Selection of the CsI(s,l) monomer enthalpy of vaporization

There is no reason for the observed differences between the 3^rd law re-calculated CsI enthalpy of sublimation obtained with the Knudsen effusion data and those obtained via transport method or total pressure measurements when considering the methods themselves since their usual uncertainties are in the same range. For total pressures and for transport method we can estimate δp/p ≈ 5 to 10% (including temperature effects), and for effusion methods δp/p ≈ 5 to 30%, the larger quoted uncertainty range coming from “parasitic” contributions as already analysed for mass spectrometric Knudsen cell coupling [56, 57]. Indeed Glushko et al.

preferred to select a dimmer to monomer ratio at 905 K, and then used the total pressure or transport measurements that appear more accurate (sic). The origin of the observed differences is thus coming more probably from other selected data, especially those for the liquid phase. The liquid thermodynamic properties are depending on the solid thermodynamic properties through the choice of the melting enthalpy of CsI(l) and the heat capacity of CsI(l), these two quantities being included in the calculated Free Energy Function of the CsI (l) used in the third law analysis of measured pressures over the liquid. Changing the melting enthalpy of CsI(s→l) has a direct effect on the vapour pressure as indicated in figure III-7 meanwhile the change of the liquid heat capacity is of second order impact. Besides, regarding the choice of the monomer vaporization enthalpy – together with the preceding dimmerization enthalpy choice – the deduced pressures over the solid influence the pressure at the melting temperature as sketched in fig. III-7.

T

-∆

H (high)

∆

H(low)

-∆

H (low)

∆

H(high) A

B

1 / T(K)

R L o g p / b ar

(high) (low)

T

-∆

H (high)

∆

H(low)

-∆

H (low)

∆

H(high) A

B

1 / T(K)

R L o g p / b ar

(high) (low)

Figure III-7: Influence of the choice of different melting enthalpies and monomer vaporization enthalpies on the vapour pressures of the CsI(s or l) compound.

If the vaporization enthalpy of the monomer is too high (in our case the one deduced from the liquid ≈ 197 kJ.mol^-1) the pressures over the solid are too low and do not join the liquid pressures at the melting (point B in fig. III-7), the measured ones being higher (point A in fig.

III-7). This is one more reason to explain that the effusion methods give a more reliable value, and indeed the Gluskho et al. selection was performed accordingly to this main analysis.

Comparison of recalculated CsI 3^rd law enthalpies of vaporization from solid and liquid phases is displayed in figures III-8 and III-9 as a function of the temperature of measurements.

CsI(s,l)=CsI(g)

193.5 194 194.5 195 195.5 196 196.5 197 197.5 198

700 750 800 850 900

T /K

CsI Enthalpy of sublimation/kJ.mol-1

Cordfunke (Transport)

Venugopal et al.(Transport)

Venugopal et al.(Effusion)

Cogin & Kimball (Effusion)

Ewing & Stern (Effusion)

Deitz (Absolute manometer)

Scheer & Fine (Effusion)

Figure III-8: Third law CsI(g) enthalpies of sublimation calculated from experimental determinations performed over the solid phase as a function of temperature of measurements.

In figure III-8 we observe that results can be divided into two groups of authors: one group corresponds to Knudsen effusion data which seems less scattered and without regular trends.

In this case, the mean enthalpy of vaporization varies between 194.66 and 195.86 kJ.mol^-1. The second group corresponds to transport and total pressure data. The mean enthalpy of vaporization varies between 196.7 and 197 kJ.mol^-1. In comparison to the first group, the enthalpy of sublimation seems less reliable because large scatter is observed especially for transport data reinterpretation (Cordfunke and Venugopal et al.). For this raison, we chose a mean CsI(g) enthalpy of vaporization of the solid phase based on effusion studies,

∆_subH(CsI,g,298.15) = 195.23 ± 0.63 kJ.mol^-1.

This value corresponds to Sheer and Fine, Ewing and Stern, Cogin and Kimball and Venugopal et al.(effusion method) mean value over CsI solid phase. The other methods more scattered are discarded. The uncertainty is based on the largest deviation between the mean selected vaporization enthalpy and other retained values.

