NOTES
3214
proton peaks are considerably broader than the other peaks,' the main relaxation is via the dipolar part of eq. 1, rather than the term depending on the hyperfme interaction. This is due to the r+ dependence of the first term in eq. 1 and the nearness of the ortho position to the metal. Using only the fist term, with (r")Bv = 6.8 X cm.B (structural parameters taken from ref. 4), g = 2.39, S = 3//z for Co,loand g = 2.32, S = 1 for Ni,I1 an upper limit to the dipolar correlation time, rc, is ~alculated.~ We obtain ro = 2 X and 6 X 10-13 sec. for the Ni and Co complexes, respectively. These r0 values are too short to be associated with the molecular tumbling time in solution, which the Debye equation estimates to be -lo-" sec., so that rC may be identified3 with the electronic relaxation time, T1. For the related complex anions,' [(phew P)Co13]- and [(phen3P)NiIS]-, similar calculations using the observed line widths' yield Tl values of about the same magnitude as for the complexes discussed above. Only very rough estimates to the ortho proton line widths are available for the anionic complexes, due to considerable overlapping of lines? It is of interest that for these complexes r > T I , where 7 is the molecular tumbling time in solution, the opposite to what has been previously assumed in the analysis of the isotropic s h i f t ~ . ~ J * ' ~ Acknowledgments. The author wishes to acknowledge the hospitality of the Bell Telephone Laboratories, Murray Hill, N. J., and thanks Mr. E. W. Anderson for obtaining the p.m.r. spectra. Valuable discussions with Profs. L. C. Allen and W. D. Horrocks, Jr., are gratefully acknowledged. (10) F.A. Cotton, 0. D. Faut, D. M. L. Goodgame, and R. H. Holm, J . Am. Chem. doc., 83, 1780 (1961). (11) F. A. Cotton, 0. D. Faut, and D. M. L. Goodgame, ibid., 83, 344 (1961). (12) H. M. McConnell and R. E. Robertson, J . Chem. Phys., 29, 1361 (1958).
The Abnormal Relation between the Velocity of Sound and the Temperature in Sodium Sulfate Solution by Tatsuya Yasunaga, Mitsuyasu Tanoura, and Masaji Miura Departmsnt of Chembtry, F d t y of Science, Hirosh&ta Univerdy, Hiroshima, Japan (Received January $6,1066)
Since the first report by one of the authors1 on the abnormality in the velocity of sound in sodium sulfate The Journal
of
Physical Chemistry
and sodium carbonate aqueous solutions near the crystal transition point of the salts, a similar abnormality has been discovered in the electric conductivity for sodium sulfate by Hirano2 and in the viscosity of sodium carbonate by F ~ j i t a . This ~ communication is to report more detail on the abnormal relation between the temperature and the velocity of sound in sodium sulfate aqueous solution. The velocity of sound was measured by an ultrasonic interferometer described in detail elsewhere. The electrical oscillations controlled by quartz crystals having each fundamental frequency 2.5, 3.5, 4.5 Mc./sec. in a thermostat were derived to the X-cut quartz crystal having its fundamental frequency 0.5 Mc. Special circuits were added to detect precisely only the change in the interference. The frequency of oscillation was measured carefully within +50 C.P.S. during each series of runs by a frequency meter. The vertical double glass tubes were sealed through a Teflon 0 ring to a holed stainless steel plate, below which was attached a gold-plated 0.5-Mc. crystal. A plane reflector made of stainless steel was connected to a micrometer and balanced for the crystal by controlling a spring. It could be moved vertically without any rotation, and its position was determined within *0.001 mm. with the micrometer having a traveling range of 6 cm. I n order to protect the sample solution from contamination during measurement, a glass tube was fixed to the shaft of the micrometer. The ultrasonic interferometer was immersed in a water bath and maintained at a constant temperature to *0.002". The velocity of sound at 3.5 Mc. for various concentrations of sodium sulfate solution at different temperatures (0.1963-1.849 M) is given in Table I and shown in Figure 1. From these results, it is clearly seen that the change in the velocity of sound with temperature below 32.4" is not the same as that for greater temperatures, even for solutions as dilute as 0.1963 M. In particular, a discrepancy in the velocity of sound waa observed for the concentrated solution at 32.4'. A similar measurement was also done for a 1.144 M solution at various frequencies. The results obtained in the process of increasing the temperature are shown in Table I1 and show no dispersion in the velocity of sound by frequency. This suggests that the abnormality is not caused by a relaxation phenom(1) T. Sa& and T. Y-aga, Kagaku To Kogyo (Tokyo), 7 , 146 (1964). (2) K.Hirrtno, Nippon Kagaku Zasshd, 79, 648 (1958). (3) K.Fhjita, Bull. C h . SOC.Japan, 32, 1005 (1959). (4) T. Yasunaga, M. Tanoura, and M. Miura, in preparation.
