ENTHALPY OF FORMATION OF AQUEOUS HYDROFLUORIC ACID: REVISION NEEDED?

Abstract

Accurate enthalpies of formation of hydrofluoric acid in the gas and liquid states as well as in aqueous solutions are critical for reduction and interpretation of combustion calorimetry data for fluorinated compounds. Analysis of current recommendations reveals inconsistencies with the existing literature that can significantly affect experimental values derived using these recommendations. Through thorough and comprehensive analysis of available experimental data, including the sources not considered before, we provide recommendations that substantially improve consistency with these results. However, the scatter in the existing data also prevents further improvements and uncertainty reduction. New experimental data, particularly for aqueous HF solutions, are needed to advance.

1. Introduction

The enthalpy of formation of HF(aq) is a key property for determination of the enthalpies of formation of fluorinated compounds by combustion calorimetry as well as other frequently-used techniques such as solution calorimetry. The reference values of Δ_fH^ο_m(F⁻(aq)), Δ_fH^ο_m(HF(l)), and Δ_fH^ο_m(HF(ideal gas)) are closely tied to Δ_fH^ο_m(HF(aq)) at various concentrations. The recommended Δ_fH^ο_m(F⁻(aq)) at T = 298.15 K has gradually evolved over the past 90 years: −327.3 kJ·mol⁻¹ in 1929,¹ −329.1 kJ·mol⁻¹ in 1952,² −332.6 kJ·mol⁻¹ in 1965,³ −(335.65 ± 0.30) kJ·mol⁻¹ in 1973,⁴ and −(335.35 ± 0.65) kJ·mol⁻¹ in 1989.⁵ These values have not been consistently used by authors, which introduces problems in interpretation and analysis of the existing literature. Also, the latter value was first reported without detailed information in 1976,⁶ which lead to ambiguous application of these recommendations to HF(aq) between 1977 and 1989.

The current recommendations by CODATA⁵ for Δ_fH^ο_m(F⁻(aq)) and Δ_fH^ο_m(HF(ideal gas)) have been widely accepted by experimentalists and adopted in the NIST-JANAF tables.⁷ These recommendations for the liquid phase are largely based on the calorimetric data on formation, dilution, and neutralization of liquid hydrofluoric acid obtained by Johnson et al.^4,8 At very low, non-zero concentrations (n(H₂O)/n(HF) > 6000), extrapolation considering dissociation of the acid should be applied because there is no experimental data in this range. The Δ_fH^ο_m(F⁻(aq)) recommended by CODATA is 0.3 kJ·mol⁻¹ higher than the original value reported by Johnson et al.⁴ To obtain this value, the additional results^{9,10,11,12,13} combined with the derived thermodynamic parameters of dissociation and association of hydrofluoric acid⁵ were used. This list of principal sources is not comprehensive and was significantly expanded in the current work. There is also an apparent inconsistency of 3 kJ·mol⁻¹ between the experimental measurements of the enthalpy of the CF₄ hydrolysis reaction^14,15,16 and the result derived using the best available Δ_fH^ο_m(CF₄(ideal gas))¹⁷ and the CODATA reference values involving Δ_fH^ο_m(HF(aq)).

The CODATA gas-phase enthalpy of formation of HF was derived using the enthalpy of vaporization to the ideal-gas state recommended by Vanderzee and Rodenburg in 1970.¹⁸ Since that time, high-resolution spectroscopic measurements have been published¹⁹ that allow one to derive a very accurate value of Δ_fH^ο_m(HF(ideal gas)). This, in turn, establishes a thermodynamic network based on this updated value. In the Active Thermochemical Tables (ATcT),²⁰ a recommendation was derived, which shifts the values of Johnson et al.⁴ by about 1.2 kJ·mol⁻¹ for liquid and aqueous HF. While the thermochemical network approach used in ATcT is rigorous, it is controlled by the input data. Specifically, data associated with thermodynamic cycles involving B, N, Mg, Si, and some other elements that are relevant to the considered property were not included. As a result, these recommendations are consistent only with a limited fraction of the available experimental data. It follows that the stated uncertainty of 0.16 kJ·mol⁻¹ for the ATcT recommendations may be optimistic.

Recently, we proposed a protocol for the efficient ab initio prediction of the enthalpies of formation for CHON-containing compounds.²¹ The expanded uncertainty at the level of (2.5 to 3.0) kJ·mol⁻¹ was found to be achievable for medium-sized molecules. The uncertainty U(Δ_fH^ο_m) = 0.7 kJ·mol⁻¹ per fluorine atom suggested in the CODATA recommendations exceeds the model-associated uncertainty of U(Δ_fH^ο_m) = 0.35 kJ·mol⁻¹ obtained by extension of this protocol to the fluorinated derivatives.²² Thus, if the quality of the recommendations on Δ_fH^ο_m(HF(aq)) could be improved, it would have a significant positive effect on the performance of the predictive procedure.

In this work, we re-analyze the existing experimental results that can be used to derive the enthalpies of formation of HF in the liquid and gas states and aqueous solution. Several problems with the existing data are shown, and consistent recommendations are given for all phases. It is also demonstrated that additional high-quality experimental data are required for further improvements.

