The Sublimation of Argon, Krypton, and Xenon

J. Chem. Thermodynamics 40 (2008) 1621–1626

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J. Chem. Thermodynamics

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The sublimation of argon, krypton, and xenon

A.G.M. Ferreira, L.Q. Lobo *

Departamento de Engenharia Química, Universidade de Coimbra, Coimbra 3030-290, Portugal article info abstract

Article history: In this paper, the sublimation pressure of Ar, Kr, and Xe are obtained as functions of temperature from an Received 18 June 2008 exactly integrated form of the Clapeyron equation. No ﬁtting to experimental data of the equilibrium Received in revised form 30 July 2008 pressure has been necessary. The deviation plots of the sublimation pressure show that the results are Accepted 30 July 2008 satisfactory. The derived enthalpy of sublimation of the three rare gases from T = 0 K up to their respec- Available online 8 August 2008 g s tive triple point temperatures are asymmetric, distorted parabolas showing maxima for Cp;m ¼ Cp;m. The g D Hm ðT ¼ 0KÞ, which is a measure of the cohesion energy of the solid crystals, is easily calculated. A gen- Keywords: s eral equation has been obtained for DgH as a function of temperature which also gives the enthalpies of Rare gases: Ar, Kr, Xe, (Ne, Rn) s m sublimation of neon and radon. The (s + ‘ + g) triple point coordinates of Rn are reassessed. Sublimation Pressure Ó 2008 Elsevier Ltd. All rights reserved. Enthalpy: Clapeyron equation

1. Introduction In this paper, we examine some of the sublimation properties of the rare gases from a more fundamental approach, since the ancil- Not long ago, we reported on the physico-mathematical lary data necessary for the calculations are available in the litera- description of the phase equilibria of pure substances from an ex- ture for Ar, Kr, and Xe. Expressions for the sublimation curves of actly integrated form of the Clapeyron equation [1]. A number of the three substances are obtained from the knowledge of those substances from rare gases to metals, and from polar compounds data with no need of ﬁtting to any experimental values of the equi- to hydrocarbons (either linear, or cyclic, or aromatic) were put to librium pressure. The derived enthalpies of sublimation are then test with satisfactory results. Almost all ﬁrst order transitions viz. easily calculated, namely at zero kelvin whose values render direct sublimation, vaporization, fusion, and solid to solid, were exam- assessment of the cohesion energy of the solid crystals of each of ined in that light. Of course, such ab initio treatment of the phase the three elements. equilibrium curves requires the knowledge of certain primary thermodynamic properties of the pure substances involved and of their 2. Theory phases: heat capacities, molar volumes, enthalpies of transition, and the coordinates of reference points (usually taken from those From the exact integration of the Clapeyron equation of the triple points of the substances). In the absence of measured g g values of these properties, one can try and describe the equilibrium dp ðDs Hm=Ds V mÞðdT=TÞ¼0; ð1Þ curves through empirical equations. Using this latter procedure, where p and T are, respectively, the equilibrium pressure and tem- we recently reported on the vapour pressure of radon [2] and on g g perature, Ds Hm is the molar enthalpy of sublimation, and Ds V m is the fusion curves of Xe, Kr, and Ar [3]. In the years of 1960s, Ziegler the molar volume change along the (solid + gas) equilibrium curve, and co-workers [4–6] analysed the experimental sublimation data an analytical representation of the sublimation curve of pure sub- for argon, krypton, and xenon, and devised a method to conjugate stances is obtained in the form [1]: the information available to describe the (solid + vapour) equilib- X4 ria. Not many experimental results on the same subject have been i1 ln p ¼ A B=T þ C ln T þ DiT þ EðTÞp=T: ð2Þ published subsequently. Leming and Pollack [7] interpreted their i¼2 own measurements on the sublimation pressure of the three hea- vier classical rare gases over large temperature intervals by using In this equation A, B, C, Di, and E(T) are parameters that can be cal- the (microscopic) principle of corresponding states. culated ab initio from measured properties of the phases at equilibrium: the heat capacities and molar volumes of the two phases, the (p,T) coordinates of a reference point on the sublimation curve (usually those of the s + ‘ + g triple point), and the enthalpy of phase

