NOTES
1153
constant, However, because of the stability of the 1:1 complex, it can be assumed that there is essentially no free T H F up to the 1 : l ratio. Consequently, the increase in equivalent conductance up to this point cannot be attributed to an increase in solvent dielectric constant. Rather it is the result of the formation of a stable 1:1 complex between the Na+ ion and the THF. The decrease in equivalent conductance after the 1:1 ratio may be attributed to a decrease in mobility of the Na+ ion arising from additional complexation. A rapid rise in equivalent conductance begins at or just prior to a 4: 1 ratio of T H F :salt and in all cases it rises to very nearly the same maximum in pure THF, as can be seen from the concentration dependent studies shown in Table I. In terms of the proposed equilibrium [Na.THF]+
+ 3THF
The increase in equivalent conductance beginning at approximately the 4: 1 ratio may then be attributed to an increase in solvent dielectric constant. However, in this region the separation of the two effects is not straightforward since the ion aggregates include the solvated rather than the free S a + ion, and a separation of the effects will require an analogous study as a function of cation size using sufliciently large cations that ion-solvent interaction can be neglected. Acknowledgment. Support of this work by National Science Foundation Grant GP 6421 and a National Science Foundation Science Faculty Fellowship for C. N. Hammonds is gratefully acknowledged.
[h’a*4THF]+
in which a relatively stable 4: 1 complex is formed, the rise in equivalent conductance after the 4: 1 ratio would be expected because of the increase in solvent dielectric constant corresponding to the increase in free T H F in the bulk solvent. In Figure 2, the equivalent conductance of the 0.1525 Jf salt solution is extrapolated to that of pure T H F as solvent. An increase is seen relative to the maximum at the 1 : 1 ratio of a factor of approximately 300. Qualitatively, ion-solvent interaction may here be interpreted in terms of an ion-size effect. The stability of the ion aggregates will decrease with an increase in the effective cation size. This will result in an increase in the number of charge carriers, but complexation by a second T H F molecule leads to a decrease in cation mobility. Thus the conductance behavior prior to the 4:l ratio of THF:salt can be considered primarily in terms of ion size rather than solvent dielectric constant.
/‘ T /
Ah8316
AE.5.3
n
Ratio THF: NaAIBuS Figure 2. Comparison of the equivalent conductance of THF:NaAlBud a t low mole ratios to the equivalent conductance of NaA1Bu4 in pure THF.
Nuclear Magnetic Resonance Study of Concentrated Lithium Chloride Solutions by Robert G. Bryant Department of Chemistry, Stanford University, Stanford, California 94305 (Received J u n e $1, 1 9 6 8 )
Nuclear magnetic resonance has made significant contributions to the study of aqueous solutions containing electrolytes. While much of the work has employed proton resonance to observe changes in the solvent, an increasing amount of information is coming from the nuclear resonance of the solute Most work thus far has focused on the more dilute solutions and the data analysis has drawn heavily on models appropriate for the limit of infinite dilution. Although the theoretical treatments of more concentrated solutions are less precise, nuclear magnetic resonance measurements in concentrated solutions reflect the environment of the nucleus observed and thus provide useful information about the structure of the solution. Since aqueous lithium chloride solutions may be made exceedingly concentrated, measurements of the ?Li+ and Wl- resonances were made as a function of lithium chloride concentration to look for unusual behavior of the solute resonances a t high concentrations. ?Li and aKC1both possess a nuclear spin quantum number of $ and nuclear quadrupole moments of 0.1 and -0.079, respectively, so that the nuclear magnetic relaxation for both is usually dominated by the interaction of the nuclear quadrupole moment with random (1) J. F. Hinton and E. S. Amis, Chem. R e v . , 67, 367 (1967). (2) R. A. Craig and R. E. Richards, Trans. Faraday Soc., 59, 1972 (1963). (3) B. F. Fabricand and 9. 9. Goldberg, Mol. Phys., 13, 323 (1967). ( 4 ) P. A. Speight and R. L. Armstrong, Can. J . Phys., 45, 2493 (1967). ( 5 ) D. E. Woesner. B. 8. Snowden, Jr., and A. G. Ostroff, J. Chem. Phys., 49, 371 (1968).