2. Analysis of experimental data

2.1. Direct determination

The enthalpy of formation of monomeric HF, Δ_fH^ο_m(HF(ideal gas)) = −(272.72 ± 0.05) kJ·mol⁻¹, can be obtained if the ionization energy of HF reported by Hu and Hepburn¹⁹ is combined with the ATcT reference values²⁰ for H⁺(g) and F⁻(g). The good precision of the spectroscopic ionization energy is obtained by combining high resolution single electron excitation with the threshold ion-pair production spectroscopy (TIPPS).²³ The older results^24,25 are consistent with this value while having a significantly higher uncertainty. Hereafter, we adopt this Δ_fH^ο_m(HF(ideal gas)). All uncertainties reported in this paper are the expanded uncertainties for 0.95 level of confidence. In most cases, they are based on the uncertainties reported in the original publications and should be considered as the lower limit of an uncertainty. The temperature is T = 298.15 K unless explicitly stated otherwise.

Wartenberg and Fitzner²⁶ directly determined the enthalpy of reaction H₂ + F₂ = 2HF(real gas). This result and other values^27,28,29 obtained in late 1920s and early 1930s have a relatively large uncertainty and are of historic interest only. However, this is not the case for the enthalpies of dilution, where larger relative uncertainties are acceptable. The enthalpy of formation for the liquid, Δ_fH^ο_m(HF(l)) = −(303.55 ± 0.27) kJ·mol⁻¹, was measured by direct reaction of the gaseous elements in a bomb calorimeter.⁸ Vanderzee and Rodenburg¹⁸ analyzed the available experimental data and suggested the enthalpy of vaporization of liquid HF into a monomeric ideal gas to be Δ_vapH^ο_m = (30.25 ± 0.10) kJ·mol⁻¹. Using Δ_fH^ο_m(HF(ideal gas)) and this enthalpy of vaporization, Δ_fH^ο_m(HF(l)) = −(302.97 ± 0.11) kJ·mol⁻¹ can be obtained. King and Armstrong¹⁰ conducted the direct reaction in the presence of water and determined Δ_fH^ο_m(HF(·50H₂O)) = −(320.83 ± 0.38) kJ·mol⁻¹.

2.2. Dissolution of HF in aqueous solutions and vaporization

Wartenberg and Fitzner²⁶ reported the enthalpies of solution of HF(real gas) in water at T = 305.15 K. The final mole ratios n(H₂O)/n(HF) varied from 354 to 675, with the average being close to 400. We recalculated all values to dissolution of the ideal gas at T = 298.15 K to form n(H₂O)/n(HF) = 400. Reference values of the real gas properties,¹⁸ the enthalpies of dilution for HF(aq)⁴ as well as the heat capacities of HF(ideal gas)⁷ and HF(aq)³⁰ were used. The barometric pressure was assumed to be P = 101.3 kPa. When the resulting value, Δ_solH^ο_m(HF(ideal gas)) = −(48.10 ± 0.23) kJ·mol⁻¹, is added to Δ_fH^ο_m(HF(ideal gas)), Δ_fH^ο_m(HF(·400H₂O)) = −(320.82 ± 0.23) kJ·mol⁻¹ is obtained.

Sometimes, the work of Roth³¹ is considered as a source of the original experimental data on the enthalpies of formation for HF(aq). Indeed, the author tabulated the enthalpies of formation for HF(l) and HF(aq) at several concentrations. However, the origin of these values was not specified, and they were likely derived from the experimental data available in the literature at that time and are not traceable at present. Therefore, we excluded these values from our analysis.

The partial pressures, p, of HF over its aqueous solutions were measured by Khaidukov et al.³², Munter et al.,³³ and Brosheer et al.³⁴ Overall, these data are inconsistent with differences as large as 0.3p. The reported partial pressures of HF are still low enough (the highest pressure is p = 3.0 kPa at T = 343.15 K) that the gas-phase association between the HF molecules can be neglected.

Khaidukov et al.³² reported Δ_vapH(HF) = 49.0 kJ·mol⁻¹ for the HF·400H₂O solution and temperatures from (298 to 313) K. This value was stated to be derived from the partial pressures of HF over the solutions with w(HF) = 0.10, 0.19, and 0.276. Some data points required to verify this value are missing in the original data table. Moreover, if one uses all experimental data points for w(HF) = 0.19 in the range (298 to 348) K, the enthalpy of vaporization to the ideal gas, Δ_vapH^ο_m = (52.1 ± 3.1) kJ·mol⁻¹, corresponding to Δ_fH^ο_m(HF(·4.74H₂O)) = −(324.8 ± 3.1) kJ·mol⁻¹ is obtained after reduction of the experimental value to T = 298.15 K using the heat capacities of HF(ideal gas)⁷ and HF(aq).³⁰ The increased Δ_vapH and large uncertainty suggest that these results should not be used.

The vapor pressures³³ exhibit significant data scatter, making only the results at w(HF) = 0.3 potentially suitable for estimation of the vaporization enthalpy. The enthalpy of vaporization of HF from this solution to the ideal gas, Δ_vapH^ο_m = (49.7 ± 0.8) kJ·mol⁻¹, was determined from the slope of the In p vs. T⁻¹ line in the range T = (303 to 343) K corrected to T = 298.15 K. This value corresponds to Δ_fH^ο_m(HF(·2.59H₂O)) = −(322.4 ± 0.8) kJ·mol⁻¹ that would be expected for the dilute solutions. The repeatability of the pressure data by Brosheer et al.³⁴ was significantly better than that in the former works. However, the enthalpies of vaporization (about 47 kJ·mol⁻¹ for w(HF) = 0.04 to 0.1) result in gas-phase enthalpy of formation Δ_fH^ο_m(HF(·10H₂O)) = −(319.7 ± 0.7) kJ·mol⁻¹ that is 1 kJ·mol⁻¹ high relative to any other experimental or recommended value in this composition range. Therefore, none of the papers reporting the partial pressures of HF is useful for the data analysis.