NOTES
~~
3215
~~~~~~~~~
~~~
~
~
~
~~
~~
~
~
~
~
~
~~~~~
~~
~
~
~
Table I: Velocity of Sound in the Aqueous Solution of Various Concentrations of NaeSOcas a Function of Temperature a t 3 5 Mc." Ha0
Temp.,
ec.
30.0 31.0 31.5 31.8 32.0 32.2 32.4 32.5 32.6 32.8 33.0 33.5 34.0
6.49948 Mo.
1509.20 1511.49 1512.63 1513.59
Sound velooity, m./sec. 0.6717 M 8.49986 Mc.
0.1963 M 6.49948 Mc.
0.9846 M Ma.
1.849 M $..@9I6 Mc.
8.49986
1538.28 (1538.30) 1540.38 1541.43 (1541.42) 1542.10 1542.51 1542.90 1543.45(1543.44)
1593.93 (1593.93) 1595.76 1596.61 1597.05 1597.25 1597.42(1597.43) 1597.98 (1597.98)
1648.80 (1648.84) 1650.41 1651.02 (1651.01) 1651.29 1651.40 1651.52 (1651.52) 1652.19 (1652.19)
1749.80 (1749.83) 1750.74 1751.06(1751.06)
1543.82 (1543.83) 1544.20 1544.47(1544.47) 1545.37 1546.19
1598.30 1598.56 1598.88 1599.70 1600.57
1652.48 1652.86 1653.18(1653.19) 1654.26 1655.42
1752.01(1752.01) 1752.11(1752.11) 1752.16 1752.40 1752.72
1751.33 1751.42(1751.41) 1751.93(1751.91)
1514.58 1515.58 1517.50
a The quantities in parentheses are the experimental values obtained by decreasing the temperature. frequency.
Italicized numerals show the
therefore, should be considered in connection with the transition phenomenon in the solid. Table II: Velocity of Sound in the Aqueous Solution of 1.144 M NalSO, a t Various Frequencies as a Function of Temperature" Temp., OC.
30.0 31.0 32.0 32.6 33.0 34.0
velocity, m./sec. 3.6 Mc.
-ound
2.5 Mo.
4.5 Ma.
-
8 . 49969
1670.81 (1670.82) Mo. 1672.07
8.49948 Ma.
1672.07
1670.79 (1670.80) 4.49991 Ma. 1672.04
8.49869
8.48984
4.49978
1672.82(1672.81) I.49969 1673.72(1673.74)
1672.81(1672.80)
1672.79 (1672.79)
8.49986
4.49978
1673.72 (1673.74)
1673.71 (1673.73)
8.49969
8.49886
4.49978
1670.80(1670.79)
1674.05
1674.05
1674.00
8 . 49969
8.49986
4.49978
1675.37
1675.36
f?.@969
8.49986
1675.34 4 . 49978
a The quantities in parentheses are the experimental values obtained by decreasing the temperature. Italicized numerals show the frequency.
30
31 32 (32.38)3 3 Temperature, O C .
3
Figure 1. Variation of the velocity of sound with temperature for various concentrations of NaZSO, aqueous solution a t 3.5 Mc.
enon. It is remarkable that the temperature which shows the discontinuity is in excellent agreement with the transition point of the saturated sodium sulfate solution coexisting with the solid. This phenomenon,
It is conceivable that an electrolyte dissolved in water exists as ions and embryonic aggregates, especially in the concentrated solution. The following scheme may be proposed for the embryo in the solution. NazS04*10H20
NazS04
+ lOH2O
That is, the embryo at the lower temperature has the same structure as that of the hydrous sodium sulfate but t u r n to the anhydrous form at the higher temperaVolume 69,Number 0 September 1966
NOTES
3216
ture. Then the change in the structure of the embryo causes the discrepancy in the velocity of sound in solution at the transition temperature. However, it is quite difficult to explain such a change in the velocity of sound as shown in the figure by consideration of the change in the structure of the embryo since the thermodynamic properties of these structures have not yet been studied. As a result of the above description, it should be considered that a very small amount of hydrous sodium sulfate embryo exists even in the dilute solution at the lower temperature and it changes to that of anhydrous at the transition temperature when the temperature is increased. It is worth noting that no hysteresis could be observed in this phenomenon as shown in Table I, and this phenomenon may be applied to accurately determine the transition point.
system, applied in part IV6 to l9Fin 1,l-difluorocyclohexane.