* Corresponding author. Tel.: +351 239 798 733; fax: +351 239 798 703. transition at that point. All these quantities contribute to the values E-mail address: [email protected] (L.Q. Lobo). of A and B while the calculation of parameter C only involves the

molar heat capacities of the two phases. The Di depends on the mo- adopted. The coordinates of the triple point of krypton were both lar volume of the solid and the difference between the molar heat taken from reference [8] after converting the temperature into capacities of gas and solid. The E(T), which is a function of temper- ITS-90 by recommended methods [9,10] giving Tt = 115.772 K, ature, is calculated from the molar volumes of both phases. The ex- and pt = (72.999 ± 0.012) kPa. The same procedure was adopted act expressions relating all these parameters and properties are for Xe yielding Tt = 161.404 K, and pt = (81.675 ± 0.011) kPa, also given and discussed in reference [1] as well as the relative magni- from reference [8]. For the present purposes, this value of Tt (Xe) tude of the terms in equation (2). The term A, which is a positive is virtually the same as Tt = (161.40596 ± 0.032) K arrived at by Hill constant, is smaller than terms involving B and C, while the summa- and Steele [11] in a recent most careful study intended to investi- tion over the Di terms is negative in every case. Although consider- gate the possible establishment of the exact triple point tempera- able partial cancellation between such terms always occurs, all their ture of Xe as a fixed point in the ITS-90. contributions are relatively important in magnitude. The term The molar enthalpy of sublimation at the triple point g involving E(T) is only relevant at temperatures not far below the tri- Ds Hm ðT ¼ TtÞ can be obtained from the general relationship ple point, since in the low temperature region the values of E(T) are small and also because they are to be multiplied by the relatively g ‘ g Ds Hm ¼ DsHm þ D‘ Hm ðat T ¼ TtÞ; ð5Þ small values of the sublimation pressure p and divided by the equi- g librium temperature T. since no direct measurements of Ds Hm ðT ¼ TtÞ seem to have been g reported, as far as we are aware. The enthalpy of vaporization of ar- The molar enthalpy of sublimation Ds Hm is obtained as a function of temperature from equation (1) by using equation (2) to cal- gon was determined experimentally by Flubacher et al. [12] at the culate (dp/dT). The following expression is obtained [1]: temperature of T = 85.67 K, slightly above Tt. Since the difference ()between the heat capacities of the vapour and the liquid phases X4 g g i 2 D‘ Cp;m is known as function of temperature, a short extrapolation Ds Hm ¼ RBþ CT þ ði 1ÞDiT þfdEðTÞ=dTgpT : ð3Þ g 1 gives D Hm ðT ¼ TtÞ¼6595 J mol . Flubacher et al. also mea- i¼2 ‘ sured the enthalpy of fusion of argon at its triple point obtaining Figure 2 in reference [1] illustrates the results for several sub- ‘ 3 1 DsHm ðT ¼ TtÞ¼1:190 10 J mol [12], not far from the value stances. A direct conclusion can be drawn from equation (3): that of 1175 J mol1 at the same temperature given by Clusius [13] the enthalpy of sublimation at T = 0 K is given simply by from his own experiments. Combining the average of these two fig- ‘ g ures for DsHm ðT ¼ TtÞ with the above mentioned value of the en- Ds Hm ðT ¼ 0KÞ¼RB: ð4Þ thalpy of vaporization at Tt, the