COMMUNICATIONS TO THE EDITOR
166 consistent with this view. These results are all negative in the aense that getting microscopic information about hydrophobic interactions from them depends more on the power of the theory which may be applied than anything else. A more promising result is shown by line C in Figure 1, which gives evidence of a probe, BPh4- interaction markedly at variance with Walden's rule behavior. This can be discussed in terms of the expression dTldm
-
Jgp,(r)epA(r)dar
where gpH is the equilibrium pair correlation function for the probe P and the other hydrophobic species H and ~ P His a measure of the effect of H upon T of P at the separation (p. It remains to learn in this case whether the extra interaction compared to line B is more due to hydrophobic binding (gpH >> 1 at some r ) or to a slowly relaxing cosphere of the hydrophobic species [large epIr(y) at some r ] . It is hoped that this can be elucidated by more detailed epr studies. A most surprising feature of the present results is the marked difference i11 behavior of BPh4- and such similar species as AsPh4-+which are found near line B. TJsing VOPiz as the probe, aqueous glycerine and tert-butyl alcohol are again indistinguishable at the same viscosity white Ru4NBr solutions deviate markedly from the Walden's rule behavior. (6) Fellow of the Nat,ional Research Council of Canada, 1969-1970. (7) The support of this research by the National Institutes of Health is gratefully acknowledged.
DEPARTMENT OF CHEMISTRY OF 'NEWYORK STATEUNIVERSITY AT STONY BROOK STONYBROOK, NEWYORK 11790
cally symmetrical molecules, w > Oe2 Any thermodynamic property of a large number of fluids (with the exception of associated fluids, or fluids containing molecules of high dipole moment) can be characterized as a function of the three parameters T r j p,, and a. Pitzer3n4has shown that a group of molecules will obey the principle of corresponding states if they obey Boltemann statistics, are approximately spherically symmetrical (i.e., the rotational, vibrational, and translational partition functions are separable), and have intermolecular potential of the same general form, i.e.
where E and u are energy and distance parameters, and f is any general function. For a molecular species obeying the above assumptions, the entropy of vaporization, As, at a constant ratio of saturated gas to liquid molar volume should be constant. This has indeed been verified by examining the inert gases Ar, Kr, and Xe, where As at a gas to liquid molar volume ratio of 335.0 has been found to be 18.67,18.60,and 18.66, respectivelyS5 Therefore, a measure of the nonideality of a given molecular species may be obtained if As is examined at a constant gas to liquid molar volume ratio. Choosing a ratio of 335.0, the inherent problem which remains is finding that point in p-V-T space where this ratio is satisfied. This can be accomplished by solving the following set of equations.
CARMEL JOLICOEUR~ HAROLD L. FRIEDMAN* 7
RlEClnIVED AUGUST10, 1970
As = 0.024218V1
The Relationship between the Acentric Factor and the Entropy of Vaporization Publication costa borne completely by The Journal of Physical Chemistry
Sir: The acentric factor, w, was introduced by Pitzer*v2 as an imperical fa,ctor to characterize the deviation of molecules from spherical symmetry. The factor is defined as OJ
=
log pr"(0.7) - '1.00
(1)
where pr"(T,) is the reduced vapor pressure at the reduced temperature, Tr. The particular method of defining w , results from the experimentally observed fact that for sphericdly symmetrical molecules such as Xe, Ar, and Kr, u is essentially zero. For nonspheriThe Joztrnal of Plq&al
Chemistry, Vol. 76, No. 1, 1971
g(2
-1
(5)
In the above, p" is the vapor pressure of the pure component, Z is the compressibility factor, M is the molecular weight, and T is the temperature. For a given ratio of V,/V,, there exists only one unique solution for T, which can be found by solving eq 2, 3, and 4. This was done using the Newton-Rapbson (1) K. 5 . Pitzer, J. Arne?. Chem. SOC.,7 7 , 3427 (1955). (2) K. 8. Pitzer, D. Z. Lippmann, R. F. Curl, C. M. Huggins, and D. E. Peterson, {bid., 77, 3433 (1955). (3) K. S. Pitzer, 1.Chem. Phys., 7 , 583 (1939). (4) G. N. Lewis and M. Randall, "Thermodynamics," 2nd ed, revised by K. S. Pitzer and L. Brewer, McGraw-Hill Book Co., New York, N. Y., 1961, p 605. (5) J. H. Hildeband and R. L. Scott, "Regular Solutions," PrenticeHall, Englewood Cliffs, N. J., 1962, p 75,
167
~ Q M M ~ J N I C TO ~ ~THE I O EDITOR ~~
