J. Phys. Chem. 1980, 84, 979-980 t/'C
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framework of Project PR 03.10.1.
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References and Notes
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(1) I. Prigogine and R. Defay, translated by D. H. Everett, "Chemical Thermodynamics", Longmans, Green and Co., New York, 1954. (2) I. Schroder, Z. Phys. Chem., Stoechiom. Verwandschaftsl., 11, 449 (1893). (3) J. H. Hildebrand and R. L. Scott, "Solubility of Nonelectrolytes", 3rd ed., Reinhold, New York, 1950. (4) N. A. Gokcen, J. Chem. Soc., Faraday Trans. 1, 438 (1973). (5) F. Kohler, G. H. Findenegg, and M. Bobik, J. Phys. Chem. 78, 1709 (1974); E. Libermann and F. Khler, hhnatsh. Chem.,9% 2514 (1968). (6) H. Buchowski, U. Domaiska, A. Ksiazczak, and A. Maczytkki, Rocz. Chem., 49, 1889 (1975). (7) H. Buchowski and A. Ksiazczak, Rocz. Chem., 48, 65 (1974); 50, 1755, 1965 (1976). (8) I f the vapor pressure of a solid is too large to be neglected, it is subtracted from the measured value of Ap. (9) H. Margenau and G. H. Murphy, "The Mathematics of Physlcs and Chemistry", 2nd ed., Van Nostrand-Reinhold, Princeton, NJ, 1956. (10) The small effect of pressure on activities in condensed phases has been neglected. (1 1) Vapor pressure over saturated solution and solubility are determined in separate experiments, and xALlst corresponding to a given temperature Is found from the smoothed solubility curve. If the curve tmt - xmtis flat, the error due to interpolation is large; S x l x (1 x) for solutions of phenols in cyclohexane is greater than 20% and determination of A is impossible. (12) H. H. Rosenbrock, Comput. J., 3, 175 (1960). (13) H. Buchowski, J. Phys. Chem., 73, 3520 (1969). (14) G. Allen, J. G. Watkinson, and K. H. Webb, Spectrochim. Acta, 22, 807 (1966). (15) F. S. Mortimer, J . Am. Chem. Soc., 45, 633 (1923); J. Chipman, ibid., 46, 2445 (1924).
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Flgure 6. Solubility curve of benzoic acid in benzene calculated from spectroscopic data (see text). Points: data by Mortimer and by ChIpman.l5
very well with the solubility curve calculated from the data given by Mortimer and by Chipman.15
Acknowledgment. The authors are grateful. for the support of this work provided by the Institute of Physical Chemistry, Polish Academy of Sciences, within the
Determination of the Critical Exponents in Liquid Ternary Mixtures by a Nonlinear Dielectric Method J. ZioYo," 2. Ziejewska, and J. Piotrowska Institute of Physics, Silesian University, Uniwersytecka 4, 40-007 Katowice, Poland (Received August 13, 1979) Publication costs assisted by the Polish Academy of Sciences
Measurements of dependence Ae/E2 (where A€ = €high field - tiow field and E is the electric field strength)~vs.T T , (T, is the critical solution temperature of the mixture at the critical point and T is that outside it) are presented. At the critical point At/E2 1 / ( T - TJf is valid, whereas outside the critical point the following is valid: At/E2 l / ( T - T*)fwhere T* C T,, One can state, using this method, that the mixture of the critical solutions of nitrobenzene-hexane and nitroethane-hexane behaves as a critical solution.
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Introduction The nonlinear dielectric effect (NDE) is defined by the quantity At/E2 (where Ae = th' h field - tlowfield and E is the electric field strength). This henomenon is used for investigations of intermolecular and intramolecular interactions in liquid dielectrics. It is also used for investigations of pretransitional effects near the phase transition, because this effect is extremely sensitive to fluctuations of the dielectric permittivity of a 1iquid.l Though the first work concerning critical solutions was carried out by Piekara2 in 1936 greater interest in using NDE for investigations of phase transition was not observed until several years later.3-6 All hitherto existing NDE investigations were limited to measurements a t the critical point. The second-order transition that is observed at a solution critical point is similar to a critical gas-liquid phase transition. For this case, near the temperature of phase separation (T,) the following dependence is ~ a l i d : ~ - ~ At E2
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( T - TJS
(1)
0022-3654/80/2084-0979$01 .OO/O
where f is the critical index, dependent on the difference in dielectric permittivities of components of the The first-order transition, similar to the liquid-gas transition, ought to be observed outside the critical solution point. The following question arises: Is NDE a method sensitive to the difference between first-order and secondorder transitions? In order to answer this question NDE measurements have been made for critical and noncritical concentrations.
