The Enthalpies of Formation of BeO(c) and BeF₂(c)

Abstract

Two of the key compounds in the evaluation and synthesis of a consistent set of thermodynamic values for the Be compounds are BeO(c) and BeF₂(c). The available measurements on the enthalpies of formation of these two compounds are presented with a detailed outline of the approach used to select the “best” values, $\Delta H{f}_{298.15\text{\hspace{0.17em}K}}^{\circ }\left[\text{BeO}\left(\text{c}\right)\right]=-145.7\pm 0.6\text{\hspace{0.17em}kcal}\cdot {\text{mol}}^{-1}\left(-609.6\pm 2.5\text{\hspace{0.17em}kJ}\cdot {\text{mol}}^{-1}\right)$ and $\Delta H{f}_{298.15\text{\hspace{0.17em}K}}^{{}^{\circ }}\left[{\text{BeF}}_2\left(\text{c},\text{\hspace{0.17em}quartz}\right)\right]=-245.4\pm 0.8\text{\hspace{0.17em}kcal}\cdot {\text{mol}}^{-1}\left(-1026.8\pm 3.3\text{\hspace{0.17em}kJ}\cdot {\text{mol}}^{-1}\right)$.

1. Introduction

Two of the key compounds in the evaluation and synthesis of a consistent set of thermodynamic values for the Be compounds are BeO(c) and BeF₂(c).

One approach used in the preparation of compilations of thermochemical data is to start with a compound for which ΔHf° (or ΔGf°) is definitive and independent of ΔHf° of any other compound of that element and preferably involves a minimum of auxiliary ΔHf°’s, and to build from the selected value for this compound. An example of this is the direct oxidation of the metal to the oxide, e.g., BeO(c), or the halogenation of the metal to the halide, e.g., BeF₂(amorp), or a set of reactions that can be combined in such a way that only one ΔHf° is unknown, e.g., Be(c) + 2HF(aq) → H₂(g) + BeF₂(aq) and BeO(c) + 2HF(aq) → BeF₂(aq) + H₂O(liq) so that by difference we can write the possible reaction, Be(c) + H₂O(liq) → BeO(c) + H₂(g); similarly Be₃N₂(c) + 3/20₂(g) → 3BeO(c) + N₂(g) and 3Be(c) + N₂(g) → Be₃N₂(c) giving Be(c) + l/20₂(g) → BeO(c). We may then relate the ΔHf°’s of other compounds of that element to the selected compound by enthalpies of reaction.

If however every subsequent ΔHf° calculated is dependent upon the value selected for one compound, although we have internal consistency, we have no crosscheck as to how good the original value is. We should then have a second compound whose ΔHf° can also be obtained independently and an enthalpy of reaction relating the two to corroborate the choices and to close the cycle.

Until the recent measurements of Kilday, Prosen, and Wagman [1]¹ on the enthalpies of solution of BeO(c) in aqueous HF solutions and the measurements of Churney and Armstrong [2] on the direct determination of the ΔHf°[BeF₂(amorph)], the data available on the direct enthalpies of formation of BeO(c) and BeF₂(c) and the data linking these values were discordant. These new investigations are a significant aid in establishing the values for BeO(c) and BeF₂(c) with more certainty. Our main efforts then, after considering the direct determinations, center upon the use of the solution measurements of BeO(c) in HF(aq) together with the solution measurements of Be(c) in HF(aq) which previously could not be fully utilized to obtain indirectly a definitive value for the ΔHF° [BeO(c)] and to relate that value to the determinations on the ΔHF° [BeF₂(c)]. Figure 1 schematically presents the reactions and paths discussed in this paper.

Figure 1:

The schematic presentation of the relationships involved in the evaluation of ΔHf° [BeO(c)] and ΔHF° [BeF₂(c)].

All auxiliary data and constants used in the calculations are given in Wagman et al. [3]. Unless otherwise specified the values quoted are at, or have been corrected to, 298.15 K. Our final selections are reported in both kJ · mol⁻¹ and kcal · mol⁻¹. However, since this evaluation is included in Parker, Wagman, and Evans [3], where values are expressed in kcal · mol⁻¹, we report the individual values and their corrections in the same units in order to preserve the consistency of the relationships.

2. Discussion of Data on BeO(c)

2.1. Bomb Combustion

The following values of ΔH(kcal · mol⁻¹) for the oxidation of Be(c) have been reported: Moose and Parr [4], −134.4; Roth, Borger, and Siemonsen [5],−147.3; Neumann, Kröger, and Kunz [6], −145.3; Mielenz and v. Wartenberg [7], −136.2; and Cosgrove and Snyder [8], −143.1. Neumann, Kröger, and Kunz [6] measured the enthalpy of combustion of Be₃N₂ (crystal form unspecified) to form BeO(c) and N₂(g) as −300.6 kcal · mol⁻¹ of Be₃N₂(c). Neumann, Kröger, and Haebler [9] directly determined ΔHf°[Be₃N₂(c)] = −134.1. By difference we obtain ΔHf°[BeO(c)] = −144.9. Of these determinations the Cosgrove and Snyder measurement appeared to be the best value and had been generally accepted; however, the measurements of Kolesov, Popov, and Skuratov [10] on the enthalpies of reaction of BeO(c) in aqueous HF and BeF₂(c) in aqueous HF indicate that the value for ΔHf° [BeO(c)] should be more negative. This is in line with the fact that Cosgrove and Snyder did not determine the completeness of the reaction; incomplete combustion would cause the value, based on the weight of metal taken, to be too positive. We turn therefore to the indirect determinations of ΔHf° [BeO(c)].

