Vapour pressure and standard enthalpy of sublimation of alkali-metal fluoroborates

Article abstract of DOI:10.1016/j.tca.2006.10.008

The temperature dependence of the vapour pressures of solid alkali-metal fluoroborates MBF₄ (M = Na, Rb or Cs) were experimentally determined using an improvised transpiration technique. The vapour pressure of NaBF₄ could be represen

Full text of DOI:10.1016/j.tca.2006.10.008

Thermochimica Acta 452 (2007) 1–6
Vapour pressure and standard enthalpy of sublimation
of alkali-metal fluoroborates
R. Pankajavalli, Ashish Jain, S. Anthonysamy∗, K. Ananthasivan, P.R. Vasudeva Rao
Fuel Chemistry Division, Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India
Received 25 May 2006; received in revised form 11 October 2006; accepted 11 October 2006
Available online 20 October 2006
Abstract
The temperature dependence of the vapour pressures of solid alkali-metal fluoroborates MBF4 (M = Na, Rb or Cs) were experimentally determined
using an improvised transpiration technique. The vapour pressure of NaBF4 could be represented by the following least-squares expressions:
log(p/Pa) [NaBF4, orthorhombic] = 7.06( 0.03) − 3734( 360) (K)/T
log(p/Pa) [NaBF4, monoclinic] = 6.03( 0.04) − 3192( 80) (K)/T
The enthalpy pertaining to the transition from the orthorhombic to the monoclinic phase at 527 K, was found to be 10.4 kJ mol−1
The measured vapour pressures of RbBF4 and CsBF4 could be represented by the following least-squares expressions:
.
log(p/Pa) [RbBF4] = 6.21( 0.04) − 4020( 87) (K)/T
log(p/Pa)[CsBF4] = 7.77( 0.04) − 5209( 108) (K)/T
By using the third law analyses of the data, ꢀH◦ of MBF4 (M = Na, Rb or Cs) at 298 K were determined to be 89.4 1.5, 123.4 1.9 and
sub
135.7 0.8 kJ mol−1, respectively.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Alkali fluoro borate; Vapour pressure; TG based transpiration technique; Enthalpy of sublimation
1. Introduction
sure of this compound was measured in our laboratory [4]. In
addition to these applications, experimental data on the vapour
pressure and enthalpies of phase transitions are required for the
basic understanding of the thermochemistry of this class of com-
pounds. Hence, in the present study, the vapour pressures of
MBF4 (where M = Na, Rb or Cs) were measured in order to study
the systematics in the vapour pressure as well as the standard
enthalpy of sublimation of these compounds.
High-density boron carbide (10B-enriched) pellets will be
used as neutron absorbers in the control and safety rods (CSR)
and diverse safety rods (DSR) of the first Indian commercial
fast breeder reactor [1]. These carbide pellets will be produced
by the direct reaction between elemental boron and graphite at
high temperature followed by consolidation by hot pressing [2].
Enriched elemental boron will be produced by the electroly-
sis of KBF4 dissolved in a molten mixture of KCl and KF [3].
Data on the vapour pressure of KBF4 would be useful for pre-
dicting and minimizing the loss of the precious enriched boron
during high temperature electrolysis. Hence, the vapour pres-
2. Experimental
2.1. Starting materials
Analytical reagent grade NaBF4 of purity better than 99.9%
(supplied by M/s Acros organics, USA) was used for the tran-
spiration experiments. RbBF4 and CsBF4 were prepared by
carrying out the following chemical reactions.
∗
Corresponding author. Tel.: +91 44 27480098; fax: +91 44 27480065.
E-mail address: sas@igcar.ernet.in (S. Anthonysamy).
0040-6031/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2006.10.008

