NOTES
June, 1959 ether causes :i m:irked change i n the heptane pattern. We have too few results of this type to attempt a detailed interpretation but three effects may be instanced as of possible importance: steric, electronic and that resulting from heterogeneity of the catalyst surface. As an example of a possible steric effect, if the surface is largely covered by propyl ether, the heptane pattern may be influenced by restrictions upon rotations about carbon-carbon bonds in species 11. In the extreme, this might make one set of secondary hydrogen atoms (one per carbon atom) more exchangeable than the other. More than one type of electronic effect is possible.
1021
X high conceiitratioii of species I would considerably affect the structure of the d-band of the catalyst. The mere effect of species I in charging the metal negatively or the presence of the surface dipoles in species I might affect the degree or even the direction of polarization of species such as 11. Finally, the ether might poison the more active sites or crystallographic planes and transfer activity to sites or planes which ordinarily make little contribution to exchange. We believe that investigation of the effect of a more strongly adsorbed molecule upon the exchange pattern of another molecule provides a hitherto unexploited source of information about the nature of chemisorbed species.
NOTES THE SOLUBILITY OF BENZENE IN WATER BY D. M . ALEXANDER Chemistry Department, University of Queensland, Brisbane, Australia Received September 8, 1968
The solubilities in water of a series of aromatic hydrocarbons, including benzene, have been determined by Bohon and Claussen' a t temperatures between 0 and 43". These authors have calculated heats of solution for the solution of one mole of liquid hydrocarbon in water. Heringtoa2 has used their results and combined them with vapor pressure values for the pure hydrocarbons to calculate the free energy change for the solution of one mole of hydrocarbon vapor a t 1 mm. pressure to form a solution of unit mole fraction. He finds a. plot of this free energy change against temperature to be linear, which means that the derived heat of solution is constant over the temperature range. This is unexpected since AC, values for a11 gases in mater are known to be large. For benzene Glew and Robertson3 using the same data and the same standard states calculate for AC, a value of 78 cal./deg. mole. Similar high values are calculated for other aromatic hydrocarbons. Examination of the plot referred to above does reveal a slight curvature larger than could be accounted for by experimental error. However, it was thought that a measurement of the solubility of benzene over an extended temperature range would greatly decrease the uncertainty in this AC, value. Experimental Analar benzene was shaken with mercury and purified according to the method of Mair, et aL4 The method of solubility measurement was based on that of Bohon and C1aussen.l The flask used for preparing the saturated solutions was not fitted with taps but with two glass U tubes containing mercury so that the solution should not come (1) R. L. Bohon and W. F. Claussen, J . Am. C h m . Soc.. 78, 1571 (1951). (2) E. F. G. Herington, ibid., 78, 5883 (1951). (3) D. N . Glew and R . E. Robertson, THISJOURNAL, 60, 332 (1956). (4) B. J . fiiair, D. J. Termini, C. B. Willingham and F. D. Rossini, J . RESEaVCh Natl. Bur. Standards, 8'7, 229 (1946).
into contact with tap grease. It was filled with water, a little benzene and a little mercury to allow better stirring. Saturation was attained after 24 hours gentle shaking and it was found that constant solubility results were obtained when the solution had stood for five hours after this. However at each temperature further shaking periods were allowed and at least one long period of standing of about 24 hours to ensure saturation and complete separation of the two phases. Samples were collected in a calibrated dilution flask filled with mercury and a known volume of water. The saturated solution was forced out of the solution flask by a head of mercury and collected over mercury in the dilution flask a t the temperature of the experiment. The volume of the diluted solution was observed when it had reached room temperature. This solution WRS transferred to a 1 cm. quartz absorption cell again by displacement of mercury, to prevent evaporation of benzene from the ~olution. The optical densities were determined with a Beckman model D.U. ultraviolet spectrophotometer a t a number of peaks in the benzene spectrum and compared with the optical densities of a series of standard solutions of benzene in mater.
