Mass spectrometric studies

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.

From ionization cross-section values and secondary electron multiplier yields relations as proposed by Drowart et al. [16], and using the sum of the ionic intensities issued from each molecule (parent plus fragment ions i.e. Cs⁺ + CsOH⁺ for the total ionic current issued from the CsOH molecule), the authors assumption has been checked and remains valid within 9%

for RbOH reference and 3% for KOH reference.

If the original thermochemical data obtained for the RbOH-CsOH systems at 673 K and KOH-CsOH at 692 K [8] are taken into consideration, using Gurvich et al. free energy functions (Fef) for the reference molecules RbOH(g) or KOH(g) [2], the dimmerization enthalpy is obtained to be: ∆ dimH^° (CsOH) = 146 ± 11 kJ.mol^-1 with RbOH as reference and 156 ± 10 kJ.mol^-1 with KOH as reference. Note that the dimmer Rb2O2H2 reference is not well known since Gurvich et al. estimated the bond using trends in the hydroxides that were then compared to flame experiments due to lack of direct vaporization studies.

Gorokov et al. (1970) [11] determined by HTMS the difference of dissociation energies of KOH and CsOH: D₀(Cs-OH)- D₀(K-OH)=31.8 ± 4.6 kJ.mol^-1. At the beginning of their experiment or in the first one, some invoked carbonates impurities (earlier studies on carbonates – including preparation of the samples - were performed by the authors) produced Cs(g) and K(g) in the gas phase. Note that this feature would be related to reducing conditions in the cell that can not be obtained by the only Pt container (used in their experiment), but necessarily by sample impurities clearly different from water pollution. As the ionization process of the hydroxides produce more Cs⁺ (or K⁺) ions than CsOH⁺ (or KOH⁺) ions, the convolution of the different contributions remains a necessary step that increases the total uncertainty of the measurements. From their equilibrium constant of the gas-phase exchange reaction (isomolecular),

Cs(g) + KOH(g) = CsOH(g) + K(g) (19)

i.e. CsOH referred to KOH from Gurvich et al. compilation [2] (D0(K-OH)=357± 3 kJ.mol^-1) , and using Fef (free energy functions) of Janaf tables for Cs and K [3], the dissociation energy of CsOH(g) has been obtained to be D0(Cs-OH) = 388.8 ± 5.6 kJ.mol^-1 (uncertainty takes into account the assumption of error compensation using √∑δx² relation and including the free energy function uncertainty= ±1 kJ.mol^-1) and ∆fH298.15CsOH(g) = -276.8 ± 5.8 kJ.mol^-1.

Born-Haber cycles from ionization processes

From Gorokov et al. (1970) [11] measurement of the Cs⁺ dissociative ionization potential using the following Born-Haber cycle (at 900 K),

CsOH(g) + e^- ↔ Cs⁺ + OH(g) + 2 e^- (dissociative ionization potential at 900 K) (3) Cs(g) + e^- → Cs⁺ + 2 e^- (known adiabatic ionization potential) (20) CsOH(g) = Cs(g) + OH(g) (deduced bond energy at 900 K) (21)

and considering the measurement performed at 900 K: D°900K(Cs-OH) = 359.8 ± 12.5 kJ.mol^-1 , dissociation energy has been calculated at 0 K using enthalpy increments,

Cs(g) 0 900 OH(g) 0 900 CsOH(g)

0 900 900

0 (Cs-OH) D (Cs-OH) (H -H ) (H -H ) -(H -H )

D° = ° K + − (22)

The enthalpy increments have been obtained from Janaf tables for OH(g) and Cs(g) and from Gurvich et al. tables for CsOH(g). The resulting dissociation enthalpy D°0(Cs-OH) = 357.6 ± 12.6 kJ.mol^-1(uncertainty takes into account the errors compensation). As Gorokhov et al., we assume no contribution of ion (and/or neutral) kinetic energy in process (3) by analogy with K⁺/KOH analyzed using electrostatic deflection at the ion source output. Our recalculated value is slightly different from the one presented in Gurvich et al. compilation (358 ± 12 kJ.

mol^-1).

From Emellyanov et al. (1967) [12] and the same Born-Haber cycle, we obtained D°0(Cs-OH) = 341 ± 13.6 kJ.mol^-1 different from the original value given by the authors at about 900 K: D°900K(Cs-OH) = 344 ± 13.5 kJ.mol^-1 . The resulting value for the enthalpy of formation is ∆fH^°298.15CsOH (g) = -229 ± 13.7 kJ.mol^-1 including the proposed uncertainty for the enthalpy increment of CsOH(g) by Gurvich et al. [2].

It is to notice that the differences in these two preceding studies have to be related to difficulties in obtaining accurate values for ionization potentials: namely 0.1 eV is rarely reached as total uncertainty (0.1 eV = 11.2 kJ).