2.2. The Enthalpies of Solution of Be(c) and BeO(c) in Aqueous HF Solutions

Matignon and Marchal [11] measured the enthalpies of solution of Be(c) and BeO(c) in 30 percent HF solutions, as have Copaux and Philips [12]. By difference, we obtain for Be(c) + H₂O(liq) → BeO(c) + H₂(g), ΔH° = −70.9 and −62.1 kcal, or ΔHf°[BeO(c)] = −139.2 and −130.4 kcal · mol⁻¹, respectively. The individual ΔH’s for solution of Be(c) in 30 percent HF are −94.2 from Matignon and Marchal and −82.2 kcal · mol⁻¹ from Copaux and Philips. For solution of BeO(c) they are −23.3 and −20.1 kcal · mol⁻¹, respectively. More recently, Bear and Turnbull [13] measured the enthalpy of solution of Be(c) in 12, 22.6, 30, and 40 percent HF solutions. The values are −101.5, −101.0, −100.5, and −100.5 kcal. Armstrong and Coyle [14] reported −99.6 kcal for solution in 25 percent HF. For solution of BeO(c) in aqueous HF we also have the results of Kilday et al., e.g., −24.2 kcal in a 30 percent HF solution, the results of Kolesov et al., in a 23 percent HF solution, −24.1 kcal, and Fricke and Wüllhorst [15] −24.3 kcal in 12 percent HF. It appears that the measurements of Matignon and Marchal and Copaux and Philips are not reliable; they give little information as to the experimental details and purity of materials. We cannot rely upon the values for ΔHf°[BeO(c)] obtained from the data of either Matignon and Marchal [11] or Copaux and Philips [12], but a judicious combination of the other measurements can yield a more reliable value.

One of the problems associated with combining reactions of Be(c) and BeO(c) in aqueous HF is that in most cases the final solutions are not the same. Not only are there no quantitative data on what Be species are in the final solutions or the percent of each, there are also no direct data on the ΔH_diln or ΔH_mix of these species in HF solutions. The measurements of Kilday et al., however, provide some insight into the effect of having solutions that do differ in both the amount and concentration of the excess HF(aq).

They have also measured the differential enthalpy of dilution in two of their final solutions,

$${\text{H}}_2\text{O}\left(\text{liq}\right)+\left[{\text{BeF}}_{\text{2}}\text{\hspace{0.17em}in excess HF\hspace{0.17em}}\cdot n{\text{H}}_2\text{O}\right]\to \left[{\text{BeF}}_2+{\text{H}}_2\text{O\hspace{0.17em}in excess HF}\cdot n{\text{H}}_2\text{O}\right].$$

These measurements are important since H₂O(in BeF₂ + HF · nH₂O) is formed in the reaction of BeO(c) with HF(aq), i.e.,

$$\text{BeO}\left(\text{c}\right)+2\text{HF}\left(\text{aq}\right)\to \left[{\text{BeF}}_2+{\text{H}}_2\text{O}\right]\text{\hspace{0.17em}in excess HF}.$$

We have compared the experimental data with those calculated from the slope dφ_L/dm^1/2 of φ_L HF at n_f H₂O from the values² tabulated by Parker [16]. These values are: at n_f = 2.68, ${\overline{L}}_1\left(\text{cal}\cdot {\text{mol}}^{-1}\right)=-178$ (calc.), and −160 ± 10 (experimental); at n_f = 3.57, ${\overline{L}}_1=-110$ (calc.) and −85 ± 5 (experimental). Since the agreement is good, we decided to ignore the presence of the BeF₂ in the final solutions and treat the solutions as if they were HF solutions. Since X (the ratio of HF to BeF₂ in the final solution) ≧ 50 this is not an unreasonable approach.

We can now set up the equation for the reaction³ in the form,

$$\text{BeO}\left(\text{c}\right)+\left(X+2\right)\left(\text{HF}+n_i{\text{H}}_2\text{O}\right)\to \left[{\text{BeF}}_2+{\text{H}}_2\text{O}+X\left(\text{HF}+n_f^{\text{'}}{\text{H}}_2\text{O}\right)\right]$$

and use the experimental ${\overline{L}}_1$ values and the φ_L values at the appropriate concentrations from [16]to calculate Δ (ΔHf°) which represents ΔHf°[BeO(c)] − ΔHf[BeF₂(aq)]. Table 1 shows the results as a function of n_f where n_f is the final ratio of H₂O to HF. It includes the mole of H₂O formed. All of their experimental ΔH’s are included, corrected to 298.15 K where necessary, using the temperature coefficient given in their work. The number in the first column corresponds to the number of the Kilday et al., experiment.

Table 1.

Data derived from measurements of Kilday et al.

