NOTES
4569
Using Po(NaF) = -2.3 ml/mole and P(Na+) = -5.7 ml/mole,' we obtain P(F-) = 3.4 ml/mole. Thus, the Vo(F-) does behave anomalously when compared to the other monatomic, monovalent ions. A possible explanation for the anomaly may be due to the strong structure-forming properties of F-. Various worker^'*^-^^ have divided P(ion) into two components P(ion) = P(int)
I
I
I
02
,
I
04
JST
I
06
t
1
1
08
I
1.0
Acknowledgment. The author wishes to thank Dr. Walter Drost-Hansen for his helpful comments and advice and also wishes to acknowledge the support of this study by the Office of Saline Water.
bath in which tahedensitometer is submersed was controlled to *0.001" with a Hallikainen regulator.
Results and Calculations The densities at various molalities, m, were fit to an equation of the form
+ Am + Bm'/' + Cm2 + Dmb/'
M
lOOOAd dsolndHIOm
(3)
From these apparent molal volumes the infinite dilution value, Ifo = 9vol was calculated using the equation +v = +vo
~~
~~
( 8 ) L. W. Tilton and J.
~
~
~~
K. Taylor, J. Res. Nail. Bur. Std., 18, 205
(1937). (9) L. Hepler, J. Phys. Chem., 61, 1426 (1957). (10) B. E. Conway, R. E. Verrall, and J. E. Desnoyers, Z. Phyeik. Chem. (Leipsig), 230, 157 (1965). (11) E. Glueckauf, ?'Tans. Faraday Soc., 61, 914 (1965).
(2)
where dHTO = 0.997075 g/mIl8A = 43.688 X lov3,B = -4.511 X C = 5.272 X lo-%,and D = -3.603 X 10-3. The deviations between this equation and the experimentally determined values range from 2 ppm in the low concentrations to 9 ppm in the high concentrations. The apparent molal volumes were calculated from the equation +v=-dsoln
(5)
where Po(int) is the intrinsic volume of the ion plus the void volume and Vo(elect.) is the decrease in volume due to electrostriction. This treatmentloQ-ll seems to work very well for most ions. However, for strongly structure-forming ions another term, flo(struct), may be necessaryll1 where VO(struct) is the volume change due to changes in the structure of HzO.
Figure 2. Plot of apparent molal volume of NaF in aqueous solution at 25' vs. l / C . Open circles are runs made with the original solution container;' filled circles are run 1 and squares are run 2, which were both made by the addition technique.
dsoln= dH20
+ P(e1ect.)
+ 1.864; + bc
(4) where c is the concentration in moles per liter, 1.86 is the theoretical limiting slope at 25°,6 and b is a constant determined from the experimental data ( b = 0.52). Figure 2 shows the apparent molal volume of NaF plotted us. & The limiting law is approached, and the infinite dilution value calculated from eq 4 wm found to be -2.29 ml/mole with an estimated uncertainty of *0.07 ml/mole.
On the Molecular Diameter of Water from Solubility and Diffusion Measurements by Paul Schatzberg Marine Engineering Laboratory, Naval Ship Research and Development Center, Annapolis, Maryland (Received J d y 25, 1967)
Uhlig' describes the energy change in placing a gas molecule into a solvent as consisting of the work to produce a spherical cavity of radius r in the solvent and the interaction energy between solute and solvent molecules. Based on this description and applying the Maxwell-Boltzmann distribution theory, he derived the equation 4rr2u l n B = --
kT
E
'G
where B is the Ostwald solubility coefficient, u is the solvent surface tension, E is the interaction energy be(1) H.H.TJhlig, J . Phys. Chem., 41, 1215 (1937).
