 O C I a n R. Shankland, Pawlttar S. Arora, and Peter J. Dunlop” Department of Physical and Inorganic Chemistry, University of Adelaide, Adelaide, South Australia, 500 1 (Received Februaty 22, 1977)
Binary diffusion coefficients have been measured for benzene and perdeuteriobenzene diffusing in n-pentane, n-hexane, n-heptane, and n-hexadecane at 25 “C, and used to study the isotope effect in these systems. The isotope effect is not proportionalto the square root of the molecular weight of the isotopic species, and appears to be related to the viscosity of the solvent as suggested by Aoyagi and Albright.
In a number of recent papers’-7 limiting binary diffusion coefficients, Do, and corresponding tracer diffusion coefficients,DT,have been reported for various isotopically labeled benzenes diffusing in various solvents at 25 “C. In most cases the data indicated a very slight linear dependence on the mass of the tracer species in concordance with the theoretical predictions of Friedmanqs However the tracer diffusion coefficients were not inversely proportional to the square root of the mass of the tracer, as has sometimes been suggested,2or to the reduced mass of the system. The purpose of this paper is to report binary dffusion coefficientsfor liquid systems containing benzene (C6H6) or perdeuteriobenzene (C6D6)with the solvents n-pentane, n-hexane, n-heptane, and n-hexadecane, which have been extrapolated to yield limiting mutual (or tracer) diffusion coefficients for both C6H6and C6D6. These solvents were chosen to complete a series of similar studies undertaken in this lab~ratory,’*~-~ in order to investigate how the mass dependence of tracer diffusion in liquids varies with the nature of the solvent.
Experimental Section and Discussion All binary diffusion coefficients were measured with a Gouy diffusiometer’O and a special diffusion cell which have been described elsewhere,’lJ2 as have also the experimental techniques and computations that are necessary to obtain the diffusion coefficients. As pentane and hexane are highly volatile solvents, the volumes above the solutions in the diffusion cell were kept saturated with The Journal of Physical Chemistty, Vol. 8 1, No. 15, 1977
TABLE 11: Values of Extrapolated Mutual Diffusion Coefficients
10” C6H6t C6H6+ C6H6+ C6H6+
n-pentane n-hexane n-heptane
n-hexadecane
109D0(mZ s-l) error 6.023 1.0 4.758
3.858 0.8860
0.8 0.7 0.1
10”
109DT(m2 s - l ) error C6D6+ C6D6+ C6D, + C,D6 +
n-pentane n-hexane
n-heptane n-hexadecane
5.951 4.7 24 3.833 0.8848
1.0 0.8 0.7 0.1
vapor from reservoirs containing mixtures a t the same concentrations. This precaution was necessary to minimize the effects of evaporation which would alter the relative concentrations of the two components during an experiment. All liquids used were analyzed by GPC and found to contain less than 0.05% impurity except the c6D6which contained less than 0.4% impurity. The n-pentane, nhexane, and n-hexadecane were obtained from Fluka, Switzerland; the n-heptane from Aldrich, Wisc.; the perdeuteriobenzene from ICN Pharmaceuticals, Calif. The latter material was stated by the manufacturers to contain 99.65% deuterium. It is believed that the binary diffusion data, summarized in Table I (see paragraph at end of text regarding supplementary material), are accurate to ap-
Isotope Effect in Diffusion of C6H6and CaD6
1519
TABLE 111: Values of A I D o and f,’AK for Benzenes Diffusing into Various Solvents
( A I D O )103 ~ (mol g-I)” ~ T A K
Solvent n-Pentane n-Hexane n-Hexane n-Heptane n - Hep tane n-Oct ane n-Dodecane n-Hexadecane n-Hexadecane Cyclohexane Cyclohexane Chlorobenzene Benzene Benzene a
2.0
1.2 1.4
1.1 1.5
1.I 0.5, 0.2, 0.4, 0.9, 1.1
0.5, 0.5, 0.0,
D o is the limiting value of D.
0.3, 0.1, 0.2, 0.1, 0.2, 0.1, 0.08, 0.03, 0.06, 0.1, 0.1, 0.083 0.08, 0.0,
Ref b b 8 b
4 6 8 b 8
6 8
0
DO where DO and Ma are the limiting tracer diffusion coef-
ficient of CsH6 and the molecular weight of C6H6,respectively,MTis the molecular weight of the tracer species, and A is a constant for a particular system. The value of ( A / D o ) (Table 111) is indicative of the magnitude of the isotope effect for tracer diffusion and a comparison between solvents can be made on this basis. Equations describing the mass dependence of tracer diffusion in solids13-15have recently beenapplied to tracer diffusion in some liquid systems; one6 of these relations can be written as
In this equation f T is a correlation factor which for impurity diffusion is not a geometrical factor since it depends on the relative jump frequencies of tracer and host, and AK is the fraction of the total kinetic energy, associated with the decomposition of a saddle point configuration, which resides in the migrating labeled species. This equation only applies to the situation where one molecule is relocated. When fTAK = 1 the tracer diffusion coefficient is inversely proportional to the square root of the molecular mass. Comparison of 1 and 2 shows that
(3)
(the values of the product f T m are given in Table 11). An estimation of AK can be made by assuming the approximate result15
-
4
5
Flgure 1. (AID’) vs. reciprocal of solvent viscosity, g, obtained from ref 16 and 17: 0,this labor at^$^^^; 0 , Albright and Aoyagi;’ X, Mills.’ +Alkanes are indicated by C,;cyclohexane, Cy; chlorobenzene, C,; benzene, B,.