2
R. Pankajavalli et al. / Thermochimica Acta 452 (2007) 1–6
2.2. Synthesis of alkali metal flouroborates
range of flow rate. However at any given temperature in this
range, the drift in mass over a period of 1 h was of the same
magnitude. The apparent mass loss was subtracted from all the
recorded isothermal mass losses. The details of the experimental
set-up and the method of measurement of the vapour pressure
are described elsewhere [4,6,7].
RbBF4 and CsBF4 were prepared through the following
chemical reactions:
4HF(aq) + H3BO3(s) → HBF4(aq) + 3H2O(l)
(1)
1
HBF4(aq) + M2CO3(aq) (M = Rb (or) Cs)
2.4. Differential scanning calorimetry (DSC)
2
1
1
A heat flux type differential scanning calorimeter (model
DSC 821 e/700, M/s. Mettler Toledo, GmbH, Switzerland) was
used for the measurement of transition enthalpy of alkali-metal
fluoroborates. The measurements were carried out at a heating
rate of 0.17 K s−1 and with a flow of 100 ml min−1 of 99.995%
pure argon. The DSC equipment was calibrated for the tempera-
ture measurement using the melting points of In, Pb, Zn, Sb, Al
and Au. The enthalpies of these transitions were in agreement
within 1 kJ with those cited in the literature [8].
→ MBF4(s) + H2O(l) + CO2(g)
(2)
2
2
Both the above reactions are highly exothermic. Hence, it
was necessary to carry out these reactions at 278 K. In the first
reaction, HBF4 was prepared by dissolving stoichiometric quan-
tity of boric acid in 27N hydrofluoric acid, by adding small lots
of H3BO3 to HF with continuous stirring. After the completion
of dissolution, a saturated solution of M2CO3 (where M = Rb or
Cs) was added to the HBF4 solution at 278 K. A gelatinous white
precipitate of MBF4 (M = Rb or Cs) was obtained. This precipi-
tate was filtered under suction using a G4 glass frit, washed with
water (278 K) and with methanol, and dried under an IR lamp
for 1 h. The XRD patterns of the compounds prepared in this
study match with the patterns reported in JCPDS [JCPDS file
no.: 11-0671 for NaBF4, 73-1521 for RbBF4 and 73-0206 for
CsBF4].
3. Results and discussion
3.1. TG and DSC measurements
Non-isothermal TG experiments were carried out with
NaBF4, RbBF4 and CsBF4 at a linear heating rate of 0.07 K s−1
using the TG/DTA thermal analyser in order to identify the
mass-loss steps and to fix the maximum temperature for
vapour pressure measurements. Typical thermograms of these
compounds are shown in Fig. 1. The range of temperature
was so chosen that they are significantly below the melt-
ing/decomposition temperature of alkali-metal fluoroborates.
The thermograms shown in Fig. 1 reveal the phase transi-
tion temperatures of NaBF4 (orthorhombic to monoclinic),
RbBF4 and CsBF4 (orthorhombic to cubic) to be 519, 527
and 442 K, respectively. These values are in excellent agree-
ment with the corresponding values of 519, 529 and 443 K,
respectively, obtained by the Differential Scanning Calorime-
try (DSC) in this study (Fig. 2). From the DSC curves the
enthalpies of phase transitions were calculated to be 7.2, 10.97
2.3. Transpiration set-up
A horizontal thermal analyzer (Model-Seiko 320) was
adapted as a transpiration set-up for vapour pressure mea-
surements. The configuration of the dual arm balance with a
narrow furnace chamber minimizes errors arising from con-
vection, buoyancy, thermo molecular and electrostatic charge
effects. A Pt-13% Rh/Pt thermocouple (Type-R) was used for
the measurement of temperatures with an accuracy of 0.5 K.
The thermocouple was calibrated at the freezing point of pure
metals such as tin, lead, antimony, aluminium, silver and gold.
These calibration experiments revealed that the measured val-
ues of the temperature conform to the scale prescribed by ITS-90
[5] within 0.5 K. Helium gas (99.995% pure) was used as the
carrier gas. Since the flow rate of the carrier gas is the critical
parameter in the transpiration experiments, precise flow cali-
bration of the carrier gas was done using a capillary glass flow
meter, which in turn was calibrated by a soap bubble method
using a horizontal burette. Though the precision in the flow rate
by the glass capillary flow meter was 0.5%, the overall preci-
sion in the integral volume was of the order of 1% of the total
volume of the carrier gas. In order to facilitate the saturation of
the carrier gas with the vapourising species, the powdered sam-
ple was spread over the surface of a shallow platinum crucible.
Further, the narrow chamber tube was found to be conducive
for the saturation of the vapour with carrier gas. Prior to the
vapour pressure measurements, blank runs were taken with flow
rates of 3–30 dm3/h of helium gas at a temperature range from
400 to 800 K keeping both the sample and the reference pans
empty. The apparent mass gain was found to be of the order
of 2–4 ␮g/100 K change in temperature encompassing the full
Fig. 1. DTA traces of MBF4 (M = Na, Rb or Cs).