enthalpy of sublimation at the This quantity, which is easily assessed in this way, is a measure of g triple point is obtained from equation (5) as Ds Hm ðT ¼ TtÞ¼ the energy necessary to transform the solid crystal at zero kelvin 7:778 103 J mol1. The enthalpy of sublimation of krypton at into the (perfect) gas at the same temperature, and it is, of course, its triple point was determined by Beaumont et al. [14] as closely related to the so-called lattice cohesion energy of the solid, g 3 1 Ds Hm ðT ¼ TtÞ¼10:791 10 J mol from their measurements a quantity of interest in the study of intermolecular forces and g ‘ of D‘ Hm ðT ¼ 116:85 KÞ and DsHm ðT ¼ TtÞ. The situation for xenon otherwise. is similar to that of argon; Clusius and Riccoboni [15] measured Equation (3) enables the calculation of DgH from zero kelvin to g 3 1 s m D‘ Hm ðT ¼ 165:13 KÞ¼12:636 10 J mol , a few Kelvin above the triple point once sufficiently accurate values of the quantities the triple point, which after a short extrapolation using the differ- necessary to the ab initio evaluation of the sublimation pressure g ence between the molar heat capacities of both phases D‘ Cp;m gives through equation (2) are available, as happens for Ar, Kr, and Xe. g 3 1 D‘ Hm ðT ¼ TtÞ¼12:725 10 J mol . By combining this with From the knowledge of the enthalpy of sublimation along the en- ‘ their measured enthalpy of fusion DsHm ðT ¼ TtÞ¼2:295 tire (solid + vapour) equilibrium temperature range, one can try 3 1 g 10 J mol , the enthalpy of sublimation Ds Hm ðT ¼ TtÞ and determine general analytical expressions accounting for that ¼ 15:020 103 J mol1 is obtained. change. Such expressions can be of use in extrapolating to the rare For the heat capacity of the three monatomic elements in the gases adjacent in the group, namely Ne and Rn, for which some gaseous state at the low pressures involved along the sublimation uncertainty is still prevailing in this respect, since neon is affected g equilibrium, the classical value Cp;m ¼ð5=2ÞR has been used in our by quantum effects and the scarce experimental data for radon do calculations. Concerning the heat capacity of each of the three ele- not withstand the confidence and quality commonly attached to ments in the solid state, the experimental values [12,14–18] have ‘ the other rare gases (helium which has no s + + g triple point is, been expressedP by simple polynomial functions of temperature: of course, out of this exercise). s 3 i Cp;m ¼ i¼0ciT . The values of the ci parameters are registered in ta- s ble 1. In the extrapolation of Cp;m (usually from T 10 or 15 K) to g 3. Results zero kelvin, necessary to refine the calculation of Ds Hm ðT ¼ 0KÞ, the Debye cubic law has been used. In the calculation of the sublimation pressure through equation Insofar as the molar volumes of the two phases are concerned, (2), finding the values of the parameters A,B,...,E(T) needs a most those of the solid have been assessed from experimental values careful evaluation of the thermodynamic properties involved. The in the literature and describedP by polynomials as a function of s 2 i (s + ‘ + g) triple point of each rare gas has been taken as reference. the temperature: V m ¼ i¼0viT . For argon, the measurements of For argon, the triple point temperature is a fixed point in the ITS- Peterson et al. [19] at low temperatures (up to the triple point)