Volume 71, Number 13 December 1967
NOTES
4570
tween solute and solvent, and k is the Boltzmann constant. If E is small and remains constant, as in a homologous series of solvents, a plot of In B against the solvent surface tension should produce a straight line. From the slope of this line one can then calculate the radius of the cavity, which is essentially the radius of the solute molecule. Equation 1has been found applicable to a number of as well as those where water is the solute in a series of normal alkane solvents from C, to C16.4 From the latter systems, the molecular diameter of water was determined at 25 and 40”. Since the solubility of water in these hydrocarbons is very low mole fraction), ideal solutions can be assumed. From the Eyring absolute reaction rate theory, a quasithermodynamic expression for the diffusion coefficient D is
L)
= edzEh exp(
T)
ex($)
(2)
carbon systems up to n-Cls. These diameters agree very, well with some literature values: 2.50,6 2.64,s 2.78,’and 2.88 A.6 I n a recent analysis of surface tension data for water,s the area of a surface water molecule was determined. From this, a molecular diameter of approximately 2.5 A was determined. The high value for the water diameter determined from the water-hexamethyltetracosane system is attributed to the six tertiary hydrogen atoms of the hydrocarbon molecule. The diffusing water molecule polarizes these atoms, resulting in a stronger solutesolvent interaction than in the normal hydrocarbon systems. Consequently, the assumption that AS* = 0 for this system is not valid. In view of the different bases for eq 1 and 3, the close agreement between the molecular diameters of water determined from the hydrocarbon solvent systems up to n-Cle is noteworthy. (2) H. L. Clever, R. Battino, J. H. Saylor, and P. M. Gross, J . Phgs. Chem., 61, 1078 (1957). (3) J. H. Saylor and R . Battino, %bid., 62, 1334 (1958). (4) P. Schatsberg, ibid., 67, 776 (1963). (5) P . Schatsberg, J. Polymer Sci., Part C, No. 10, 87 (1965). (6) N. E. Dorsey, “Properties of Ordinary Water Substance,” ACS Monograph, Reinhold Publishing Corp., New York, N. Y., 1940. (7) C. J. F. Bottcher, Rec. Trav. Chim. (Rotterdam), 65, 14 (1946). (8) W. F . Claussen, Science, 156, 1226 (1967).
where e is the Napierian base, k is the Boltzmann constant, h is Planck’s constant, Q is the activation energy for diffusion, and AS* the entropy of activation for diffusion. The term d is the distance between successive equilibrium positions of the diffusing particle and is of the order of a molecular diameter. From a plot of log D against 1/T, the activation energy Q can be evaluated. This has been done for water diffusing through n-hoxadecane and 2,6,10,15,19,23-hexamethyltetracosane.’ It can be assumed that the diffusion A New Method for the Synthesis of Radical process for water through saturated hydrocarbon Cations of Aromatic Hydrocarbons’ liquids is analogous to a unimolecular reaction so that EquaAS* = 0 and exp(AS*/R) of eq 2 goes to unity. tion 2 can then be rearranged so that by Axel Reymond and George K. Fraenkel
(3) Using eq 3 and values of D and Q previously determined,5the molecular diameter of water was calculated. Table I compares results for water diameters based on eq 1 and 3. A remarkably close agreement is seen to exist between the diameters determined from the water-hydro-
Table I : Water Diameters, d, in Angstroms Eq 3--
O C
Eq 1 Watern-alkanes CI-ClS
Watern-hexadecane
Water hexamethyltetraooeane
25 40
2.74 2.72
2.77 2.69
4.52 4.41
Temp.
The Journal of Phgsieal Chemistry
Department of Chemistry, Columbia Unitersity, New York, New York 10067 (Received July 31, 1967)
Radical cations of aromatic hydrocarbons have been produced and studied using electron spin resonance (esr) by a number of investigators employing several different procedures,2-12 but many of the species are (1) This research was supported in part through U. S. Air Force Office of Scientific Research Grant No. AF-SFOSR-285-65. (2) D. H. Geske and A. H. Maki, J . A m . Chem. SOC.,82, 2671 (1960). (3) A. Carrington, F . Dravnieks, and M. C. R. Symons, J . Chem. SOC.,947 (1959). (4) Y. Yakosawa and I. Miyashita, J. Chem. Phys., 25, 796 (1956). (5) M. T . Melchior and A. H. Maki, &id., 34, 471 (1961). (6) 9. I. Weissman, E. de Boer, and J. J. Conradi, ibid., 26, 963 (1957). (7) 3. R. Bolton and G. K. Fraenkel, ibid., 40, 3307 (1964).
