Sublimation pressures of hydrogen chloride

M-2472 J. Chem. Thermodynamics 1990, 22. 407412

Sublimation chloride FREDERIC

pressures

of hydrogen

SER and YVES LARHER

CEA-IRDI-DESICP-DLPC-SCM, CEN-Saclay, 91191 Gifsur Yvette Cedex, France (Received 24 January 1990; in final form 20 February 1990) New measurements of the sublimation pressure of HCI have been carried out between 120 K and 150 K. They appear more reliable than previously published results, at least below 140 K. From our results and the heat capacities of Chihara and Inaba,t9) we derive for the molar cohesion energy of HCI at T = 0 a value of - (20222 &-20) J. mol- I.

1. Introduction We find it useful to complement our adsorption-isotherm measurements by adsorbate saturation-pressure measurements. By doing this systematically over a period of years, we obtained new results concerning temperature ranges not yet investigated”) and results more reliable than those previously published.@* 3, Both these kinds of results were obtained for the vapour-pressure measurements on hydrogen chloride carried out by us to supplement an investigation of the adsorption seemed to us of hydrogen chloride on graphite,‘4) so that their publication worthwhile.

2. Experimental The experimental device is almost the same as used in our adsorption studies, the only difference being that the adsorption cell is empty of the adsorbent. A detailed description of the cryostat can be found. (‘I The temperatures were measured with a vapour-pressure thermometer containing Xe; we used the results of Leming and Pollack@’ which are reliable in the range of temperatures investigated, i.e. from 120 K to 150 K. The Xe pressures were measured with a U-tube manometer containing either Apiezon oil below 143 K or mercury above. The HCl pressures were measured with a capacitive gauge: a Barocel manometer from Datametrics with a sensor having a range 0 to 133 kPa and especially treated for corrosive gases by the manufacturer. The HCl gas, purchased from Prodair, was pure to 99.995 moles per cent. However, since we transferred it to the adsorption apparatus in a glass bottle having a greased stopcock, prior to each experiment we trapped all the gas in a cold 0021-9614/90/040407 +06 $02.00/O

0 1990 Academic Press Limited

408

F. SER AND

Y. LARHER

finger at liquid-nitrogen temperature and pumped out of it the volatile impurities, H, for instance, which could possibly result from the reaction of HCl with grease or other contaminants. Since our adsorption apparatus had a glass burette whose volume could be varied by raising mercury, we checked that the vapour pressure remained independent of the condensate quantity to better than 0.2 per cent. 3. Results and discussion The experimental results are given in table 1. They are accounted for, to better than 0.3 per cent, by the two linear regressions: lg(p/Pa) = - 1029.6.K/T+

10.627,

(121 K < T < 133 K),

lg(p/Pa) = - 1023.0.K/T+

10.577,

(134 K < T < 150 K).

and

We analysed them, along with previously published results,‘7 9, in the same way as earlier for other gases,(1~3) by using the equation expressing the equality of the chemical potentials of the crystal (left-hand side) and of the vapour (right-hand side): T f&n(O)

-

G,,(O)

C,,, dT-T

+

s0 TABLE

T (C,,,,/T)dT

1. Sublimation

pressures

T K

L

KS’) FGF

121.04 122.60 124.10 125.49 126.91 128.49 129.93 131.42 132.03 132.98 134.57 136.07 137.16 137.55 139.12 140.52 142.03 143.47 145.03 146.54 147.99 149.45

132.0 169.3 213.9 264.4 327.3 410.5 504.0 620.5 673.4 766.5 941.9 1143.9 1312.9 1383.3 1676 1988 2372 2799 3337 3944 4616 5388

-20217.8 -20219.5 -20221.0 -20221.3 -20219.8 - 20223.7

’ Equation

Pa

(3) is used with

= AP,8+RT+Bp,

(1)

s0

H,,,(O)= - 20222

&ale.)” Pa

-20223.2 -20222.0 -20223.5 -20222.0 -20226.4 -20225.6 - 20225.7 -20221.7 -20223.3 - 20220.7 -20222.1 - 20222.7 - 20222.5 -20221.7 - 20220.5 -20219.9 J. mol-

of HCl

I

131.4 168.9 213.6 264.2 326.6 411.2 504.6 620.5 674.4 766.5 945.7 1147.6 1317.1 1382.9 1678 1986 2372 2800 3338 3943 4610 5379

A 102-LI

P

-0.4 -0.2 -0.1 -0.1 -0.2 +0.2 +0.1 0.0 +0.1 0.0 +0.4 +0.3 +0.3 0.0 +O.l -0.1 0.0

+0.05 0.0 0.0 -0.1

-0.2

SUBLIMATION

PRESSURES

OF

HCI

409

where H,(O) and S,,,(O)are the molar enthalpy and entropy of the crystal at T + 0, and C,,, its molar heat capacity at constant pressure. A: is the molar Helmholtz free energy of the gas considered as perfect. A small correction to imperfection is represented by Bp in which B is the second virial coefficient. R is the gas constant. We know from statistical mechanics(“) that 4Zg = - (RTIWn((v/A

3)N(~rot)N(~viJN/~ !}.