R. Pankajavalli et al. / Thermochimica Acta 452 (2007) 1–6
3
Fig. 2. DSC traces of MBF4 (M = Na, Rb or Cs).
and 8.26 kJ mol−1, respectively for NaBF4, RbBF4 and CsBF4.
These values are in excellent agreement with the values of 6.7,
11.96 and 8.11 kJ mol−1 recommended by Dworkin and Bredig
[9]. The experimentally determined quantities along with those
reported in earlier investigations are compared in Table 1.
where‘W’isthemass-lossofthesample, Vc isthetotalvolumeof
the carrier gas (saturated with the vapour species), Tc is the ambi-
ent temperature of the carrier gas and M is the molecular weight
of the vapour species. In the case of KBF4, the vapour phase
in equilibrium with the solid compound contains monomeric
species [10,11]. This supposition is substantiated from the obser-
vation made in our earlier work [4]. In the present study, we
derived the enthalpy of transition and transition temperature of
NaBF4 from the vapour pressure measurements assuming that
the gaseous species were only monomeric. It is observed that
there is a good agreement between the enthalpy values derived
from vapour pressure measurements (free vapourization) and
closed capsule DSC measurements. Similarly, we derived the
enthalpy of transition and transition temperature of RbBF4 and
CsBF4 from DSC measurements. It is observed that there is a
good agreement between the enthalpy values derived from DSC
measurementsmadeinthisstudyandtheenthalpyvaluesderived
from calorimetric measurements reported in the literature [9].
Thus, the absence of gas phase decomposition of the vapour
species, as well as preferential removal of any particular species
(other than the monomeric species) from the gas phase during
the vapour pressure experiments is confirmed. This testifies the
validity of the assumption that the vapourization is congruent
in MBF4 and that the vapour comprises only monomers. The
vapour pressures of alkali-metal fluoroborates were measured
after establishing the equilibrium conditions. In order to estab-
lish that the measured values of papp are the equilibrium vapour
pressure values at a given temperature, it is necessary to demon-
strate the existence of a chair-shaped curve in the plot of papp
versus flow rate of the carrier gas. This chair-shaped curve is
characteristic of isothermal equilibrium vapourization in a tran-
spiration technique. Such plots for MBF4 (M = Na, Rb or Cs)
are shown in Fig. 3. The plateau in these plots shows that the
vapourizationratewasadequatetosaturatethecarriergasforany
3.2. Transpiration experiments
The apparent vapour pressures, papp, over solid NaBF4,
RbBF4 and CsBF4 were calculated from the mass-loss of the
sample using the relation:
WRTc
papp
=
(3)
MVc
Table 1
Comparison of ꢀH◦
and Ttrans of MBF4 (M = Na, K, Rb or Cs)
trans
M
ꢀH◦trans(kJ mol−1
)
Ttrans(K)
Reference
Na
6.7
7.2
10.4
–
516
519
527
519
[9]
This work—DSC
This work—TG transpiration
This work—DTA
K
14.1
16.8
14.1
14.5
–
556
556
561
561
560
[9,11]
[10]
[4]—TG Transpiration
[4]—DSC
[4]—DTA
Rb
Cs
11.96
10.97
–
518
529
527
[9]
This work—DSC
This work—DTA
8.11
8.26
–
443
443
442
[9]
This work—DSC
This work—DTA

