Experimental determination of enthalpies of sublimation

Materials Chemistry 6 (1981) 187 - 196

EXPERIMENTAL DETERMINATION OF ENTItALPIES O F SUBLIMATION*

W. BROSTOW*, D.M. McEACHERN** t, J.A. VALDEZ** *

D e p a r t m e n t of.Materials Engineering - Drexel University, P H I L A D E L P l t l A , PA 19104, U . S . A .

**

Center for A d v a n c e d Studies - National Polytechnic I n s t i t u t e - A.P. 14-740, Mexico 14, D.F.

Received 6 April 1981; accepted 4 May 1981 Summary - Experiments were made with a restricted molecular flow method and by differential scanning calorimetry (DSC). The two methods are compared and discussed together with other methods described in the literature. A specific experimental procedure is established for the use of DSC to obtain enthalpies of sublimation HSUbl; the technique is accurate as well as fast. Values of Hsubl/(kJ mol -l ) obtained for anthracene and benzoic acid are respectively 97.4-+ 1.1 and 93.45-+ -+ 1.1. A claim is made that these values should supersede those reported by other authors.

INTRODUCTION There exist several methods o f experimental determination of the enthalpies o f su blimation. For instance, in papers from the Aziz laboratory ~, 2, a claim is made that "provided sufficiently precise and copious results are available, the enthalpies and internal energies calculated from vapor pressures are at least as accurate if not more * A part of this work was presented at the XII1 Mexican Congress of Pure and Applied Chemistry in Tijuana, Baja California Norte, July 10-13, 1978. t Deceased. 0390-6035/81/030187-0952.00/0 Copyr~ht © 1981 by ~ S.ILI.. All ~iihts of reproduction in any form reserved

188 accurate than those obtained from calorimetric measurements" 2. This point of view is doubtlessly related to the fact that the systems studied in I and 2 consisted of argon, krypton and xenon, with equilibrium vapor pressures P of several hundreds Torr. As noted by one of us and Sandoval 3, for many organic compounds the vapor pressures of interest are below 0.1 Torr; the popular methods of measuring P then either require elaborate equipment or are unreliable. We thus find that the choice of a method is related to the kind of material we are dealing with. The main use of thermodynamics - as characterized by McGlashan 4 - then comes into play: some thermodynamic properties are easier to measure than others. We have compared two methods of determination of enthalpies of sublimation Hsubl: an indirect one, based on a molecular flow evaporation procedure; and a direct one, based on the use of a differential scanning calorimeter. We discuss the results of the comparison. We also report in the present paper values of H subl for anthracene and benzoic acid; we claim that these values should supersede those obtained by earlier authors.

MATERIALS USED Anthracene used was Reagent Grade, manufactured by Eastman Organic Chem. icals. It was purified by recrystallization from absolute ethanol. The total mole fraction of impurities x was determined by differential scanning calorimetry (DSC) from the equation for melting point depression: Ts ---To

NAkT2x HfUS F

(1)

where T s is the instantaneous temperature of the sample, To the melting point of infinitely pure sample, N A the Avogadro constant, k the Boltzmann constant, H fus the enthalpy of fusion and F the fraction of the total sample melted at Ts. Validity of assumptions leading to equation (1) has been discussed by Barrall and Diller 5 The value obtained for our anthracene was 1 - x-- 0.9998. Our benzoic acid sample was Thermometric Standard Grade prepared by Fisher Scientific Co. The purity determined by DSC with equation (1) was 1 - x = 0.9995.

MOLECULAR EVAPORATION METHOD The free molecular evaporation method was devised by Langmuir 6 to meas-

189 ure P o f wolfram. He has assumed that the rate o f evaporation o f a substance in vacuum is equal to the rate o f its condensation. This can be true when the two processes under consideration are independent from each other, that is for P ~< 1 Torr. Then the condensation rate of a pure material under its equilibrium vapor pressure is given by the kinetic theory of gases as the number of molecular collisions per unit area per unit time for a given P. Thus, the rate o f sublimation may be used to calculate P, and then p _

ln(

_

H subl i

Torr )

I

ssubl +

I

NAkT

(2)

NAk

where S is entropy. In reality, only a fraction of molecules colliding with a surface actually stick tO it. The condensation rate is less than the rate o f collisions by a factor ct, called the e/aporafion coefficient (in 3 a was termed the condensation coefficient). While tile case of a = 1 is possible too, in general 0 < a ~< 1. The l_angmuir procedure can be called the free molecular flow method. However, the modification of it developed in 3 and used in the present work involves a restricted molecular flow (RMF) apparatus. There is a 38 cm tube between the sample container and the condenser, and some molecules which had evaporated simply never reach the condenser. To take care o f this phenomenon, a correction factor f, called the apparatus restriction factor, has to be introduced. The equilibrium vapor pressures can then be calculated as P Tort

f = 50.877

a

r m o l . s"

a 1

cm 2

NAk M•

J • K'1 . tool'1

T •

(~

1/2 )