Experimental Section The spin-echo apparatus and experimentalprocedures used in this study were the same as those described previ~usly,~"as are the experimental errors. The dample of perfluorocyclohexane was obtained from Pierce Chemical Co., Rockford, Ill,, with indicated b.p. 52" and m.p. 51'. It was used without further purification. The pure liquid was studied between 54 and 112', in a sealed tube under its own vapor pressure. Also, measurements were made between 54 and 23" upon extending the liquid range by adding 30% by weight of isopentane as a diluent; this sample was degassed. A suitable solvent was not found for measurements at lower temperatures.'
Results and Discussion In the methods e m p l ~ y e d , ~the - ~ decay constant Spin-Echo Nuclear Magnetic Resonance Studies of Chemical Exchange. V. Perfluorocyclohexane' by H. S. Gutowsky and Fu-Ming Chen Noyes Chemiwd Laboratory, University of Illinois, Urbana, Illinois (Received April 99,1966)
The chair-chair isomerization of perfluorocyclohexane has been investigated by Tiers,2 who used steady-state, high-resolution n.m.r. methods for the purpose. However, neglect of internuclear coupling in determining exchange rates from high-resolution spectra tends to give systematic errors which make the apparent rates too high at lower temperatures near the slow exchange limit. This can be circumvented by using a complete line shape method which includes the effects of the coupling.* Another, simpler approach is afforded by spin-echo technique^,^-^ for which it has been demonstrated recently that homonuclear coupling, J, in cycles per second, between exchanging nuclei does not affect the apparent exchan e rate 1/27 provided that 1/27 2 3a, where a = 2~1,Jy.~ The finding by Tiersa of a relatively large, negative entropy of activation, about -10 e.u., for the perfluorocyclohexane isomerization led us to suspect the accuracy of his results, for reasons discussed in part 111.5 Because of this, we have used perfluorocyclohexane as a further test of the spin-echo methods developed to study intramolecular exchange of a coupled AB The Journal of Physical Chemistry
1/T2 for the amplitudes of successive echoes in a Carr-Purcell trains is determined as a function of the pulse separation top. The parameters for perfiuorocyclohexane are such that we observed only region A of the 1/T2 us. l/top curve^,^ in which ~ / T is z relatively insensitive to l/top and has for l/i& -t 0 the limiting value
(1/Tz) = (1/TZ0)
+ (1/27) - [(1/2712 q(6w)211'* 1
(1)
Thus, independent values are required for l/Tzo and for the chemical shift 6w in order to determine the exchange rate 1/27 from the 1/T2data. The low-temperature, high-resolution value of 18.2 p.p.m. for the axial-equatorial l9F chemical shift2 was used to calculate 6 w ; and l/Tzo for each temperature was obtained by measuring the IgFl/T1 with the null methods and assumingss6 that 1/T1 = l/Tzo. With these values as input parameters, the computer pro(1) This research waa supported by the U. s. Office of Naval Research and by the National Science Foundation. (2) G. V. D. Tiers, Proc. C h m . Soc., 389 (1960). (3) J. JonK, A. Allerhand, and H. 8. Gutowsky, J. Chem. Phys., 42, 3396 (1965). (4) 11: A. Allerhand and
H. S. Gutowsky, ibid., 42, 1587 (1965). See also prior work cited therein. (5) 111: A. Allerhand, F. M. Chen, and H. 8. Gutowsky, ibid., 42, 3040 (1965).
(6) I V : A. Allerhand and H. 8. Gutowsky, ibid., 42, 4203 (1964). (7) The CFCls used as a solvent in the low-temperature high-resolu-
tion work interferes with the spin-echo measurements. In principle, the spin-echo method of IV6 could give accurate values for the perfluorocyclohexaneisomerization rate down to about Oo. (8) H. Y. Carr and E. M. Purcell, Phys. Rev., 94, 630 (1954).
