Investigation of the Vaporization of Boric Acid by Transpiration

Oct 9, 2008 - Fuel Chemistry DiVision, Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam,. Tamil Nadu 603102, India. ReceiVed: July...
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J. Phys. Chem. B 2008, 112, 13873–13884

13873

Investigation of the Vaporization of Boric Acid by Transpiration Thermogravimetry and Knudsen Effusion Mass Spectrometry R. Balasubramanian, T. S. Lakshmi Narasimhan, R. Viswanathan,* and S. Nalini Fuel Chemistry DiVision, Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu 603102, India ReceiVed: July 4, 2008; ReVised Manuscript ReceiVed: August 27, 2008

The vaporization of H3BO3(s) was studied by using a commercial thermogravimetric apparatus and a Knudsen effusion mass spectrometer. The thermogravimetric measurements involved use of argon as the carrier gas for vapor transport and derivation of vapor pressures of H3BO3(g) in the temperature range 315-352 K through many flow dependence and temperature dependence runs. The vapor pressures as well as the enthalpy of sublimation obtained in this study represent the first results from measurements at low temperatures that are in accord with the previously reported near-classical transpiration measurements (by Stackelberg et al. 70 years ago) at higher temperatures (382-413 K with steam as the carrier gas). The KEMS measurements performed for the first time on boric acid showed H3BO3(g) as the principal vapor species with no meaningful information discernible on H2O(g) though. The thermodynamic parameters, both p(H3BO3) and ∆subH°m(H3BO3,g), deduced from KEMS results in the temperature range 295-342 K are in excellent agreement with the transpiration results lending further credibility to the latter. All this information points toward congruent vaporization at the H3BO3 composition in the H2O-B2O3 binary system. The vapor pressures obtained from transpiration (this study and that of Stackelberg et al.) as well as from KEMS measurements are combined to recommend the following: log [p(H3BO3)/Pa] ) -(5199 ( 74)/(T/K) + (15.65 ( 0.23), valid for T ) 295-413 K; and ∆subH°m ) 98.3 ( 9.5 kJ mol-1 at T ) 298 K for H3BO3(s) ) H3BO3(g). 1. Introduction Numerous studies exist in the literature on boric acid on account of its many application areas,1–4 but only some pertinent to the present work are referred in this paper. Since H3BO3 (orthoboric acid) is the most common form of boric acid, the others being HBO2 (metaboric acid) and H2B4O7 (tetraboric acid or pyroboric acid), the term boric acid will be used in this paper to mean orthoboric acid. To our knowledge, the most detailed vaporization study performed yet on the H2O-B2O3 system was that by Stackelberg et al.5 70 years ago. They passed steam over solid boric acid and determined the amount of boric acid carried over by the steam, as a function of temperature (382-453 K) at the steam pressure of 1 atm, and also as a function of the steam pressure (1.33 × 104 to 1.01 × 105 Pa) at various temperatures. They observed that under a steam flow at 1 atm pressure, orthoboric acid converted into metaboric acid at T > 413 K. Furthermore, they also observed that while the water vapor pressure (from 1.20 × 104 to 1.01 × 105 Pa) had no influence on the rate of sublimation of orthoboric acid (mean p(H3BO3) ) 79 Pa at T ) 382 K), increase in the water vapor pressure caused a nearly linear increase in the boron volatility of the metaboric acid. From the measurements performed at a constant steam pressure of 1.01 × 105 Pa, they gave the p(B)boron species)-T relations corresponding to the reactions H3BO3(s) ) H3BO3(g) (382-413 K) and HBO2(s) + H2O(g) ) H3BO3(g) (415-453 K) and deduced the enthalpies for various reactions. They also constructed a p-T-x diagram for this binary system from measurements performed at other steam pressures. Just ahead of Stackelberg et al., Bezzi6 had performed similar vaporization * To whom correspondence should be addressed. Fax: 91 44 27480065. E-mail: [email protected].

experiments over boric acid at different p(H2O) pressures and observed that the p(H3BO3) at 373 K was constant (mean value ) 42 Pa) as the p(H2O) was varied from 1.72 × 104 to 5.40 × 104 Pa. On the basis of this, Bezzi concluded that the volatilization of boric acid under steam environment occurred not because of formation of a volatile hydrate but because of its own vapor pressure. The values of p(H3BO3) determined by Bezzi (from 363 to 383 K) and Stackelberg et al. (382-413 K) are reasonably consistent within these temperature ranges, but the temperature dependence of vapor pressures being different, the enthalpy of sublimation of boric acid deducible from Bezzi’s results (70.7 kJ mol-1) is about 30 kJ mol-1 lower than that from Stackelberg et al. (100.0 kJ mol-1). Meschi et al.7 used the Knudsen effusion mass spectrometric method (KEMS) to study the reaction between B2O3(l) and H2O(g) in the temperature range from 1060 to 1450 K, leading to the formation of HBO2(g). The trimeric species (HBO2)3(g) constituted about 1% of the monomer and so also was H3BO3(g). Randall and Margrave8 also studied the vapor equilibria in the B2O3(l)-H2O(g) system in the temperature range from 1000 to 1273 K by using the transpiration method. No measurable mass loss of B2O3 occurred when only dry nitrogen was flowed; and the mass loss occurred when saturated moisture containing nitrogen gas was flowed was attributed to gaseous boron hydroxides. West9 compiled the results of vapor pressure and solution calorimetric measurements performed at NIST (formerly NBS). The decomposition pressures were measured on a two-phase mixture of orthoboric acid and metaboric acid by using a U-tube mercury manometer. The p(H2O)-T relation for three two-phase mixtures (each consisting of a different form of metaboric acid) are given. The enthalpy of formation of metaboric acid (for all

