J. DANIELKELLEYAND FRANCIS OWENRICE
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in this system is 4y0 from a deviation from Raoult's law of 5.6%. It should be noted that in two of these systems, heptane-hexadecane and hexane-dodecane, the deviation from Raoult's law is negative while, in the other two, hexane-carbon tetrachloride and cyclohexanecarbon tetrachloride, the deviation is positive. Figure 4 shows the system hexane-hexadecane, from data reported previously by the authors.I7 In this case, the activity term appears to correct the Dv curve for nonideality ; however, from the results of the other four systems, it is apparent that this agreement is fortuitous. It may be that with deviations from
ideality this small, the effect of size and shape of the diffusing inolecule on the hydrodynamic resistance of the molecule is greater than that of solution nonideality. I n any case, it is apparent that the term (d In a/d In X) does not account for nonideal diffusion behavior whether the system is associative or not. Acknowledgment. This work was supported by a grant from the Petroleum Research Fund, administered by the American Chemical Society. Grateful acknowledgment is hereby made to the donors of the fund. (17) D . L. Bidlack and D. K. Anderson, J . Phys. Chem., 68, 206 (1964).
The Vapor Pressures of Some Polynuclear Aromatic Hydrocarbons'
by J. Daniel Kelley2 and Francis Owen Rice Department of Chemistry, Georgetown University, Washington, D . C. (Received June 22, 1964)
The vapor pressures of anthracene, 1,2-benzanthracene, 9,10-dimethyl-1,2-benzanthracene, and 20-methylcholanthrene have been measured over the following temperature ranges, respectively: 69 to 86O, 104 to 127") 106 to 135O, and 128 to 152'. The rerJlts are expressed in the form log P,,, = A - B/T°K. where A and B are 12.068 and 5145 for anthracene, 11.528 and 5461 for 1,2-benzanthracene, 13.168 and 6643 for 20-methylcholanthrene, 16.108 and 7051 for solid 9,10-dimethyl-1,2-benzanthracene, and 12.232 and 5897 for liquid diinethylbenzanthracene. The average heats of sublimation over the experimental temperature ranges are obtained, and the results for anthracene are compared to previous work.
The vapor pressures of anthracene, 1,2-benzanthraand 20-methcene, 9,10-dimethyl-1,2-benzanthracene, ylcholanthrene have been measured in the pressure regions 0.001-0.01 nim. for the former two compounds and 0.0004-0.006 mm. for the latter two. The vapor prcssure of anthracene has been previously studied in higher pressure region^.^-^ The vapor pressures of the other three compounds have apparently not been investigated in any pressure region. Experimental C o m p o u n d s . The compounds used in these vapor pressure studies were of the highest purity commercially Th,e Journal of Physical Chemistry
available. Each was further purified by vacuum sublimation, and the melting point ranges of the samples (1) This work is taken from t h e dissertation submitted by J. D . Kelley t o the Graduate School of Georgetown University for the degree of Doctor of Philosophy. This work was supported in part by the National Institutes of Health, N I H Grant No. C-5411. (2) Brookhaven Xational Laboratory, Upton, N. Y.
(3) C. A. Nelson and C. E. Senseman, I n d . Eng. Chem., 14, 58 (1922). (4) F. 6. Mortimer and R. V. Murphy, ibzd., 15, 1140 (1923). (5) G. W. Sears and E. R. Nopke, J . Am. Cbem. Sac., 71, 1632 (1949). (6) B. Stevens, J . Chem. SOC.,2973 (1953). (7) V. P. Klochkov, Zh. Fiz. Khim., 32, 1177 (1958).