Walrafen et al.³⁵ determined the enthalpy of vaporization of HF from its aqueous solution with x(HF) = 0.50 to the monomeric gas using Raman spectroscopy. Depending on the mathematical treatment of their results and the subset of data used, the Δ_vapH^ο_m value varied from (36.5 to 44.5) kJ·mol⁻¹. Thus, this work is of interest only as an example of applying an unusual technique for thermodynamic measurements, and it is not useful for the purposes of the present study.

Vanderzee and Rodenburg⁹ derived the enthalpy of solution of HF in the ideal-gas state in water at infinite dilution Δ_solH^ο_m = −(61.59 ± 0.42) kJ·mol⁻¹ from their experiments on dissolution of the real gas in excess sodium hydroxide solution, which resulted in Δ_fH^ο_m(F⁻(aq)) = −(334.31 ± 0.42) kJ·mol⁻¹. These authors also derived the value Δ_solH^ο_m = −(61.97 ± 0.42) kJ·mol⁻¹ from the thermodynamic data^36,37 associated with the reaction KHF₂(cr) = KF(cr) + HF(g) and dissolution of the salts in aqueous KOH. Using this enthalpy of solution and Δ_fH^ο_m(HF(ideal gas)) yields Δ_fH^ο_m(F⁻(aq)) = −(334.69 ± 0.42) kJ·mol⁻¹. The enthalpy of solution in water of the monomeric gaseous HF to form HF·6017H₂O, Δ_solH^ο_m = −(55.11 ± 0.28) kJ·mol⁻¹ derived through the thermodynamic cycle using LiF and LiHF₂ ³⁸ is inconsistent with any other value despite an excellent agreement of the enthalpies of most intermediate steps with the available literature or theoretical models. The only exception is the enthalpy of dissolution of LiHF₂ in water, which, we believe, is a source of the problem. Johnson et al.⁴ calorimetrically determined the enthalpy of HF neutralization with NaOH(aq) and derived Δ_fH^ο_m(F⁻(aq)) − Δ_fH^ο_m(HF(l)) = −(32.10 ± 0.16) kJ·mol⁻¹.

Higgins and Westrum³⁹ reported the enthalpies of the following processes:

$${\mathrm{NH}}_3(\text{real gas},127\text{kPa})+n\text{HF}(\text{l})={\mathrm{NH}}_3·n\text{HF}(\text{l}),n=238\Delta {H^o}_{\text{m}}=-(177.61\pm 0.25)\text{kJ}·{\text{mol}}^{-1}$$ (1)

$${\mathrm{NH}}_4{\mathrm{HF}}_2(\text{cr})+(n-2)\text{HF}(\text{l})={\mathrm{NH}}_3·n\text{HF}(\text{l})\Delta {H^o}_{\text{m}}=-(24.10\pm 0.13)\text{kJ}·{\text{mol}}^{-1}$$ (2)

The enthalpy difference between the real- and ideal-gas states of NH₃ at these conditions is ΔH = 0.13 kJ·mol⁻¹.⁴⁰ From these data,

$${\mathrm{NH}}_3(\text{ideal gas})+2\text{HF}(\text{l})={\mathrm{NH}}_4{\mathrm{HF}}_2(\text{cr})\Delta {H^o}_{\text{m}}=-(153.64\pm 0.28)\text{kJ}·{\text{mol}}^{-1}$$ (3)

Schütza et al.⁴¹ calorimetrically measured

$${\text{NH}}_3(\mathrm{aq},0.85\text{mol}·{\mathrm{kg}}^{-1})+2\text{HF}(\mathrm{aq},0.21\text{mol}·{\mathrm{kg}}^{-1})={\text{NH}}_4{\text{HF}}_2(\mathrm{aq},0.0925\text{mol}·{\mathrm{kg}}^{-1})\Delta {H^o}_{\text{m}}=-(63.71\pm 0.50)\text{kJ}·{\text{mol}}^{-1}$$ (4)

and

$${\text{NH}}_4{\text{HF}}_2(\mathrm{cr})={\text{NH}}_4{\text{HF}}_2(\mathrm{aq},0.0925\text{mol}·{\mathrm{kg}}^{-1})\Delta {H^o}_{\text{m}}=-(20.54\pm 0.35)\text{kJ}·{\text{mol}}^{-1}$$ (5)

Combination of eqs. (4) and (5) gives

$${\text{NH}}_3(\mathrm{aq},0.85\text{mol}·{\mathrm{kg}}^{-1})+2\text{HF}(\mathrm{aq},0.21\text{mol}·{\mathrm{kg}}^{-1})={\text{NH}}_4{\text{HF}}_2(\text{s})\Delta {H^o}_{\text{m}}=-(84.25\pm 0.61)\text{kJ}·{\text{mol}}^{-1}$$ (6)

The difference of eqs. (3) and (6) is

$${\mathrm{NH}}_3(\text{ideal gas})+2\text{HF}(\text{l})={\text{NH}}_3(\mathrm{aq},0.85\text{mol}·{\mathrm{kg}}^{-1})+2\text{HF}(\mathrm{aq},0.21\text{mol}·{\mathrm{kg}}^{-1})\Delta {H^o}_{\text{m}}=-(69.39\pm 0.83)\text{kJ}·{\text{mol}}^{-1}$$ (7)

The enthalpy difference between NH₃(aq, 0.85 mol·kg⁻¹) and NH₃(ideal gas) ΔH = −(31.38 ± 0.08) kJ·mol⁻¹ can be calculated using its enthalpy of dissolution and ionization in water⁴²,⁴³ for the enthalpies of formation in the ideal gas and solution and the data of Parker³⁰ for the apparent enthalpies. Finally,

$$\text{HF}(\text{l})=\text{HF}(\mathrm{aq},0.21\text{mol}·{\mathrm{kg}}^{-1})\Delta {H^o}_{\text{m}}=-(19.01\pm 0.42)\text{kJ}·{\text{mol}}^{-1}$$ (8)

Note that this thermodynamic cycle gives only the enthalpy of dilution.