CsI(s,l)=CsI(g)

193 194 195 196 197 198 199 200

900 1000 1100 1200 1300 1400 1500

T/K

CsI Enthalpy of sublimation/ kJ.mol-1

Topor (Transport) Cordfunke(Transport) Ewing & Stern (Effusion)

Murgulescu & Topor (Robedusch Dixon) Venugopal (Boiling point)

Figure III-9: Third law CsI(g) enthalpy of sublimation calculated from experimental determinations performed over the liquid phase as a function of temperature of measurements.

Figure III-9 presents the CsI(g) 3^rd law enthalpy of sublimation obtained from original data over the liquid phase. Results seem very scattered. In fact the enthalpy of vaporization varies between 194.44 and 198.92 kJ.mol^-1. Moreover we observe some trends with temperature which can be attributed to errors in Free Energy Function of the reaction – presently for the liquid phase. Since the selected enthalpy of vaporization over solid is closer to the first value (obtained with Ewing and Stern data), we chose it as the mean CsI(l) enthalpy of sublimation over liquid phase and discard the higher values.

Finally, the CsI mean enthalpy of sublimation selected over solid and liquid is thus equal to,

∆_subH(CsI,298.15) = 194.83 ± 4 kJ.mol^-1.

The uncertainty is based on the largest differences between the mean selected vaporization enthalpy and other retained values. Using the retained vaporization enthalpy, we recalculated via the 3^rd law of thermodynamics the monomer and dimmer partial pressures as well as the apparent pressures. Results are presented in figures III-10, III-11 and III-12 altogether with experimental data.

-8 -7 -6 -5 -4 -3 -2

9 10 11 12 13 14 15

10⁴/ T /K^-1 log10 Papp / bar

Glushko et al.1982 table via 3rd law Ewing & Stern 1974

Scheer & Fine 1962 Cogine & Kimball 1948 Venugopal 1985 recalculated data

Figure III-10: CsI apparent pressure determinations over solid and liquid given by different authors using the effusion method and comparison with recalculated data using our new dimmerization constant and the selected vaporization enthalpy of the monomer.

With the present selected CsI(s,l) vaporization enthalpy, recalculated data are in good agreement with those determined by different authors over the solid phase.

-6 -5 -4 -3 -2 -1 0

6 7 8 9 10 11 12 13

10⁴/T /K^-1 Log10 Papp / bar

Topor 1972 (Fit) Venugopal 1985 Cordfunke solid 1986*

Glushko et al. 1982 via 3rd law Cordfunke liquid 1986 recalculated data

T_m

Figure III-11: CsI apparent pressure determinations over solid and liquid given by different authors using the transport method and comparison with recalculated data using our selected dimmerization constant and our selected enthalpy of vaporization for the monomer.*

As shown in figure III-11, the present selected CsI(g) enthalpy of vaporization increases the apparent pressures over solid in comparison to Cordfunke and Venugopal et al. and are also slightly higher than Cordfunke above the melting point. Over liquid, recalculated pressures remain slightly higher in comparison to those determined by Cordfunke and join apparently Topor’s data at elevated temperature (T > 1600 K).

-8 -7 -6 -5 -4 -3 -2 -1 0

6 7 8 9 10 11 12 13 14

10⁴/ T /K Log10 Ptot / bar

Murgulescu & Topor 1970 (Robedusch Dixon) Venugopal et al. 1985 (boiling method) Glushko et al. 1982 table via 3rd law recalculated data

Deitz 1936 (Absolute manometer)

Figure III-12: Total pressure determinations over CsI given by different authors and comparison with recalculated data using our selected K_dim and CsI(s,l) enthalpy of vaporization = 194.83 kJ.mol^-1

In figure III-12, the recalculated total pressures with the CsI(s,l) selected enthalpy of vaporization are higher than Deitz over solid phase and Venugopal et al. over liquid phase.

However, at elevated temperature, the recalculated data tend to join Venugopal et al.

determined ones as well as Murgulescu and Topor.

In order to reduce the difference between experimental data and the recalculated data using the present selected CsI(g) enthalpy of vaporization and to find a better compromise between the different experimental methods (Knudsen effusion, transport and total pressure measurements), we propose to select a new CsI(sl) melting enthalpy rather than keeping the Glushko et al. selected one.