1	2	3	4	5	6	7	8	9	10	11	12
No.	%HF in initial solution	$-\Delta H_{298.15\text{\hspace{0.17em}K}}^{\text{a}}$	X	nf	Δ(Δ Hf) [BeO(c)- — BeF2(aq)]	Mean Δ(Δ Hf)	Mean nf	Δ(Δ Hf) from smooth curve, fig. 2	Δ(Δ Hf) corrected toX=100	Mean Δ(Δ Hf)	Δ(Δ Hf) from smooth curve, fig. 3
		Kcal·mol−1			Kcal·mol−1	Kcal·mol−1		Kcal·mol−1	Kcal·mol−1	Kcal·mol−1	Kcal·mol−1
20	29.76	24.301	112.58	2.6765	106.710				106.717
22		24.292	117.42	2.6742	106.707	106.716	2.676	106.70	106.717	106.723	106.71
23		24.315	113.12	2.6762	106.731				106.738
24		24.299	113.16	2.6762	106.714				106.721
2	24.33	24.200	94.60	3.5374	107.041				107.038
4		24.221	96.47	3.5359	107.055	107.051	3.534	107.07	107.053	107.051	107.07
5		24.235	107.53	3.5274	107.057				107.061
25	24.23	24.221	93.05	3.5581	107.109				107.105
26		24.197	97.97	3.5538	107.082				107.081
27		24.176	94.17	3.5571	107.064	107.080	3.555	107.08	107.061	107.078	107.08
28		24.202	91.36	3.5597	107.096				107.091
29		24.182	114.23	3.5423	107.057				107.065
30		24.187	92.47	3.5586	107.071				107.067
1	24.13	24.183	88.82	3.5817	107.113				107.112
3		24.141	95.48	3.5753	107.070	107.090	3.578	107.09	107.068	107.087	107.09
9		24.163	94.19	3.5765	107.103				107.100
10		24.183	93.52	3.5771	107.072				107.068
7	19.80	24.103	75.23	4.6310	107.475	107.475	4.631	107.46	107.461	107.461	107.47
11	19.80	24.055	234.68	4.5407	107.389				107.463
13		23.955	232.05	4.5412	107.296	107.378	4.540	107.43	107.369	107.454	107.44
18		24.089	247.99	4.5384	107.448				107.529
6	19.66	24.108	76.47	4.6699	107.473	107.468	4.672	107.47	107.460	107.456	107.48
8		24.091	74.60	4.6731	107.462				107.452
12	19.66	24.062	237.12	4.5806	107.397				107.472
17		24.158	256.22	4.5773	107.497	107.404	4.579	107.44	107.583	107.485	107.46
19		23.968	251.47	4.5781	107.318				107.401
14	14.05	23.787	53.85	7.0644	107.753				107.728
15		23.862	55.49	7.0563	107.830	107.782	7.061	107.78	107.806	107.758	107.78
16		23.794	54.42	7.0616	107.764				107.739

^aCorrected for BeSO₄ impurity.

The values for Δ(ΔHf) within each group are in excellent agreement with one another, within the precision of the experimental data although there are some differences in X and n_f in the final solutions. The values appear to be primarily dependent upon the concentration of HF within the range 50 ≦ × ≦ 250. Figure 2 shows a plot of Δ(ΔHf) as a function of n_f. For the Δ(ΔHf) we obtain a smooth curve. The smoothed values are also given in table 1. The variation of ΔH as a function of the concentration of HF without regard to the variation of X may be expressed as ΔH = −24.092−0.113(4.50−n_f) kcal · mol⁻¹ for 7.1 > n_f >2.6.

Figure 2:

The ΔHr[BeO(c)] and Δ(ΔHf)[BeO(c) − BeF₂(aq)] (uncorrected for the variation in X) as a function of the concentration of HF in the final solution (HF + n_fH₂O).

For ΔHr: ● data of Kilday et al.

■ data of Kolesov et al.

For Δ(ΔHf): ○ data of Kilday et al.

□ data of Kolesov et al.

Kolesov, Popov, and Skuratov [10] also measured the enthalpy of solution of BeO(c) in aqueous HF. Their reaction corresponds to:

$$\text{BeO}\left(\text{c}\right)+342\left(\text{HF}+3.801{\text{H}}_2\text{O}\right)\to \left[{\text{BeF}}_2+{\text{H}}_2\text{O}+340\left(\text{HF}+3.823{\text{H}}_2\text{O}\right)\right].$$

The ΔH = −24.158 kcal · mol⁻¹ of BeO(c) results in Δ(ΔHf) = 107.085 kcal · mol⁻¹ (using the same treatment as before). From our straight line plot of ΔH from Kilday et al.’s data, we obtain −24.168 kcal · mol⁻¹ where the final solution contains BeF₂ in 90(HF + 3.826 H₂O). From our plot of Δ(ΔHf) versus n_f we obtain Δ(ΔHf) = 107.185 kcal · mol⁻¹. The agreement in ΔH is excellent, fortuitously so; in Δ(ΔHf°) it is not, but still within the experimental uncertainties. In addition X differs by 250 moles HF in the two solutions.

Kilday and Churney, private communication (1971), also made some measurements on the enthalpy of solution of BeF₂(amorph) in HF concentrations of 3.63 H₂O and 5.06 H₂O where X varied from 400 to 2700. From these measurements we obtain the following:

$$\Delta H_{\text{soln}}=-8,430+0.50X\text{\hspace{0.17em}cal}\cdot {\text{mol}}^{-1}\text{\hspace{0.17em}for\hspace{0.17em}}n=3.63$$

$$\Delta H_{\text{soln}}=-8,680+0.60X\text{\hspace{0.17em}cal}\cdot {\text{mol}}^{-1}\text{\hspace{0.17em}for\hspace{0.17em}}n=\mathrm{5.06.}$$

Although the precision of these measurements is not high they do enable us to obtain an approximate correction to Δ(ΔHf) for the variation in X. As a reference solution we have chosen this X to be 100 and have added −0.55(100 − X) cal · mol⁻¹ (an average value) to the Δ(ΔHf)’s (see table 1, columns 10, 11, and 12 and fig. 3). The new Δ(ΔHf)’s are in slightly better agreement with one another. For the Δ(ΔHf°) from Kolesov et al., we obtain 107.217 kcal · mol⁻¹ as compared to 107.180 from figure 3, in much better agreement; this lends support to the use of this treatment on the Bear and Turnbull measurements [13] on Be(c) in excess HF solutions, where the final ratio of HF to BeF₂ is greater than 340.

Figure 3:

The Δ(ΔHf) [BeO(c) − BeF₂(aq)] and the ΔHf[BeF₂(aq)] as a function of the concentration of HF in the final solution (HF + n_fH₂O).

For Δ(ΔHf): Δ Kilday et al. data, corrected to X = 100.

▲ Kolesov et al. data, corrected to X = 100.

For ΔHf[BeF₂(aq)] : ○ Bear and Turnbull data, corrected to X = 100.

