NOTES
4412
through a n F & M chromatograph with a silica gel column and by measuring the COz peak. Fluorocarbonyl compounds decompose quantitatively to C02 on this column; thus, the COZ corresponds to the CFClO introduced. The absorption coefficient, to base 10, a t 5.35 p is 0.019 cm.-I mm.-l. Assuming the CFClO and the CFC12N0 yields to be unity in t.he CFCL-02 and the CFCl,-NO photolyses, respectively, yields values 0.0087 and 0.012 mm.-I for the absorption coefficients, to base 10, for the 6.19- and 8.8p bands of CFCI2NO,respectively.
Acknowledgment. The authors wish to thank Mrs. Barbara Peer for assistance with the manuscript.
Self-Diffusion Coefficients of Water by Jui H. Wang Kline Chemistry Laboratory, Yale University, New Haven, Connecticut (Received August 2, 1965)
The self-diffusion coefficients of water are of interest in many physicochemical and biological studies. A series of measurements of the self-diff usion of liquid water with HIzO1*as tracer by means of the controlled-stirring, open-capillary method was carried out in 1954 in connection with our study of the solutions of proteins1 and electrolytes.2 I n view of the frequent use by other workers of the two published self-diff usion coefficients of water, it seems desirable to report the other values determined in our earlier series of measurements. The experimental details were already described in an earlier p ~ b l i c a t i o n . ~The OIs atom per cent in the diffusion samples varied from 0.5 to 1.5%. The temperature was controlled to within i0.01". The results are summarized in Table I. The constancy of Dq/T shows that the effective volume of the diffusing species remains constant be-
tween 5 and 25". Therefore, in spite of the tetrahedrally hydrogen-bonded structure of waterl416 it is entirely adequate to describe its self-diffusion in terms of the movement of individual H20 molecules.6 A linear plot of In D vs. 1/T gives an apparent activation energy of 4.8 kcal./mole. Since each hydrogen bond is shared between two water molecules, this apparent activation energy is large enough to rupture completely two hydrogen bonds per activated molecule. For a polar liquid with loose-packed structure such as the ice-like structure of water, self-diffusion and dielectric relaxation may involve essentially the same activation mechanism. If this is the case, then the dielectric relaxation time r and self-diff usion coefficient D should be related by the simple equation, D = X2/r, where X is the average distance between two successive equilibrium positions of a diffusing molecule. Since the density of water at 25' is only 0.3%smaller than that a t 5") X2 should remain practically constant in this temperature range. The dielectric relaxation data of Collie, Hasted, and Ritson' enable us to compute X2 as listed in Table 11. Using the average of the above values of PT = X2, we obtain a mean jumping distance of 3.7 A. for self-diffusion in liquid water. This value compares interestingly with the observed 0-0 distances in ice I which are 2.76 A. for the nearest neighbors and 4.51 8. for the next nearest neighbors. Table I1 Temp.,
7
x lo1',
DT
x
1016,
C.
880.
cm.2
5
9.43 7.96 6.87 5.23
13.4 13.3 13.5 13.4
10 15 25
Experimentally, the constancy of D r / T and D r with respect to T enables one to estimate with reasonable accuracy both D and 7 at other temperatures from the viscosity data of water by either interpolation or even short extrapolation of these values.
Table I
Temp.,
OC.
5.00 10.00 15.00 25.00
Number of measurements
8 6
8 6
Self-diffusion coefficient of water, D X 105, cm.s/sec.
Viscosity, 1 X 108, poise
1.426 f 0.018 1.675 f 0.025 1.97 i.0.020 2.57 i.0.022
15.188 13.077 14.404 8.937
The Journal of Physical Chemistry
DdT
x
1010
7.77 7.73 7.79 7.70
(1) J. H. Wang, J. Am. Chem. SOC., 76, 4755, 6423 (1954). (2) J. H. Wang, J . Phys. Chem., 58, 686 (1954). (3) J. H. Wang, C. E. Anfinsen, and F. M. Polestra, J. Am. Chem. SOC.,76, 4763 (1954). (4) J. D. Bernal and R. H. Fowler, J. Chem. Phys., 1, 515 (1933). (5) L. Pauling, J. Am. Chem. SOC.,57, 2680 (1935). (6) J. H. Wang, {bid., 73,510 (1951). (7) C. H. Collie, J. B. Hasted, and D. M. Ritson, Proc. Phys. SOC. (London), 60, 145 (1948).