4
R. Pankajavalli et al. / Thermochimica Acta 452 (2007) 1–6
Fig. 3. Plots of papp vs. flow rate of the carrier gas for NaBF4, RbBF4 and CsBF4.
Table 2
Table 3
Vapour pressure of NaBF4
Vapour pressure of RbBF4
Experiment
number
Temperature (K)
Ambient Experimental
Mass lossa Vc (dm3) Pressure
Experiment
number
T (K)
Mass lossa (␮g)
(cumulative)
Vc (dm3)
Pressure
(mPa)
(␮g)
(mPa)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
550
555
566
576
581
592
602
613
622
622
622
629
641
655
676
697
34
46
56
74
86
106
142
188
180
217
248
260
320
442
600
936
12.414
12.414
12.414
10.909
12.414
10.909
12.414
12.414
9
10.909
12.414
12.414
10.909
12.414
10.909
12.414
39.3
53.2
64.7
97.3
99.4
139.4
164.1
217.3
287.0
285.4
286.7
300.5
420.9
510.9
789.2
1081.9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
297
297
295
297
299
301
299
299
299
299
299
299
299
299
299
299
295
299
295
299
295
295
295
295
483
493
498
503
514
519
523
533
544
545
554
554
554
554
554
566
575
576
580
586
602
612
622
663
107
133
140
192
320
306
420
570
800
710
778
716
1000
957
10.909
9.955
9.0
10.909
10.909
10.909
10.909
10.909
10.909
9.0
221.5
300.8
347.9
396.3
664.9
640.1
872.7
1184.3
1662.2
1475.2
1959.4
1803.3
1825.9
1847.7
1878.3
2561.3
2638.4
3027.2
3512.9
3838.2
3512.9
5890.8
8782.2
15817
9.0
9.0
12.414
11.662
10.909
9.0
10.909
9.0
12.414
9.0
12.414
12.414
12.414
6.200
904
1017
1287
1202
1950
1524
3090
3270
4875
4390
Ambient temperature is 297 K.
a
Initial weight of the sample: 45 mg.
Table 4
Vapour pressure of CsBF4
Experiment
number
T (K)
Mass lossa (␮g)
(cumulative)
Vc (dm3)
Pressure
(mPa)
a
Initial weight of the sample: 70 mg.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
586
592
602
608
611
623
627
627
627
627
634
648
654
666
682
692
703
705
40
46
73
93
92
12.414
12.414
12.414
12.414
12.414
12.414
10.909
12.414
15
18
12.414
15
12.414
12.414
12.414
15
10.909
10.909
36.3
41.7
66.2
84.3
83.4
flow rate within this range. It is well known that at higher flow
rates the carrier gas is under-saturated with slow vapourization
of the sample while at lower flow rates than that in plateau region
papp is greater than pequilibrium owing to diffusion of the heav-
ier species down the temperature gradient at a different mean
velocity than the carrier gas atoms [12]. The mass losses, T, Vc
and papp calculated using the expression (3) for MBF4 are listed
in Tables 2–4. The measured data could be represented by the
following least-squares expressions:
156
116
142
172
204
201
348
383
394
617
1030
868
920
141.4
119.7
128.7
129.0
127.5
182.2
261.1
347.2
357.2
559.3
772.7
895.4
949.0
log(p/Pa) [NaBF4, orthorhombic]
= 7.06( 0.03) − 3734( 360) (K)/T
(4)
(5)
log(p/Pa) [NaBF4, monoclinic]
Ambient temperature is 297 K.
a
Initial weight of the sample: 45 mg.
= 6.03( 0.04) − 3192( 80) (K)/T

R. Pankajavalli et al. / Thermochimica Acta 452 (2007) 1–6
5
Fig. 5. Systematic trend in Enthalpy of transition (axis Y1) and enthalpy of
sublimation at 298 K (axis Y2) with lattice energy of the alkali metal.
Fig. 4. Temperature dependence of equilibrium vapour pressure of MBF4
(M = Na, K, Rb or Cs).
when enthalpies of transitions are plotted as a function of lat-
tice energy of the alkali-metal fluroborates, as can be seen from
Fig. 5 except for NaBF4. In the case of NaBF4, the phase trans-
formation is from orthorhombic to monoclinic whereas in other
alkali fluoroboates, the transformation is from orothorhombic
to cubic and therefore the deviation exists. The present vapour
pressure results of MBF4 (M = Na, Rb or Cs) are compared in
Table 5 along with the data on KBF4 reported earlier from this
laboratory.
log(p/Pa) [RbBF4] = 6.21( 0.04) − 4020( 87) (K)/T
(6)
log(p/Pa) [CsBF4] = 7.77( 0.04) − 5209( 108) (K)/T (7)
The vapour pressures of NaBF4 were represented by the
expressions (4) and (5) in the temperature ranges, 483–513
and 518–663 K, respectively. From these expressions a value of
527 K was obtained for the orthorhombic to monoclinic trans-
formation temperature of NaBF4, which is in good agreement
with the value of 516 K cited in Ref. [9]. From the slopes of the
above equations, values of 71.5 1.5 and 61.1 6.9 kJ mol−1
could be derived for the enthalpy of sublimation, ꢀH◦
of
3.3. ꢀH◦sub of MBF4 (M = Na, Rb or Cs)
sub
orthorhombic and monoclinic phases of NaBF4, respectively
at the mean temperature of the measurements, i.e., 498 and
591 K, respectively. The difference between these results yielded
a value of 10.4 kJ mol−1 for the enthalpy of phase transition of
NaBF4 which is in good agreement with the data reported in Ref.
[9] as well as those obtained using DSC, in the present work.
From the slopes of the Eqs. (6) and (7), the mean enthalpies of
sublimation (ꢀH◦sub) of RbBF4 and CsBF4 in the respective
temperature ranges of 550–697 K and 586–705 K, were derived
In order to assess the temperature dependent errors in the
present measurements, a third-law analysis of the vapour pres-
sure data was carried out. The change in the Gibbs energy
functions for the vapourization reaction was calculated using
the Gibbs energy functions of each participating member of the
reaction in the temperature range of the present measurements.
Among the fluroborates studied the values of the free energy
functions were available only for KBF4 [10] and not for the
other alkali-metal fluoroborates. For MBF4 (M = Na, Rb or Cs)
solids, the Gibbs energy functions were calculated using data
given in Ref. [9]. Since data on the Gibbs energy functions for
gaseous MBF4 (M = Na, Rb or Cs) are not available in the litera-
ture, they were estimated by using respective thermal functions
of MF(s)(M = Na, Rb or Cs)andBF3 (g) [10,11] andconsidering
to be 77.0( 1.7) and 99.7( 2.1) kJ mol−1
.
The plots of log p against 1/T for the compounds MBF4
(M = Na, Rb or Cs) are given in Fig. 4 along with our results
for KBF4 [4] for the purpose of comparison. It is clear from
Fig. 4 that the vapour pressure of the alkali-metal decreases sys-
tematically from Na to Cs. A similar systematic trend is observed
Table 5
Comparison of vapour pressure and enthalpy of sublimation at 298 K for MBF4 (M = Na, K, Rb or Cs)
M
log p (Pa) = A − B/T (K)
T range (K)
p (Pa) at 600 K
ΔH◦
(kJ mol−1
)
Reference
sub,298 K
A
B
Na
K
7.06
6.03
8.16
6.85
6.21
7.77
−3734
−3192
−4892
−4158
−4020
−5209
483–513
518–663
538–560
576–660
550–697
586–705
6.9
5.3
1.0
0.8
0.3
0.1
89.4
89.4
104.5
104.5
123.4
135.7
This work
This work
[4]
[4]
This work
This work
Rb
Cs

