846
S. J. Thornton and Peter J. Dunlop
Foundation for Grant No. GP-20605 in support of this work. Supplementary Material Available. The data 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 of $2.00 for microfiche, referring to code number JPC-74839. References and Notes (1) M. K. Chantooni, Jr., and I . M. Kolthoff, J. Phys. Chem., 77, 527 (1973). (2) i. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Chem. SOC., 95, 8539 (1973). (3) I. M. Kolthoff, S. Bruckenstein, and M. K. Chantooni, Jr., J. Amer. Chem. SOC., 83,3927 (1961). (4) I. M. Kolthoff and M. K. Chantooni. Jr., Anal. Chem., 44, 194 (1972). (5) M. K. Chantooni, Jr., and i. M. Kolthoff, J. Amer. Chem. SOC., 92, 7025 (1970). (6) I. M . Kolthoff. J. J. Lingane, and W. Larson, J. Amer. Chem. SOC., 60, 2512 (1938). (7) The Sadtler Standard Spectra, Sadtler Research Laboratories, Philadelphia, Pa. (8) L. Lang, Ed., "Absorption Spectra in the Ultraviolet and Visible Region," Academic Press, New York. N. Y., 1961. (9) M. K. Chantooni, Jr., and I. M. Kolthoff, J. Phys. Chem., 77, 1 11973) - -, (IO) I. M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Chem SOC., 87, 4428 11965). (11) I. M . 'Kolthoff and M. K. Chantooni, Jr., J. Phys. Chem., 76, 2024 (1972). (12) G. KortOm, W. Vogel, and K. Andrussow, "Dissociation Constants of Organic Acids in Aqueous Solution," Butterworths, London, 1961. (13) J. Dippyand S. Hughes, Tetrahedron, 19, 1527 (1963). (14) J. Juillard, Ph.D. Thesis, University of Clermont-Ferrand, 1967; J. Juillard and N. Sirnonet, Bull. SOC.Chim. Fr., 1883 (1968). \
(15) J. Elliott and M. Kiipatrick, J. Phys. ?%em., 45, 454, 466 (1941). (16) I. M. Kolthoff and L. Guss, J. Amer. Chem. Soc., 61, 330 (1939). (17) I. M. Kolthoff, J. J. Lingane, and W. Larson, J. Amer. Chem. SOC., 60,2512 (1938). (18) W. Brightand H. Briscoe, J. Phys. Chem., 37, 787 (1933). (19) L. Minnick and M. Kilpatrick, J. Phys. Chem., 43, 259 (1939). (20) H. Goldschmidt and F. Aas, 2.Phys. Chem., 112, 423, 429 (1924). (21) M. Kilpatrick, J. Amer. Chem. SOC., 75, 584 (1953). (22) I . Tabagua, Tr. Sukhum. Gos. Pedagog. lnst., 15, 119 (1962). 92, (23) M. K. Chantooni, Jr., and I. M. Kolthoff, J. Amer. Chem. SOC., 7025 (1970). (24) See paragraph at end of paper regarding supplementary material. (25) 0. Konovalov, Russ. J. Phys. Chem., 39,364 (1965). (26) J. Christensen, R. Izatt, and L. Hanson, J. Amer. Chem. Soc., 89, 213 (1967). (27) P. D. Bolton, K. Fleming, and F. Hall, J. Amer. Chem. SOC.,94, 1033 (1972). (28) E. King, "Acid-Base Equilibria," Macmillan, New York, N. Y. 1965, p211. 163 (1962), (29) A. J. Parker, Quart. Rev., Chem. SOC., (30) J. W. Larson and C. Hepler in "Solute-Solvent Interactions." J. F. Coetzee and C. D. Ritchie, Ed., Marcel Dekker, New York, N. Y., 1969, p 37. (31) See, for example, L. P. Hamrnett, "Ph,ysical Organic Chemistry," 2nd ed, MacGraw-Hill, New York, N. Y., 1970, p 368; E. Gouid, "Mechanism and Structure in Organic Chemistry," Holt, Rinehart and Winston, New York, N. Y., 1959, p 256; H. Brown in "Determination of Organic Structures by Physical Methods," Vol. 1, E. Braude and F. Nachod, Ed., Academic Press, New York, N. Y., 1955, p 604. (32) L. P. Hamrnett, ref 31, p 371. (33) J. Steigman and I , Sussrnan, J. Amer. Chem. Soc., 89, 6406 (1967). (34) L. Wooten and L. P. Hamrnett, J. Amer. Chem. SOC., 57, 2289 (1935). (35) J. M. Wilson, N. Gore, J. Sawbridge, and F. Cardenas-Cruz, J. Chem. SOC.8,852 (1967). (36) M. W. Dietrich, J. Nash, and R. Keiler, Anal. Chem., 38, 1479 (1966). (37) M. Tribble and J. Traynham, J. Amer. Chem. SOC.,91, 379 (1969). (38) C. P. Srnyth, "Dielectric Behavior and Structure," McGraw-Hili, New York, N. Y., 1955, p 253. (39) R. W. Taft in "Steric Effects in Organic Chemistry," M. Newman, Ed., Wiley, New York, N. Y., 1956, p 581; R. Taft, J. Amer. Chem. SOC., 74, 3120 (1952). (40) I . M. Kolthoff and M. K. Chantooni, Jr., J. Amer. Chem. SOC., 93, 3843 (1971).
