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derived from the plots, of kHketo = 1.3 1. mole-’ sec-I, and k ~ ~ = ~ ’0.2 ” 1. mole-’ sec-’. Since even a t the highest acidities the rate of tautomerism is comparable with the exchange rate, it is possible that a large part of the observed enol exchange rate is due to prior exchange of the keto form and subsequent tautomerism. I n this case, the actual rate of oxygen exchange of the enol form will be considerably lower than the figure quoted above. A rigorous analysis of the exchange kinetics could be made in principle, but would necessitate a large number of runs and a correspondingly large amount of 170enriched water. However, the large difference in exchange rates of the keto and enol forms is demonstrated. The commonly accepted mechanism for oxygen ex-
change of a carbonyl group involves the nucleophilic attack of the oxygen atom of a water molecule on the carbon atom of the protonated carbonyl group to give a tetrahedral intermediate.’ The keto form has two carbonyl groups available for protonation, while the enol has formally only one carbonyl group, and therefore, other factors being neglected, there is twice as great a chance of the keto form being protonated and subsequently exchanging. The actual ratio of the rates is at least 6:l. Presumably, electronic effects play an important part in determining the relative rates; in particular, the carbonyl group in the enol form will be less susceptible to protonation than the keto carbonyl group, since it is already internally hydrogen bonded.
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Comment on the Article “On the Theory of the Dielectric Dispersion of Spherical Colloidal Particles in Electrolyte Solution”’ Sir: Spherical colloidal particles suspended in an electrolyte solution display a dispersion of very high dielectric constants at low frequencies.2 A mechanism due to the polarization of the counterion atmosphere was shown to account very well for the observed experimental facts.3 The underlying model theory has recently been criticized by Schurr’ for not taking into account the surface conductivity due to free charge carriers as introduced by O’Konski.* We would like to make clear that this “free” surface conductivity X can be neglected as far as the subject of the criticized paper is concerned, that is, the low-frequency dielectric dispersion of spherical colloidal particles suspended in a fairly well conducting electrolyte solution. It had dready been pointed outZt5that the “free” surface coiiductivity cannot explain the low-frequency dielectric dispersion since it results in relatively small dielectric increments which display a dispersion a t far higher frequencies. Therefore, the effect of X was not taken into account in the above-mentioned model theory, but only the complex conductivity due to bound counterions. Schurr has included the “free” surface conductivity in his calculations, thus obtaining T h e Journal ,of Physical Chemistry
a somewhat more general theory. His result differs from that of ref 5 only by the fact that the conductivity inside the particle K~ is replaced by an apparent con2X/R (R = radius of the sphere). ductivity K~ This might be of significance for certain other phenomena, but not for the phenomenon in question. Since the quantity 2X/R can be assumed to be small in comparison with the external conductivity K,, it will have no noticeable effect on the low-frequency dielectric dispersion as may be seen from eq 26 and 27 in ref 5, Schurr has suggested dielectrophoretic measurements of the dipole moments of the particles to test the theories. According to him, there should be an extremely large difference in these dipole moments (almost five orders of magnitude in one case) depending on which of both model theories is applied. Such a big difference in the dipole moments would indeed be very remarkable in view of the fact that the over-all dielertric increment is virtually the same. It can be shown, however, that this big difference does not exist. I n order to calculate the dipole moments for his model Schurr used the true surface charge density as deter-
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(1) J. M. Schurr, J . P h y s . Chem., 68, 2407 (1964). ( 2 ) H. P. Schwan, G. Schwarz, J. Maczuk, and H. Pauly, ibid., 66,2626 (1962). (3) G. Schwarz, ibid., 66,2636 (1962). (4) C.T.O’Konski, ibid., 64,605 (1960). (5) H.P.Schwan, Advan. BWZ. Med. P h y s . , 5,183 (1957).
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the compressibility of xenon in the critical region, Habgood and Schneider6 found the critical isotherm considerably flatter than that corresponding t o a van der Waals fluid. The function (b2P/bV2) T, vs. density has an inflection at or very near the critical density indicating that (b4P/bV4) To must vanish if the isotherm is continuous. The third derivative was shown to be small, and they suggested that it may also vanish. Zimm,l from an analysis of his light-scattering data in the critical-solution region of the system perfluoromethylcyclohexane carbon tetrachloride, found evidence that the third derivative of the chemical T,,P, tends toward zero. potential, (b3p1/b213) Recent experiments in our laboratory on the volume of mixing, V, for the system perfluoro-n-heptane isooctane (2,2,4-trimethylpentane) lo and the enthalpy nof mixing, H, for the system perfluoro-n-hexane T,,P hexane" show that the third derivatives (b3V/bz13) and (b3H/bx13)~,,p also vanish in the neighborhood of their respective critical-solution points. ( T , = 23.7", X C , F ~= ~ 0.374; T , = 22.64", XC~F,,= 0.370.) Partial molar volumes for perfluoro-n-heptane and (6) C. J. F. Bottcher, "Theory of Electric Polarization," Elsevier isooctane were determined a t several concentrations Publishing Co., Amsterdam, 1952. through the critical-solution region and at infinite DEPARTMENT OF BIOMEDICAL ENGINEERING G. SCHWARZ dilution using a technique similar t o that of Shinoda MOORESCHOOL H. P. SCHWAN and Hildebrand.12 The enthalpy of mixing for the UNIVERSITY OF PENNSYLVANIA second system was determined using an improved diPHILADELPHIA, PENNSYLVAXIA phenyl ether calorimeter. The data in both studies RECEIVED AUGUST24, 1965 were sufficiently precise to justify four coefficients in analytical functions of the form y = 2 1 2 2 a,(xl mined from the divergence of the dielectric displacement vectors. In the case of the model of ref 3 he took into account only the charge density due to the bound counterions and not the true surface charge density as he consequently should have done. I n that case he would have found little difference in the dipole moments. They then differ only by the missing 2X/R in the apparent conductivity of the inner conductivity of the sphere, We may point out, however, that the apparent dipole moment of the particle is not only due to the true surface charges but also to "apparent" surface charges ('(apparent" surface charges are, for instance, responsible for the dipole moment of a purely dielectric sphere in a purely dielectric medium6). In the case of interest here the apparent dipole moment as seen in the electrolyte solution can easily be obtained from the equation for the outside electric potential +a which is simply a supposition of the potential of the external field and the potential of the apparent dipole moment of the sphere (eq 13 in ref 1, eq 34 in ref 3).
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2 2 ) m.
Shapes of Critical Isotherms
Sir: The conditions which characterize the liquidvapor critical point on the P-V-T surface for a pure substance are: (bPlbV)~, = 0, ( b 2 P / b V 2 ) ~ =, 0, . . . , (b"P/dV")T~ 0. If the critical isotherm is to be a continuously differentiable function, thermodynamic stability requires n t o be an odd integer in the first nonzero derivative.' For a van der Waals or classical fluid, the familiar value of n is 3. The thermodynamic similarities of single- and twocomponent systems have been discussed by Rice.2 The corresponding conditions for a critical-solution