Vaporization studies

Konings and Cordfunke [10] total apparent pressure papp from the transpiration experiment – calculated on the basis of the transported and analyzed Cs atoms at the condenser - gives the partial pressure of the monomer and dimmer using our dissociation constant Kd (inverse of dimmerization constant) for the reaction (CsOH)₂(g)↔2CsOH(g) according to the following relations,

2

1 2 p

p

p_app = + (23)

2 2 1

p

K_d = p (24)

Kd

p p

2 1

2 = (25)

d

app K

p p p

2 1 1+2

= (26)

0

2p₁² +K_d ⋅p₁−K_d ⋅ p_app = (27)

(

^{d app}

)

d app d

d K p K K p

K ²+8 ⋅ = +8

=

∆ (28)















− + +

⋅ + =

+

= −

d d app

app d

d d

K K p

p K K

p K 8

1 4 1

4

) 8 (

1 (29)

p1 and p2 correspond respectively to monomer and dimmer pressures.

As the monomer remains the main species, third law calculation of the CsOH(cr,l) = CsOH(g) equilibrium is chosen as the main result : ∆sublH^°298.15 = 162.8 ± 0.9 (standard deviation) kJ.mol^-1. The third law results are presented in figure II-1 as a function of the measured temperature and compared to authors results with their assumption that monomer is the only present component in the gaseous phase. Our corrected values discarding the dimmer contribution lead to a less scattered mean value and to a smaller trend (thermodynamics should show no trend). The original pressures and corrected ones are presented in table II-3.

The total uncertainty is calculated from the third law relation:

δ∆_sublH = δT.( ∆ _sublH/T_mean) + δ(∆_sublFef).T_mean + R.T_mean.δP/P = ± 6.5 kJ.mol^-1 (30)

We estimated - (i) the total monomer pressure uncertainty on the basis of maximum deviation of the original apparent pressure (δP/P = ± 0.46 in fig. II-2 of Konings and Cordfunke [17]) for papp, adding the uncertainty on the dimmer existence or not (0 < p2 / p1 < 0.6 leading to δP/P = ± 0.3), the total δP/P = ± 0.76, - (ii) T_mean = 800 K and δT = ± 5 K, - (iii) δ(∆sublFef) = 2 + 2 according to Gurvich et al. tables. The assumption of errors compensation has been used for the calculation of total uncertainty. The deduced enthalpy of formation

∆fH^°298.15CsOH(g) is equal to -253.4 ± 6.5 kJ.mol^-1 (uncertainty takes into account the errors compensation and ∆fH^°298.15CsOH(s,l)= 416 ± 0.5 kJ.mol^-1 from Gurvich et al. [2].

Konings and Cordfunke (1988) - DeltaHsubl(CsOH, g, 298 K) monomer

154 156 158 160 162 164 166 168 170

660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980

T(K)

DeltaHsubl/kJ.mol-1

recalculed with our Kd mean value Papparent = Pmonomer mean value

Figure II-1: Third law enthalpy of the vaporization reaction CsOH(l) = CsOH(g) versus temperature for Konings & Cordfunke data [10] and Konings & Cordfunke corrected values discarding the dimmer contribution to the total apparent pressure data .

T(K)

Measured pressure = Papp

(Pa*) Konings

Konings assumption:

P1 = Papp

∆subH298.15(Konings) kJ.mol^-1

Our calculation:

P1 = Papp-2P2

(bar)

Without dimmer

∆subH^°298.15

(recalculated) kJ.mol^-1

675.7 1.4 158.9 7.13E-06 162.7

686.4 2.42 158.0 1.17E-05 162.1

699.1 5.08 156.2 2.23E-05 161.0

705.6 3.13 160.3 1.74E-05 163.8

737.3 12.22 158.2 6.17E-05 162.4

756.9 21.5 158.2 1.10E-04 162.4

769.4 20.73 160.6 1.21E-04 164.1

781.6 38.34 158.8 2.06E-04 162.8

799.6 67.16 158.0 3.53E-04 162.3

804.8 85.09 157.3 4.34E-04 161.8

819.4 124.57 157.0 6.36E-04 161.6

820 106.76 158.2 5.76E-04 162.4

854.6 191.77 159.4 1.12E-03 163.2

880.5 267.36 160.8 1.69E-03 164.1

902.6 432.6 160.3 2.73E-03 163.8

919.4 575.43 160.5 3.69E-03 163.8

922.2 723.88 159.1 4.43E-03 162.8

922.3 720.23 159.1 4.42E-03 162.9

922.4 633.74 160.1 4.03E-03 163.6

940.8 972.77 159.2 6.08E-03 162.9

958.1 1199.93 159.8 7.75E-03 163.3

975.6 1627.13 159.5 1.06E-02 163.0

Mean value at 298 K 158.9 162.8

Standard deviation 1.3 0.9

* the published unit in table 1 of Konings and Cordfunke paper [17] is Pascal and not kPa as mentioned.