90: Tt = 83.8058 K. For its respective equilibrium pressure the value have been used, while for krypton the molar volume of the solid pt = (68.898 ± 0.011) kPa selected by Staveley et al. [8] was phase has been calculated from the X-ray values of the lattice

TABLE 1 s Molar heat capacities of the rare gases in the solid state Cp;m as functions of temperature P s 1 1 3 i1 Rare gas Coefﬁcients ci in the molar heat capacity polynomials, Cp;m=ðJ mol K Þ¼ i¼1ci ðT=KÞ Temperature range of the measurements References 2 4 Ar c0 = 10.5324; c1 = 1.5932; c2 = 2.5100 10 ; c3 = 1.5047 10 T P 10 K [12,16] 2 4 Kr c0 = 3.3243; c1 = 1.2128; c2 = 1.6443 10 ; c3 = 0.7750 10 T P 10 K [14] 2 4 Xe c0= 7.3947; c1 = 0.6018; c2 = 0.6170 10 ; c3 = 0.2227 10 T P 15 K [15,17,18] A.G.M. Ferreira, L.Q. Lobo / J. Chem. Thermodynamics 40 (2008) 1621–1626 1623

TABLE 2 s Molar volumes of the solid rare gases V m as functions of temperature P s 3 1 2 i Rare gas Coefﬁcients vi in the molar volume polynomials, Vm=ðcm mol Þ¼ i¼0vi ðT=KÞ Temperature range of the measurements (T/K) References 3 4 Ar v0 = 22.554; v1 = 0.4457 10 ; v2 = 3.0144 10 2.4 6 T/K 6 83.2 [19] 3 4 Kr v0 = 27.034; v1 = 6.7195 10 ; v2 = 1.5565 10 4 6 T/K 6 Tt [20] 2 5 Xe v0 = 34.560; v1 = 1.2232 10 ; v2 = 8.1847 10 0 6 T/K 6 160 [18]

TABLE 3 Second virial coefficients B of the rare gases as functions of temperature P 3 1 2 i Rare gas Coefficients bi in the second virial coefficient polynomials, B=ðcm mol Þ¼ i¼0bi=ðT=KÞ Temperature range of the values of B 3 6 Ar b0 = 4.0385; b1 = 0.8666 10 ; b2 = 1.7325 10 77 6 T/K 6 163 3 6 Kr b0 = 23.2774; b1 = 4.4027 10 ; b2 = 4.6342 10 107 6 T/K 6 210 3 6 Xe b0 = 25.9110; b1 = 3.5338 10 ; b2 = 10.7670 10 160 6 T/K 6 300

parameters given by Losee and Simmons [20] spanning the tem- that the sublimation curves of Ar, Kr, and Xe in figure 1 are calcu- perature interval from T = 4 K to the triple point. For xenon, the lated from equation (2) with the numerical values of its parameters measurements given in reference [18] up to T = 160 K have been indicated in table 4. No fitting to any sublimation pressure mea- selected. The coefficients vi are registered in table 2. surements has been necessary to find these curves in spite of the g 8 The molar volumes of the gaseous phases V m have been calcu- fact that they encompass equilibrium pressures from (10 to lated with the Berlin form of the virial equation of state truncated after the second term, the second virial coefficients B of the three substances being taken from those recommended in the compila- 106 tion by DymondP and Smith [21] adjusted through polynomials of 2 i the form B ¼ i¼0bi=T . The values of the coefficients bi in these 5 Ne Ar Kr Xe Rn polynomials are given in table 3. 10 Having assessed as carefully as possible the information on the properties needed in the evaluation of the parameters in equation 104

(2), the subsequent calculations give the values of A, B, C,Di, and E(T) indicated in table 4. The calculations show that the molar vol- 103 umes of the solid phases have a negligible effect on the final results while the influence of the second virial coefficients on the molar 102 volumes of the gas should only be taken into account at temperatures not far below that of the triple point of each substance, in 101 accordance with the conclusions of our previous work [1]. Figure 1 shows a representation of the sublimation curves of Ar, Kr, and 100 Xe calculated in the way described above. The points in this figure are experimental, from various sources. The deviation plots in fig- 10-1 ure 2 elucidate more clearly on the quantitative aspects in this p / Pa context. 10-2 After numerically complete forms of equation (2) had been g -3 established for the three classical rare gases, the values of Ds Hm 10 are easily calculated as functions of temperature by using equation (3). The results obtained at T = 0 K and T = Tt are registered in table 10-4 g 5, and the change of Ds Hm with temperature is shown in figure 3. 10-5 4. Discussion 10-6 Figures 1 and 2 are complementary. For clarity only part of the experimental points are shown in both. It should be emphasized 10-7