VAPORPRESSURES OF POLYNUCLEAR AROMATIC HYDROCARBOKS
actually employed were: anthracene, 217.0 to 217.5’; 1,Bbenzanthracene, 161.O to 161.5’ ; 9,lO-dimethyl1,2-bensanthracenel 3 22.9 to 123.5”; and 20-methylcholanthrene, 179.0 to 179.5’. Appayatus. These vapor pressure data were obtained by a dynamic method, in which the vapor a t its equilibrium pressure above the sample was allowed to effuse through a small orifice and condense on a liquid nitrogen cooled cold finger above the orifice. This apparatus was similar to that employed by Verhoek and Marshall8 to measure vapor pressures of nonvolatile esters. The sample chamber was a 25-ml. Pyrex bulb with an arm sealed to a short section of Kovar tubing, about 2.0 cm. in diameter and 1.5 cm. long; a disk of copper foil 0.013 cm. thick with an orifice of area 0.0615 was soldered across thLe top of this tubing, and another short section of Kovar tubing was attached. The top portion of the apparatus was sealed to the free end of this tubing section. During a run this apparatus was immersed up to the vacuum side arm in an oil bath kept a t temperatures constant to 0.1 ’. Procedure. To begin a typical set of determinations, the small arm on the saniple bulb was opened and approximately 1 g. of sample was introduced; since the compounds were all in the form of fine, loosely packed crystals, a large evaporating surface was assured. The arm was then closed and the apparatus inimersed in the oil bath and connected to the vacuum line through a two-channel stopcock which could be closed, opened to vacuum, or opened to a tank of dry nitrogen gas for subsequent breaking of vacuum. The fresh sample was then pumped a t room temperature for a t least 2 hr.; the temperature of the bath was then slowly raised to 60°, the cold finger filled with liquid nitrogen, and pumping continued a t that temperature for about 30 min. At this point vacuum was broken by admitting nitrogen gas, the cold finger was removed, and a clean cold finger substituted. The oil bath was then allowed to warm to the temperature desired for a vapor pressure determination. ’When the oil bath had stabilized at this temperature, which was read on a calibrated mercury-in-glass thermometer to the nearest 0. I O including the emergent stem correction, the apparatus was quickly evacuated and, when the pressure had fallen to 0.1 mm., the cold finger was filled with liquid nitrogen. Timing of the run was started as the cold finger was filled. When a sufficient amount of sample, 20-30 mg., had condensed on the finger, vacuum was broken by admitting nitrogen and the timing of the run stopped. The condensed sample was then carefully washed from the finger with a minimum amount of spectral
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grade acetone into a preweighed weighing bottle. The bottle with sample was placed in a vacuum desiccator and carefully dried and weighed. All weights were obtained on a Mettler Type H one-pan balance read to the nearest 0.1 mg. The determinations were not carried out in any particular order with regard t o temperature; 30 to 40 points were used in the determination of each vapor pressure curve. During the course of the investigation of a conipound, the melting points of the charged samples and condensates were periodically checked to ensure that no change in the nature of the inaterial had occurred. Calculations. From kinetic t h e ~ r y the , ~ number of gas molecules, 2, entering an orifice of area a in time t is given by 2
(nu/4)at (1) where n is the number of molecules per unit volume and u is the average velocity of the molecules. Substituting for n and u their values in terms of pressure, p , temperature, T, molecular mass m, and Boltzniann s constant, k, one obtains from (1) Z
=
atp(l/zrrmkT)’” (2) The mass of material entering the orifice, G, may be obtained by niultiplying (2) by iV/N0, where N o js Avogadro’s number. Renienibering that Nok is equal to R, the gas constant, we obtain for G =
G = atp(M/2nRT)”’ (3) Since the orifice has a finite thickness, not every molecule which enters passes through, so that (3) must be multiplied by W , the probability that an entering molecule leaves the orifice. Values of W for channels of various dimensions have been tabulated by ClausinglO; W proved to be 0.978 for this orifice. Rearranging (3), the equilibrium vapor pressure is given by p = G’T”‘[(l/aW) (2nR/M)”’] (4) where the quantity in brackets is constant for a given compound in a given apparatus, and G’ is equal to G/t.
Results The vapor pressures of the four substances investigated were measured over the following temperature ranges: anthracene, 69 t o 86’ ; l12-benzanthracene, ~
~~~
( 8 ) F. H. Verhoek and A. L. Marshall, J . Am. Chem. Soc., 61, 273’7
(1939). (9) R. D. Present, “Kinetic Theory of Gases,” McGraw-Hill Book Co., Inc., New York, N. Y., 1958, Chapter 2.