□ Bear and Turnbull data, uncorrected for variation in X.

Bear and Turnbull used solutions of 12, 22.6, 30, and 40 percent HF. Their results can be treated three ways:

(1) using their ΔH_r with the ΔH_r from our straight line plot of the Kilday et al., data on BeO in HF at the appropriate n_f, with the experimental ${\overline{L}}_1$, obtaining the reaction, Be(c) + H₂O(aq) → BeO(c) + H₂(g);

(2) calculating the ΔHf°[BeF₂ in X(HF + n_f H₂O)] and using the appropriate Δ(ΔHf) [BeO − BeF₂(aq)] at n_f from figure 2;

(3) correcting ΔHf[BeF₂(aq)] to X = 100 and using the comparable corrected Δ(ΔHf) from figure 3.

The results are summarized in tables 2 and 3. It is obvious that the values for ΔHf°[BeO(c)] are in better agreement using the third way of calculating. Figure 3 shows a plot of ΔHf[BeF₂(aq), in 100(HF + n_f H₂O)] and also the uncorrected values derived from the Bear and Turnbull measurements.

Table 2.

Data derived from the measurements of Bear and Turnbull and the corresponding values from Kilday et al.

1	2	3	4	5	6	7	8	9	10	11
% HF	X	nf	ΔHr° Be(c)	Δ Hf [BeF2(aq)]	Δ Hr° of BeO(c) st. line plot, fig. 2	X for (6)	${\overline{L}}_1$H2O	Δ(Δ Hf) [BeO- BeF2(aq)] fig. 2	Δ Hf [BeF2(aq)] corrected to X= 100	Δ (Δ Hf) [BeO(c)— BeF2(aq)] fig. 3
			Kcal·mol−1	Kcal·mol−1	Kcal·mol−1		Kcal·mol−1	Kcal·mol−1	Kcal·mol−1	Kcal·mol−1
12	358	8.184	− 101.47	− 253.84	− 23.68	50	0	107.81	− 253.98	107.78
22.6	677	3.811	− 101.02	− 252.51	−24.17	90	−0.07	107.18	− 252.83	107.18
30	899	2.597	− 100.52	−251.89	−24.31	115	−0.18	106.68	− 252.33	106.68
40	1079	1.670	− 100.5	a−251.0	− 24.42	130	−0.3 (est’d)	106.2	−251.54	106.2

^aThis is based on an estimate for ΔH_diln = −0.9 kcal · mol⁻¹ for 1079(HF + 1.666H₂O) → 1079(HF + 1.670H₂O) and φ_L for HF + 1.666H₂O = 3.8 kcal · mol⁻¹.

Table 3.

ΔHf°[BeO(c)] in kcal · mol⁻¹ as calculated by various methods from data in table 2

Method 1 (4, 6, and 8)	Method 2 (5 and 9)	Method 3 (10 and 11)
− 146.11	− 146.03	− 146.20
− 145.24	− 145.33	− 145.65
− 144.70	− 145.21	− 145.65
− 144.7	− 144.8	− 145.3

For confirmation of the above values we may use the enthalpy of solution of the samples of BeF₂(amorph) cited earlier whose ΔHf° is known (−244.3 kcal · mol⁻¹, directly determined by Churney and Armstrong [2]) from which we obtain ΔHf[BeF₂(aq) in 100(HF + 3.63H₂O)] = −252.68 kcal · mol⁻¹ and ΔHf[BeF₂(aq) in 100(HF + 5.06 H₂O)] = −252.92 kcal · mol⁻¹ (cf −252.75 and −253.38 kcal · mol⁻¹ from the smoothed curve (fig. 3) of Bear and Turnbull’s corrected ΔHf’s). Using Δ(ΔHf) = 107.11 and Δ(ΔHf) = 107.57 kcal · mol⁻¹ from figure 3, we obtain ΔHf° BeO(c) = −145.57 and −145.35 kcal · mol⁻¹, respectively.

In all the above cases we have used the Δ(ΔHf) [BeO(c)−BeF₂(aq)] derived from the Kilday et al. measurements. If we use Δ(ΔHf) = 107.217 kcal · mol⁻¹ from the Kolesov et al. measurements and ΔHf BeF₂(aq) = −252.93 kcal · mol⁻¹ from figure 3 we obtain ΔHf° BeO(c) = −145.71 kcal · mol^−1.

There is another reaction involving the enthalpy of solution of Be(c) in HF(aq), that by Armstrong and Coyle [14]. They reported that there was an unexplained deficiency of H₂ on the order of 0.5 percent. They ascribe an uncertainty of not more than 0.2 percent to the enthalpy of reaction for this contribution. The measurements are on the reaction: Be(c) + 6.470(HF + 3.309 H₂O) → [BeF₂ + 4.470(HF + 4.789 H₂O)] + H₂(g) for which ΔH = −99.64 kcal · mol⁻¹ and ΔHf[BeF₂(aq) in 4.470(HF + 4.789 H₂O)] = − 251.1 kcal · mol⁻¹. Using the same three approaches as for Bear and Turnbull’s data we obtain ΔHf°[BeO(c)] = −143.9 (1); −143.6 (2); and −143.5 kcal · mol⁻¹ (3), where X is corrected to 100. In all cases we assume that the species in the two solutions are the same; in the third case we also assume our correction is applicable to X = 4.47, which is probably not justified.

There are two other approaches we can use on their data:

(4) Heretofore we have neglected the effect of the BeF₂ on the HF dilution correction. If we assume that the BeF₂ present in the solution may be replaced by an equivalent number of moles of HF solution, then we may consider the HF to be in 3.913H₂O. This results in ΔHf[BeF₂(aq)] = −251.4 kcal · mol⁻¹ and ΔHf° [BeO(c)] = −143.9 kcal · mol⁻¹.