The calorimetric results of Higgins and Westrum⁴⁴ allow one to obtain the enthalpy of the reaction:

$$\text{NaF}(\text{cr})+\text{HF}(\text{l})={\text{NaHF}}_2(\text{cr})\Delta {H^o}_{\text{m}}=-(43.1\pm 0.18)\text{kJ}·{\text{mol}}^{-1}$$ (9)

Miller⁴⁵ measured apparent vapor pressures in the system

$${\text{NaHF}}_2(\mathrm{cr})=\text{NaF}(\text{cr})+\text{HF}(\text{ideal gas})$$ (10)

using the Knudsen effusion method. The determined vapor pressures increased with decreasing the orifice diameter, which is not surprising for the measurements over solids. We derived the enthalpy of the reaction ΔH^ο_m = (74.1 ± 3.0) kJ·mol⁻¹ by weight-averaging the lnp vs. T⁻¹ slopes for two smaller orifices and correcting the result to T = 298.15 K using the heat capacities of the participants^46,47,7 at this temperature. The diameter of the third orifice was 20 % of the cell diameter and the enthalpy obtained with this orifice was 5 kJ·mol⁻¹ lower than the value above. Combination of eqs. (9) and (10) yields the enthalpy of vaporization to the monomeric gas Δ_vapH^ο_m = (31.0 ± 3.0) kJ·mol⁻¹ consistent with the value reported by Vanderzee and Rodenburg.¹⁸ The enthalpy of reaction (10), ΔH^ο_m = (82 ± 2) kJ·mol⁻¹, determined by the transpiration method⁴⁸ is, therefore, incorrect.

2.3. Boron trifluoride and oxide

Δ_fH^ο_m(BF₃(ideal gas)) = −(1136.0 ± 0.8) kJ·mol⁻¹ was derived from a thermodynamic network for boron compounds.⁵ This value is mainly based on three values^49,50,51 derived from the experiments on boron combustion in fluorine. Combination of the results on dissolution in aqueous HF of boron in the presence of O₂¹¹ and BF₃¹² gives

$$\text{B}(\mathrm{cr})+0.75{\text{O}}_2+18.67\text{HF}·57.22{\text{H}}_2\text{O}={\mathrm{BF}}_3(\mathrm{ideal\; gas})+15.67\text{HF}·58.72{\text{H}}_2\text{O}\Delta {H^o}_{\text{m}}=-(607.2\pm 0.9)\text{kJ}·{\text{mol}}^{-1}$$ (11)

Using the enthalpies of dilution of HF(aq),⁴ the enthalpy of the following reaction can be derived

$$\text{B}(\mathrm{cr})+0.75{\text{O}}_2+3\text{HF}(·3.065{\text{H}}_2\text{O})={\mathrm{BF}}_3(\mathrm{ideal\; gas})+1.5{\text{H}}_2\text{O}(\text{l})\Delta {H^o}_{\text{m}}=-(602.7\pm 0.9)\text{kJ}·{\text{mol}}^{-1}$$ (12)

If one combines this value with Δ_fH^ο_m(BF₃(ideal gas)) and Δ_fH^ο_m(H₂O(l)), the enthalpy of formation Δ_fH^ο_m(HF(·3.065H₂O)) = −(320.68 ± 0.40) kJ·mol⁻¹ can be obtained. Johnson and Hubbard⁵² suggested a thermodynamic cycle involving B₂O₃(cr), H₃BO₃(cr), BF₃(ideal gas), and HF(aq), which results in Δ_fH^ο_m(HF(·3.000H₂O)) = −(320.49 ± 0.32) kJ·mol⁻¹.

2.4. Nitrogen trifluoride

The enthalpy of hydrogenation of NF₃ to form N₂ and HF(·123H₂O), ΔH^ο_m = −(834.7 ± 0.9) kJ·mol⁻¹, ⁵³ and the enthalpy of decomposition of this compound, ΔH^ο_m = (131.5 ± 1.3) kJ·mol⁻¹,⁵⁴ can be combined to give Δ_fH^ο_m(HF(·123H₂O)) = −(322.1 ± 0.5) kJ·mol⁻¹

2.5. Carbon tetrafluoride

The enthalpy of formation of CF₄ in the ideal-gas state, Δ_fH^ο_m = −(933.2 ± 0.8) kJ·mol⁻¹, was derived by Greenberg and Hubbard¹⁷ from experiments on combustion of graphite in fluorine. The values obtained by Domalski and Armstrong using a similar technique⁵⁵ and those in the references therein are consistent with this result. The enthalpy of reaction

$${\text{CF}}_4(\mathrm{ideal\; gas})+2{\text{H}}_2\text{O}={\text{CO}}_2(\text{ideal gas})+4\mathrm{HF}(·20{\text{H}}_2\text{O})\Delta {H^o}_{\text{m}}=-(173.2\pm 1.3)\text{kJ}·{\text{mol}}^{-1}$$ (13)

can be derived from the results of experiments^14,15,16 in which poly(tetrafluoroethylene) and perfluorobicyclohexyl were burnt in oxygen with some water present. Combination of these values with Δ_fH^ο_m(H₂O(l)) results in Δ_fH^ο_m(HF(·20H₂O)) = −(321.14 ± 0.38) kJ·mol⁻¹.

