CONTRIBUTIONS TO THERMODYNAMICS: THE ANOMALOUS HEAT OF VAPORIZATION OF HEPTANE
A FEW yearsago, some very precise data, painstakingly
TABLE 1
determined, were reported for the vapor pressures and Some Vapor Pressure Data for n-Heptane boiling points of 52 highly purified hydrocarbons (1). Point Pressure, From such data can be determined heats of vaporizaTemp., T. mm. numbw tion. Assuming that the heat of vaporization may he 1 98.781 768.08 represented by the relation 2 98.217 755.31 3 97.710 744.11 aH = A' + B'T (1) 4 97.160 732.12 over a moderate temperature range, the Clapeyron 5 92.060 627.98 6 84.832 500.75 equation, 14 42.597 103.66 dp dT
AIf = TAV
(2)
16 18
35.993 29.648
77.28 57.42
may be integrated, following the usual procedures, to obtain
tested.) No adequate explanation of why the heat of vaporization should increase has yet been found, but it is certainly not a result of errors in neglecting the In p = - A ' / R T + ( X ' I R ) In 7' + C' liquid volume and in assuming that the ideal gas laws or are valid; the temperature is well below the critical, logp=C-~/7r+Blop~ (4) and the pressure below atmospheric. It may be noted in this connection that heptaneis the In determine IVhether surh a equa- only straight-chain hydrocarbon that is foundin tion would be satisfactorily precise over the entire pine trees instead of, or in addition to, the terpenes ranges of pressure and temperature for which data. are usually present, and it occurs in only two species: the given, or whether it should he applied only to portions Jeffrey pine (Pinus jeffreyi) and the digger pine (P. of the data. (for each pure hydrocarbon), the equation sabiniana) ( 2 , 3). would expect a Cs or C1ohydr+ was solved for the constants ,' and for several carbon rather than heptane, since Csis the structural groups of three selected points. unit of the terpenes (4, 5, 6, 7, 8). It may be that the For it was that values of AH!R appearance of heptane is related to this thermodynamic calculated by extrapolating down with the equat~on peculiarity, The temperature at which this anomabased on points L 5 , and 6 (Table 1 reproduces some of lous heat effect to be apparent is well above any the data from reference (1) and Table 2 gives values of the constants derived) agreed fairly well with those TABLE 2 calculated by extrapolating up with the equation based Calculated Results for n-Heptane on points 14,16, and 18. This indicated that the equation would he satisfactory. Points ztsed A B But from the values of A and B, and the relation 1,2, 3 -11,087.7 +79.7335 1,3, 5 855.568 + 5.69779 that
*,
+
A H / R = 2.3.4
+ BT,
(5)
the surprising fact is brought out that as the temperature increases, the heat of also increases, a t least at temperatures ahove about 9 2 0 ~ .~ h is, ~ B has a positive value. ~h~ factthat R increases with temperature is itself anomalous; that it becomes positive is quite startling, F~~ normal liquids, the heat of vaporizatiou decreases monotonous~yto a t the critical point. So far, n-he~taneis the only liquid tested that shows this anomalous increase if AH with T' far' n-heptane is the Only liquid EDITOR'S NOTE: This is mother of "Dr. McQuirg's" papers intended to test our rcaders' ingenuity and insight. For s. cornrncnt, on this paper, turn to pngc 377.
b5, 6 14, 16, 18
+
+
2355.13 2726.38
- 3.67069 - 6.19821
that is likely to be encountered by a pine tree. Nevertheless t there may be a catalytic phenomenon within !he tree that takes advantage of this anomaly, with ~tsconsequenteffect on the free energy of formation of this hydrocarbon from the precursor chemicals which 1" a pine tree normally give terpene compounds. The matter be instigated LITER~TURECITED ( 1 ) WILLINGHAM, C. B., W. J. TAXOR,J. M. PIGNOCCO, AND F. D. Rossr~r,J. Research Natl. Bur. Standards, 35, 21944 (1945). (2) G ~ R Y E.,, A N D J. A. HALL, Plant Physiol., 1 0 , 5 3 7 4 3 (1935).
348
JOURNAL OF CHEMICAL EDUCATION
(3) M~nov,N. T., J. Forestry, 44,13-16 (1Y46). (4) BERNTHSEN, A,, AND J. J. SUDBOROUGH, "A Textbook of
(6) FIESER,L. F., AND M. FIESER, "Organic Chemistry," D. C. Heath and Co., Boston, 1944.
Organic Chemistry," D. Van Nostrand Co., Ino., New York, 1931. (5) CONANT,J. B.,"The Chemistry of Organic Compaunds," The Maemillan Co., New Yark, 1933, pp. 339 ff., 566.
(7) G I L ~ NH. , T., "Organie Chemistry," John Wiloy B Sons, Inc., New York, especially Vol. IV, 1953. (8) SIMONSEN, J. L., "The Terpenes," 2nd ed., Cambridge University Press, 3 vols., 1947-52.