(5) We can calculate a ΔH_mix for the addition of more of the initial solution, [HF + 3.309 H₂O], to their final solution, using the ϕ_L values of HF, and obtain:

[BeF₂(aq) + 4.470(HF + 4.789H₂O)] + 95(HF + 3.309H₂O) → [BeF₂(aq) + 99.470(HF + 3.375H₂O)]; ΔH_mix = −0.264 kcal · mol⁻¹. Combining this with their reported ΔH leads to: Be(c) + 101.470(HF + 3.309H₂O) → [BeF₂(aq) + 99.470 (HF + 3.375H₂O)] + H₂(g); ΔH = −99.95 kcal · mol⁻¹. This value is now in closer agreement with Bear and Turnbull’s measurements. For the same reaction with BeO(c) we obtain ΔH = −24.22 kcal · mol⁻¹, so that ΔHf°[BeO(c)] = −144.1 kcal · mol⁻¹. A variation of this would be to use a ΔH_mix based on our fourth approach, i.e., to assume the HF is in 3.913 H₂O, then ΔH = −100.23 and ΔHf° [BeO(e)] = − 144.4 kcal · mol⁻¹.

2.3. The Enthalpies of Solution of Be(c) and BeO(c) in Aqueous HCl Solutions

The problem of nonidentical final solutions is also present in the Be(c) − BeO(c) − HCl aqueous systems. Kilday et al. [1] have obtained ΔH = −12.8 and −12.7 kcal · mol⁻¹ for the solution of BeO(c) in 18 and 22.6 percent HCl, respectively. The complete reactions are:

$$\text{BeO}\left(\text{c}\right)+40.9\left(\text{HCl}+9.21{\text{H}}_2\text{O}\right)\to \left[{\text{BeCl}}_2\left(\text{aq}\right)+{\text{H}}_2\text{O}\left(\text{aq}\right)+38.9\left(\text{HCl}+9.69{\text{H}}_2\text{O}\right)\right]$$

and

$$\text{BeO}\left(\text{c}\right)+47.8\left(\text{HCl}+6.93{\text{H}}_2\text{O}\right)\to \left[{\text{BeCl}}_2\left(\text{aq}\right)+{\text{H}}_2\text{O}\left(\text{aq}\right)+45.8\left(\text{HCl}+7.23{\text{H}}_2\text{O}\right)\right].$$

(The experimental ${\overline{L}}_1$ value = −272 cal · mol⁻¹ of H₂O (see ref. [1], sec. 5.4) checks well with the ${\overline{L}}_1$ calculated from the ϕ_L values of HCl [16] at n = 7.23H₂O).

From these reactions we obtain for BeCl₂(aq) in 38.3(HCl + 9.72H,O) Δ(ΔHf)[BeO(c) − BeCl₂(aq)] = 18.6 kcal · mol⁻¹ and 16.6 kcal · mol⁻¹ for BeCl₂(aq) in 45.8(HCl + 7.25H₂O).

Thompson, Sinke, and Stull [17] reported ΔH = −89.61 kcal · mol⁻¹ for Be(c)+8.38(HCl + 8.111H₂O) → [BeCl₂(aq) + 6.38(HCl + 10.654H₂O) + H₂(g), from which we obtain ΔHf[BeCl₂(aq)] = −163.79 kcal · mol⁻¹. Blachnik, Gross, and Hayman [18] reported ΔH_383K = −90.00 kcal/mol for:

$$\text{Be}\left(\text{c}\right)+8.86\left(\text{HCl}+7.991{\text{H}}_2\text{O}\right)\to {\text{H}}_2\left(\text{g}\right)+\left[{\text{BeCl}}_2\left(\text{aq}\right)+6.86\left(\text{HCl}+10.320{\text{H}}_2\text{O}\right)\right].$$

This value, corrected to 298.15 K is in good agreement with the Thompson et al. value.

Using the same approaches as for HF we have:

(1) With ΔH of solution of BeO(c) ≈ −12.8 kcal · mol⁻¹ when n_f = 10.65, ΔHf° [BeO(c)] = −145.2 kcal · mol⁻¹.

(2) From an extrapolation of Δ(ΔHf°) [BeO(c) − BeCl₂(aq)] we obtain Δ(ΔH f°) = 19.4 kcal · mol⁻¹ where the BeCl₂ is in 34(HCl + 10.65H₂O) and ΔHf°[BeO(c)] = −144.4 kcal · mol⁻¹.

(3) Not used since we have no correction for the variation in X.

As in our treatment of the Armstrong and Coyle [14] results we may try the following:

(4) If we assume that the BeCl₂ present may be replaced by an equivalent number of moles of HCl solution we may consider the HCl to be in 9.21 H₂O. Then ΔHf[BeCl₂(aq)] = −165.0 and ΔHf[BeO(c)] = −145.6 kcal · mol⁻¹.

(5) We can calculate a ΔH_mix by adding more of the initial HCl solution to the final solution. We obtain:

$$\left[{\text{BeCl}}_2\left(\text{aq}\right)+6.38\left(\text{HCl}+10.654{\text{H}}_2\text{O}\right)\right]+35.54\left(\text{HCl}+8.111{\text{H}}_2\text{O}\right)\to \left[{\text{BeCl}}_2\left(\text{aq}\right)+41.92\left(\text{HCl}+8.499{\text{H}}_2\text{O}\right)\right];\Delta H=-0.64\text{\hspace{0.17em}kcal}\cdot {\text{mol}}^{-1}$$

and ΔH = − 90.3 kcal · mol⁻¹ for:

$$\text{Be}\left(\text{c}\right)+43.92\left(\text{HCl}+8.111{\text{H}}_2\text{O}\right)\to {\text{H}}_2\left(\text{g}\right)+\left[{\text{BeCl}}_2\left(\text{aq}\right)+41.92\left(\text{HCl}+8.499{\text{H}}_2\text{O}\right)\right].$$