6
R. Pankajavalli et al. / Thermochimica Acta 452 (2007) 1–6
enthalpy of sublimation of orthorhombic and monoclinic phases
of NaBF4 were derived to be 71.5 1.5 kJ mol−1 (valid over
483–513 K) and 61.1 6.9 kJ mol−1 (valid over 518–663 K),
respectively. Likewise, enthalpy of sublimation of RbBF4 and
CsBF4 were derived to be 77.0( 1.7) and 99.7( 2.1) kJ mol−1
valid over the temperature ranges 550–697 and 586–705 K,
respectively. Third-law analysis of the experimental data yielded
enthalpy of sublimation values of 89.4 1.5, 123.4 1.9 and
135.7 0.8 kJ mol−1, respectively for Na, Rb and Cs fluorobo-
rates at 298 K.
Acknowledgements
The authors express their sincere gratitude to Shri. R.
Venkatakrishnan for DSC analysis of the samples. Authors are
also thankful to Shri. R. Madhavan for recording XRD patterns
for the alkali metal fluoroborates.
Fig. 6. Third-law plots for the enthalpy of sublimation of MBF4 (M = Na, Rb
or Cs).
References
the following chemical equilibrium:
MF(s) + BF3(g) → MBF4(g)
The enthalpy of sublimation at 298 K was then derived using
Eq. (8).
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ꢀ
ꢁ
G◦T − H◦
298
ꢀH◦sub(MBF4) = ꢀG◦vap − Tꢀ
.
(8)
T
For the vapourization process, the values of ꢀH◦sub of MBF4(s)
were calculated for the experimental data given in Tables 2–4.
Plots of ꢀH◦sub of MBF4(s) against experimental temperatures
are shown in Fig. 6. The mean values of ꢀH◦sub at 298 K were
found to be 89.4 1.5, 123.4 1.9 and 135.7 0.8 kJ mol−1 for
NaBF4, RbBF4 and CsBF4, respectively. The plots indicate that
the systematic errors in the present measurements are insignif-
icant. The values of ꢀH◦ at 298 K are compared in Table 5
sub
and also plotted in Fig. 5. It is seen from Fig. 5 that there is a
systematic increase in the enthalpy of sublimation at 298 K for
the alkali-metal fluoroborates as the lattice energy of the alkali-
metal fluroborates decreases.
4. Conclusion
[12] D.E. Cater, Vapour pressure measurements, in: R.A. Rapp, D.A. Shores
(Eds.), Physico-Chemical Measurements in Metals Research, vol. IV, Cal-
ifornia, USA, Part I, 1970, p. 21.
The vapour pressures of solid NaBF4 RbBF4 and CsBF4
were measured by transpiration technique for the first time. The