2.6. Magnesium difluoride

Rudzitis et al.⁵⁶ measured Δ_fH^ο_m(MgF₂(cr)) = −(1124.2 ± 1.3) kJ·mol⁻¹ by combination of the elements in a bomb calorimeter. Torgeson and Sahama⁵⁷ experimentally determined the enthalpies of the processes

$$\text{Mg}(\mathrm{OH}{)}_2(\mathrm{cr},298.2\text{K})+2\text{HF}(·4.42{\text{H}}_2\text{O},346.9\text{K})={\mathrm{MgF}}_2(\mathrm{cr},346.9\text{K})+2{\text{H}}_2\text{O}(\text{soln.},346.9\text{K})\Delta {H^o}_{\text{m}}=-(121.71\pm 0.08)\text{kJ}·{\text{mol}}^{-1}$$ (14)

$${\text{H}}_2\text{O}(\text{l},298.2\text{K})={\text{H}}_2\text{O}(\text{soln.},346.9\text{K})\Delta {H^o}_{\text{m}}=(3.39\pm 0.02)\text{kJ}·{\text{mol}}^{-1}$$ (15)

The difference between the final solutions in these reactions was due to a small amount (0.08 % by mass) of SiO₂ dissolved in the latter. This difference is small and can be neglected for the purposes of this study. To derive the enthalpy of the reaction at 25°C

$$\text{MgO}(\mathrm{cr})+{\text{H}}_2\text{O}(\text{l})=\text{Mg}(\mathrm{OH}{)}_2(\mathrm{cr})\Delta {H^o}_{\text{m}}=-(37.03\pm 0.10)\text{kJ}·{\text{mol}}^{-1},$$ (16)

they combined the experimentally determined enthalpy of the Mg(OH)₂ dissolution in aqueous hydrochloric acid with that of MgO taken from the literature.⁵⁸ The enthalpy of formation of MgO(cr) Δ_fH^ο_m = −(601.60 ± 0.30) kJ·mol⁻¹ was recommended by CODATA.⁵ To calculate the enthalpy required to cool the HF solution and MgF₂ to 25°C, the apparent heat capacity of HF C_p = 31 J·K⁻¹·mol^{−1 30} and the heat capacity of MgF₂ C_p = 61.5 J·K⁻¹·mol^{−1 5} were used. These experimental data above were combined to derive Δ_fH^ο_m(HF(·4.42H₂O)) = −(321.49 ± 0.63) kJ·mol⁻¹.

2.7. Silicon tetrafluoride and dioxide

Wise et al.⁵⁹ and later Johnson⁶⁰ reported the enthalpies of formation for SiF₄(ideal gas) determined by direct reaction between Si(cr) and F₂(g) to be −(1614.94 ± 0.79) and −(1615.78 ± 0.46) kJ·mol⁻¹, respectively. Although Johnson⁶⁰ suspected some problems with the older results,⁵⁹ no convincing arguments were given. Thus, the weighted-average value Δ_fH^ο_m(SiF₄(ideal gas)) = −(1615.57 ± 0.40) kJ·mol⁻¹ was adopted here. Wise et al.⁵⁹ also reported the enthalpy of a direct reaction of α-SiO₂ with F₂ in the absence of water to be ΔH^ο_m(298 K) = −(704.0 ± 1.2) kJ·mol⁻¹. From these results, Δ_fH^ο_m(α-SiO₂) = −(911.6 ± 1.3) kJ·mol⁻¹ can be derived.

The enthalpy of solution of SiF₄(ideal gas) in HF(aq) was found to be Δ_solH^ο_m = −(142.34 ± 0.17) kJ·mol⁻¹.⁶¹ The experiments were performed a few kelvin below T = 298 K, and the temperature dependence of the enthalpy was neglected. The authors⁶¹ specified in the text that this value corresponded to the dissolution in the acid with w(HF) = 0.19, however, the reported thermochemical equations implied w(HF) = 0.20. In this work, we adopt w(HF) = 0.19. The uncertainty for w(HF) increases U(Δ_solH^ο_m) from 0.17 kJ·mol⁻¹ to about 0.35 kJ·mol⁻¹. The enthalpy of solution depends on the final concentration of the solute. Using the experimental data presented in the original paper, we estimated the volume of the solution in the calorimeter to be 0.22 dm³ and the molarity of the dissolved Si (in any form) to be 0.068 mol·dm⁻³. This estimate is needed for further thermochemical cycles.

The slopes of the enthalpies of dissolution of α-SiO₂⁶² and SiO₂(sisilicalite)⁶³ with respect to w(HF) near T = 298 K were −0.35 and −0.226 kJ·mol⁻¹·(wt. % HF)⁻¹, respectively. These are significantly weaker than what one would expect for the dilution of the acid only. This suggests that the contribution of H₂SiF₆ should be considered for rigorous data evaluation. We are not aware of any experimental data necessary for this analysis. Another option, which cannot be fully excluded, is that the composition dependence of Δ_fH^ο_m(HF(aq)) at w(HF) = (0.1 to 0.4) might be even weaker than the currently recommended one.⁴ In this work, we used the increment −(0.226 ± 0.005) kJ·mol⁻¹·(wt. % HF)⁻¹ obtained from the linear regression of the more precise results by Johnson et al.⁶³ More shallow slopes can be derived from the results on dissolution of SiF₄⁶¹ and Si.⁶⁴ However, in those works, this increment derivation would involve the two-point extrapolation with one of the points measured at the very low concentration of the acid. The solvated form of silicon in these solutions might significantly differ from that in the more concentrated ones.

