James Speros Chickos
University of Missouri-St. Louis St. Louis, 63121
A Simple Equilibrium Method for Determining Heats of Sublimation
Heat of combustion data have provided chemists with a wealth of information regarding the chemical bond. However, before this data can be used in any meaningful way, heat of vaporization (AH,) or sublimation (AH,) corrections to a standard state are necessary. A frequently used method is calculation of AH,, or AH, from the vapor pressure-temperature relation by means of the Clapeyron eauation ( I ) . A number of methods of estimating these qLantities have also been described (2, 3). More recently, heat of vaporization calorimeters have been developed (4. 5). The measurement of low vapor pressure on the order of 1 fi bas generally been accomplished by transpiration studies (gas saturation method), measurement of rates of effusion from a Knudsen cell, or direct measurement by use of pressure gauges such as the Bourdon gage (6). All these methods require a considerable amount of sophisticated equipment and a great deal of effort is required before vapor pressure measurements can he made routine. Furthermore as cautioned by Thomson (6J, the presence of systematic errors and disagreement between alternative approaches has rendered many of the results reported in the literature by these methods highly suspect. Although the presence of such errors in vapor pressure measurements need not necessarily introduce substantial error in the heats of the sublimation (AH,), it is clear that rather large discrepancies in AH, do exist. As an example, AH, reported for naphthalene ranges from a low of 8.0 (7) to a high of 19.6 kcal/mole (8) with a number of other values scattered in between (9). Recently, vapor pressure measurements have been carried out indirectly by using a spectrophotometric technique (12). The curriculum of many physical chemistry laboratories, ours included, includes some study of the vapor pressure-temperature relationship. We would like to report a modification of a simple method previously described for determining enthalpies of sublimation (12) and to comment on some of the method's inherent limitations. The apparatus used is shown in Figure 1. The method consists of allowing a sample at temperature, TI, to equilibrate with an evacuated ballast tank maintained a t some higher temperature, Tz. After equilibration has been achieved, the sample compartment is isolated, and the vapor in the ballast tank is condensed in an evacuated cold finger. Removal of the cold finger, admission of a known weight or volume of solvent affords a solution which can he ana-
Figure 1. Apparatus.
lyzed spectroscopically. Adjustment of the quantity of solvent assures absorbance readings in the range where the Beer-Lamhert law is obeyed. We have routinely used quantitative infrared and ultraviolet spectroscopy in measuring sample size. In addition to spectroscopic methods, gas chromatographic analysis could also he used provided an internal standard (in the solvent) was included. This method differs from the one previously described in that we found i t advantageous to maintain the ballast tank a t temperatures above those of the sample compartment. This was necessary to minimize what is believed to be adsorption of the vapor on the glass surface and to eliminate the possibility of condensing the vapor in the ballast tank, an occurrence which was observed in some instances when both sample and vapor were maintained a t a uniform temperature. Our experimental results are included in Figures 2 and 3 and Table 1. Figure 2 includes the results obtained where good straight lines could be passed through all the data. Figure 3 lists the two cases recorded where straight lines were not obtained and Table 1 summarizes our AH, results, the best literature results as compiled by Davies, and calculated AH, from the following equation AH,
=
AH, + AH,,.,,,,
This equation is rigorously correct only for enthalpies ob-
Table 1. Heats of Sublimation This Workd
Literature AH,
Compound
AH* (kesl/molej
In A (atm)
Temp Range (OC)
Corn coef
AH, (keal/mole)
In A (atm)
20.4 (21.3)
23.9 (25.3)
20 40 (20 -r 40)
-
0.9969 (0.9969)
21.73"
26.07
Temp Range ("C)
kcal/moleb (ealcd)
camphor Phenol Naphthalene Biphenyl
........ Thymol
,. ......
0
+ 40
D s t n from Weaat, R. C., (Ediror), "Handbook of Chemistry and Physics," 52 Ed., m e Chemical Rubber Co., Cleueland, Ohio, 1972, p. C-716. b F ~ o t n o t a, e pp. C-717.719 and D-151-170. 'Sellers, P., Aeto. Chem. Scond., 26, 2291 (1971). Heats of sublimation calmdated from a leaet+quares analysis of the data.
134 / Journal of Chemical Education
17.5
Figure 3. Lag P versus 1 / T , 0 ballast temperature 75% ballast temperature25'C. (a) Thymol. (b) Biphenyl. I,,
110'