10.1021/jp8058883 CCC: $40.75  2008 American Chemical Society Published on Web 10/09/2008

13874 J. Phys. Chem. B, Vol. 112, No. 44, 2008 three crystalline forms) are deduced and compared with those obtained by solution calorimetry. Ogden and Young10 characterized the molecular boric acid by matrix isolation spectroscopy and mass spectrometry. They could obtain satisfactory flux of molecular species of boric acid for matrix isolation spectroscopic study by gentle warming of the substance to only 308-318 K. The mass spectrometric study of crystalline boric acid showed that when heated in a vacuum at 313 K, it vaporizes to yield molecular H3BO3. The intensity of the parent ion B(OH)3+ was ∼2.4 times smaller than the fragment ion B(OH)2+. The intensity due to the only other boron-containing species H3B3O6+ was Ts,1), and the mean temperature [Ts,m ) (Ts,1 + Ts,2)/2], and the coefficients A and B corresponding to each run. The (dm/dt) at mean temperature Ts,m was computed from the least-squares fit relation and subsequently a normalization factor f was deduced by employing the eq 3:

f ) [Papp/(dm/dt)] at Ts,m

(3)

The values of Papp required for this purpose was computed from eq 2. Table 2 gives the values of f corresponding to each run.

Figure 5. Temperature dependence of the rate of mass loss of H3BO3(s) and p(H3BO3): (a) rate of mass loss vs 1/T (open symbols: exit stopcock fully open; filled symbols: exit flow constricted); (b) p(H3BO3) vs 1/T (filled symbols are “plateau values” from Figures 3 and 4; open symbols correspond to all the data in part a).

The Papp at each Ts was then computed by multiplying f with the measured (dm/dt) at Ts. Figure 5, a and b, shows respectively how the (dm/dt) and the normalized Papp values (76 points) varied with temperature. Figure 5b also contains the six Papp values from the flow dependence runs (plateau region values). The least-squares-fitted straight line corresponding to all the Papp values (82 points) shown in Figure 5b yields the following p-T relation:

log(Papp/Pa) ) -(5939 ( 176)/(T/K) + (17.90 ( 0.53) (4) The above relation gives an apparent enthalpy of sublimation of 113.7 ( 3.4 kJ mol-1, which is slightly higher than what eq 2 or the p-T relation of Stackelberg et al. yields. A third-law evaluation of these Papp values was performed by employing Gibbs free energy functions for H3BO3(s) from JANAF,18 and those for H3BO3(g) from JANAF as well as from Bowsher et al.11 As Figure 6a,b reveals, the third-law enthalpies of sublimation ∆subH°m(298 K) do not show any distinct trend with temperature: mean third-law value ) 100.3 ( 0.9 kJ mol-1 (with thermal functions for H3BO3(g) from JANAF) and 91.4 ( 1.0 kJ mol-1 (with thermal functions for H3BO3(g) from Bowsher et al.).

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Figure 6. Third-law enthalpy values for the reaction H3BO3(s) ) H3BO3(g) from the transpiration experiments (a and b) and the Knudsen effusion mass spectrometric experiments (c and d). Gibbs energy functions for H3BO3(s) from JANAF;18 Gibbs energy functions for H3BO3(g) from JANAF (a and c) and from Bowsher et al.11 (b and d).

Figure 7. Mass (of the sample plus the crucible) vs time plot corresponding to a long isothermal transpiration experiment at T ) 316 K under a constant flow of argon carrier gas (∼123 mL/ min).

3.1.3. Vaporization Experiment at a Fixed Temperature and a Fixed Flow for Long Duration. Figure 7 shows how the mass of the boric acid sample varied as vaporization was effected at 316 K and the argon carrier gas flow was maintained at ∼123 mL/min with the stopcock fully opened. The rate of mass loss, dm/dt, computed for the different segments of time that generated a total mass loss of 0.02 mg at least, practically remained the same through out the duration of the experiment: (3.2 ( 0.2) × 10-7 mg/s. The results of this experiment served to confirm that at T as low as 316 K, boric acid is volatile enough to show measurable mass loss when the vapor is transported out and that vapor pressure would remain invariant with time for such long duration as 60 h. Invariant vapor pressure at a constant temperature for a two-component system would mean that the sample was a congruently vaporizing single phase or an incongruently vaporizing two-phase mixture. That the dm/dt values of this experiment corresponds to a vapor pressure that would be hundreds of times lower than what NIST group9 report for the two-phase mixture H3BO3(s) + HBO2(s) makes us believe that vaporization of boric acid was congruent.

