PART II: CRITICAL ASSESSMENT OF THERMODYNAMIC DATA FOR CSOH
II.3. CRITICAL ASSESSMENT OF THERMODYNAMIC DATA FOR THE GAS PHASE
II.3.1. CsOH(g) flames studies
In order to obtain the enthalpy of formation of CsOH(g), H2 + O2 + N2 + CsOH (dopant) flames dissociation studies were performed assuming the main dissociation reaction (2):
Cs(g) + H2O(g) = CsOH(g) + H(g)
Assumptions - based on this unique reaction or on a simplified set of elementary reactions - have been chosen for interpretation of measurements. Usually, CsOH is introduced in the
flames as a spray of diluted solution in water and the ionization of Cs into Cs+ liberates electrons at high temperature. The proportion of Cs+ is small as well as the CsOH(g) formed at equilibrium, and the introduced concentration of Cs is often chosen as a first approximation to be the existing one in the flame - sometimes including different species -. Different detection systems were used - electron concentration by attenuation method using radiofrequency waves [5], resonant cavity for electron concentration measurement, absorption spectroscopy for atoms [6] and double-beam atomic absorption using Cs hollow-cathode lamps [7] - .
Smith and Sugden (1953) [5] observed that the Saha relation for equilibrium ionization of alkaline components,
[CsOH] = Cs+ + e- + [OH] (6)
was not observed for Rb and Cs hydroxides, even with a modified burner protecting the flame by a nitrogen flow against atmospheric interferences, or using different mixtures. As temperature uncertainties could not explain the difference between measurements and attended results, a competitive reaction was proposed, i.e. the electron capture by the hydroxyl radical,
OH + e- → OH- (7)
that decreases the electron concentration as detected by radio frequency. The enthalpies of the two reactions assumed to occur altogether – ionization of Cs and electron capture by OH– were deduced from determination of the attenuation coefficient. But yet the electron affinity of OH was estimated to be 288.7 kJ.mol-1 instead of 175.7 kJ.mol-1 as presently retained from more recent and accurate measurements using laser methods as compiled by Lias et al. (1988) [14]. This difference implies that the OH- concentration is underestimated, then the Cs+ concentration overestimated. Finally the obtained value for the Cs-OH dissociation is overestimated as shown in table II-2 when compared to cotton and Jenkins [7] (at least 3 kJ) using a different method.
In fact, in this study the Cs-OH bond dissociation was not determined directly but referred to the Li-OH bond dissociation, these two metals having similar dissociation values. As a result,
chosen to be entirely decomposed for calibration of the electron concentration in the flame.
Thus, the CsOH dissociation was referred in a trend to LiOH dissociation which is well known (value so far unchanged).
Besides, the molecular parameters for the two molecules LiOH and CsOH – used in the pre- exponential factor of the equilibrium constant (partition function) – have been estimated by the authors. For this reason and using the presently known parameters – from JANAF98 [3]
for LiOH and Gurvich et al. [2] for CsOH – free energy function has been recalculated by using JANAF formula for a linear polyatomic molecule [3] and compared to those calculated with the same manner by using Smith and Sugden molecular parameters for LiOH and CsOH [5]. The free energy function contribution difference into the dissociation energies has been calculated for the reaction LiOH(g) + Cs(g) → CsOH(g) + Li(g) with the following relations:
) (
)
( 0
0 ) ) (
0( RTLnKp T fef D Li OH D Cs OH
H° Smith =− + ∆ Smith = ° − − ° −
∆ (8)
) ( ) ( ) ( )
(CsOH fef Li fef LiOH fefCs
fef
fef = + − −
∆ (9)
.) ( )
) ( 0( )
0(corr H Smith T fef smith T fef ourcal
H° =∆ ° − ∆ + ∆
∆ (10)
( ) ( )
[
( ) ( ) ( ) ( ) ( ) ( ) . ( ) ( )]
.) ( )
( )
(
Cs Janaf Li
Janaf cal
LiOH our Cs CsOH
Janaf Li
Janaf Smith
LiOH CsOH
cal our Smith
fef fef
fef fef
fef fef
fef fef
T
fef fef
T
− +
− +
+
− +
−
=
∆ +
∆
−
(11)
( ) ( )
[
( ) ( ) ( ) ( ) .]
.) ( )
( )
( fefSmith fefourcal T fefCsOH fefLiOH Smith fefCsOH fefLiOH ourcal
T −∆ +∆ = − + + − (12)
∆H°0(corr) is the corrected enthalpy, ∆H°0(smith) is Smith and Sugden enthalpy, ∆fef(smith) the free energy function calculated with Smith and Sugden molecular parameters for CsOH(g) and LiOH(g), ∆fef our cal. our recalculated free energy function using Janaf parameters for LiOH(g) and Gurvich et al. parameters for CsOH(g) (see appendix II-B), free energy functions of Li(g) and Cs(g) considered taken from Janaf tables [3].