Volume 75,Number 4 April 1989
1154
NOTES
fluctuations in the electric environment of the nucleus observed. In the limit of extreme narrowing, the relaxation time for a nucleus of spin 4 is given by 1 = (1 TT~ 5
~
+
z)
(ezqQ)2
260 240
220 200
-
1
1
1
1
1
,
1
1
1
,
- IO
4 180-
- 9
-
160140-
3
120-
loo-
13
-11
-
2
-
14
- 12
-
- 78
0 8%
- 6 - 5
’LI
k!!
8Ot
!? =+
c
1 4
[LI CI] rnoles/liter
Figure 1. The W l line width and ’Li longitudinal relaxation time us. lithium chloride concentration. The Journal
of
Physical Chemistry
I
1
1
1
1
I
4 I
a I
28
Experimental Section Lithium chloride purchased as Baker Analyzed reagent was recrystallized from water to remove a colored impurity apparent in concentrated solutions. Two solutions standardized by potentiometric titration with silver nitrate were used as stock solutions from which others were made volumetrically. The nmr measurements were made on a Varian Model V-4300 nmr spectrometer operating a t 4.33 MHz coupled with a Princeton Applied Research Model JB-4 Lock-in-Amplifier and audio amplifier built in this 1
c
~ c
where T1 is the nuclear spin lattice relaxation time, q is the electric field gradient a t the nucleus of quadrupole moment Q, n is the asymmetry parameter, and rc is the correlation time for reorientation of the field gradient with respect to the direction of the applied magnetic field.6 In the limit of extreme narrowing the line width, Av, measured in hertz as the full line width a t halfheight is equal to l/nT1. Changes in the relaxation time or line width thus reflect either changes in the symmetry of the electric environment about a nucleus or changes in the average reorientation time for the nucleus with respect t o the laboratory axis system. To a first approximation the correlation time is proportional to the bulk viscosity, 7; however, the validity of this approximation depends critically on how exactly the bulk viscosity reflects the microscopic viscosity that dominates the r o term of eq 1. The quantity 1/Tm is thus a measure of the remaining effects including terms strongly dependent on the electric symmetry a t the observed nucleus.
280
36
HrOlLICl le10 6 7 6 6
4
24
Figure 2. The *5Clline width divided by viscosity us. lithium ahloride concentration; the ratio of water molecules to lithium chloride molecules is indicated across the top.
laboratory to permit various modulation and detection options. The W 1 line width was measured as the full width a t half-height of the absorption signal displayed as the first side band a t 550 or 750 Hz; the deviations reported are the average deviations from the mean calculated from a t least eight measurements at each concentration, ‘Li T1 measurements were made using adiabatic rapid-passage techniques. Recovery of the bulk magnetization was followed below saturation using a Model 151 Sanborn recorder. T1 values reported are the average of a t least three separate determinations and the deviations reported are the average deviations from the mean. Samples were contained in 14-mm 0.d. Pyrex tubes and measured a t the temperature of the magnet gap, 25 f 2’. Values for the viscosity were obtained from the “International Critical Tables.”
Results and Discussion The results of the 7Li+ and 36Cl- measurements are presented in Figure 1. Although the changes in the slope of both plots in the region of 9 M are striking, interpretation is difficult since the data reflect changes in viscosity as well as changes in the electric environment of the nucleus observed. The curves shown in Figures 2 and 3 represent the data in Figure 1 divided by the viscosity; the lithium TI data have been plotted as 1/T17 so that it may be compared more directly with the chlorine line widths. The chloride plot reaches a minimum when the ratio of water molecules to lithium chloride molecules is approximately 12, and the curve shows a marked increase in slope at concentrations above which there are less than six water molecules per lithium chloride molecule. Because the 7Li+ signal is weak a t 4.3 MHz below ( 6 ) A . Abragam, “The Principles of Nuclear Magnetism,” The Clarendon Press, Oxford, 1961, p 314.
NOTES
I
1155 HgWUCI let0 8 7 6 8 I
8
I
I
I
,
I
4
a
8
8
must be deferred until the solvent resonance data a t these concentrations are more complete.