(2)

Taking into account that the molecular volume V/N = kT/p and A = (h/27cmkT)‘12, where h and k are Planck’s constant and Boltzmann’s constant, respectively, and m = M/L, where M is the molar mass of HCl and L is Avogrado’s constant, then equation (1) can be written: T

H,(O)-

T&,(O) = -

C,,, dT+ T s 0

T (C,,JT)dT s0

- RT. ln((kT/p)(2xmkT/h2)3’2}

- Bp- RT. In qrot-- RT. In qvib, (3)

where qro, and qvib are the rotational and vibrational partition functions, respectively, of one molecule. The first excited vibrational state of HCl, at ! = 2990 crn-l,(ll) has a negligibly small occupation probability at 150 K, the highest temperature we worked at, so that we can take qvib = 1. The rotational partition function is written:“” 4 r,,t =

f

(25 + l)exp( -J(J + 1)0,/T),

.I=0

where the rotational

characteristic temperature

8, is defined by:

9, = h2/8n21k = B,hc/k, where I and B, are the molecule’s moment of inertia respectively, and c is the speed of light in vacuum. The rotational-vibrational spectra are respectively 10.592 and H37C1.02’ Taking the mean value 10.584cm-’ approximated (4) by

and rotational constant, values of B, derived from 10.576 cm-’ for H35C1 and yields 8, = 15.23 K. We

4rot = J$o (2.1+ l)exp{ - J(J + 1)6,/T} + (7.5 + T/Qexp( - 56&/T), In this expression, summation is carried out up to J = 6, and the remainder, which represents, at any temperature, less than 1 per cent of qrot, is taken as an average of two integrals surrounding $‘, (2-J+ l)exp( -J(J+

1)&/T}.

The second virial coefficient B was calculated according to a semi-empirical formula due to Guggenheim* .(13) B/V, = 0.44 + 1.40{ 1 -exp(0.75TJT)} in which the critical constants V, = 81 cm3 .moll’ and T, = 324.7 K.(i4)

F. SER AND Y. LARHER

410

The two integrals on the right-hand side of equation (3) can be calculated once the heat capacities are known. We used the results of Chihara and Inaba.“) From their table 7 we extract: 130K

C,,, dT = 32.68 x 130 J.moll’ s0 and 130K

(C,,,,/T)dT

= 54.93 J.K-‘.mol-’

s0 (see their table 7). The additional contribution analytically, using for C,,,, the linear regression: C,,,,/(J.K-‘.mol-‘)

to the integrals

was calculated

= 0.1619(T/K)+23.45,

which represents within experimental accuracy the results of Chihara and Inaba”’ from 120 to 150 K. It appears that, once the vapour pressures are known, {H,(O)- TSJO)) can be calculated as a function of T. The values derived from our vapour pressures and from those of Karwat, Giauque and Wiebe, and Chihara and Inaba are represented in figure 1. For the whole set of our results {H,(O)- T&,(O)} remains constant, which shows that the zero-temperature entropy is zero, in agreement with a conclusion previously deduced by Giauque and Wiebe@) in a slightly different way. The vapour-pressure results of Karwat”’ and of Giauque and Wiebe@’ have a scatter larger than ours, but are also consistent with this conclusion. On the other hand, the results of Chihara and Inaba, with a scatter comparable with ours, if not better, cannot be represented by a straight line which means that at

FIGURE 1. Variation with temperature of {-H,,,(O)+ T&(O)} results; V, reference 7; 0, reference 8; +, reference 9.

