PURIFICATION AND PHYSICAL PROPERTIES OF ORGANIC COMPOUNDS. VI
SOMEAPPLICATIONS AND LIMITATIONS OF AS A
THE SPECIFICHEATMETHOD “NON-COMPARATIVE CRITERION OF PURITY”
EVALD L. SKAU1
Received July 19, 1984
Part 111 (8) of this series of papers contains a discussion of the enormous rise in the values of heat content and specific heat of a solid a t constant , just below its melting (freezing) pressure, ( A H ) , and ( C P ) ~respectively, point owing to the presence of impurity. In Part V (0) it was pointed out that only a small amount of impurity is necessary to raise the value of (Cp), above that of (Cp)i, the specific heat of the liquid, at the freezing we may a t once suspect the point, and it was shown that if ( C p ) , > (cp)~, presence of impurity in the sample. The purpose of the present communication is to point out certain possibilities which must be kept in mind in applying such heat content and specific heat data as a %on-comparative (10) criterion of purity.” Although there is a high probability that a given compound is quite pure if the value of ( C P )increases ~ almost linearly with temperature and so as not to exceed that of (Cp)t a t the freezing point, actual exceptions and apparent exceptions exist. The actual exceptions comprise all the cases of impure samples where the change from the liquid to the solid state takes place completely a t constant temperature, e.g., a eutectic mixture. The apparent exceptions are comprised of cases in which the change from the liquid to the solid state takes place over a temperature range but where this temperature range lies completely above the highest temperature for which the data for the heat content, and therefore for the specific heat, of the solid have been determined experimentally. This can best be seen by reference to a diagram. In figure 1the dotted lines and the upper full line represent the heat contents in calories per gram, A H , of pure benzene in the liquid and solid states 1 Guggenheim Fellow a t Bayerische Akademie der Wissenschaften, Munich; Chemisches Institut der Universitat, Frankfurt am Main; and Bureau Idternational des Etalons Physico-chimiques, Brussels. Present address: Department of Chemistry, Trinity College, Hartford, Connecticut. 541
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EVALD L. SKAU
a t various temperatures near the freezing point, 5.5"C.;AH for the pure liquid a t 5.5"C. is taken as zero. The full lines represent the heat contents of a l-g. sample of benzene containing 1.48 mole per cent of naphthalene, i.e., enough to lower its freezing point 1°C. (See paper I11 of this series, samples I and V, respectively.) The eutectic temperature of this binary system is -3.5"C., i.e., 8°C. below the freezing point of the sample being considered, and the eutectic composition is about 13 mole per cent, 19.7 weight per cent, of naphthalene (12). The total heat change for 1 g. of the impure sample during its complete solidification can be calculated on
FIQ.1. HEATCONTENT-TEMPERATURE CURVEFOR A PUREAND SAMPLE OF BENZENE
FOR AN
IMPURE
the basis of Washburn and Read's values and on their conclusion that the system behaves ideally. One gram of eutectic liquid would give up about (0.197 X 36.4 0.803 X 30.1) or 31.35 calories during solidification, that is, about 1.25 calories per gram more than pure benzene. For the particular sample in question the amount of benzene crystals which would separate on cooling to -3.5" is 0.88 g. per gram of sample (8), so that there remains 0.12 g. of eqtectic solution. This gives up 0.12 X 1.25 or about 0.15 calorie per gram more on solidification than the same amount of pure benzene. Thus it is obvious that the heat content of the sample completely solidified at the eutectic temperature is 0.15 calorie per gram lower than that for
+
PURIFICATION AND PHYSICAL PROPERTIES O F ORGANIC COMPOUNDS
543