10-8 0 50 100 150 200 250 TABLE 4 P 4 i1 T / K Parameters in equation (2):lnðp=PaÞ¼A B=ðT=KÞþC lnðT=KÞþ i¼2DiðT=KÞ þ 2 3 EðTÞðp=PaÞ=ðT=KÞ, where {E(T)/(T/K)} = E1 + E2(T/K) + E3/(T/K) + E4/(T/K) + E5/(T/K) FIGURE 1. Sublimation curves of the rare gases. Legend: the solid lines (—) are 2 4 7 Rare gas AB C10 D2 10 D3 10 D4 calculated from equation (2) with the parameters given in table 4. The dashed lines (– – –) are calculated from equation (9). The symbols are experimental. For argon: , Ar 10.9131 930.108 3.7667 9.5811 5.0314 15.081 reference [22]; , reference [12]; j, reference [23]; M, reference [7]; +, reference Kr 14.2350 1344.287 2.8998 7.2934 3.2960 7.7679 [24]; h, reference [25]; ., reference [8]. For krypton: e, reference [26]; , reference Xe 18.5232 1916.032 1.6106 3.6187 1.2368 2.2324 [27]; d, reference [14]; j, reference [23]; N, reference [28]; h, reference [29];+, 10 11 6 4 10 E1 10 E2 10 E3 10 E4 E5 reference [24]; ., reference [8]. For xenon: d, reference [30]; , reference [31]; N, j M . Ar 0.5361 3.6255 3.1971 1.0422 0.2084 reference [32]; , reference [23]; , reference [33]; +, reference [24]; , reference d h e Kr 8.0816 1.8720 6.0510 5.2952 0.5574 [8]. For neon: , reference [34];+, reference [35]; , reference [36]; , reference . M . Xe 14.712 0.9844 7.2877 4.2501 1.2950 [37]; , reference [8]. For radon: +, reference [38]; , reference [39]; , this work (triple point). 1624 A.G.M. Ferreira, L.Q. Lobo / J. Chem. Thermodynamics 40 (2008) 1621–1626

3 the original work at integer values of temperature from (63 to 80) K also have attached deviations too large to be included in ﬁg- } 2 Ar exp ure 2 which shows that with those two exceptions there is com- p

)/ 1 fortable agreement between our calculated curves and the exp p

- 0 experimental values registered in the literature. calc

p Figure 2 in reference [1] makes it clear that the enthalpy of sub- -1 limation of pure substances that are much different in nature from

100{( -2 each other is a distorted, inverted parabola as function of T with its s g -3 maximum at the temperature at which Cp;m ¼ Cp;m. Both the exper- 0.5 0.6 0.7 0.8 0.9 1.0 g imental measurements of Ds Hm and the values calculated from T / Tt various methods and theories agree with those resulting from our calculations. Figure 3 conﬁrms that this same trend is observed 3 for the three classical rare gases. The calculated values at the two

} 2 Kr extremes of the parabola, at T = 0 K and T = Tt, registered in table exp

p 5 leave little room for discussion. However, pertinent comments

)/ 1 g

exp should be addressed when the change in Ds Hm over the entire tem- p - 0 perature range is analysed. This change can be expressed by a func- calc p -1 tion of the form:

g c

100{( -2 Ds Hm=ðRTtÞ¼að1 TrÞþbTr ; ð6Þ -3 0.5 0.6 0.7 0.8 0.9 1.0 where Tr = T/Tt, and a and b are parameters which assume well de- g g ﬁned values: a ¼ Ds Hm ðT ¼ 0KÞ=ðRTtÞ, and b ¼ Ds Hm ðT ¼ TtÞ= T / Tt ðRTtÞ. For the three rare gases, the average value of the latter parameter is b = 11.1884. On the other hand, both a and c can be related to 3 new quantities h1 =(M MAr)/M, where M is the atomic mass of the

} 2 Xe particular gas, and MAr is the same for argon, and h2 =(Tt Tt,Ar)/Tt, exp p

)/ 1 where exp p - 0 a ¼ 11:1269 þ 0:9348h1; ð7Þ calc p -1 c ¼ 0:8755 þ 0:0648h2: ð8Þ