as defined by equation (3). SC,Our

SUBLIMATION

PRESSURES

OF HCI

411

least some of them are unreliable. Since above 146 K their {H,,,(O)- 7’S,(O)} value seems to become constant, we feel that some artefact progressively comes into play in their measurement below this temperature. Considering that their values are correct above 145 K, then they would be too high by A~/p = AH~(O~/~~ z 56/(8.3 x 132) z 0.05 at their lowest temperature, 132 K. It is very improbable that this difference could be ascribable either to the thermometer or to the manometer (at 132 K, the pressure, being higher than 665 Pa, is easily measurable with an accuracy better than 0.5 per cent. The presence of a non-condensable impurity in HCl, for instance H,, could be a possible explanation of an error in pressure which increases as temperature decreases. For this reason, but also because our H,(O) is constant over the largest temperature range and because we had the advantage of having at our disposal the purest hydrogen chloride (99.995 moles per cent purity instead of 99.0 moles per cent for Chihara and Inaba before purification), we consider our estimate of HJO) as the most precise and reliable. Our average value is H,(O) = - 20222 J *mol- ’ with a root-mean-square deviation of 2.1 J+mol-‘. Now if we take into account the results of Chihara and Inabatg’ for temperatures above 146 K we obtain a value H,(O) = -20210 J. mold1 which differs very little from ours: by 0.06 per cent only. This corresponds to a deviation on pressure of Ap/p = AH,,,(O)/RT z 0.01, which is quite satisfying, considering that we used in our temperature measurements the vapour pressure of Xe determined by Leming and Pollack, (6f It is worth noting that these authors calibrated their thermometer against the same temperature scale as Chihara and Inaba:“) the IPTS-68. But of course a slight inaccuracy in the pressure measurements of Xe could explain part of the difference between our vapour pressures and those of Chihara and Inabac9) above 143 K. The difference between our values and those of the two older studies, which can be seen in figure 1 as a difference in ( -Ha(O) + T&,(O)), remains within reasonable limits. In fact, Karwat’s results agree with ours within experimental uncertainty. Those of Giauque and Wiebe are about 2 per cent higher than ours. The difference in temperature scale, difficult to correct, would not be sufficient to reconcile their results and ours. Since Giauque and Wiebe insist on the difficulty of preparing pure HCl, it may be that some volatile impurity is responsible for their vapour pressure being slightly higher than ours. A second source of error of H,,,(O) arises from the uncertainty of heat capacities. We estimated graphically the quantity:

T T (AC,,,,/T)dTs0 in which AC,,, is the difference Wiebe”) and Chihara and Inaba;‘g) that the experimental uncertainty uncertainty to that associated with that H,,,(O) is known to better -(20222-j--20) Jsmol-‘.

T AC,., dT, s0

between the values obtained by Giauque and it amounts to + 9 J 1mol-‘. It seems improbable would be higher than this value. Adding this the vapour-pressure measurements, we conclude than 20 J.mol-‘. So we propose H,(O) =

412

F. SER AND

Y. LARHER

The zero-temperature enthalpy is a quantity currently used in assessing the interaction potential between atoms or molecules.os) We do not know of any previous attempt to propose an experimental estimate of it for HCl. It can also be useful in calculating vapour pressures, especially in a temperature range in which they are not yet known, for instance below 121 K. Equation (3) must be used, along with the experimental heat capacities used to determine H,(O), to eliminate the effect of an error on these heat capacities. Table 1 contains the values of vapour pressures calculated in this way. They differ by less than 0.4 per cent from the experimental values. REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. IO.

II. 12. 13. 14. 15.

Terlain, A. J. C&t. P&s. 1983, 80, 805. Larher, Y. J. Chim. Phys. 1968,6.5, 1683. Tessier, C.; Terlain, A.; Larher, Y. Physica 1982, 113A, 286. Ser, F. Thesis, to appear. Gilquin, B. Thesis NANCY (1979), CEA-N-2091 Report (1979). Leming, C. W.; Pollack, G. L. Phys. Rev. B 1970, 2, 3323. Karwat, E. Z. Phys. Chem. 1924, 112, 486. Giauque, W. F.; Wiebe, R. J. Am. Chem. Sot. 1928,50, 101. Chihara, H.; Inaba, A. J. Chem. Thermodynamics 1976,8, 915. McQuarrie, D. A. Statistical Mechcmies. Harper and Row: New York. 1976. Huber, K. P.; Her&erg, G. Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules. Van Nostrand Reinhold: New York. 1979. Levy, A.; Rossi, I.; Joffrin, C.; Van Than, N. J. Chim. Phys. 1964, 70, 600. Guggenheim, E. A. Applicutions of Statistical Mechanics. Clarendon Press: Oxford. 1966. Ambrose, D. VupQ~r-~jqujd Critical Properties. NPL Report Chem. 107: Teddington. 1980. Barker, J. A.; Klein, M. L.; Bobetic, M. V. I.B.M. J. Res. Devel. 1976, 20, 222.