3.2. Mass Spectrometric Measurements on Boric Acid. The main ionic species detected in the mass spectrum of the equilibrium vapor over boric acid were H2BO2+ and H3BO3+. The ions HBO2+ and H3B3O6+ were also detected at high temperatures as very minor species. With the ionic species H3BO3+, the natural isotope abundances of 10 and 11 for boron were readily confirmed from I+ m/z ) 61 and 62. In the case of H2BO2+ while I+ at m/z ) 45 would correspond wholly to 11B, that at m/z ) 44 could correspond to the sum of I(H210BO2+) and I(H11BO2+). Because I(H10BO2+) at m/z ) 43 , I(H211BO2+) at m/z ) 45, I+ at m/z ) 44 was often close to that expected for H210BO2+, and consequently, the contribution of H11BO2+ could not be always ascertained. The ion H2O+ also showed the “shutter effect” and at the highest temperature of our investigation it was easily 4 times higher than the most abundant boron-containing ionic species I(H2BO2+). However, since the background intensity itself was rather high, and the net I(H2O+) showed no meaningful dependence on temperature unlike both H2BO2+ and H3BO3+, we are not sure of the origin of H2O(g), nor can we make any meaningful estimate of its abundance relative to boron-containing species. The ionization efficiency curves for H2BO2+ and H3BO3+ have been determined on a few times, and their appearance potentials (AP) deduced by linear extrapolation method with reference to the AP of the high background ion H2O+. The AP of H2BO2+ (14.6 ( 0.5 V) was consistently ∼2-2.5 V higher than that of H3BO3+ (12.6 ( 0.5 V), in accord with the observation of Ogden and Young,10 although the latter’s actual AP values were a little lower: 13.8 ( 0.5 V for H2BO2+ and 10.8 ( 0.5 V for H3BO3+. The higher AP for H2BO2+ together with the fact that both ions showed nearly the same temperature dependence (shown below) make us believe that at the electron energy of 30 eV used by us, H3BO3+ was formed by simple ionization of H3BO3(g) while H2BO2+ was generated by dissociative ionization of H3BO3(g), although I(H2BO2+) was easily 2.0 to 2.8 time higher than I(H3BO3+) in different runs.

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Balasubramanian et al.

Figure 8. Temperature dependence of ion intensities (a-e) and of p(H3BO3) (f, corresponding to the results of (e) with pressure calibration using mercury).

TABLE 3: Details Pertinent to Temperature Dependence Experiments on Solid Boric Acid (KEMS Experiments) H211BO2+ series no. 1 (3, 4, 5 Jan 2008) 2 (17, 18, 21, 22 Jan 2008)

temp no. of pointsa range (K)

H311BO3+

log (IT) ) A/T + B -A

B

∆subHapp no. of temp (kJ mol-1) pointsa range (K)

log (IT) ) A/T + B -A

B

∆subHapp (kJ mol-1)

26

Sample 1 291-332.5 4772 ( 117 15.11 ( 0.38

91.4 ( 2.2

25

291-334

4979 ( 130 15.33 ( 0.42

49

294-326

Sample 2 5187 ( 189 16.67 ( 0.61

99.3 ( 3.6

48

294-326

5301 ( 178 16.59 ( 0.58 101.5 ( 3.4

56

294-324

5396 ( 181 16.98 ( 0.59 103.3 ( 3.5

95.3 ( 2.5

3 (15, 19, 20, 21, 22, 25, 26 Feb 2008)

58

293-324

Sample 3 5288 ( 157 17.08 ( 0.51 101.2 ( 3.0

4 (11, 12 Mar 2008)

13

299-317

Sample 4 5456 ( 290 17.81 ( 0.95 104.5 ( 5.6

12

299-317

5437 ( 215 17.35 ( 0.70 104.0 ( 4.1

295-342

Sample 5 5354 ( 188 17.76 ( 0.59 102.5 ( 3.6

35

295-342

5226 ( 211 17.03 ( 0.67 100.0 ( 4.0

5 (3, 4, 7, 8, 9 Apr 2008) a

38

They correspond to total number of intensity measurements performed at different temperatures on different days given in column 1.

Figure 8 shows the temperature dependence of I(H211BO2+) and I(H311BO3+) observed over different experiments (Figure 8a-e). Table 3 gives the details pertinent to these measurements and also the apparent enthalpies of sublimation of these ions obtained by the second law method. The latter were computed from the log (IT) ) -A/T + B relations given in the same table. The mean value of apparent enthalpy of sublimation for H211BO2+ is 99.8 ( 5.1 kJ mol-1 and for H311BO3+ 100.9 ( 3.5 kJ mol-1. These values are very close to what we obtained in our transpiration measurements (see sections 3.1.1 and 3.1.2). The difference between the vaporization environments in the two types of experiments is essentially that, while in the transpiration the vaporization was effected from an open cell and under argon flow, in the KEMS experiment the vaporization was effected from a Knudsen cell (closest to a closed cell) and