Isotope Effect in Diffusion of I4C-Substituted Benzenes in Benzene, n-Heptane,
n- Octane, and Cyclohexane at 25" S. J. Thornton and Peter J. Dunlop* Department of Physical lnorganic Chemistry, University of Adelaide, Adelaide, South Australia 5007 (Received October 26, 7973)
Tracer diffusion coefficients are presented for 14C-substituted benzenes of different molecular weights diffusing in benzene, n-heptane, n-octane, and cyclohexane at 25". The data which were obtained with one magnetically stirred diaphragm cell indicate that, in agreement with previous results, a small isotope effect is present in each system.
In a previous paper,l tracer diffusion coefficients, DT, were presented for 14C-substituted benzenes of varying molecular weight diffusing in unlabeled benzene. Those results indicated that, while the tracer diffusion coefficients were not inversely proportional to either the square root of the mass of the tracer species or to the square root of the reduced mass of the system, a very slight linear The Journal of Physical Chemistry, Vol. 78, No. 8, 1974
mass dependence was present. This information is contrary to both the theoretical prediction^^.^ and experimental findings4 for binary gaseous systems, to recent results for benzene tracers diffusing in benzene crystals, and to the results of Eppstein and Albright,6 who also studied benzene tracers diffusing in liquid benzene, but in agreement with the conclusions of PikaL7
047
Isotope Effect in Diffusionof 14C-SubstitutedBenzenes TABLE I: Values of Tracer Diffusion Coefficients (DT) of 14C-Substituted Benzenes in Benzene, n-Heptane, n-Octane, and Cyclohexane a t 25 DT X 106,cm* sec-1
(Error X 105); cm* sec-1
2.215 2.214 2.213 2.206 2.203 2.202
14C-Benzene in Benzene f 0 .004 fO .013 f O ,005 f0 .002 fO .002 f0 .004
3.796 3.816 3.799
14C-Benzene in n-Heptane f0.015 fO ,024 fO .016
3.136 3.121 3.143 3.114 3.117 3.121 1.853 1.859 1.854
W-Benzene in n-Octane f0.005 f0 .010 ~ 0003. fO .001 fO .003 f0.003
Mol wt
84.6 84.6 84.6 88 88 88
...ij'----i
88 88 88
\
(Cl
1.84
84.6 84.6 84.6 88 88 88
W-Benzene in Cyclohexane f O .008 88 f0.007 88 f0 ,001 88
Or Average molecular weights were calculated for labeled benzenes from details of the synthesis supplied by the manufacturers. Mean error of two, three, or four analyses for each experiment.