Kilday and Prosen¹³ reported the enthalpies of dissolution of α-SiO₂ (NBS Standard Reference Material 1654) in the aqueous HF with w(HF) = 0.244 to be −(136.69 ± 0.11) kJ·mol⁻¹. To get the same final state as in the experiments with SiF₄, 4 g (0.067 mol) of SiO₂ should be dissolved in 1 dm⁻³ of the solution with w(HF) = 0.194. The adjustment for the HF dilution using the data of Johnson et al.⁶³ for silicalite increases the experimental value by 1.13 kJ·mol⁻¹. Transformation of the mass concentrations of the dissolved material from 5 g·dm⁻³ used by Kilday and Prosen¹³ to 4 g·dm⁻³ requires no correction. The value Δ_fH^ο_m(HF(·4.60H₂O)) = −(321.61 ± 0.35) kJ·mol⁻¹ is obtained from these results with the use of the enthalpies of SiF₄ dissolution in HF(aq), formation of SiF₄ and α-SiO₂ from the elements, and dilution for HF(aq).⁴ Johnson et al.⁶⁵ determined ΔH^ο_m = −(135.59 ± 0.18) kJ·mol−1 for dissolution of the same material in the solution with w(HF) = 0.244 at the mass concentration of 1.1 g·dm⁻³. Per their results on silicalite, a correction of −0.24 kJ·mol⁻¹ is required to make an adjustment to 4 g·dm⁻³. The uncertainty of this term is probably close to 0.1 kJ·mol⁻¹. Based on these results, Δ_fH^ο_m(HF(·4.60H₂O)) = −(321.82 ± 0.35) kJ·mol⁻¹. For the statistical analysis, the resulting two values were averaged.

Johnson et al.⁶³ reported the results of a calorimetric study of silicalite, a SiO₂ polymorph. This material has a larger specific surface than α-SiO₂. This increases its dissolution rate in HF(aq) and adds a significant surface energy contribution to the calorimetric results. If this compound is used in a thermodynamic cycle, it is very important to use the same samples for all experiments. The enthalpy of the silicalite combustion in fluorine to form SiF₄(ideal gas) was determined to be ΔH^ο_m = −(710.58 ± 0.70) kJ·mol⁻¹. The enthalpy of the silicalite dissolution in aqueous HF with w(HF) = 0.194 derived from the data⁶³ is ΔH^ο_m = −(143.98 ± 0.14) kJ·mol⁻¹. When these results are combined with the enthalpy of solution for SiF₄ and the HF(aq) enthalpies of dilution,⁴ Δ_fH^ο_m(HF(·4.60H₂O)) = −(321.17 ± 0.20) kJ·mol⁻¹ is obtained.

Good et al.⁶⁴ measured the enthalpy of combustion of silicon in oxygen in the presence of HF(aq) with w(HF) = 0.2328 to be −(1047.3 ± 1.0) kJ·mol⁻¹. If one uses the extrapolation approach described above, ΔH^ο_m = −(1046.4 ± 1.0) kJ·mol⁻¹ can be derived for w(HF) = 0.194. With the two-point linear interpolation based on the original results,⁶⁴ ΔH^ο_m = −(1046.9 ± 1.0) kJ·mol⁻¹ is obtained. The values derived with these two procedures agree within their uncertainties. Using the former for consistency with the other compounds, Δ_fH^ο_m(HF(·4.60H₂O)) = −(321.79 ± 0.28) kJ·mol⁻¹ can be derived.

A good consistency of all four enthalpies of formation implies two important outcomes. First, the final solution used by Good et al.⁶⁴ was equivalent to one formed by dissolution of 16 g of SiO₂. A very good agreement of this enthalpy of formation with those derived for the solutions with the lower SiO₂ mass concentration indicates that this quantity is almost independent of the silicon content in the final solution if more than 4 g of SiO₂ is dissolved in 1 dm³ of the acid. Second, there was a discussion^63,66 that indicated potential problems in the published enthalpies of solution of α-SiO₂ in HF(aq) near T = 298.15 K. The observed data consistency does not support this suspicion, and we see no reason to ignore the four values derived with silicon compounds.

2.8. Iodine pentafluoride

Settle et al.⁶⁷ suggested a thermodynamic cycle for calculation of Δ_fH^ο_m(IF₅(l)) involving IF₅(l), IF₅(aq), HIO₃(aq), and HF(aq). Reversing this cycle results in Δ_fH^ο_m(HF(·261.17H₂O)) = −(322.50 ± 0.35) kJ·mol⁻¹.

The uncertainty of the enthalpy of formation of HF(aq) determined from the thermodynamic cycle involving UF₆ suggested by Johnson et al.⁴ is comparable to the discussed difference of about 1 kJ·mol⁻¹. This cycle and some other suggested cycles where the enthalpies of processes are expected to have large uncertainties (for example, those with tetrafluoroethylene) are not considered here. A summary of all results discussed above is given in Table 1 and in Figure 1.