benzene. This is represented in figure 1 by the sharp drop in the heat content curve at -3.5°.2 Below this temperature the curve would be expected to run practically parallel to that for pure benzene since the slope, i.e., the specific heat, will not be much different, the specific heat of crystalline mixtures being an additive property (7). The uppermost curve in figure 1, i.e., that for the liquid and supercooled liquid states, can be considered as the same for the pure and slightly impure benzene. Fromfigure 1 it is obvious that i f the heat data for the impure sample in question did not include any values for the temperature range -3.5' to +4.5"C., the data would be interpreted as proving that the sample was highly pure, since the specific heat of the solid would be almost linear with respect to the temperature and apparently (Cp), < (Cp)l at the melting point. This would also be true in case the benzene contained any concentration of naphthalene as impurity up to 20 per cent by weight and indeed, since the same condition would exist on the other side of the eutectic, it would be impossible to distinguish by means of this heat data alone between a pure compound and a sample containing as high as 30 to 40 weight per cent of naphthalene. The case of cerotic acid reported by Garner and King (4) probably falls in this category. These authors pointed out that although the sample was a mixture of at least two acids, probably C Z ~ H ~ and ZOZ C2sHssO2,as shown by x-ray analysis (3), the curves for the specific heat up to within 6°C. of the freezing point failed to show the usual abnormalities indicative of the presence of impurities. It seems probable therefore that the eutectic temperature for the mixture falls within 6°C. of the freezing point. Indeed this is in accord with the fact that an equimolecular mixture of the straight 4 0 ~a melting point only 6.1"C. below chain acids C,H2,02 and C n + 2 H ~ n +has the freezing point of the C, acid when n = 16; 5.5"C. when n = 18; 4.4"C. when n = 20; 4.3"C. when n = 22; and 4.2"C. when n = 24 (3). For the mixture of the Cza and CZSacids, therefore, the melting point would be expected to be about 4°C. below the freezing point of the C26acid.3 Let us finally point out a possible misinterpretation of the heat content and specific heat data when the data for the range just below the melting point are complete. The curve for the sample of benzene containing 1.48 mole per cent of naphthalene as impurity, given in jigure 1 , might be mistaken .for that for a nearly pure compound with a transition point at -S.S"C., the 2 In actual practice this drop does not take place at a constant temperature since, as in the case of the pure substance, even a trace of impurity causes the solidification t o take place over a range. a The fact that the heat of fusion for this sample as obtained by Garner and King (4) is much lower than that of either the pure Cne or acid, indicates, if we assume that !he sample contained no other impurity, t h a t this binary system is not ideal.
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EVALD L. SKAU
P-form being stable below that temperature and the a-form above? It is therefore at once obvious that such a heat content curve with a break below the melting point cannot safely be accepted as definite proof of a transition point unless the curve just below the meEting point (instead of below the supposed transition point) indicates that the sample is highly pure. REFERENCES (1) BOGOJAWLENSKI: Schriften Naturforsch. Ges. Universitat Jurjeff (Dorpat) 13, 1 (1904); Chem. Zentr. 76, 11, 945 (1905). (2) DICKINSON AND OSBORNE: Bur. Standards Sci. Papers, No. 248; SOC.Refrigerating Engrs. 1, 32 (1915); J. Franklin Inst. 179, 489 (1915). (3) FRANCIS, PIPER, AND MALKIN:Proc. Roy. SOC.London l%A, 214 (1930). (4) GARNER AND KING: J. Chem. SOC.1929, 1849. (5) TAMMANN: Krystallisieren und Schmeleen, p. 14. Barth, Leipzig (1903). (6) Reference 5, pp. 14 and 25. (7) TAMMANN AND ROHMANN: 8. anorg. Chem. 190, 227 (1930). (8) SKAU:J. chim. phys. 31, 366 (1934). See also references 1,2, 5, and 11. (9) SKAU:Bull. SOC. chim. Belg. 43, 287 (1934). See also reference 5, pp. 14 and 25. (10) SKAU:Proc. Am. Acad. Arts Sci. 67, 551 (1933). (11) SMITH:Phys. Rev. Ill 17, 193 (1903). (12) WASHBURN AND READ:Proc. Nat. Acad. Sci. 1, 191 (1915).
The heat of fusion of thea-form would then be taken as the difference in the heat content of the liquid a t +4.5"C. and t h a t of the "solid form'' obtained by extrapolating the curve for the solid from just above -3.5"C. up t o +4.5"C. The heat of transition would be taken as the difference between the heat content of the "solids" and the "solid 8'' a t f4.5"C. by extrapolation of the corresponding curves up t o +4.5"C.