under vacuum. The two different environments did not appear to influence the vaporization behavior of solid boric acid, both the enthalpy of sublimation (discussed above) and the vapor pressures (see section 3.3.2 and Table 1) in the temperature range of our study. 3.3. Studies on Mercury. To ascertain the reliability of vapor pressures of boric acid obtained in our transpiration measurements over boric acid, similar measurements were performed over mercury (with the same quartz cell used for boric acid), nearly at the same temperatures. However, in view of the limitation of our apparatus that the total mass on the pan cannot exceed 1 g and that the mercury sample itself will just be one single globule, it was not possible for us fill the crucible in the same manner as we could with boric acid powder. KEMS measurements were also performed to examine (1) how well

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Figure 9. Results of the vaporization experiments on mercury: (a and b) transpiration experiments (a, flow dependence run at T ) 349 K; b, temperature dependence run from 309 to 349 K); (c) Knudsen effusion mass spectrometric run for pressure calibration from 291 to 308 K.

the enthalpy of sublimation of Hg compares with the known value; and (2) what is the vapor pressure one would get for boric acid with the pressure calibration constant that could be deduced from measured I(Hg+) and known p(Hg) over mercury. Essentially, the measurements on mercury were undertaken to remove any doubt that different kinds of errors (especially that in temperature) combined such that we could get mutually consistent results from transpiration and KEMS experiments. 3.3.1. Transpiration Measurements on Mercury. Figure 9 shows the results from one of the three flow dependence runs (Figure 9a) and from one of the four temperature dependence runs (Figure 9b). The three flow dependence runs were performed at three different temperatures. The mean plateau region pressures are as follows: 0.32 ( 0.01 Pa (309 K); 1.29 ( 0.04 Pa (329 K); 4.49 ( 0.12 Pa (349 K). These values are by a factor of 2 less than those deduced from the p-T relation recommended by Alcock et al.27 and yield the following p-T relation:

log[p(Hg)/Pa] ) -(3078 ( 14)/(T/K) + (9.47 ( 0.04) (5) This relation yields an enthalpy of sublimation of 58.9 ( 0.3 kJ mol-1, close to the value deducible (61.1 kJ mol-1; 298-400 K) from the equation (log [p(Hg)/Pa] ) - 3190/(T/K) + 10.12) given by Alcock et al.27 The values of apparent enthalpy of sublimation deduced from the slopes of log(dm/dt) vs 1/T corresponding to the four temperature dependence runs are 57.2 ( 1.0, 58.1 ( 1.2, 58.0 ( 0.3, and 56.5 ( 0.4 kJ mol-1, in reasonable accord with the literature value. We believe that the lower p(Hg) obtained by us could be due to the fact that we could not fill the crucible with the sample up to its brim, or perhaps, Hg taken by us was also not very pure. Nevertheless, the transpiration experiments on mercury served to demonstrate that even if our vaporization studies corresponded to low temperatures or only a small temperature range, the vapor pressures and the enthalpy of sublimation deducible from our transpiration experiments could be relied

upon: the vapor pressures within a factor of 2 and the enthalpy of sublimation within ∼5 kJ mol-1. 3.3.2. Mass Spectrometric Measurements on Mercury and EWaluation of Vapor Pressures and Enthalpy of Sublimation of H3BO3(g). The AP of Hg+ agreed with the ionization potential IP of Hg(g)28 with the AP of H2O+ normalized to IP of H2O(g).29 The initial temperature dependence measurements were performed without altering the focusing conditions for Hg+ (from those optimized for H3BO3+). The values of apparent enthalpies of sublimation obtained in these three runs were as follows: 68.5 ( 2.2 kJ mol-1 (302.5-334 K), 68.6 ( 3.1 kJ mol-1 (302-328 K), 70.3 ( 2.0 kJ mol-1 (301-321 K). These values are about 7-9 kJ mol-1 higher than that deducible from the p-T relation recommended by Alcock et al.27 For the purpose of pressure calibration, immediately after the last series of boric acid experiments, we loaded a fresh sample of mercury and performed a temperature dependence run after altering the focusing conditions to get maximum ion intensity for 202Hg+. Figure 9c shows the temperature dependence of 202Hg+ corresponding to this run (temperature range 291-308 K). The second law enthalpy of sublimation deducible from this plot is 65.1 ( 6.5 kJ mol-1, in reasonable accord with the p-T relation.27 The pressure calibration constant for Hg was obtained from the relation

k(Hg) ) [p(Hg)/Pa]/[I(Hg+)(T/K)]

(6)

where p(Hg) at temperature T was obtained from the p-T relation recommended by Alcock et al. and I(Hg+) was the measured ion intensity of Hg+ at 30 eV. The mean of 21 values of k(Hg) was (6.45 ( 1.31) × 10-2 Pa K-1. Using the above value of pressure calibration constant in conjunction with the ion intensities measured over boric acid in series 5, the vapor pressures of H3BO3(g) corresponding to the series 5 sample of boric acid were deduced. The following relations were employed for that purpose:

13882 J. Phys. Chem. B, Vol. 112, No. 44, 2008

p(H3BO3) ) k(Hg){σ(Hg)γ(202Hg+)n(202Hg+)} {I+(total H3BO3)T}/σ(H3BO3) (7) where

I+(total H3BO3) ) [I(X+)/{γ(X+)n(X+)}] + [I(Y+)/{γ(Y+)n(Y+)}] (8) where X+ ) H311BO3+, the parent ion, and Y+ ) H211BO2+, the fragment ion. In eqs 7 and 8, σ refers to the relative electron impact ionization cross section for the gaseous species given in parentheses; and γ and n refer to the relative detector response and the relative isotopic abundance of the ionic species given in parentheses. The γ was assumed to be inversely proportional to square root of the mass number of the ion measured. The value of σ for Hg was taken from Mann30 while that for H3BO3 was computed as 0.75 times the sum of the ionization cross sections for the elements; the values again were taken from Mann. Table 4 gives the ion intensities corresponding to series 5 measurements, the computed p(H3BO3) values, and also the

Balasubramanian et al. third-law enthalpy of sublimation value deduced for each p(H3BO3) value. The third-law values show absolutely no trend with temperature whether the Gibbs free energy functions used for H3BO3(g) were from JANAF18 or from Bowsher et al.11 The third-law values are also shown in Figure 6c,d to emphasize that the results of mass spectrometric and transpiration measurements are consistent. Figure 8f contains a plot of log p(H3BO3) vs 1/T deduced from KEMS which yields the following relation:

log p(H3BO3)/Pa) ) -(5226 ( 204)/(T/K) + (15.73 ( 0.65)

(9) This relation yields the second-law enthalpy as 100.0 ( 3.9 kJ mol-1 (at Tm ) 318.5 K) and 100.7 ( 3.9 kJ mol-1 (at T ) 298 K). This is in excellent agreement with the mean third-law value (see Table 4) with JANAF thermal functions. The p(H3BO3) values at some selected temperatures deduced from this relation are listed in Table 1 (column 6). 3.4. Recommended p(H3BO3)-T Relation and Enthalpy of Sublimation to H3BO3(g). The mean third-law sublimation ∆subH°m(298 K) values from our transpiration measurements

TABLE 4: Vapor Pressure of Boric Acid Derived from KEMS Measurements in Series 5 third-law ∆subH°m(298 K)c/(kJ mol-1)

T/K

I(H211BO2+)

I(H311BO3+)

I+(total H3BO3)a

p(H3BO3)/Pab

310 311 312 312 313 314 315 316 304 307 307 309 311 313 314 315 316 318 321 299 301 313 327 308 311 315 316 321 324.5 331 333 295 334 334 336 339 342 338 mean

1.06 × 10-2 1.26 × 10-2 1.17 × 10-2 1.31 × 10-2 1.28 × 10-2 1.30 × 10-2 1.59 × 10-2 1.89 × 10-2 3.13 × 10-3 4.72 × 10-3 4.26 × 10-3 7.78 × 10-3 1.02 × 10-2 1.12 × 10-2 1.41 × 10-2 1.98 × 10-2 2.50 × 10-2 2.72 × 10-2 3.18 × 10-2 4.75 × 10-3 4.99 × 10-3 7.13 × 10-3 1.04 × 10-1 1.25 × 10-2 1.67 × 10-2 2.09 × 10-2 2.56 × 10-2 4.45 × 10-2 6.17 × 10-2 1.24 × 10-1 2.50 × 10-1 1.21 × 10-3 1.57 × 10-1 1.81 × 10-1 2.34 × 10-1 3.16 × 10-1 2.70 × 10-1 1.63 × 10-1

4.63 × 10-3 5.08 × 10-3 5.05 × 10-3 5.52 × 10-3 5.77 × 10-3 5.81 × 10-3 7.65 × 10-3 8.02 × 10-3 1.87 × 10-3 2.06 × 10-3 2.16 × 10-3 3.66 × 10-3 4.60 × 10-3 6.46 × 10-3 7.74 × 10-3 1.01 × 10-2 1.24 × 10-2 1.54 × 10-2 1.77 × 10-2 2.48 × 10-3 2.33 × 10-3 3.76 × 10-3 5.53 × 10-2 6.50 × 10-3 7.50 × 10-3 1.09 × 10-2 1.24 × 10-2 2.39 × 10-2 3.22 × 10-2 6.70 × 10-2 6.16 × 10-4 1.06 × 10-1 1.37 × 10-1 1.21 × 10-1 7.49 × 10-2

1.34 × 10-1 1.56 × 10-1 1.48 × 10-1 1.64 × 10-1 1.64 × 10-1 1.66 × 10-1 2.09 × 10-1 2.37 × 10-1 4.47 × 10-2 5.99 × 10-2 5.70 × 10-2 1.01 × 10-1 1.31 × 10-1 1.62 × 10-1 1.94 × 10-1 2.65 × 10-1 3.32 × 10-1 3.80 × 10-1 4.41 × 10-1 6.42 × 10-2 6.48 × 10-2 9.68 × 10-2 1.42 1.69 × 10-1 2.14 × 10-1 2.83 × 10-1 3.37 × 10-1 6.08 × 10-1 8.34 × 10-1 1.70 1.62 × 10-2 3.01 4.00 3.45 2.10