The purpose of this paper is to report further experimental data which agree with the results of our previous study.l Experimental Section and Discussion Using a diaphragm cell of Stokes design,8 we measured the tracer diffusion coefficients of one and sometimes two 14C-labeled benzenes in benzene, n-heptane, n-octane, and cyclohexane at 25". One of the labeled samples (mol wt 88) was the same as that used in the previous study. The reader is referred to that paper and elsewhereg3l0 for experimental details, for techniques used to purify the solvents, for the methods used to calculate the tracer diffusion coefficients, and for the method used to calibrate the diaphragm cells. All solvents were analyzed by gpc techniques and were found to contain less than 0.05% impurities. The experimental DT values together with the corresponding molecular weights are summarized in Table I. We believe the overall average experimental error to be approximately &0.3%. The data for 14C-benzene in benzene are in excellent agreement with our previous results1 which indicated the presence of a slight mass dependence. The tracer results for the other three systems are included in Figure 1, together with the limiting mutual diffusion coefficients, Do, of benzene in n - h e ~ t a n ein , ~ n-octane,ll and in cyclohexane.ll These Do values, which are listed in Table 11, were extrapolated from experimental data measured in this laboratory by means of a Gouy diffusiometer12 and the same solvents used in the present study. We believe the errors in each value of Do to be approximately *0.3%. The Do values should be identical with the values of DT extrapolated to the molecular weight of normal benzene. The graphs of DT us. molecular weight in Figure 1 indicate a slight mass dependence for each system. Several theories13-15 suggest that the self-diffusion coef-
10.3%
\,
\
78
02 04 86 MOLECULAR WEIGHT
80
88
Tracer diffusion coefficients for 14C-substitutedbenzenes diffusing in (a) n-heptane, (b) n-octane, and (c) cyclohexane: 0, experimental DT points; 0 , limiting experimental mutual diffusion coefficients, Do. The dashed and dotted lines indicate the limiting mass dependences expected if the tracer diffusion coefficients of the labeled species are assumed to be inversely proportional to the square root of their mass and the reduced mass of the system, respectively. Figure 1.
TABLE 11: Values of DO and A z for Use in E q 2
Benzene-n-heptane Benzene-n-octane Benzene-cyclohexane
3.864 3.145 1.865
0.0059 0.0023 0.0010
-1.5 -0.7 - 0.5
ficients of liquids should be inversely proportional to the square root of the mass of the molecular species. Our results indicate that tracer diffusion coefficients in liquids are not such sensitive functions of mass in agreement with the recent predictions of Friedman, who used the time correlation function to derive an expressionla which may be rearranged to yield
DT = Ds
-
A,(MT
-
M,-,) .I- . * *
(1) for the case of a tracer of labeled benzene diffusing in benzene, and DT = Do - A,(MT MO) (2) for the case of a tracer of labeled benzene diffusing in a different solvent. In these equations Ds is the self-diffusion coefficient, Do is the limiting mutual diffusion coefficient, A1 and Az are constants, and MT and M o are the molecular weights of the labeled and unlabeled species, respectively. The form of eq 1 is identical with eq 1 of ref 1, while eq 2 accurately describes the slight mass dependence of labeled benzenes diffusing in n-heptane, n-octane, and cyclohexane. The coefficients A2 for these systems are listed in Table 11. For the benzene tracer with molecular weight 88 the values of the percentage change in the tracer diffusion coefficient, [100(D~- D O ) / D O ]for , these systems are very close to the corresponding quantity [ 1 0 0 ( D ~- Ds)/Ds] obtained in ref 1, and much less than the values required to describe either an inverse mass or an inverse reduced mass dependence. These values of [100(D~- DO)/Do]are listed in Table 11. The two inverse mass dependences are
-
+
The Journal of Physical Chemistry, Voi. 78,NO. 8, 7974
a48
Communications to the Editor
clearly indicated in Figure 1. A reduced mass dependence has recently been predicted by O’Reilly.17
Acknowledgment. This work was supported in part by a grant from the Australian Research Grants Committee. The authors are grateful for helpful discussions with Professor H. L. Friedman, Dr. D. E. O’Reilly, and Dr. K. R. Harris.
References and Notes (1) G. G. Allen and P. J. Dunlop, Phys. Rev. Lett., 30, 316 (1973). (2) S. Chapman and T. G. Cowling, “The Mathematical Theory of Nonuniform Gases, Cambridge University Press, New York, N. Y., 1952. (3) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids,” Wiley, New York, N. Y., 1954.
