CONTINUITY O F THE MET ASTABLE STATE ANDREW VAN HOOK Department of Chemical Engineering, Lafayette College, Easton, Pennsylvania Received September 28, 1996 INTRODUCTION
There is no reason to expect a discontinuity of properties of a system on passing through the limit of complete equilibrium into the metastable equilibrium state. Ostwald (1883), Roozeboom (1889), Rothmund (1907), and most recently Liesegang (4)have discussed this behavior in general, while numerous workers have offered abundant experimental evidence, mostly on the change of properties in the supersaturated region. In addition, the density, vapor pressure, and viscosity of supercooled water, the viscosity of superheated water, and the flow properties of fluids have been reported as continuous from the “stable” region, so that voluminous data indicate the truth of the above statement. A lone exception to this principle has been interpreted (4)in the work of Nayar (6), who claims a variation in volume of ammonium oxalate, oxalic acid, and potassium nitrate solutions on passing through the saturation point. It was the purpose of this investigation to repeat and extend Nayar’s work. He (7) confirms the results of this paper, and states that his object was not to question the principle of continuity of properties, but “to study the behavior of solutions before and during crystallization (and not to prevent crystallization).” EXPERIMENTAL
Dilatometers, of about 75-ml. capacity with thermometers centrally located, were employed. Sixty to 70 ml. of solution was added and the remaining volume and capillary completely filled with a deaerated mineral oil which was proven to be immiscible, even in the case of the alcoholic solution. The whole was brought to a steady state a t a temperature 10’ to 15°C. above the saturation temperature, and cooled slowly over the course of one and one-half to three hours in a large well-stirred water bath. Recrystallized solutes of reagent quality were used. An amount of solute and water proper to saturation at the chosen temperature was heated for an hour in a closed vessel with agitation a t a temperature far in excess of saturation, brought to a boil, and filtered directly into the scrupulously clean and warmed dilatometer. In almost 593
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all cases the first portion of filtrate served as wash liquid. The solution was covered immediately with oil, and the saturation temperature determined. This was accomplished by slowly cooling the vigorously agitated solution, when, in most cases, a spontaneous crystallization occurred a t the saturation temperature. This point was confirmed by supercooling the solution to 0.25' to 0.5'C. without stirring, and seeding. I n all cases a n immediate crystallization occurred. As a further guarantee of the correctness of the accepted values for the saturation temperature, the solutions were seeded while a t a temperature 0.25" to 0.5"C. above this temperature. In no case did crystal growth occur. DISCUSSION
The results are presented in figures 1, 2, and 3. A blank with the oil (figure 2) demonstrates that the cooling curve of oil and apparatus is
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FIG.1. Cooling curves van Hook Potassium nitrate.. . . . . . . . . . . . . . . . . . No. 1 83.5"C. Ammonium oxalate . . . . . . . . . . . . . . . . . . No. 2 83.5"C. Oxalic acid .......................... No. 3 57.0"C.
Nayar No. 4 85°C. No. 5 85°C. No. 6 55°C.
regular, and equilibrates with the bath temperature within 0.3'C. Therefore any irregularity must be due to the cooling properties of the solution. All the curves representing this work are smooth and continuous from well above saturation to the crystallization temperature. No indication of change in direction at the saturation point, such as reported by Kayar (6) and presented schematically for coniparison in figure 1, is apparent.
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The results are in accord with the scant data available on the values of density of supersaturated solutions. The values reported by Scott and
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FIG.2. Cooling curves. 1, calcium nitrate, 34°C.; 2, acetamide in water, 35°C.; 3, acetamide in 95 per cent ethyl alcohol, 34°C.; 4, urea, 34°C.; 5, oil blank.
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FIG.3. Oxalic acid, 57°C. A, cooled very slowly, three hours; B, cooled in air, 30 minutes; C, cooled in ice, 3 minutes.
Badger (8) for calcium nitrate, sucrose solutions (3), potassium chlorate solutions (l),and supercooled water (2) are all continuous without marked change in slope at the saturation point.
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The results presented in figure 3 are all for the same solution in the same dilatometer. The indications are that very rapid cooling induces crystallization, due to localized undercooling, a t a point closer to the saturation temperature, thus causing a depression in the cooling curve. The same apparent behavior would result from thermometric lag. Or, what is more likely, accidental inoculation with crystallization nuclei may have caused Nayar’s observed results ( 5 ) . The fact that Nayar’s first inflection generally corresponded with the first appearance of a thin shower of crystals is strongly suggestive of this. I n this work no such thin shower of crystals was observed. SUMMARY
The temperature-dilation curves for supersaturated solutions of potassium nitrate, ammonium oxalate, oxalic acid, calcium nitrate, acetamide, and urea show no non-uniformity at the saturation point. This uniformity is confirmed by the scant data available in the literature. The principle of continuity of properties into the metastable state is generally valid. REFERENCES (1) International Critical Tables, Vol. 111, p. 86. McGraw-Hill Book Co., Inc., New York (1928). (2) International Critical Tables, Vol. 111, p. 26. McGram-Hill Book Co., Inc., New York (1928). (3) Landolt-Bornstein Tabellen, Vol. I, p. 464 (1923). (4) LIESEGANG, R. E.: Scientia 67,345, 110 supplement (1935). ( 5 ) hIIERS, H. A., AND ISAAC: J. Chem. SOC.89, 413 (1906); Rice Institute Pamphlet 6, 222 (1914). (6) NAYAR, M. R.: Bull. acad. sci. United Provinces Agra Oudh Allahabad, India 1,100-1 (1931); Chem. Abstracts 26,5816 (1932). LIESEGASG:Reference 4. (7) NAYAR, M. R.: Private communication. (8) SCOTT A N D BADGER: J. Phys. Chem. 40, 461 (1936).