(3)

where r is the sublimation rate, a the effective sample area and M the relative molar mass of subliming gas. We have used samples of approximately 500 rag. They were introduced as powders into an A1 sample container. The apparatus was the same as described in 3, with one improvement: in earlier work 3, 7-9 each sample had to be removed from the system to be weighed; we have provided for a continuous control of the weight o f the sample. A Calm R-100 balance was attached to the system. The electrobalance functions in a reliable way under vacuum conditions. The experimental procedure we have followed is described in detail in 3, and also in 1o The experimental values obtained were substituted in turn into equations (3) and (2). Values o f the apparatus restriction factor f were calculated on the basis of an idealized model of the system shown in Fig. 3 in 3 and represented by a system

190 of equations (6)-(16) in the same paper. Essentially, f is calculated by tracing a number of imaginary planes so as to divide the system into a number of compartments. The compartments are assumed to be rectangular, and total material balances along each plane are calculated. The evaporation coefficient ct was assumed to be equal to unity. For both compounds, the values of H subl thus obtained were obviously charged with large errors. Disappointing as this was, the problems encountered were hardly new. The procedure of calculating the apparatus restriction factor outlined above is clearly an oversimplification. The situation with the evaporation coefficient is still much worse. The assumption a = 1 is simply a default option, and might be a source of gross errors. We have made measurements for benzoic acid in the course of the present work, but the same compound was also studied in the original project a in which the RMF apparatus has been constructed. Calculation of ct on the basis of equilibrium vapor pressure data from the literature has then produced the values 3 of 0.002 ~< t~ ~< 0.05. In a related context, de Kruif and his colleagues 11 note the existence of what they call irregularities in the effusion process. Their particular solution of the problem consists in the use of the simultaneous torsion - and weighing - effusion technique. This increases the change of detecting the irregularities. The RMF method has ted to at least acceptable values for some compounds 7"9. At the same time, it was reported also in the first paper on RMF 3 that the apparatus failed to reproduce the known vapor pressure behaviour of naphtalene. Of course, naphtalene is a par excellence compound which "prefers" sublimation to consecutive melting and vaporization. We can only conclude that the RMF method works for some materials, but not for some other ones. Under the circumstances, we have decided to develop an alternative technique which would not have such limitations. The results are described below.

DIFFERENTIAL SCANNING CALORIMETRY METHOD Quantitative DSC is known to have many successful applications. In particu, lar, it is an important tool of polymer characterization 12. There have been, however, only very few attempts to use DSC to determine enthalpies of sublimation. These attempts have produced contradictory results: Dyson 13 has concluded that the DSC technique fails to produce reproducible and accurate values of HsUbl; by contrast, Beech and Lintonbon 14 have obtained results they consider satisfactory.

191 We have used a Perkin-Elmer differential scanning calorimeter, model DSC-1B. Essentially, there are two independent electrical circuits. One o f them controls the average temperature according to a preprogrammed heating rate; readings of Pt resistance thermometers in the sample cell and in the reference material cell are translated into adjustments of energy outputs of heaters in both cells. The oth. er circuit provides amplification and registration of the difference in absorbed energy between the two cells. We have used a Speedomax W recorder with two pens, manufactured by Leeds and Northrup of Philadelphia. We have used samples with mass up to 5 mg; best results were obtained for 3 mg samples. Each sample was distributed fairly uniformly at the bottom of the sample holder, then the holder filled completely with A1 powder, and closed with an A1 foil cover (subsequently, perforations in the cover were made). This procedure, recommended by Beech and Lintonbon 14, turned out to be very important. The presence of the A1 powder has minimized temperature gradients. The reproducibility of the results, which had been only fair without the powder, became very good after the powder filling procedure was instituted. After trying various combinations of adjustable parameters, we have found that the best results were obtained with the temperature rates 5 K/min and 10 K/min; the heating rates were 4 and 8 mcal/s; the best recorder paper velocity was a slow one, 15 in./hour. A sample of indium provided by the manufacturer was used as the standard. We do not give here any further details of the experimental procedure, since they have been amply discussed in the literature, and we have followed the instructions of the manufacturer I 5. The enthalpies were calculated from the equation: HSUb1= A ' W I n - Aln" W

. fus

"t tin

"M

(4)

where the quantities without indices refer to the material studied, while the subscript In refers to the indium standard; the superscript fus as before refers to fusion; W is the sample weight and A the surface area below the recorded curve. With the best operational parameters indicated above, several experiments for each sample have given values of the enthalpy of sublimation reproducible within 1.1 kJ • mol "1 . In a careful analysis of the entire experimental procedure we have not discovered any source of systematic errors. Therefore, not only the precision but also the accuracy of our DSC determination of H subl is within 1.1 kJ • mol "I. The results obtained are reported in the following Section.