For the reaction with BeO(c) we can say ΔH = −12.7 kcal · mol⁻¹ for BeO(c) + 43.92(HCl + 8.111H₂O) → [BeCl₂(aq) + H₂O + 41.92(HCl + 8.499H₂O)], so that ΔH = −77.56 kcal · mol⁻¹ for Be(c) + H₂O(aq) → BeO(c) + H₂(g) and ΔHf°BeO(c) = −146.0 kcal · mol⁻¹. A variation of this would be to calculate a ΔH_mix = −1.81 kcal · mol⁻¹ on the basis of (4). Then ΔH for the reaction with Be(c) = −91.4 and ΔHf°[BeO(c)] = −147.2 kcal · mol⁻¹.

Averaging these five values we obtain −145.7 kcal · mol⁻¹ for ΔHf° [BeO(c)].

2.4. Other data

From the cell measurements of Smirnov and Chukreev [19] in the temperature range 955 to 1313 K, we obtain a second law ΔH° = −94.6 kcal · mol⁻¹ and a third law ΔH° = −93.7 kcal · mol⁻¹ for Be(c) + ½CO₂(g) → BeO(c) + ½C(graphite), or ΔHf° [BeO(c)] = −141.6 and −140.8 kcal · mol⁻¹, respectively.

2.5. The Selection of the ΔHf°[BeO(c)]

It is appropriate at this point to tabulate the values of ΔHf°BeO(c), both the direct and indirect determinations (table 4). As is evident, except for the Smirnov and Chukreev value, all the indirect determinations support a more negative value than that of Cosgrove and Snyder. The “best” value now appears to be −145.7 kcal · mol⁻¹ in good agreement with the Neumann et al. [6] direct determination. The uncertainties are discussed in section 4.

Table 4.

Summary of values of ΔHf° [BeO(c)]

Investigator	ΔHf°
Direct Determinations	kcal · mol−1
Moose and Parr [4]	−134.1
Roth et al. [5]	−147.3
Neumann et al. [6]	−145.3
Mielenz and v. Wartenberg [7]	−136.2
Cosgrove and Snyder [8]	−143.1
Indirect Determinations
Neumann et al. [6,9]	−144.9
Smirnov and Chukreev [19]	−141.1
Kilday et al. [1] and Bear and Turnbull [13]
Kilday et al. [1], Kilday and Churney, private communication (1971) and Churney and Armstrong [2]
Kolesov et al. [10] and Bear and Turnbull [13]	−145.7
Kilday et al. [1] and Armstrong and Coyle [14]	−143.9
Kilday et al. [1] and Thompson et al. [17]	−145.7

2.6. The Decomposition of Beryllium Hydroxide as Supporting Evidence

Bear and Turnbull [13] have also measured the enthalpy of solution of Be(OH)₂ (β, orthorhombic) and Be(OH)₂ (α, tetragonal) in 22.6 percent HF, [679(HF + 3.80H₂O)]. From these measurements and their measurements on Be(c) we obtain ΔH = −79.83 kcal · mol⁻¹ for Be(c) + 2H₂O(liq) → Be(OH)₂(β) + H₂(g) and ΔHf° = −216.5 kcal · mol⁻¹; similarly for Be(OH)₂(α) we obtain ΔH = −79.10 kcal · mol⁻¹ and ΔHf° = −215.7 kcal · mol⁻¹. Using these values for ΔHf° and our tentative “best” value for BeO(c) we obtain:

$$\text{BeO}\left(\text{c}\right)+{\text{H}}_2\text{O}\left(\text{liq}\right)\to \text{Be}{\left(\text{OH}\right)}_2\left(\text{c},\beta \right);\Delta H^{\circ }=-2.5\text{\hspace{0.17em}kcal\hspace{0.17em}}\cdot {\text{mol}}^{-1}$$

$$\text{BeO}\left(\text{c}\right)+{\text{H}}_2\text{O}\left(\text{liq}\right)\to \text{Be}{\left(\text{OH}\right)}_2\left(\text{c},\alpha \right);\Delta H^{\circ }=-1.7\text{\hspace{0.17em}kcal\hspace{0.17em}}\cdot {\text{mol}}^{-1}.$$

Fricke and Wüllhorst [15] measured the enthalpies of solution of BeO(c), Be(OH)₂(c, β), and Be(OH)₂(c, α) in 11.59 percent HF. From these measurements we obtain ΔH° = − 2.5 and −1.8 kcal · mol⁻¹, respectively, in excellent agreement with our ΔH°. Matignon and Marchal [20, 21], from measurements in 30 percent HF, obtained $\Delta H_{\text{hyd}}^{\circ }\left(\text{Be}{\left(\text{OH}\right)}_2,\text{form unspecified}\right)=-3.2\text{\hspace{0.17em}kcal}\cdot {\text{mol}}^{-1}$, in fair agreement. Fricke and Severin [22] measured the equilibrium vapor pressure at 378 K to be 100 mm H₂O(g) over Be(OH)₂(c, β). Using a Nernst equation they calculate ΔH = 15.5 kcal · mol⁻¹ of H₂O(g), which results in ΔH° = −5.0 kcal · mol⁻¹ for the hydration of BeO(c). However they reported that the BeO formed had a distorted lattice which should require a ΔHf° more positive than −145.7 kcal · mol⁻¹. Also since the ΔH calculated is based on only one point it can not be considered a definitive value.

It is evident that the related data are supportive of our value for ΔHf°[BeO(c)] = −145.7 kcal · mol⁻¹.