100{( -2 With this set of parameters, the enthalpies of sublimation are given -3 as functions of temperature by the dashed lines in figure 3 for Ar, Kr, 0.5 0.6 0.7 0.8 0.9 1.0 and Xe. g g T / Tt Having obtained a general expression for Ds Hm ¼ Ds HmðTÞ, equation (6), one can try and use it to integrate equation (1) g FIGURE 2. Deviation plots for the sublimation pressure of Ar, Kr, and Xe. pcalc is assuming that Ds V m is given by the perfect gas law. Then, the sub- calculated from equation (2), and pexp are experimental from various authors. limation pressure comes out as Legend: symbols as in figure 1. 0 0 c1 lnðp=ptÞ¼ða b Þa=Tr a ln Tr þ b Tr ; ð9Þ where b0 = b/(c 1). The deviation plots of the sublimation pressure 105) Pa over relatively moderate temperature ranges for each one of Ar, Kr, and Xe calculated from equation (9) are only marginally of the gases involved. The steepness of the curves in figure 1 does worse than those indicated in figure 2. not help in assessing the quality of the results. In any case, this fig- From a different point of view, it can be envisaged that equa- ure may legitimately support the conclusion that the measure- tions (6)–(9) would be of use if applied to neon and radon which ments made by Leming and Pollack [7] for Ar at the lower are adjacent to Ar, Kr, and Xe in the group of rare gases, but have temperatures in their experiments are clearly off. It is not surpris- not been involved in the above calculations. This extrapolation ing that the results (shown in graphical form) by Levenson [23,33] exercise might be useful for two main reasons: (i) those equations at the lowest temperatures for the three gases exhibit much larger do not demand the knowledge of any quantum parameter in deal- deviations than those of the remaining authors. Similarly the mea- ing with neon, since parameter h1 plays a role similar to that of a surements made by Fisher and McMillan [27] for Kr indicated in quantum correction; and, (ii) the values of the sublimation

TABLE 5 g Molar enthalpy of sublimation Ds Hm of the rare gases

g 1 Rare gas Ds Hm=ðJ mol Þ

T =0K T = Tt This work Literature Reference This work Literature Reference Ar 7755 7732 ± 42 [40] 7778 7733 ± 11 [41] 7722 ± 11 [41] 7786 ± 21 [14] 7740 ± 50 [42,43] 7740 [4] Kr 11,172 11,158 ± 50 [40] 10,791 10,791 ± 13 [14] 11,148 ± 13 [41] 11,155 ± 29 [14] Xe 15,815 15,839 ± 91 [40] 15,020 15,039 ± 22 [41] 15,816 [44] A.G.M. Ferreira, L.Q. Lobo / J. Chem. Thermodynamics 40 (2008) 1621–1626 1625

18000 ence [8]. With these data, equations (7)–(9) lead to the sublimation curve of neon represented in ﬁgure 1, and the deviation plot in ﬁgure 4. The result is most satisfactory. Turning now to the case of radon, a previous issue must be examined. In reference [2], an iterative method to estimate the values of the coordinates of the (s + ‘ + g) triple point of Rn has been devised, and in calculating the sublimation curve of the substance 16000 the data published by Stull [38] were used. Meanwhile our attention has been drawn to the existence of additional information on radon properties, namely to an article by Grosse [39] in which this element is still named as Emanation (symbol Em). By combin- Xe ing the values of the sublimation pressure provided in both references [38,39], and using the same iteration procedure as before [2],

14000 we arrive at Tt = 207.7 K, and pt = 84.0 kPa for the coordinates of the triple point of Rn. This value of Tt is to be compared with T = 208.3 K estimated by Grosse [39]. It should be noted that con- -1 trary to the conclusions of reference [2] the triple point pressure

now obtained is pt(Rn) > pt(Xe), as one should expect, and the dif-

/ J.mol ference between the boiling and the triple point temperatures is m

H (211.9 207.7) K = 4.2 K which is about the average value of the

s 12000

Δ same difference (3.7 K) for Ar, Kr, and Xe. These two facts support the conclusion that the triple point coordinates of radon obtained in this work should be preferred to those indicated in our previous

work [2]. The new value of Tt leads to h2 = 0.5966, which combined Kr with h1 = 0.8201 allow the calculation of the sublimation pressure of radon trough equation (9) as represented in ﬁgure 1. The calcu- 10000 lated curve lies in between the two sets of vapour pressure results from the literature [38,39]. From equation (6) and the above mentioned values of parame-