Table II-3 : In the third column, the third law enthalpy is calculated with the Fef of Gurvich et al.[2]

and with Konings assumption of only monomer in the gas phase. In the fourth column, the monomer pressure is calculated using our dissociation enthalpy for the dimmer. The last column corresponds to the calculated third law enthalpy for the sublimation of the only monomer (CsOH(cr,l) = CsOH(g)).

Blackburn and Johnson (1988) [9] vaporized CsOH(l) by HTMS (quadrupole mass spectrometer) and calibrated the mass spectrometer using the mass loss of the sample during the experiment. When compared with earlier mass spectrometric studies and our determinations [1] performed with a conventional magnetic mass spectrometer, their dimmer ionic intensities are much lower - at least by a factor 100. As we confirmed the values for the ionic intensities dimmer to monomer ratio of Schoonmaker and Porter [8] performed with a magnetic mass analyzer, we agree with the existence of an uncontrolled mass discrimination in the quadrupole MS as invoked by Gurvich et al. [2]. Indeed, Blackburn and Johnson attempted to check this mass discrimination “using perfluorotripentylamine for the mass range 50 to 602” but they were not convinced by their tests and did not use the mass discrimination results. So, the Blackburn and Johnson determinations cannot be used for the determination of the dimmerization equilibrium constant. Moreover, due to their attributed small contribution of dimmer in their gas phase, Blackburn and Johnson calculated the monomer vaporization from the full mass loss and so doing they over-evaluated the monomer’s pressure. Gurvich et al. took off the dimmer contribution to the monomer pressure, but no details are published about the correction done probably to the total mass loss. Similar process has been done using our selected dimmerization (or dissociation) constant in the following way:

• the total relative mass loss (from tables II-1 and II-2 in Blackburn and Johnson paper [9]) have been recalculated due to the monomer and dimmer effusion according to the Hertz-Knudsen equation,

• The total pressure in the effusion cell - defined as apparent pressure from the only mass loss - is then used to recalculate the monomer partial pressure using our equilibrium constant K_d (dissociation of the dimmer into two monomers) according to the following relations,

2

1 2 p

p

p_app = + (31)

2 0

1 2

1 + − app =

d

p p

K p (32)

app d

K p 4 2 1− ⋅

=

∆ (33)

Kd

p 2 2/ 1

1

∆ +

= − (34)

and finally, using relation (32) dimmer pressure p₂ is deduced according to the following relation:

2

1 2

p p p^app−

= ⁽³⁵⁾

The so calculated ratio p_1/p_app amounts to about 0.96. For low temperature range, no dimmer pressures have been published by Blackburn and Johnson and as a first approximation, their monomer pressure can be considered as equal to the apparent pressure. Meanwhile in the high temperature range, the apparent pressure has been recalculated from the two contributions (presence of monomer and dimmer in the gaseous phase). Then, from this recalculated apparent pressure (as measured by mass loss) and using our dissociation constant K_d, the real monomer pressure has been recalculated.

The original pressures and corrected ones are presented in table II-4 and figure II-2. From the corrected partial pressure of the monomer, the third law sublimation enthalpy for the reaction CsOH(cr,l) = CsOH(g) has been calculated to be: ∆sublH^°298.15 = 164.4 ± 1.3 (standard deviation) kJ.mol^-1. The estimated total uncertainty has been taken as for Roki et al. mass spectrometric same experiments (± 6.5) and finally the total uncertainty is δ(∆sublH) = ± 7.8

-1

∆_fH^°_298.15CsOH(s,l)= 416 ± 0.5 kJ.mol^-1, the deduced formation enthalpy is ∆_fH^°_298.15CsOH (g) = -251.8 ± 7.8 kJ.mol^-1 (uncertainty takes into account the errors compensation).

N.B. The authors did not mention any experimental observations concerning the creeping or overflow of the material - as analyzed by Roki et al.[1] - but we observe a relatively large scatter of the original published data (see fig. II-2). Consequently, the third law enthalpy results of the main reaction CsOH(s,l) = CsOH(g) are largely scattered as presented as a function of temperature measurements in figure II-3.

In order to test the influence of a possible overflow of about 50% in the total mass loss, we calculated also the sublimation enthalpy when the apparent pressure is divided by two (fig II-3). Results show that the enthalpy is increased by about 3kJ but the results show a small trend (comparison between the mean value and the least square fit). Our first calculation with apparent pressure seems better. As the authors used silver Knudsen cell – a material Roki et al. did not test in their experiments – we can conclude that either there is compensation between the overflow and their measured ionic intensities (genuine effusion plus parasitic contribution) or there is no significant overflow with silver cells.