The product T(∆Fef(our cal.)+ ∆Fef(Smith)) at the flame temperature (T = 2245 K) amounts to - 16.7 kJ.mol-1 that has to be added to the proposed value by Smith and Sugden: D°0 (Li-OH) - D°0 (Cs-OH) = 46 - 16.7 = 29.3 kJ.mol-1 . The resulting dissociation energy D°0 (Cs-OH) = 398.8 kJ.mol-1. D°0 (Li-OH) has been calculated from Janaf tables [3] for the dissociation reaction LiOH(g) → Li(g) + OH(g) at 0 K using the following relation:
) , ( )
, ( )
, ( )
( 0 0 0
0 Li OH H Li g H OH g H LiOH g
D° − =∆f +∆f −∆f (13)
∆Fef0(i) is the formation enthalpy of the gas i (i = Li(g), OH(g) and LiOH(g)) at 0 K. The dissociation energy D°0 (Li-OH) has been obtained to be 428.1 kJ.mol-1. D°0 (Cs-OH) has been transformed into D°298.15 K(Cs-OH) according to relation (14):
CsOH(g) → Cs(g) + OH(g) D°0 (Cs-OH) at 0 K
CsOH(g) → Cs(g) + OH(g) D°298.15 (Cs-OH) at 298.15 K
)CsOH(g) H
- (H - )OH(g) H
- (H )Cs(g) H
- (H OH) - (Cs D OH) - (Cs
D°298.15 = °0 + 298.15 0 + 298.15 0 298.15 0
(14)
D°0(Cs-OH) dissociation enthalpy at 0 K, D°298.15(Cs-OH) dissociation enthalpy at 298.15K, (H298.15-H0)enthalpy increment taken from Janaf tables for Cs(g)and OH(g) and from Gurvich et al. table for CsOH(g).
The formation enthalpy of CsOH(g) at 298.15 K has been calculated within the following relations:
) , (
) , ( )
, ( )
( 298.15 298.15 298.15
15 .
298 Cs OH H Cs g H OH g H CsOH g
D° − =∆f +∆f −∆f (15)
) (
) , ( )
, ( )
,
( 298.15 298.15 298.15
15 .
298 CsOH g H Cs g H OH g D Cs OH
H f f
f =∆ +∆ − ° −
∆ (16)
The enthalpies of formation of Cs(g) and OH(g) have been taken from Janaf tables [3].
Results before and after correction of Smith and Sugden free energy functions are presented in table II-2.
Jensen and Padley (1966) [6] values further corrected by Jensen (1970) [15] for the linear Cs- O-H structure used high temperature flames (2475 K) and determined electron concentration by resonant cavity, with special calibration procedure and keeping values in the linear range response of the cavity versus the inverse of temperature in the range 2000 – 2500 K.
The alkaline component concentration was determined by optical absorption measurements using the first resonant doublets of the alkaline component. For the Cs study, the authors added small quantities of Cs in Rb in order to suppress the Cs ionization – feature which was not reached – and in addition the residual concentration of CsOH(g) could not be neglected.
Finally the Cs concentration has been increased – according to the ionization theoretical equilibrium – in order to decrease the CsOH concentration below the detection threshold. The
balance between the Cs introduced concentration in the flame and the one deduced from electron concentration measurements amounts to a factor ≈ 6. This factor will induce a decrease of the dissociation energy of about RTln6 = 33 kJ.mol-1 (at T = 2250 K, R: gas constant) (see table II-2). Besides, we can question about the formation of the OH- ion as postulated by Smith and Sugden (1953) [5] that may decrease the electron concentration.
Cotton and Jenkins (1969) [7] used low flame temperature (1570 K) in order to avoid (or limit) the ionization of Cs, and obtained the Cs concentration by atomic absorption (Cs lamps) using a double-beam for calibration. Some usual techniques were used to measure the H flame concentration. The equilibrium constant is deduced from the trend of the ratio H2O/H as a function of the introduced volume (and thus concentration) of the solution in the flame.
Entropies are those from Jensen and Padley (1966) [6], consequently the correction to be applied is ≈ - 1kJ as re-calculated by Jensen (1970) [15] (see table II-2).
Authors D°0 original (kJ.mol-1)
D°0 corrected (kJ.mol-1)
∆f H°(298.15 K) (kJ.mol-1)
Method Smith & Sugden [5] 380.7a± 12.6
(2nd law)
398.8 ± 12.6
-268.7 ± 12.7 -286.8 ± 12.7
electron concentration by resonant cavity Jensen & Padley [6]
Jensen [15]
380a ± 12 (3rd law)
347 ± 12
-268 ± 12 -235 ± 12
electron concentration by resonant cavity Cotton & Jenkins [7] 376.6a ± 8.4
(3rd law)
375.6 ± 8.4
-264.6 ± 8.5 -263.6 ± 8.5
Flame photometry
a original authors data and estimated uncertainty
Table II-2. Summary of flame studies of the Cs-OH bond dissociation and our corrected values as discussed in the text. Corrected values are presented in bold. δ∆f H°(298.15 K) has been calculated with assumption of error compensation using the √∑δx2 relation
Concerning the flame studies, excited states are not necessarily identified when existing, and equilibrium conditions are difficult to ascertain since the only observed evolution in the flame does not warranty sufficient long time to achieve equilibrium till fundamental electronic level of the reactants and products even when analysis are performed along the flame propagation.
Moreover, Gurvich et al. [2] invoked a significant uncertainty on third law analysis due to the high temperatures used in flames (2475 K for Jensen & Padley [6], Jensen [15]) but this is not so significant for Cotton & Jenkins [7] who worked at rather low temperatures ≈ 1570 K. In
fact the pre-exponential factor – taking into account the rotational and vibrational states - in the equilibrium constant for the main postulated reaction has been estimated on the basis of no electronic contribution (sigma ground state), and this assumption may introduce large errors in the third law analysis if some low laying states exist. Farther, the choice of a single reaction or of a simplified set of reactions (usually only two main reactions) does not correspond to the real complex equilibria occurring in the flames within the temperature and concentration ranges of the experimental determinations. Clearly flame studies necessitate a panel of technical analysis in view to consider the complexity of the gaseous phase.
For all these reasons, we believe that the above flame studies are likely to be approximate values. Indeed their results differ significantly from those obtained using more conventional methods as Knudsen effusion, transpiration and mass spectrometry.