Table 1.

Standard enthalpies of formation of HF in different phases at T = 298.15 K available in the literature^a

Composition	w(HF)	Involved compounds or process	ΔfHοm / kJ·mol−1	Year	Dev. from Ref. 4	Dev. from this work	Ref.
HF(g)	1	HF(g) = H+(g) + F−(g)	−(272.72 ± 0.05) b	2006	0.58 b	0.31	19
HF(g) – HF(l)	1	HF(l) vaporization	30.25 ± 0.10 b,c	1970			18
HF(g) – HF(l)	1	NaF, NaHF2, HF(l)	30.0 ± 3.0c,d	1961,1967
HF(l)	1	H2 + F2	−(303.55 ± 0.27)	1973	0	−0.27	4,8
HF·50H2O	0.0217	H2 + F2 + H2O	−(320.83 ± 0.38)*	1968	1.47	1.20	10
HF·400H2O	2.77·10−3	HF(g) solution in water	−(320.82 ± 0.23)*	1926	1.79	1.52	26
HF·4.74H2O	0.190	HF(aq) vaporization	−(324.8 ± 3.1)	1936	−3.18	−3.55	32
HF·2.59H2O	0.300	HF(aq) vaporization	−(322.4 ± 0.8)	1949	−1.62	−1.99	33
HF·10H2O	0.100	HF(aq) vaporization	−(319.7 ± 0.7)	1947	2.33	1.96	34
HF·H2O	0.526	HF(aq) vaporization	see text	1997			35
F−(aq)	0	HF(g) + NaOH(aq)	−(334.31 ± 0.42)	1971	1.34	0.48	9
F−(aq)	0	KHF2, KF, HF(g), KOH(aq)	−(334.69 ± 0.42)	1949,1961	0.96	0.10	36,37
HF·6017H2O	1.85·10−4	LiF, LiHF2, HF(g), H2O	−(327.83 ± 0.28)	1965	−2.78	−3.15	38
F−(aq) – HF(l)		HF(l) + NaOH(aq)	−(32.10 ± 0.16) e	1973	0	−0.59	4
HF·3.065H2O	0.266	B, BF3(g), O2, HF(aq)	−(320.68 ± 0.40)	1965,1966	0.40	0.13	11,12
HF·3.000H2O	0.270	B2O3,H3BO3, BF3(g), HF(aq)	−(320.49 ± 0.32)	1969	0.55	0.28	52
HF·123H2O	8.95·10−3	NF3(g) + H2 + H2O; NF3 decomposition	−(322.1 ± 0.5)	1965,1967	0.28	0.01	53,54
HF·20H2O	0.0526	CF4 + H2O	−(321.14 ± 0.38)	60s&50s	1.04	0.77	17,55,14,15,16
HF·4.42H2O	0.201	MgF2, MgO, Mg(OH)2, HF(aq)	−(321.49 ± 0.63)	40s&60s	0.06	−0.21	56,57,58
HF·4.60H2O	0.194	α-SiO2, SiF4, HF(aq)	−(321.61 ± 0.35) f	1973	−0.02	−0.29	13
HF·4.60H2O	0.194	α-SiO2, SiF4, HF(aq)	−(321.82 +0.35)f	1982	−0.23	−0.50	65
HF·4.60H2O	0.194	Si, SiF4, O2, HF(aq)	−(321.79 ± 0.28)	1964	−0.20	−0.47	64
HF·4.60H2O	0.194	SiO2(silicalite), SiF4, HF(aq)	−(321.17 ± 0.20)	1987	0.42	0.15	63
HF·261.2 H2O	4.23·10−3	IF5(l), IF5(aq), HIO3(aq), HF(aq)	−(322.50 ± 0.35)	1976	−0.02	−0.29	67

^aValues printed in italics were not used in averaging. The values marked with * were excluded by statistical analysis. All gases are assumed to be in the ideal-gas state

^bΔ_fH^ο_m(HF(l)) based on these values was used in averaging

^cstandard enthalpy of vaporization

^dcorresponds to Δ_fH^ο_m(HF(l)) = −(302.72 ± 3.0) kJ·mol⁻¹

^eΔ_fH^ο_m(F⁻(aq)) − Δ_fH^ο_m(HF(l))

^fconsidered as a single entry for averaging

Figure 1.

Standard enthalpies of formation of aqueous HF at T = 298.15 K. Blue line, ATcT recommendation;²⁰ green line, recommendations of Johnson et al.;⁴ yellow circles, experimental results used for averaging; blue squares, experimental points excluded due to large deviation; pink triangles, data points excluded during statistical analysis. The results at w(HF) = 0 and pure HF are not shown.

2.9. Enthalpies of dilution

The enthalpies of dilution recommended by Johnson et al.⁴ are in excellent agreement with the enthalpy of reaction (8) derived above, the enthalpy of dilution HF(·8.33H₂O) = HF(·6017H₂O),³⁸ and the results by Roth et al.⁶⁸ reduced to T = 298.2 K. A reasonable agreement is also observed with the other dilution results.^69,70,71 In 1883, Guntz⁷² measured the enthalpy of solution of HF(l) and enthalpies of dissolution of HF(aq) to form HF·400H₂O at T = 290 K. The values adjusted to T = 298.15 K using the apparent heat capacities³⁰ of the aqueous solution and the heat capacity of HF(l)⁷³ agree with those of Johnson et al.⁴ within ±0.35 kJ·mol⁻¹. This should be considered as a very good agreement as the sensitivity of the Guntz’s calorimeter is close to 0.5 kJ·mol⁻¹, per our estimate based on his results.