192

RESULTS In Table 1 we give our value of the enthalpy of sublimation of anthracene together with values obtained by other authors. In each case we indicate whether Tab. 1 - Enthalpies of sublimation of anthracene. Hsubl Method

Authors

Year

Ref.

kJ • mol "1

Indirect

Bradley and Cleasby

1953

16

97.6

Indirect

Kelly and Rice

1964

17

98.6

Direct

Beech and Lintonbon

1971

14

126 -+ 4

Indirect

Wiedemann

1972

18

84.0

Indirect

McEachern and Sandoval

1973

3

95.8 -+ 6

Indirect

de Kruif

1980

19

100.4 -+ 1

Direct

this work

97.4 -+ 1.1

a direct or an indirect method has been used. On the basis of the results presented, we claim that our value is better and should supersede the earlier ones. In Table 2 a similar oresentation is given for benzoic acid. Again, we claim Tab. 2 - Enthalpies of sublimation of benzoic acid. Hsubl Method

Authors

Year

Ref.

Indirect

Davies and Jones

1954

20

91.5

Indirect

Ashcroft

1971

21

89.1

Direct

Beech and Lintonbon

1971

14

Indirect

Wiedemarm

1972

18

86.6

Indirect

McEachern and Sandoval

1973

3

88.3 -+ 3

Direct

this work

kJ ' mol "1

100 + 5

93.45 + 1.1

193 that the value obtained in this work should supersede the results of other authors.

DISCUSSION Tile simplest method of obtaining the enthalpy of sublimation consists, of course, in using the relation H subl = H fus (Tin) + H vapn (Tb)

t5)

where T m denotes the melting point, T b the normal boiling point, and the superscript vapn refers to vaporization. Equation (5) has been discussed by Zivojinov 22 in connection with her P values for Ar at temperatures from 20 K upwards. The main disadvantage of (5) is that it t u r n s H subl into a temperature-independent constant. Moreover, the use of (5) is limited to "decent" materials which undergo fusion first, and cannot be applied to solids which tend to sublime. Therefore, the experimental procedures we have tested did not involve the use of (5). The results of our experiments indicate clearly that the DSC method is distinctly better than the restricted molecular flow procedure. We did not have any preconceived preference for direct (calorimetric) rather than indirect (equation (2)) method. In fact, one of us argues elsewhere 23 advantages of methods which go across phase transition points, as constrasted with methods which are limited to the study of the transitions. We were aware of some direct determinations of H subl by conventional calorimetry 24. As for the DSC, even putting aside the report of Dyson 13, Beech and Lintonbon 14 have claimed only moderate accuracy. At the same time, and as already mentioned earlier, those calculating H subl from vapor pressure determinations, were stressing advantages of their procedures. Now, in view of the results obtained in this work, the following points ought to be noted. First, those who have indeed obtained very good results from equation (2) were working mainly with argon ~, 2, 22. For materials which tend to sublime directly rather than to melt the restricted molecular flow procedure might be used, but it does not work in every case. Turning now to calorimetric procedures, DSC is distinctly faster than conventional calorimetry. As already noted by Beech and Lintonbon 14, the difficulties encountered by Dyson 13 are probably due to the condensation of evolved material on some relatively cold parts of the sample holder assembly. Beech and Lintonbon 14 have enriched the DSC method with the A1 powder filling procedure, an improvement important indeed. The reason we have ob-

194 tained better results than they did can be attributed to our detailed study of the effect of the heating rate on the reproductibility of the results. Staying with the optimum heating rate range indicated in Section 4 appears essential. As also noted in Section 4, even the recorder paper velocity plays a role in the accuracy of the results obtained. If appropriate attention is given to these factors, then the DSC technique for H subl becomes reliable as well as fast. Almost needless to say, having established a convenient experimental procedure, we have obtained values not only for two materials. Values of enthalpies of sublimation of several compounds will be reported later 2 s, together with a discussion of significance of these values from the point of view of bonding energies.

A ckno wledgements This research was supported financially by the National Council o f Science and Technology (CONACyT), Mexico Oty, D.F. Some support has been also provided by the National Association o f Universities and Institutions o f Higher Education (ANUIES), Mexico City. One of us (J.A. K) acknowledges a leave o f absence from the Autonomous University o f the State o f Sinaloa, Culiacan. Mr. Omar Solorza has participated in some o f the experiments.

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