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experiments. However, should hydrogen bonding to solvent exist, it does not greatly alter the coordinates of the helical polypeptide.
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physical properties to determine the temperature dependence of al. Compressibility seems to be a less questionable property to use for this purpose than is surface tension. AMERIC-ANMEDICAL ASSOCIATION FRANCO QUADRIFOQLIO D~~ w. uRRY The greatest problem with compressibilities is that INSTITUTE FOR BIOMEDICAL RESEARCH CHICAGO, ILLINOIS 60610 reliable data are difficult to obtain. Nevertheless, if one examines position number 2 of the figure in ref 1, RECEIVED FEBRUARY 23, 1967 it is found that while the actual values of soare altered as a result of the temperature dependence of al obtained from compressibilities, the relative differences between solvents are pretty much preserved. It is On the Scaled-Particle Theory of this difference that distinguishes water as a solvent Dilute Aqueous Solutions different from say ether or benzene. The problem still remains, however, that if one accepts the values of Sir: Recently, Ben-Naim and Friedman’ discussed the 3, obtained from their assumption number 2, then at application of the scaled-particle theory of fluids to least the fair numerical agreement found2s3 is lost dilute aqueous solutions of nonpolar g a s e ~ . ~ JTheir unless as they suggest the entropy of interaction, Si, argument is that the scaled-particle theory does not is important. It is interesting to note that if the 3s: give the correct temperature dependence for the surunder their assumption 2 are correct, then a larger face tension of water and hence the entropy of cavity contribution from Si will be required for the nonformation, S,, calculated using this theory cannot be aqueous solvents than for water. correct. They base their argument upon the work of Now it is this writer’s belief that the temperature Mayer4s5in which it was found that in order to obtain dependence of the ai's given by Rlayer are unreasonthe correct temperature dependence of the surface ably large because of the interface problem mentioned tension using the scaled-particle theory it was necesabove. There is no question that al should have some sary to assume that the hard-sphere parameter, al, was temperature dependence especially for nonspherical temperature dependent. In fact, Pierotti examined molecules, but the very nature of a collision diameter the temperature dependence of a1 and found it to be implies that there exists a large energy gradient with very small and hence unimportant in the calculation of respect to distance and hence a small change in kinetic the free energy and entropy of cavity f ~ r m a t i o n .The ~ energy should not appreciably change the collision question appears to be whether or not the scaled pardiameter. ticle theory can adequately account for the entropy of A more consistent approach to the temperature decavity formation if it does not adequately account for pendence of al is to use the extrapolation method dethe temperature dependence of the bulk surface tension scribed in ref 2 and 3. This method is equivalent to of a fluid. determining the solubility of a nonpolarizable hard The first point to be made is that the scaled-particle sphere and is therefore a direct and proper test of the theory strictly applies only to rigid wall cavities, a adequacy of the scaled-particle theory. If data for the situation met well when the cavity is filled by a molesolubility of the rare gases in a given solvent are availcule but not so well when the cavity is filled with a able a t several temperatures, then it is possible to comdilute gas. As pointed out by Ben-Naim and Friedpute al for the solvent at each temperature from the man in footnote 7 of their note, the surface tension intercept of a plot of In K H vs. CY, where K H is the given by the theory is for the interface between the Henry law constant and CY is the polarizability. This liquid and a rigid wall. Ordinary surface tension has been done for water and benzene and the results measurements involve an interface between the liquid are shown in Table I along with values of a1 calculated and a dilute gas. Although it is often assumed for from surface tension and compressibility. Examination of this table indicates that at least insofar as the lack of anything better that these two surface tensions solubility of a hard sphere is concerned, ul for these are not very different, no evidence is available to indicate the magnitude of their difference. Of even more (1) A. Ben-Naim and H. L. Friedman, J . Phys. Chem., 71, 448 importance to the argument of Ben-Naim and Fried(1967). man is the effect of temperature on the nature of the (2) R. A. Pierotti, ibid., 67, 1840 (1963). gas-liquid int,erface and to what extent this effect is (3) R. A. Pierotti, ibid., 69, 281 (1965). being ascribed to the term dal/dT. This is a serious (4) 9. W.Mayer, J. Chem. Phys., 38, 1803 (1963). difficulty and hence one should perhaps look to other (5) S. W.Mayer, J. Phys. Chern., 67, 2160 (1963). The Journal of Physieal Chemistry
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Table I : The Variation of al with Temperature
OK
ai (A), surface tensiona
288 298 315
5.05 5.02 4.94
277 298 323 343
(2.94) 2.88 2.83 2.77
Temp,
ai (A), compressibility a
ai (A), solubility*
5.02 5.00 4.96
5.24O 5.24 5.24
2.71 2.72 2.71 2.70
2 . 75d 2.75 2.75 2.74
esr spectrum of the transient radicals produced is predominantly a septet' (A). Evidence presented previously' led to this being assigned to the radical cation I (R = Me). If the acetaldehyde is mixed with the
Benzene
Water
From ref 5. From extrapolation method described in the text. This number is in excellent agreement with values determined from other sources (see Table 111 of ref 2). The bulk of data for a1 in the literature fall very close to 2.7 A (see references in ref 3).
solvents is at most only very slightly temperature dependent. The fact pointed out by Ben-Naim and Friedman that 3, is a fairly strong function of al is not surprising. The most remarkable thing about positions 3, 4, and 5 on their figure is that even with the wide choice of a