Results and Discussion The results agree well with those of Bohon and C1nussen.l AGO values were calculated for the change benzene vapor (fugacity = 1 mm.) -+ soln. of benzene in water (M.F. = 1, hypothetical)
Values for the vapor pressure of benzene6 were converted to fugacities by using published values of the second virial coefficient.6 The vapor pressure of benzene above a saturated solution of water in benzene was calculated by Raoult's law. This involved an extrapolation to other temperatures of the results of Joris and Taylor' for the solubility of water in benzene. The values of AGO, the standard free energy of solution, may be represented by the equation AGO = -229380 + 541.273T - 169.000T log T where T is the absolute temperature. Values of AGO calculated from this equation are given in column 4 of Table I. The value of AC, corresponding (5) A. F. Forziati, W. R . Norris and F. D. Roesini, ibid., 48, 555 (1949). (6) P. G. Francis, BI. L. BIcGlashen, S. D . Hainann and W. J. McManamey, J. Chem. P h g s . , 20, 1341 (1952). (7) G. G . Joris and H. S. Taylor, ibid., 16, 45 (1948).
NOTES
1022
to this equation is 73 cal./deg. mole. It is estimated that the error in c, the concentration, could be f0.5%, in each AGO value *0.1% and in the ACp value .t5 cal./deg. mole. TABLE I SOLUBILITY OF BENZENE I N WATER AU',
e,
26.
&/I.
Obsd.
Vol. 63
for c1 > co and 0 < IL: 5 1, then F'(c) would be positive for all c. (4)is equivaleht to
-* & cp(C0)
or, if PC
cal./mole Calcd.
0.8 1.84a 6037 6032 9.4 1.79 6496 6500 16.8 1.77 6893 6894 24.0 1.80 7259 7259 31.0 1.83 7606 7603 38.0 1.92 7936 7936 44.7 2.03 8240 8242 51.5 2.14 8544 8542 58.8 2.34 8856 8854 65.4 2.57 9121 9120 In some experiments at 0.8' benzene (m.p. 5.5') was present as the supercooled liquid. This figure refers to theae experiments. In others solid benzene was present and its solubility found to be 1.71 g./l. at this temperature.
THE TIME LAG I N DIFFUSION. 111 BY H. 0. POLLAK A N D H. L.FRISCH Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey Received November 29, 1968
This note is concerned with deriving a sufficient condition that the reduced time lag's2 for the (onedimensional) diffusion of a species through a membrane (with fixed surface concentrations c and 0, respectively, and initially free of the diffusing species) under the concentration dependent diffusion coefficient ~ ( c is ) a non-decreasing function of c. The reduced time lag F(c) has been shown to be2
a(zc1)
cp(zC0)
= eSo, cl = esl,
x
= e-,
In d e Y ) =
and
dv)
(5)
to d s o ) - d s o - U) 5 dsi) - g(si - u) (6) for any SO < s1 and u > 0. But (6) is equivalent to g'(y) being an increasing function, i e . , g is convex. We have thus proved the following theorem: If
In
Ioey
P(u) du = g(g)
(7)
is a convex function of y, then F'(c) 2 0 for all positive c. The physical importance of this result stems from the fact that if F'(c) 2 0 and lim D(c) = Do, a constant e-0
then the inequality stated by equation 15 of reference 2 can be replaced by the stronger
-61 -< F(c) 5 31
(8)
This is true for example if D(c) is a polynomial (or infinite series) with positive coefficients bj n
P(c) =
bjCi j-0
Then
J[ wP(w) Ji P(u)du dw
F(c)
=
c
(K
(1) du)l
Integration by parts shows this to equal since the numerator by the Schwarz inequality is non-negative. Setting
ADSORPTION OF CETYLPYRIDINIUM CHLORIDE ON GLASS BYA. E. WESTWELL AND E. W. ANACKER
and w
=
Chemistry Department, Montana State College. Bozeman, Montana Receiaed October 28, 1868
xc
we find that (2) becomes
Our aim is to test whether F'(c) 2 0. This will certainly be true if F ( c l ) > F(CO)if c1 > co. Thus if it should be the case that (4) H. L. Frisch, THISJOURNAL, 61, 93 (1957). (2) H. L. Frisch. ibid., 62, 401 (1958); the nomenclature and definition8 used throughout this paper are in accord with those of reference 1, 2. (1)
I n a recent light scattering study1 of cetylpyridinium chloride (CPC)-sodium chloride-water mixtures, two breaks in the scattering curve a t low surfactant concentrations were found. This is illustrated in Fig. 1. The usual behavior a t low surfactant concentrations is indicated by the broken line. Since all solutions had been filtered through fritted glass prior to the light scattering measurements, adsorption of CPC on the filter was suggested2 as a possible explanation of the observed departure from (1) E. W. h a c k e r , THISJOURNAL, 62, 41 (1958). (2) By referee of 1.