Acknowledgment. The author wishes to thank Professor John D. Baldeschwieler and the other members of his research group for very helpful discussions. Support of the National Institutes of Health under Grant GM 14752-02,the Center for Materials Research, Stanford University, and the National Science Foundation under Grant GP 4924x is gratefully acknowledged.
jot a Q w
+
b3
(7) Woesner, Snowden, and Ostroffb have shown that the dipole contribution to the 7Li+ T I in aqueous solutions of lithium chloride is approximately equal to the quadrupole contribution. They have also shown that the quadrupole contribution dominates the shape of the curve TI us. concentration. Therefore the treatment in terms of quadrupole relaxation is sufficient for this qualitative discussion. (8) H. G. Hertz, 2.Elektrochem., 65, 20 (1961). (9) C. Deverell, D. J. Frost, and R. E. Richards, Mol. Phys., 9,
(Li
c g molcC/litU
Figure 3. The reciprocal of the 7Li longitudinal relaxation time divided by viscosity us. lithium chloride concentration; the ratio of water molecules to lithium chloride molecules is indicated acrom the top.
concentrations of about 5 M , it is difficult t o define the lithium l/T1q curve below this concentration. At approximately 8.5 M , however, there is a dramatic transition followed at higher concentrations by a region of almost zero slope. At concentrations above 13 M , where the water to lithium chloride ratio is less than 4, the slope again increases rapidly. The general behavior of these curves suggests that the electrical environments of the nuclei observed experience significant changes a t concentrations where the average number of water molecules available to associate with a lithium chloride molecule reaches critical values such as 12, 6, 5, or 4. That both resonances experience significant changes a t concentrations where the water to lithium chloride ratio is less than 6 most likely indicates changes in the nature of ion pairing. The almost zero slope of the l/Tlq curve between water to lithium chloride ratios of 5 and 4 suggests a primary coordination number for Li+ of 4; however, such conclusions must be tempered with a realistic appraisal of the approximations involved. To attribute the behavior of 1/Tlq or Av/v to changes in the environmental symmetry of a magnetic nucleus with a quadrupole moment is admittedly a very simplified interpretation of these results.' However, more detailed models for the relaxation mechanism of quadrupolar nuclei have drawn heavily on the asumption that the correlation time is linearly related to the viscosity and most measurements have confirmed this behavior.&1° Without making complex assumptions, these data imply that basic changes occur in lithium chloride solutions a t high concentrations. While these measurements point to certain aspects of thwe changes, interpretation in terms of detailed ion-pairing schemes
565 (1965). (10) K. A. Valiev and 1118 (1961).
E. M . Khabibullin, Russ. J. Phys. Chem., 35,
Diffusion of Alcohols and Amides in Water from 4 to 37" la by C. M. Gary-BoboIb and Heather W. Weber Biophysical Laboratory, Harvard Medtcal School, Boston, Massachusetts (Received June 1 6 , 1 9 6 8 )
A large amount of data for the diffusion of small nonelectrolytes in water is scattered throughout the literature, but these data were obtained under such different conditions that their comparison is often difficult. Furthermore, there are very few data concerning diffusion in dilute solution that is pertinent to the diffusion and permeability measurements carried out today with radioactive tracers. The need for such a systematic study prompted our investigation. In the present work, the diffusion coefficients of a series of alcohols and amides were measured by the capillary-cell method designed by Wang and co-workers2 using a modified technique described by Saraf, Witherspoon, and Cohed and Witherspoon and Saraf.4 The measurements were carried out at 4, 12.5, 24.8, and 37'. These temperatures were regulated within f 0 . 0 5 . The solute concentration was fixed at M (including 14C-labeled and nonlabeled solute). The labeled solutes were obtained from New England Nuclear Corp., except nbutyramide and isobutyramide, which were obtained from International Chemical and Nuclear Corp. (1) (a) This project was supported in part by the Atomic Energy Commission. (b) Laboratoire de Physiologie Cellulaire, Coll&gede France Paris Ve, France. (2) G. H. Wang. S. Amer. Chem. Soc.. 7 3 , 510. 4181 (1951); (b) J". H. Wang, 0 . V. Robinson, and I. 9. Edelman, ibid., 75, 466 (1953). (3) D. N. Saraf. P. H. Witherspoon. and L. H. Cohen, Science,
144, 955 (1963). (4) P. H. Witherspoon and D. N. Saraf, J . P h y s . Chem., 69, 3752 (1965).
Volume 79, Number 4 April 1969