7.50 × 10-2 8.71 × 10-2 8.30 × 10-2 9.21 × 10-2 9.24 × 10-2 9.39 × 10-2 1.18 × 10-1 1.35 × 10-1 2.44 × 10-2 3.31 × 10-2 3.15 × 10-2 5.63 × 10-2 7.31 × 10-2 9.10 × 10-2 1.10 × 10-1 1.50 × 10-1 1.89 × 10-1 2.17 × 10-1 2.55 × 10-1 3.45 × 10-2 3.51 × 10-2 5.45 × 10-2 8.35 × 10-1 9.34 × 10-2 1.20 × 10-1 1.60 × 10-1 1.91 × 10-1 3.51 × 10-1 4.87 × 10-1 1.01 8.60 × 10-3 1.82 2.44 2.13 1.28

thermal functions for H3BO3(g) from JANAF18

thermal functions for H3BO3(g) from ref 11d

100.1 100.1 100.5 100.3 100.6 100.8 100.6 100.5 101.1 101.3 101.4 100.6 100.5 100.6 100.4 99.9 99.7 99.9 100.4 98.5 99.2 101.9 99.0 98.9 99.3 99.8 99.6 99.6 99.8 99.7 100.6 99.6 99.6 100.9 101.2 100.2 ( 0.8

91.8 91.7 92.1 91.9 92.2 92.4 92.1 92.0 92.9 93.0 93.1 92.3 92.2 92.2 92.0 91.5 91.2 91.4 91.8 90.5 91.1 93.5 90.3 90.7 90.9 91.3 91.1 90.9 91.0 90.8 92.7 90.6 90.5 91.7 92.1 91.7 ( 0.8

a Computed according to eq 8; n(H211BO2+) ) n(H311BO3+) ) 0.80; γ(H211BO2+) ) (1/45)0.5; γ(H311BO3+) ) (1/62)0.5. b Computed by using eq 7; k(Hg) ) 0.0645; n(202Hg+) ) 0.298; γ(202Hg+) ) (1/202)0.5; σ(Hg) ) 5.83; σ(H3BO3) ) 0.75 [3σ(H) + σ(B) + 3σ(O)] ) 0.75 [ 3 × 0.215 + 2.52 + 3 × 0.892] ) 4.381. c For the sublimation reaction H3BO3(s) ) H3BO3(g). d Thermal functions for H3BO3(s) from JANAF.18

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(JANAF functions,100.3 ( 0.9 kJ mol-1; Bowsher et al. functions, 91.4 ( 1.0 kJ mol-1) and from KEMS measurements (JANAF functions, 100.2 ( 0.8 kJ mol-1; Bowsher et al. functions, 91.7 ( 0.8 kJ mol-1) are mutually consistent. They are also consistent with the six p(H3BO3) points from Stackelberg et al.’s work (JANAF functions, 101.4 ( 0.2 kJ mol-1; Bowsher et al. functions, 90.6 ( 0.3 kJ mol-1). This fact together with the already mentioned absence of noticeable trend in the third-law ∆subH°m(298 K) values encouraged us to pool together 123 values of p(H3BO3): 88 from transpiration method (76 normalized Papp values from six temperature dependence runs; six mean Papp values from six flow dependence runs; and six p(H3BO3) values from Stackelberg et al.) and 35 from KEMS method (given in Table 4). We obtained the following p-T relation:

log p(H3BO3) ) -(5199 ( 74)/(T/K) + (15.65 ( 0.23)

(10) Since the above relation combines the mutually consistent data from different types of vaporization experiments and corresponds to a large temperature range from 295 to 413 K, it may be considered as an equation that best represents the vaporization of boric acid. The p(H3BO3) values at some selected temperatures deduced from this relation are listed in Table 1 (column 7). The second-law enthalpy of sublimation resulting from eq 10 is 99.5 ( 1.4 kJ mol-1 (at Tmean ) 354 K). With auxiliary thermal functions from JANAF for both solid and gaseous H3BO3, we obtain the second-law enthalpy at 298 K as 100.7 ( 1.4 kJ mol-1. The mean third-law enthalpy corresponding to the two sets of thermal functions are 100.3 ( 0.9 kJ mol-1 (JANAF) and 91.4 ( 1.0 kJ mol-1 (Bowsher et al.). Although the mean third-law value deduced with JANAF thermal functions is closer to our second-law value, the thermal functions from Bowsher et al. being more recent, we would give equal consideration for the values obtained using either set of thermal functions, and take the mean value (95.9 ( 6.3 kJ mol-1) as that resulting from the third-law evaluation. We would recommend the mean of second- and third-law values for sublimation of H3BO3(g) from H3BO3(s) at 298 K: 98.3 ( 9.5 kJ mol-1. The uncertainty in the recommended enthalpy is estimated as described below. 3.5. Uncertainties in Temperature, Pressure, and Enthalpy of Sublimation. Our measurements were performed at such low temperatures that the temperature measurements by the Pt-Rh thermocouple (in transpiration experiments) might not be quite reliable. One does not require Ts to calculate Papp in a transpiration method (see eq 1), but the Papp needs to be ascribed to a Ts to become meaningful. Although, maintaining the sample temperature at any set value of Tset was never a problem with our apparatus, the temperature calibration performed with the melting temperatures of indium, aluminum, and silver did show that at low temperatures, there is a lag of 10-13 deg between the Tset and the value computed by the temperature calibration equation as Ts (Ts - Tset = 10-13 K). This could be set right by the software itself by exercising a suitable option, but we chose to measure the temperatures Ts for different Tset values (in a separate series of experiments) by an external chromel-alumel thermocouple, placed right where normally the sample crucible would be lying on the pan (but without touching any part of the pan). These experiments were run under argon flow conditions similar to those employed in actual transpiration measurements with the stopcock fully opened. Each Tset was maintained for sufficiently long time that the steady readings