.
= 1- (2/2)
3
7
proximately 0.2% Limiting binary diffusion coefficients were obtained by extrapolating the experimental data to R = 0, where R is the mean mole fraction of C6H6 (C6D6) (see Table 11) used in an experiment. In both these cases the coefficients obtained in this way are limiting binary coefficients, Do; in the case of c&, however, the coefficient obtained is also the tracer diffusion coefficient, DT, of the isotope of benzene. As reported previously6the tracer diffusion coefficients of 14C-substitutedand perdeuterated benzenes in a number of organic solvents can be represented by an equation of the form A (DT/ D o )= 1- -(MT - M o )
fT
2
rl-’
This work.
( A I D o )= ( ~ T A K / ~ M I J )
1
6 3
(4)
where 2 is the coordination number. If 2 10 (a reasonable choice for the liquids studied) then f T = 0.8 and the corresponding values of AK are all quite small, so only
(CP’)
a small fraction of the kinetic energy associated with the jump is retained by the migrating molecule. Thus as mentioned before6 a small value of AK may indicate that during the migration process momentum is transferred to the surrounding molecules, suggesting that the mass effect for tracer diffusion in liquids may possibly be related to the viscosity of the solvent. The values of ( A / D o )are plotted against the reciprocal of the solvent viscosity, q, in Figure 1,where one can see that (within the experimental error of 10-50%) the isotope effect decreases with increasing solvent viscosity. The data can be represented by the least-squares line
x 10-4 + 3.4 x 10-4q-1
(5) with an average deviation of 3 X The standard deviations of the intercept and slope were 2 X and 8 X W 5respectively. , This linear relationship may be fortuitous as other functions of viscosity (e.g., v-~,g-3) can also be used. Albright and Aoyagi8 have also suggested a correlation between solvent viscosity and the isotope effect for tracer diffusion in different solvents. Acknowledgment. This work was supported in part by a grant from the Australian Research Grants Committee. Supplementary Material Available: Table I containing the mutual diffusion coefficients at 25 “C for C6H6and C6D6in various solvents (2 pages). Ordering information is available on any current masthead page.
( A / D O=)
References and Notes (1) K. R. Harris, C. K. N. Pua, and P. J. Dunlop, J. Pbys. Cbem., 74, 3518 (1970). (2) L. B. Eppsteln and J. G. Albright, J. Pbys. Cbem., 75, 1315 (1971). (3) 0.G. Allen and P. J. Dunlop, Pbys. Rev. Lett., 30, 316 (1973). (4) S. J. Thornton and P. J. Dunlop, J. Pbys. Cbem., 78, 346 (1974). (5) I. R. Shankland and P. J. Dunlop, J. Pbys. Cbem., 79, 1319 (1975). (6) I. R. Shankland, P. J. Dunlop, and L. W. Barr, Pbys. Rev.
B, 12,
2249 (1975). (7) R. Mllls, J. Pbys. Cbem., 79, 852 (1975). (8) K. Aoyagi and J. G. Albright, J. Cbem. Phys., 64, 81 (1976). (9) H. L. Friedman in “Molecular Motions in LiquMs”, J. Lascombe, Ed., Reldel Publlshing Co., Dordrecht, Netherlands, 1974. (IO) J. Kegeles and L. J. Gosting, J. Am. Cbem. Soc., 69, 2516 (1947). (11) H. D. Ellerton, G. Reinfelds, D. E. Mulcahy, and P. J. Dunlop, J. Pbys. Cbem., 68, 403 (1964). (12) G. R. Staker and P. J. Dunlop, J . Cbem. Eng. Data, 18, 61 (1973). (13) A. H. Schoen, Pbys. Rev. Lett., 1, 138 (1958). (14) A. D. LeClaire, Phi/. Mag., 14, 1271 (1966). (15) A. D. LeCbre in “Physical Chemisty”, Vd. X, H. Eyring, H. Henderson, and W. Jost, Ed., Academic Press, New York, N.Y., 1970. (16) F. D. Rossini et al., “Selected Values of Physical and Thermodynamic Propettiesof Hydrocartons and Related compOunds”, Camegie Press, Pittsburgh, Pa., 1953. A.P.I. Research Project 44. (17) J. Tlmmermans. “Physic0 Chemical Constants of Pure Organic Compounds”, Elsevier, Amsterdam, 1950. The Journal of Pbysical Cbemlstty, Voi. 81, No. 75, 1977