(4) K. R. Harris, T. N. Bell, and P. J. Dunlop, Can. J. Phys., 50, 1874 (1972). (5) R. Fox and J. N. Sherwood, Trans. Faraday Soc., 67, 1 (1971). (6) L. B. Eppstein and J. G. Albright, J. Phys. Chem., 75, 1315 (1971). (7) M. J. Pikal,J. Phys. Chem., 76, 3038 (1972). (8) R. H. Stokes, J. Arner. Chem. SOC.,72, 763 (1950). (9) K. R. Harris, C. K. N. Pua, and P. J. Dunlop, J. Phys. Chem., 74, 3518 (1970). (IO) T. N. Bell, E. L. Cussler, K. R. Harris, C. N. Pepela, and P. J. Dunlop, J. Phys. Chern., 72, 4693 (1968). (11) P. J. Dunlop, unpublished data. (12) H. D. Ellerton, G. Reinfelds, D. E. Mulcahy, and P. J. Dunlop, J. Phys. Chem., 68, 403 (1964). (13) H. C. Longuet-Higgins and J. A. Popie, J. Chem. Phys., 25, 884 (1956). (14) R. C. Brown and N. H. March, Phys. Chem. Liquids, 1, 141 (1968). (15) H. G. Hertz, Ber. Bunsenges. Phys. Chern., 75, 183 (1971). (16) See eq 14 of H. L. Friedman in “Molecular Motion of Liquids,” J. Lascombe, Ed., Reidel Publishing Co., Dordrecht, Netherlands, 1974. (17) D. E. O’Reilly, J. Chern. Phys., in press.
COMMUNICATIONS TO THE EDITOR
Relaxation Spectra of 6-Methylpurine in Aqueous Solution
’
Publication costs assisted by the National Science Foundation
Sir: Numerous studies dealing with the molecular interactions which maintain the secondary structure of nucleic acids have appeared in recent years. Work by Ts’o and others on the monomeric units of nucleic acids in aqueous solution2 indicate that (a) mononucleosides associate in “stacks” made up of layers of the essentially planar base moiety, (b) the stacks are held together primarily by so called “hydrophobic” interactions rather than by hydrogen bonding, and (c) the formation of stacked bases can be described by a model which assumes that the free-energy change and enthalpy change for the addition of a single base molecule to a stack is independent of the size of the stack. In order to elucidate the dynamics of the stacking process we have measured the sound absorption spectra of aqueous solutions containing 0.025-0.22 M 6methylpurine at 25”. The measurements, which employed a pulse technique covering the frequency range of 7-500 MHz, show excess absorption due to the presence of solute. Although the resulting relaxation curves are somewhat wider than allowed by a single relaxation, the absorption data can be used to calculate an observed, or average, relaxation time 7 and amplitude A according to
measured; Table I gives the least-squares values of the relaxation parameters as a function of formal concentration of solute. The background absorption for all solutions is equal to that of pure water, so that the relaxation time observed is the shortest time of the chemical system. A number of equilibrium studies3-5 have been done in which the data are evaluated by considering a step-wise association model
P,
(2 1
j 2 1
+
1)mer from jmer and is related to the concentrations of the reacting species by K]+l
=
c]+l/clC,’
C1, C,, and C J + l are the molar concentrations of monomer, jmer, and (j l)mer, respectively. The model is usually applied by assuming that the free-energy change for the addition of a monomer to a stack is independent of the size of the stack, i.e.
+
K,,
=
KZ3 = ... = K,’,,’ + I
=
... = K ,
K , is thus the common association equilibrium constant for the aggregation of solute molecules. The rate equations for the kinetic model are
dt
The Journal of Physical Chemistry, Vol. 78, No. 8, 1974
PI+,
K J , ] +is~ the equilibrium constant for the formation of (I’
-dC,’+ where a is the absorption coefficient and f is the sound frequency. Since r is concentration dependent, indicating a second-order process, the observed relaxation is attributed to the aggregation of purine molecules. Figure 1 shows plots of a/f“ us. log f for several of the solutions
+ PI Z
I -‘I
,’+lclc]
-
(‘I+,,,’
+ ‘,’+lI+,C1)Cj+, + k,+2,+lC,+1
j 1 1
The rate constants of the model are represented by the various k; for example, the forward and reverse rate constants of reaction 2 are k J , ] + land k J + 1 , , , respectively, and are related to the equilibrium constant by K J , J + =~