from the external thermocouple could be relied upon to be indicative of the constant temperature Ts′. The difference between Tset and Ts′ was noted for a number of Tset values. In the temperature range of our investigations, Ts′ - Tset ranged from 9 to 11 K, confirming that the lag found in the software output at the end of an experiment was real. Thus, the Ts which figures in eq 1 is actually [Tset + (Ts′ - Tset)]. We ascertained the reliability of our Ts values further by performing a melting temperature run on HIBA (hydroxyisobutyric acid; melting temperature 77-81 °C). With all these inputs, we estimate that the maximum uncertainty in our temperature measurements is (3 K. Any error in Ts would not alter Papp, but the value of Papp determined could be at Ts/K ( 3 K. The flow dependence measurements at 336 and 349 K showed that the plateau region Papp values differ by 0.3 Pa, which makes it that P at 336 K has an uncertainty of 20% and that at 349 K has an uncertainty of 6%. Our transpiration results differ by about 30% from those of Stackelberg et al. Considering all these facts, we would assign an overall uncertainty of 40% for the values of p(H3BO3) from transpiration experiments. Although it is gratifying that the values of p(H3BO3) from KEMS measurements are well consistent with those from transpiration measurements, we do realize that the uncertainties in the values of k, σ, and γ often introduce a factor of 2 (and perhaps even more) uncertainty in the KEMS pressures. The k(Hg) has a statistical uncertainty of 20%. The value of the σ ratio {σ(Hg)/σ(H3BO3)} fortunately do not vary by more than 3% between 20 and 40 eV, and therefore, the value we used for 30 eV (σ(Hg)/σ (H3BO3) ) 1.33) does not suffer much from an error in electron energy calibration. If σ(H3BO3) is taken as [3σ(H) + σ(B) + 3σ(O)] instead of 0.75 times the sum of the terms within the brackets, the resulting p(H3BO3) will be about 33% lower than those computed by us now. Considering all these aspects, we would assign an overall uncertainty of (50% in the value of p(H3BO3) from KEMS measurements. Since the recommended p-T relation resulted from both transpiration and KEMS measurements, we would estimate that the maximum uncertainty in the values of p(H3BO3) is ∼65%. An uniform error of δT ) (3 K would alter the second law value only by ≈2 kJ mol-1, but a differential error of -1.5 K at the high-temperature end and +1.5 K at the low-temperature end of our KEMS or transpiration measurements range will cause an error in the second-law enthalpy as high as 8 kJ mol-1. The error in third-law values due to error in T or in p(H3BO3) will be comparatively insignificant. The mean third-law value differed by ∼4.5 kJ mol-1 from the mean values obtained with the two sets of thermal functions for H3BO3(g). Considering all these aspects, we would assign a maximum uncertainty of ∼9.5 kJ mol-1 in our recommended value of enthalpy of sublimation of H3BO3(g). 4. Conclusions The vaporization of boric acid was investigated by the transpiration gravimetry (with argon as the carrier gas and the mass loss of the condensed phase continuously measured) and Knudsen effusion mass spectrometry. The enthalpy of sublimation and vapor pressures of H3BO3(g) obtained by both these methods are consistent among themselves as well as with those determined seventy years ago by Stackelberg et al.5 using the transpiration method at relatively higher temperatures (with steam as carrier gas and the condensate of the transported vapor analyzed for boric acid content). While our mass spectrometric study represented the first investigation on boric acid by KEMS,