(10) P. Clausing, Ann. f’hysik, 12, 961 (1932).
Volume 68, Number 1.92 December, 196,;
J. DANIELKELLEYAND FRANCIS OWENRICE
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104 to 127" ; 9,10-dimethyl-1,2-benzanthracene, 106 to 135"; and 20-methylcholanthrene, 128 to 152'. The data for anthracene are represented by the equation logp,,
=
12.068 - 5145/T (L, = 23.54 kcal./mole)
(5)
where Le is the average heat of sublimation over the experimental temperature range. The data for 1,2-benzanthracene are represented by logp,,
=
11.528 - 5461/T (Le = 24.99 kcal./mole)
(6)
The data for 20-methylcholanthrene are represented by log
pmm
=
13.168 - 6643/T (L, = 30.40 kcal./mole)
(7)
The temperature range over which 9,lO-dimethyll12-benzanthracene was studied included the melting temperature, so that a discontinuity appeared in the slope of the log p , , us. 1/T plot corresponding to the heat of fusion, Lf. The data for the sublimation of solid dimethylbenzanthracene and the evaporation of liquid dimethylbenzanthracene are represented, respectively, by the two equations log p,,
=
15.108 - 705l/T (L, = 32.26 kcal./mole)
(8)
12.232 - 5897/T (Le = 26.98 kcal./mole)
(9)
and log p,,
=
where L, is the average heat of vaporization over the experimental temperature range. The heat of fusion is given to a good approximation by L, - Le and was found to be 5.28 kcal./mole. The above equations were obtained by obtaining the best straight line through the experimental points by the method of least squares. The mean percentage errors were 2.3, 4.4, 1.9, 1.8, and 1.0% for anthracene, 1,2benzanthracene, 20-niethylcholanthren~,and solid and liquid 9,10-dimethyl-l,2-benzanthracene, respectively.
Discussion The vapor pressure of anthracene has been studied over several temperature ranges, 3-7 all above the range covered in this work. Sears and H ~ p k e and , ~ Klochkov,? have made measurements in the range 105 to
The Journal of Physical Chemistry
125". The agreement between these experimenters was only fair, Klochkov's results being about 15yo higher on the average over the experimental range. Table I shows a comparison of these two determinaTable I T ,O C .
p ,Pa
p , Pb
p , PC
95 100 105
15.0 21.4 32.5
11.9 18.5 28.3
12.5 19.1 29.1
L8
L B
LB
23.35
23.90
23.45
a Data of Sears and Hopke.6 study.
* Data of Klochkov.'
c
Present
tions with the present one for vapor pressures, given in microns, calculated at three temperatures intermediate between the two experimental ranges ; the average heats of sublimation in kcal./mole for the three determinations are shown as well. As the table shows, the pressures calculated from Klochkov's vapor pressure equation agree with those calculated from eq. 5 to within a few per cent for these intermediate temperatures; the pressures calculated from the equation of Sears and Hopke are about 10% higher. The average heat of sublimation calculated from these data is close to that obtained from the data of Sears and Hopke, and slightly higher, as would be expected from the fact that the heat of sublimation is not constant but in general increases with decreasing temperature. The heat of sublimation obtained by Klochkov is higher than that found here, although Klochkov's experimental temperature range was, as was that of Sears and Hopke, 35" higher on the average than that of the present investigation. The heat of fusion calculated from the data on 9,lOdimethyl-1,2-benzanthracene, 5.28 kcal./mole, leads to a value for the entropy of fusion (Lf/T,,,lt,,g) of 13.1 cal./deg.-mole. Mortimerll noticed that the entropies of fusion for a number of aromatic hydrocarbons related to anthracene and phenanthrene were close to' 12.8 cal./deg.-mole. The above value for 9,10-dimethyl-1,2-benzanthracene seems to be in good agreement with this empirical observation. (11) F. S. Mortimer, J . Am. Chem. Soc., 44, 1429 (1922).