3. The Enthalpy of Formation of BeF₂(c)

3.1. The Enthalpy of Transition of BeF₂(gl) and BeF₂(amorph) to BeF₂ (α, quartz)

There are no published direct determinations of the ΔHf°[BeF₂(c)] from combustion of Be(c) in F₂(g); the combustion of Be(c) in F₂(g) results in amorphous material. The indirect reactions, in which BeF₂ forms, produce a glassy state.

Taylor and Gardner [23] determined the enthalpy of solution of both the α, quartz form, and the glassy form in acetic acid-sodium acetate solutions to be − 3.64 and −4.76 kcal · mol⁻¹, respectively. This leads to a ΔH_trans quartz → glass = 1.12 kcal · mol⁻¹. If we assume that the amorphous and glassy states are equivalent we can convert both to ΔHf°[BeF₂(α, quartz)].

3.2. The Reaction of Be(c) With F₂(g)

Churney and Armstrong [2] measured the enthalpy of reaction of Be(c) in F₂(g) to be −244.3 kcal · mol⁻¹. They report BeF₂(amorph) to be their product. This results in ΔHf°[BeF₂(c)] = −245.4 kcal · mol⁻¹. In a preliminary report (1965) they cite the unpublished measurements of Simmons (1961) on the conversion of Be(foil) to partially glassy BeF₂, leading to AHf°[BeF₂(c)] = −257.0 kcal · mol⁻¹.

3.3. The Reaction of Be(c) With PbF₂(c)

Gross [24] reported ΔH° = −84.0 kcal for the reaction of Be(c) with PbF₂(c) to form BeF₂(c) and Pb(c). Although no crystallographic identification was made the direction of the results under varying conditions indicates that the value is for the formation of BeF₂(c). Since there is some uncertainty in our selection for PbF₂(c) we will avoid its use by relating the reaction to the reaction from Gross, Hayman, and Levi [25]:

3/2PbF₂(c) + Al(c) → AlF₃(c) + 3/2Pb(c); ΔH = −118.53 kcal from which we obtain:

3/2Be(c) + AlF₃(c) → Al(c) + 3/2BeF₂(c); ΔH = −7.47 kcal and using ΔHf°[AlF₃(c)] = −359.5 kcal · mol⁻¹ [3], ΔHf°[BeF₂(c)] = −244.6 kcal · mol⁻¹. However, a more recent direct determination of ΔHf°[AlF₃(c)] = −361.0 kcal · mol⁻¹ by Rudzitis et al. [26] would lead to ΔHf°[BeF₂(c)] = −245.6 kcal · mol⁻¹.

3.4. Other Data

There is a path to Δ(ΔHf°) [BeO(c) − BeF₂(c)] and another to ΔHf°[BeF₂(c)] both of which involve BeF₂(g) in high temperature gas phase equilibria. These can be referred to BeF₂(c) with the enthalpy of sublimation of BeF₂. Table 5 summarizes the second and third law $\Delta H_{\text{subl}}^{\circ }{\text{BeF}}_2$ calculated from the vapor pressure measurements on the crystal and liquid. From these data we have chosen $\Delta H_{\text{subl}}^{\circ }=55.7\text{\hspace{0.17em}kcal\hspace{0.17em}}\cdot {\text{mol}}^{-1}$. Because the thermal functions of BeF₂(g) are based on an estimate for one of the three vibrational frequencies and the thermal functions of the condensed phases at high temperature are only approximate, we estimate an uncertainty of ±2.0 kcal · mol⁻¹. The gas phase equilibria calculations are summarized in table 6. Because of the many uncertainties inherent in these data, we have not assigned any weight to these measurements. The thermal functions used are given in [27].⁴

Table 5.

Summary of values for $\Delta {\text{H}}_{subl}^{\circ }\left[{\text{BeF}}_2\left(\text{c}\right)\right]$ at 298 K

Investigator	Temp. Range of Measurements	Second Law ΔH°	Third Law ΔH°
	K	kcal · mol−1	kcal · mol−1
Cantor [28]	1146−1372	56.03	55.70
Khandamirova et al. [29]	846−950	58.7	56.07
Sense and Stone [30]	1075−1293	55.37	55.65
Sense, Snyder, and Clegg [31]	1019−1076	60.8	55.58
	1076−1241	55.9
Hildenbrand and Theard [32]	821−942	55.98	55.40
Blauer et al. [33]	713−795	58.1	53.70
Greenbaum et al.[34]	823−1053	56.66	54.86
Novoselova et al. [35]	1040−1376	52.3	55.8

Table 6.

Gas phase equilibria involving BeF₂(g)

Reference	Reaction	Δ(ΔHf°)[BeO(c) — BeF2(c)]		ΔHf° [BeF2(c)]
		2d Law	3d Law	2d Law	3d Law
		Kcal·mol−1		Kcal·mol−1
[36]	BeO(c) + 2HF(g) → BeF2(g) + H20(g)	105	101
[32]	BeF2(g) 4– 2Al(c) → Be(c) + 2AlF(g)			−242	−238

3.5. The Selection of ΔHf°[BeF₂(c)] and Δ(ΔHf°)[BeO(c) − BeF₂(c)]

From the values for ΔHf°[BeF₂(c)] in 3.2 and 3.3 our “best” value for BeF₂(c, quartz) appears to be −245.4 kcal · mol⁻¹. Tentatively, then our Δ(ΔHf°) [BeO(c) − BeF₂(c)] = 99.7 kcal · mol⁻¹.