13884 J. Phys. Chem. B, Vol. 112, No. 44, 2008 the transpiration gravimetric study served to complement the results of Stackelberg et al. which were adopted by JANAF18 but sought to be superseded with very different results by the most recent transpiration gravimetric study.17 In view of the many pieces of evidence pointing toward H3BO3 vaporizing congruently to yield H3BO3(g) as the principal vapor species, it will be interesting to investigate the vaporization of the adjacent two-phase region in the H2O-B2O3 phase diagram, which is [H3BO3(s) + HBO2(s)]. The evolution upon continuous vaporization of such samples could provide further insight into the vaporization chemistry of the H2O-B2O3 binary system. Acknowledgment. We thank the electronics group for maintenance of the mass spectrometer, the X-ray group for characterization of the samples, and the glass-blowing facility for making the quartz cell for transpiration measurements. We also thank Dr. Christian Chatillon for a very useful discussion on some aspects of the vaporization of boric acid. References and Notes (1) Remy, H.; Anderson, J. S.; Kleinberg, J. Treatise on Inorganic Chemistry, Vol. 1, Introduction and Main groups of the Periodic Table; Elsevier: Amsterdam, 1956; p 337. (2) Patnaik, P. Handbook of Inorganic Chemicals; McGraw-Hill: New York, 2002; p 119. (3) Encyclopedia of Inorganic Chemistry; King, B. R., Ed.; Wiley: Chichester, UK, 1994; p 362. (4) Bowsher, B. R. Prog. Nucl. Energy 1987, 20, 199. (5) Stackelberg, M. V.; Quatram, F.; Dressel, J. Z. Elektrochem 1937, 43, 14. (6) Bezzi, S. Gazz. Chim. Ital. 1935, 65, 766. (7) Meschi, D. J.; Chupka; W, A.; Berkowitz, J. J. Chem. Phys. 1960, 33, 530. (8) Randall, S. P.; Margrave, J. L. J. Inorg. Nucl. Chem. 1960, 16, 29. (9) West, E. D. ARL Technical report 60-276, NBS (now NIST), 1960. (10) Ogden, J. S.; Young, N. A. J. Chem. Soc., Dalton Trans. 1988, 1645.

Balasubramanian et al. (11) Bowsher, B. R.; Dickinson, S.; Ogden, J. S.; Young, N. A. Thermochim. Acta 1989, 141, 125. (12) Andrews, L.; Buckholder, T. R. J. Chem. Phys. 1992, 97, 7203. (13) Gailardet, J.; Lemarchand, D.; Go¨pel, C.; Manhe`s, G. Geostand. Geoanal. Res. 2001, 25, 67. (14) Zachariasen, W. H. Acta Crystallogr. 1954, 7, 305. (15) Yan, Li.; Ruoff, R. S.; Chang, R. P. H. Chem. Mater. 2003, 15, 3276. (16) Sevim, F.; Demir, F.; Bilen, M.; Okur, H. Korean J. Chem. Eng. 2006, 23, 736. (17) Pankajavalli, R.; Anthonysamy, S.; Ananthasivan, K.; Vasudeva Rao, P. R. J. Nucl. Mater. 2007, 362, 128. (18) Chase M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; McDonald, R. A. JANAF Thermochemical Tables, 3rd Edition. J. Phys. Chem. Ref. Data 1985, 14; Supplement No. 1, p 231 for H3BO3(g) and p 230 for H3BO3(s). (19) Viswanathan, R. In Thermans 2008, Proceedings of the sixteenth National National Symposium on Thermal Analysis; Varma, S., Kutty, K. V. G., Mukerjee, S. K., Gnanasekaran, T., Bharadwaj, S. R., Venugopal, V., Eds.; SIRD, BARC: Mumbai, India, 2008; p 53. (20) Lakshmi Narasimhan, T. S.; Viswanathan, R.; Balasubramanian, R. J. Phys. Chem. B 1998, 102, 10586. (21) Lakshmi Narasimhan, T. S.; Sai Baba, M.; Balasubramanian, R.; Nalini, S.; Viswanathan, R. J. Chem. Thermodyn. 2002, 34, 103. (22) Lakshmi Narasimhan, T. S.; Sai Baba, M.; Viswanathan, R. Thermochim. Acta 2005, 427, 137. (23) Lakshmi Narasimhan, T. S.; Sai Baba, M.; Viswanathan, R. J. Phys. Chem. B 2002, 106, 6762. (24) Lakshmi Narasimhan, T. S.; Sai Baba, M.; Nalini, S.; Viswanathan, R. Thermochim. Acta 2004, 410, 149. (25) Lakshmi Narasimhan, T. S.; Viswanathan, R.; Balasubramanian, R. J. Phys. Chem. A 2006, 110, 13705. (26) PDF-2 Database, JCPDS-ICDD (Pensylvania, Copyright 19871994). Indexing number for H3BO3(s) is 30-0199. (27) Alcock, C. B.; Itkin, V. P.; Horrigan, M. K. Can. Metall. Q. 1984, 23, p 309. (28) Moore, C. E. NSRDS-NBS 34, 1970, 22. (29) CRC Handbook of Chemistry and Physics, 59th ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1978-79; p E-74. (30) Mann, J. B. Recent DeVelopments in Mass Spectrometry. Proceedings of the International Conference on Mass Spectrometry; Ogata, K., Hayakawa, T., Eds.; University of Tokyo Press: Tokyo, 1970; p 814 (Tables of ionization cross sections as a function of electron energy were obtained on request).

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