ters h1 and h2 for neon and radon, the molar enthalpy of sublimation for both substances can be obtained, either at zero kelvin {(2.085 103 and 19.788 103)J mol1, respectively} or at their g 8000 respective triple point temperature: Ds HmðTt ¼ 24:555 KÞ¼ 3 1 g 2:284 10 J mol for neon, and Ds HmðTt ¼ 207:7KÞ¼ Ar 18:605 103 J mol1 for radon. The calculated values for neon g 3 1 are to be compared with Ds Hm ðT ¼ 0KÞ¼2:120 10 J mol g 3 1 0 20 40 60 80 100 120 140 160 180 [40] or Ds Hm ðT ¼ 0KÞ¼1:929 10 J mol [46], and with g 1 Ds Hm ðTt ¼ 24:555 KÞ¼ð2129 25Þ J mol [40]. For radon T / K g 1 Grosse [39] estimated: Ds Hm ðT ¼ 0KÞ¼19:958 J mol and g 3 1 g D Hm ðTt ¼ 207:7KÞ¼18:912 10 J mol . FIGURE 3. Plot of molar enthalpies of sublimation Ds Hm of Ar, Kr, and Xe as s functions of temperature. The solid lines are calculated from equation (3). The dashed lines are calculated from equation (6). Acknowledgements

The authors wish to thank J.W. Arblaster for having drawn their 3 attention to the existence of the paper by Grosse [39], and for his most helpful comments on the triple point of radon [2]. } 2 exp p

)/ 1 xp

e References p

- 0 calc

p [1] L.Q. Lobo, A.G.M. Ferreira, J. Chem. Thermodyn. 33 (2001) 1597–1617. -1 [2] A.G.M. Ferreira, L.Q. Lobo, J. Chem. Thermodyn. 39 (2007) 1404–1406. [3] A.G.M. Ferreira, L.Q. Lobo, J. Chem. Thermodyn. 40 (2008) 618–624.

100{( -2 [4] W.T. Ziegler, J.C. Mullins, B.S. Kirk, Calculation of the vapor pressure and heats -3 of vaporization and sublimation of liquids and solids, especially below one 0.50.60.70.80.91.0 atmosphere pressure. II. Argon. Technical Report No. 2. Project No. A-460, T / T Georgia Institute of Technology, Atlanta, 1962. t [5] W.T. Ziegler, D.W. Yarbrough, J.C. Mullins, Calculation of the vapor pressure and heats of vaporization and sublimation of liquids and solids, especially FIGURE 4. Deviation plot for the sublimation pressure of Ne. palc is calculated from below one atmosphere pressure. VI. Krypton. Technical Report No. 1. Project equation (9), and pexp are experimental from various authors. Legend: symbols as in No. A-764, Georgia Institute of Technology, Atlanta, 1964. figure 1. [6] W.T. Ziegler, J.C. Mullins, A.R. Berquist, Calculation of the vapor pressure and heats of vaporization and sublimation of liquids and solids, especially below one atmosphere pressure. VIII. Xenon. Technical Report No. 3. Project No. A- pressure of radon published in the literature, which still carry 764 and E-115, Georgia Institute of Technology, Atlanta, 1966. [7] C.W. Leming, G.L. Pollack, Phys. Rev. B 2 (1970) 3323–3330. non-negligible uncertainty [2], can be tested in this way. [8] L.A.K. Staveley, L.Q. Lobo, J.C.G. Calado, Cryogenics 21 (1981) 131–144. Examining first the case of Ne, the following information is re- [9] R.N. Goldberg, R.D. Weir, Pure Appl. Chem. 64 (1992) 1545–1562. [10] R.L. Rusby, J. Chem. Thermodyn. 23 (1991) 1153–1161. quired: h1 = 0.9796, calculated using the internationally adopted [11] K.D. Hill, A.G. Steele, Metrologia 42 (2005) 278–288. atomic weights [45]; h2 = 2.4130, by taking Tt,Ne = 24.555 K, [12] P. Flubacher, A.J. Leadbetter, J.A. Morrison, Proc. Phys. Soc. (London) 78 (1961) which is a fixed point in the ITS-90, and pt = 43.356 kPa from refer- 1449–1461. 1626 A.G.M. Ferreira, L.Q. Lobo / J. Chem. Thermodynamics 40 (2008) 1621–1626

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