Results The subjects of our measurements were solutions of nitrobenzene in hexane (NB-H) and nitroethane in hexane (NE-H). Coexistence curves for NB-H (open circles) and NE-H (closed circles) are presented in Figure 1. Figure 2 shows results of measurements of (At/E2)-lvs. T - T, for different NB-H solution concentrations (critical solution: 0.43 (crosses); and noncritical solutions: 0.35 (closed circles), 0.5 (open circles)). A qualitative difference between results 0 1980 American Chemical Society
980
The Journal of Physical Chemistry, Vol. 84,
No. 9,
1980
Ziolo, Ziejewska, and Piotrowska
Ffgure 3. The dependence of (At/,!?-’ vs. T - T, (circles) and (Ad,!?)-’ vs. T - T‘ (crosses) (where T’ = T, - 0.6 K) for NB-H solution with a concentration of 0.35. I
Flgure 1. Phase diagrams for a solution nitrobenzene-hexane (open circles), nitroethane-hexane (closed circles), and ternary solution nitrobenzene-nitroethane-hexane (crosses).
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Flgure 4. Dependence of (AdE2)-’ vs. T - T, (log-log plot) for a concentration of 0.63 nitrobenzene-hexane in nitroethane-hexane.
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Flgure 2. The dependence of vs. T - T, (log-log plot) for the following solutions of nitrobenzene-hexane with the concentrations: critical, 0.43 (crosses); and also 0.35 (closed circles) and 0.50 (open circles).
for critical and uncritical solutions is seen. Results become similar for all concentrations at temperature T* C T,. Figure 3 shows the dependence of (Ac/E2)-l vs. T - T, (circles) and (Ac/E2)-l vs. T - T* (crosses) (where T* = T, - 0.6 K) for NB-H solution with a concentration of 0.35 (T* is determined by fitting).6 Therefore, it can be accepted that the formula describing temperature dependence of NDE has the following form: A€ 1 (2) E2 ( T - T*)f where T* C T,.
for the phase transition isotropic liquid-nematic,4i6 which was a first-order transition. For a first-order transition in solid state, the temperature T* also occurs.’ Then, the existence of T* can be treated as an indicator of a firstorder transition. Therefore, the dependence2can be admitted as an experimental confirmation of the fact that the phase transition outside the critical solution point is a first-order transition. Since phase transitions far away from critical points are known to be of first order, dielectric measurements demonstrate that a critical mixture behaves otherwise. Figure 1 shows the coexistence curve (crosses) for different concentrations of solution, which is the mixture of NE-H in NB-H. Figure 4 presents the results of measurements of (Ac/E2)-1vs. T - T,, for one point belonging to the coexistence curve of a ternary solution (0.63 mole fraction NE-H in NB-H). It is seen that the results obtained can be depicted by eq 1. Therefore, the mixture of two critical solutions behaves as a critical solution.
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Discussion The results presented herein of NDE measurements for uncritical solutions indicate the necessity of introducing the temperature T* in order to describe the temperature dependence AelE2. The temperature T* was introduced
References and Notes (1) A CheYkowski, “Fizyka Dielektrykbw”, PWN, Warszawa, 1972 (in Polish). (2) A. Piekara and B. Piekara, C.R . Acad. Sci. Paris, 203, 1058 (1936). (3) W. Pyiuk and K. ZboiAski, Cbern. Pbys. Lett., 52, 577 (1977). (4) J. MaYecki and J. ZioYo, Cbern. Pbys., 35, 187 (1978). (5) J. C. Filippini and Y. Poggi, J . Pbys. C7, 36, 137 (1975). (6) J. ZioYo, Cbern. Phys. Lett., 84, 570 (1979). (7) C. Kittel, “InWductionto Soli State Physics”, Wiley, New York, 1966. (8) J. ZioYo, Pbys. Lett. A , 73, 41 (1979).