it]erative procedure, on the SDS 940 computer. The density constants a,@, and 6 were taken from ref 6. The vapor presswe constants for the Antoine equation, A , -LE, and 6 , were taken from NBS Bulletin 510.’ The results of this procedure, for a gas to liquid molar volume ratio of 335.0, are shown in Table I. As can be Table I Compound
n-Cz n-6.2 82-G
n-cs n-Cs 12-C7
n-c* n-69
?&-@lo
n-G n-Gz n-G
T ,OK
As, eu
w(os1cd)
0
180.7 224.4 261.4 294.8 325.6 352.3 376.5 398.3 418.8 437.8 456.0 472 0 488.1 502.1 515.9 529.9 562.8 266.9 346.1 348.1 332.5 333.9 340.1 334.6 362.1 359.4
19.05 19.85 20.32 21.14 21.52 22.40 22.72 23.48 23.88 24.46 24.76 25.37 25.75 26.21 26.52 26.95 27.96 20.61 21.83 21.82 21.33 21.60 21.33 21.11 21.38 20.99
0.0815 0.147 0.189 0.255 0.285 0.358 0,383 0.445 0.478 0.525 0.550 0.598 0,630 0.667 0.693 0.728 0.81 0.212 0.311 0,310 0.271 0.293 0.271 0,253 0,275 0.243
0.105 0.152 0,201 0.298 0.290 0.352 0.398 0.441 0.586 0.530 0.553 0.593 0.626 0.650 0.704 0.763 0.710 0.195 0.327 0.314 0.300 0.307 0.284 0.260 0.275 0.244
I
n-614
n-CE n-c26 n-617
n-czo Neopentane 3-Methylhexane %Ethylpen tane 2,ZDimethylpentane 2,4-Dirnethylpentane 3,BDimethylpentane 2,2,3-Trirnethylbutane E thylcyclopentane Methylcy clohexane
seen, a linear relationship does exist between the empirically derived acentric factor, u, and the entropy (AsVAP - 18.00) required to vaporize a nonspherically symmetrical molecule. For spherically symmetrical atoms or molecules both (AsVAP - 18.00) and o approach zero. From these results, it appears that 88331,
-*
A5O33jj
(12.7)~
in a value for of -0.057. From eq 6, a value of 0.057 is equivalent to 0.7 eu. This is in excellent agreement with the value (18.65-18.00) eu found experimentally. Thus for these measurements, represents the entropy of vaporization of the carbon atom core, for whichw = 0. For those data points which vary considerably from the linear relationship, it appears that the w values are inconsistent rather than As. For example, n-CloHzz has an acentric factor that is significantly greater than either n-CgHzoor n-C11H2., whereas A s values increase in a continuous fashion. For polar and associated molecules, there i s essentially no correlation between the acentric factor and As335. The reason for this is inherent in the initial assumptions. The intermolecular potential for polar molecules cannot be approximated by a simple twoparameter equation, since two parameter potential functions ignore dipole-dipole interactions. Thus any sui table intermolecular potential (such as the Stochmeyer potential function) involves an additional term and is no longer of the same general form as ey 4 . I n conclusion, it does appear that the acentric factor, for normal fluids, is a direct measure of the deviation of the entropy of vaporization from the spherically symmetrical molecule. Acknowledgment. I would like to acknowledge the help of R. Moore in conceiving this study and D. Lebaw for his assistance in programming. (6) E. W. Washburn, Ed., “International Critical Tables,” McGrawHill Book Co., New York, N. Y., 1926. (7) Rossini, et al., “Selected Values of Properties of Hydrocarbons and Related Compouiids,” American Petroleum Institute Research Project 44, Thermodynamic Research Center, Texas A & M University, College Station, Texas. (8) R. C . Reid and T. K. Sherwood, “The Properties of Gases and Liquids,” McGraw-Hill Book Co., New York, N. Y., 1966, p 571. (9) R. C. Weasl,, Ed., “Handbook of Chemistry and Physics,” Chemical Rubber Publishing Co., Cleveland, Ohio, 1969, p D-145.
SHELLCHEMICAL Go. MORTON SCHRAGER PLASTICS AND RESINSTECHNICAL CENTER NEWJERSEY 08096 WOODBURY, RECEIVED AUGUST19, 1970
(6)
where Asoa36 denotes the entropy of vaporization of spherically symmetrical atoms (or molecules) as met+ sured at a gas to liquid molar volume ratio of 335.0. It was previously noted that at a gas to liquid molar volume ratio of 335.0, the entropy of vaporization of the inert gases Ar, Kr, and Xe are approximately 18.65, and have acentric factors of 0. Equation 6 would project for these elements acentric factors of 0.053. This discrepancy can be resolved by examining the neon atom. The acentric factor, a, for neon has previously been estimated to be Q U 8 Ne can, however, be determined using eq 1. Over the range 1 < p o < 10 atm, neon vapor pressure datag can be accurately fitted to the Clausins-Clapeyron equation, resulting
Concerning “Kinetics of Isopropyl Alcohol Radicals by Electron Spin Reson,ance-Flow technique^'^ Publication costs assisted by the National Research Council of Canada
Sir: I n their recent paper, James and Siciliol purport to have measured the rates of reaction of the radicals (CH&cOH (RI) and CHsCHOH6H2 (Rz) with HzOz (1)
R. E. James and F. Sicilio, J . Phys. Chem., 74, 1166 (1970). The JotiTml of Physical Chemistry, Vol. 76,No. 1I lsTl