As cited earlier the data from Kolesov et al. [9 ] yielded Δ(ΔHf) [BeO(c) − BeF₂(aq)] = 107.085 kcal · mol⁻¹, where the BeF₂(aq) is in 340(HF + 3.826H₂O). They also measured the enthalpy of solution of BeF₂(c, β-cristobalite) to the same final solution, ΔH = − 8.07 kcal · mol⁻¹. If we combine these results with our selected value for BeO(c), ΔHf° = −145.7 kcal · mol⁻¹ we obtain for BeF₂(c, β-cristobalite)−244.7 kcal · mol⁻¹. This indicates an enthalpy of transition of 0.7 kcal · mol⁻¹ between the two forms. Reported values for similar transitions in SiO₂ [3], CaF₂ [37], and BeCl₂ [38] are 0.37, 1.14 and 1.32 kcal · mol⁻¹, respectively.

4. Assigned Uncertainties

We have tried to indicate some measure of the uncertainty in the reported values of ΔH and in the derived ΔHf°’s by the number of significant figures given, following the convention that the overall uncertainty lies between 2 and 20 units of the last figure. The uncertainty in the ΔHf°’s depends on the uncertainties of all the determinations in the total chain of reactions used to establish the value. But the values also are given so that the experimental data from which they are derived may be recovered with an accuracy equal to that of the original experimental quantities.

The overall uncertainties in the ΔH’s are based on many factors – the experimental technique used, the details given, the number of measurements, the standard deviation of the reported results, the magnitude and reliability of the corrections to 298.15 K, and the reliability of previous work of the investigators. A strictly mathematical evaluation can therefore not be made. For this reason we shall consider only the discussion of the assignment of uncertainties to our “best” values for ΔHf°[BeO(c)] and ΔHf°[BeF₂(c)].

Kilday et al. reported the uncertainty in their measurements of ΔH of solution of BeO(c) in aqueous 24 percent HF to be ±0.05 kcal · mol⁻¹. Kolesov et al. state their uncertainty to be ±0.12 kcal · mol⁻¹. Bear and Turnbull state the uncertainties in their measurements to be ±0.6, ±0.3, ±0.6, and ±0.9 kcal · mol⁻¹ for the solution of Be(c) in 12, 22.6, 30, and 40 percent HF solutions, respectively. In calculating the Δ(ΔHf) [BeO(c) − BeF₂(aq)] and ΔHf[BeF₂ aq)] we introduced errors due to the uncertainties in our values for ΔHf° F⁻(aq) and φ_L HF, but these errors essentially cancel in obtaining ΔHf° [BeO(c)]. We introduce a ±0.05 kcal · mol⁻¹ uncertainty by our correction of ΔHf[BeF₂(aq)] to X = 100. This is negligible. The overall uncertainty obtained from the combined results of Bear and Turnbull and Kilday et al. is ±0.6 kcal · mol⁻¹; similarly from the results of Kolesov et al. and Bear and Turnbull. The ΔHf° [BeO(c)] derived from the combination of the results of Kilday et al., and Churney and Armstrong, is dependent upon ΔHf° [F⁻(aq)]; hence the overall uncertainty must be ±1.2 kcal · mol⁻¹.

The uncertainty in the Armstrong and Coyle measurement is ±0.2 kcal · mol⁻¹. However, the final solution here is not dilute with respect to the BeF₂(aq). Even with the estimated mixing correction to the measured ΔH, the uncertainty in the derived ΔHf° [BeO(c)] must be ±1.5 kcal · mol⁻¹. Similarly, although the uncertainty in the measurements of Thompson et al., on Be(c) in HCl is ±0.1 kcal · mol⁻¹ (for BeO in HCl from Kilday et al. it is ±0.5 kcal · mol⁻¹) the overall uncertainty in the derived ΔHf° [BeO(c)] is + 1.5 kcal · mol⁻¹. For our “best” value for ΔHf° [BeO(c)] we assign an uncertainty of ±0.6 kcal · mol⁻¹. Churney and Armstrong assigned ±0.8 kcal · mol⁻¹ to their value for ΔHf° [BeF₂(amorph)]. The indirect determination from the measurements of Gross et al. have an overall uncertainty of ±0.8 kcal · mol⁻¹. We assign an overall uncertainty of ±0.8 kcal · mol⁻¹ to our “best” value for ΔHf° [BeF₂(c)].

5. A Key Assumption

The interpretation of the data and the values given are internally consistent with our value for ΔHf° [HF(aq, std. state)] [3], and lend support to this value; eg., the values for Δ(ΔHf°) [BeO(c)−BeF₂(quartz)] from our ‘selected’ values, independent of HF(aq) are in excellent agreement with that derived from the Kolesov et al. difference, HF dependent, if one assumes a ΔH_trans of 0.7 kcal · mol⁻¹ for the β cristobalite to the quartz form. Also the ΔHf[BeF₂(aq, in HF)] from the Bear and Turnbull measurements, dependent upon HF are in excellent agreement with that derived from the ΔH_soln (measured by Kilday and Churney) of a BeF₂ (amorph) sample whose ΔHf° was measured directly by Churney and Armstrong and is thus independent of ΔHf° [HF(aq)]. However there is also evidence [39, 40, 41] that the ‘selected’ value for HF may be too positive by 0.3 to 0.4 kcal · mol⁻¹. If so, this would involve a reinterpretation of the data.

In summary:

$$\Delta H{f}^{\circ }\left[\text{BeO}\left(\text{c}\right)\right]=-145.7\pm 0.6\text{\hspace{0.17em}kcal}\cdot {\text{mol}}^{-1}\left(-609.6\pm 2.5\text{\hspace{0.17em}kJ}\cdot {\text{mol}}^{-1}\right)$$

$$\Delta H{f}^{\circ }\left[{\text{BeF}}_2\left(\text{c},\text{\hspace{0.17em}quartz}\right)\right]=-245.4\pm 0.8\text{\hspace{0.17em}kcal}\cdot {\text{mol}}^{-1}\left(-1026.8\pm 3.3\text{\hspace{0.17em}kJ}\cdot {\text{mol}}^{-1}\right).$$