CsOH(l) vaporization

-7,5 -7 -6,5 -6 -5,5 -5 -4,5 -4 -3,5

1,2 1,3 1,3 1,4 1,4 1,5 1,5 1,6 1,6 1,7

1000/(T/K)

Log10(P/bar)

monomer(Blackburn)

dimmer(Blackburn)

monomer corrected

dimmer corrected

Figure II-2 : Decimal logarithm of partial pressures in equilibrium with CsOH(l) versus 10³/T for Blackburn and Johnson data [9] and corrected pressures as explained in the text.

T(K) Monomer pressure (Bar)

Blackburn

Dimmer pressure (bar)Blackburn

Apparent Pressure

(bar)

Monomer pressure corrected with our

Kd

∆sublH(298 K) (kJ.mol^-1)

622 5.60E-07 5.60E-07 3,81E-07 166.2

654 7.82E-06 7.82E-06 3,64E-06 161.7

672 5.53E-06 5.53E-06 3,56E-06 165.8

681 1.49E-05 3.94E-07 1.55E-05 8,13E-06 163.1

684 1.68E-05 1.68E-05 8,92E-06 163.2

684 1.28E-05 1.28E-05 7,39E-06 164.2

686 1.24E-05 1.24E-05 7,38E-06 164.7

702 3.19E-05 1.53E-06 3.41E-05 1,78E-05 162.9

714 3.23E-05 3.23E-05 1,94E-05 164.8

736 5.70E-05 5.70E-05 3,58E-05 165.5

743 8.04E-05 1.81E-06 8.30E-05 4,99E-05 164.8

759 1.16E-04 1.88E-06 1.19E-04 7,41E-05 165.3

772 1.71E-04 4.21E-06 1.77E-04 1,10E-04 165.1

164.4 Mean value at 298 K

Standard deviation 1.3

Table II-4: Re-calculations of apparent pressure from monomer and dimmer pressure values of Blackburn and Johnson [1] and deduced monomer pressure using our dissociation enthalpy for the dimmer. The last column corresponds to the calculated third law enthalpy for the sublimation of the monomer CsOH(cr,l) = CsOH(g).

Blackburn and Johnson (1988) - DeltaHsubl(CsOH, g, 298 K)monomer

155 157 159 161 163 165 167 169 171 173 175

600 620 640 660 680 700 720 740 760 780

T (K)

DeltaHsubl/kJ.mol-1

from apparent pressure mean value

p apparent /2 p app/2 mean value

Figure II-3: Third law enthalpy of the reaction CsOH(cr,l) = CsOH(g) from Blackburn and Johnson data recalculated using our dissociation constant for the dimmer (full line). Dashed lines correspond to an arbitrary decrease of mass loss (50%) associated to the assumption of an overflow contribution in the total effusion process.

Roki et al. (2007) [1] performed mass spectrometric vaporization of pure CsOH(l) (see appendix II-A for experimental pressures of CsOH(g) and Cs₂O₂H₂(g)) and propose for the sublimation reaction CsOH(cr,l) = CsOH(g) a value ∆_sublH^°298.15 = 163.3 ± 6.5 kJ.mol^-1 . Using Gurvich et al. enthalpy of formation for the solid: ∆_fH^°298.15CsOH(s) = -416.2 ± 0.5 kJ.mol^-1, the CsOH(g) enthalpy of formation has been obtained to be: ∆fH^°298.15CsOH(g) = - 252.9 ± 6.5 kJ.mol^-1, uncertainty takes into account the error compensation √(6.5²+0.5²) (published value in [1] -252.7 ± 6.5, the 0.2 difference is simply due to an error of calculation). The direct determinations of the sublimation enthalpy are compared in table II-5.

Results show that all third law enthalpies become more consistent when taking into account our dissociation constant.

Reaction : CsOH(cr,l) = CsOH(g)

Temperature range (K)

∆sublH(298 K, 2^nd law) /kJ.mol^-1

∆sublH(298 K, 3^rd law) /kJ.mol^-1 Authors 622-772

(Tmean = 700)

160.9 ± 9.7 151.9 ± 1.9 Blackburn, Johnson

[9]

Corrected 163.6 ± 7.0 164.4 ± 1.3^a

Authors 676-976 (Tmean = 830)

152.2 ± 2.6 158.9 ± 1.3 Konings, Cordfunke

[10]

Corrected 157.9 ± 1.8 162.8 ± 0.9^a

Roki et al. [1] This work 496-765 146.8 ± 10.1^b 163.3 ± 2.1^b

a: 1 experiment, ^b: 4 experiments standard deviation

Table II-5: Comparison between literature data and recalculation of sublimation enthalpy with 2^nd and 3^rd law (with standard deviation).

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