NOTES
June, 1963 are summarized in Table 11. These values, in common with all values of ion-pair dissociation constants, are subject to a n unavoidable determinate error, since they depend on tlie particular model chosen for calculating the long-range interionic effects. Thus, for KCl in TOYo dioxane-30yo water at 25O, our potentiometric value of lo3& is 2.35 f 0.16, while the conductometric value reported recently by Lind and Fuoss5 is 6.0 f 0.2, or more than twice as large. A substantial part of this discrepancy results from a difference of models: Lind and Fuoss limit the concept of "ion pair" to a pair of ions a t distance of closest approach, while the model used by us is more inclusive, allowing the interionic distance in the ion pair to extend to the Bjerruni distaiice q = -zxlzze2/2DkT. We do not claim a fundamental superiority for tlie model on which the present values are based; nor do we profess a strong aesthetic preference, except that this model does fit the data better than other models we have tried.3 TABLE I1 POTENTIOMETRIC Kd VALUES FOR CHLORIDE SALTS IN DIOXANE-30.00 WT. % WATER AT 25'
70.00 WT.
70
Salt
HCl LiCl NaCl KC1
1 0 3 ~ ~
6.6'1'~ 2.87 f 0.10 5.32 f .14 2 . 3 5 f .163
Salt
loaKd
RbCl CSCl (CH3)4KC1
2.57 f 0 . 1 3 2 . 7 0 f .09 2 . 1 8 f .O&
While the absolute values of K d are thus uncertain, the relative values should be a t least qualitatively correct. We may, therefore, infer from Table I1 that the dissociation constants for the various alkali halides are all quite similar in 70% dioxane-30Yo water, except for the rnarkedly higher value obtained for NaCl. However, the relative tendency of alkali metal salts to dissociate depends rnarkedly on the solvent. For example, the sequence of K d values is Li > Na > K for iodides in methyl ethyl ketone16K > Li > Na for picrates nn pyridine, and K > Na >> Li for picrates in nitr~benzene.~ ( 5 ) J. E. Lind, Jr., and R. 34.Fuoss, J . Phys. Chem., 61, 999 (1961). (6) S.R. C. Hughes, J. Chem. Soc., 634 (1947). ( 7 ) C. A. Kraus, J. Phys. Chem., 60, 129 (1956).
N.M.R. SPIN-ECHO SELF-DIFFUSION MEASUREMENTS ON FLUIDS UNDERGOING RESTRICTED DIFFUSION BYD. E. WOESSXER Socony itlobil Oil Company, Inc., Field Research Laboratory, Dallas, Texas Received December 10,196B
The spin-echo technique for measuring self-diffusion coefficients in l i q ~ i d s l -involves ~ the attenuation of the spin-echo amplitude resulting from the diffusion of the molecules into regions having different values of applied magnetic field. For a two-pulse spin-echo from a liquid sample which experiences a uniform magnetic field gradient this attenuation is given by the relation
E/Eo = exp(- 2 / 3 y 2 G 2 D ~ 3 ) (1) in which y is the nuclear gyromagnetic ratio, D is the bulk liquid self-diffusion coefficient, r is the time interval between the two pulses, G is the magnetic field (1) H. Y . Carr and E. M. Purcell, Phys. Rev., 94, 630 (1954). (2) D. C. Douglass and D. MoCall, J . Phys. Chem., 62, 1102 (1958). (3) D. E. Woessner, J . Chem. Phys., 34, 2067 (1961).
W.
1365
gradient along the direction of the applied magnetic field, Eo js the echo amplitude when G is zero, and E is the spin-echo amplitude for the given G value. The derivation of this expression assumes that the diffusing molecules move in an infinite reservoir so that the Einstein relation ((Ax)2),, = 2Dr holds. Suppose, now, that the reservoir is not infinite so that the molecules experience physical barriers to their diffusive movements. The average displacement a molecule undergoes during a time interval 7 should be less than that for an infinite reservoir. But as T is decreased toward zero, the displacement of the average molecule should approach that for an infinite reservoir because fewer and fewer molecules move far enough to experience the barriers. The size of the infinite reservoir to which eq. 1 applies is great enough so that the average distance bletween molecules and constrictive barriers is very large compared to ~ ( D T ) ' the / ~ , average distance a molecule moves in any direction during the time 27. For water at room temperature, this diffusion distance is 14 p for r = 0.02 sec. The size which a reservoir must attain i;o that eq. 1 applies then, increases with increasing r values. Systems such as porous rocks and viscous colloidal suspensions should provide barriers so that eq. 1 no longer applies. This has been observed for water in a geological core and for water in aqueous suspensions of silica spheres. For 7 values in the range of 0.01 tlo 0.03 see., the values of E/Eowere measured4 as a funation of G for fixed r values. Plots of In (E/Eo) us. G2 showed that In ( E / E o )is directly proportional to G2, as is the case for bulk liquids. These data can thus be interpreted by use of eq. 1 with the bulk liquid selfdiffusion coefficient D replaced by a spin-echo diffusion coefficient D'. For a qualitative discussion, one may use the relation D' = ((Ax)2),v/(4~),where A AX)^),, refers to the mctlecular disp1acemen.t during 27. From the above considerations, one would expect D' t o be a function of the ~ of the distance from diffusion distance ~ ( D T ) ' 'and molecules to barriers. I n particular, D' should decrease as the ratio of diffusion distance to the molecubto-barrier distance increases. Also, in the limit when r = 0, it is expected. that D' = D; and with increasing values of T, D' should decrease. These expectations are in agreement with the following data. When 'T becomes long enough so that the diffusion distance is very large compared to the average molecule-to-barrier distance, D' should become independent of r and be the diffusion coeffilcient obtainable by conventional means. This will occur when the relation = 2D't holds for all 1 > t, such that t, clopropane in the 1-butene-mercury system. 2