To our knowledge, the dilution enthalpies reported by Thourey et al.⁷⁴ have not been considered in prior evaluations. These results cover the range from HF·27H₂O to HF·5500H₂O. At n(H₂O)/n(HF) < 140, they agree with the values by Johnson et al.⁴ within ±0.1 kJ·mol⁻¹. For the more diluted final solutions, the enthalpies are typically more negative than those from Ref. 4. Both the deviations and the observed scatter are consistent with the expanded uncertainty of 0.3 kJ·mol⁻¹ in this range. These authors also reported the enthalpies of dissolution of fluorides and hydrogen fluorides of ammonium, sodium, and potassium in HF(aq).⁷⁵ The mutual inconsistency of the data for the fluorides and their hydrogen fluoride counterparts was up to 4 kJ·mol⁻¹.

Thus, the revision of the current recommendations on the enthalpies of dilution for HF(aq) is not warranted.

2.10. Dilute solutions

The dilution data⁴ cover the composition range from HF(·5500H₂O) to pure HF(l). Based on their experimental results, Johnson et al.⁴ reported the enthalpy increment between HF(·5500H₂O) and HF(·∞H₂O) to be ΔH^ο_m = −(10.71 ± 0.15) kJ·mol⁻¹. In an aqueous solution, HF undergoes the following processes:

$$\text{HF}={\text{H}}^{+}+{\text{F}}^{-}$$ (17)

$${{\text{HF}}_2}^{-}=\text{HF}++{\text{F}}^{-}$$ (18)

The equilibrium constants of process (17) was reported in multiple works. The value pK₁₅ = 3.18 ± 0.02 was recommended by Hefter⁷⁶ after critical evaluation of the available results. pK₁₆ = 0.61 ± 0.08 was found by averaging of the results from Refs. 81,80,77, and 78. Process (18) has a small effect (below 1.2 %) on the dilution enthalpy for the dilute solutions. The enthalpy of reaction (17), ΔH^ο_m = −(13.31 ± 0.13) kJ·mol⁻¹, was measured calorimetrically.⁷⁹ This value is supported by the electrical conductivity⁸⁰ and potentiometric⁸¹ measurements. The enthalpy of reaction (18), ΔH^ο_m = −(18 ± 2) kJ·mol⁻¹, was estimated from the equilibrium constants.^81,80,82 We calculated the molalities of all species in the HF(·5500H₂O) solution using the Debye-Hückel limiting law for the mean ionic activity coefficients γ_± and calculated the enthalpy increment between HF(·5500H₂O) and HF(·∞H₂O) to be ΔH^ο_m = −(10.16 ± 0.10) kJ·mol⁻¹. This value differs from that used by CODATA⁵ by about 0.3 kJ·mol⁻¹ that cannot be explained by the differences in the input parameters. According to our analysis, the CODATA value can be recovered if one assumes that 1/γ_± was erroneously used instead of γ_±. Without this mistake, the CODATA Δ_fH^ο_m(F⁻(aq)) would be 0.3 kJ·mol⁻¹ closer to the experimental results at infinite dilution derived by Vanderzee and Rotenburg.⁹

3. Discussion

The recommendations by Johnson et al.⁴ on the enthalpies of dilution at n(H₂O)/n(HF) < 5500 (w(HF) > 2·10⁻⁴) are supported by the available experimental data and do not need revision. We believe the relative expanded uncertainty for this property does not exceed 0.01 (1 % of the value).

Deviation of the available Δ_fH^ο_m values from the recommendations⁴ are shown in Figure 2. The values recommended by Johnson et al.⁴ are below the majority of data points. However, with the uncertainty suggested by CODATA (0.65 kJ·mol⁻¹),⁵ they are consistent with 11 of 16 values within the combined uncertainties. The ATcT recommendations²⁰ agree with the results at infinite dilution and those obtained from the direct reaction in the presence of water and CF₄ hydrolysis.

Figure 2.

Deviation of the standard enthalpies of formation of aqueous HF at T = 298.15 K from the recommendations of Johnson et al.⁴ (green line): blue line, ATcT recommendation;²⁰ yellow circles, experimental results at w(HF) > 0 used for averaging; green squares, experimental results at w(HF) = 0 used for averaging; pink triangles, data points excluded during statistical analysis.

The value of Wartenberg and Fitzner²⁶ (1.79 kJ·mol⁻¹) is inconsistent with both recommendations. Simple averaging of all points results in a shift value of 0.48 kJ·mol⁻¹. Robust statistics treatment that provides resistance to outliers in the data set by analyzing the scatter, the SMDM approach of Koller and Stahel,⁸³ yields the value of 0.43 kJ·mol⁻¹, suggesting lower weights for points (1.47 and 1.79) kJ·mol⁻¹ in the data set. The latter is also suggested to be an outlier according to the Tukey’s fences⁸⁴ and single-outlier Grubbs⁸⁵ statistical tests.

The point 1.47 kJ·mol⁻¹ is based on the enthalpy of the direct reaction¹⁰

$${\text{H}}_2(\mathrm{ideal\; gas})+{\text{F}}_2(\mathrm{ideal\; gas})+100{\text{H}}_2\text{O}(\text{l})=2(\text{HF}·50{\text{H}}_2\text{O})(\text{l})$$ (19)

The authors of that work also determined the enthalpy of the process

$${\text{OF}}_2(\mathrm{ideal\; gas})+2{\text{H}}_2(\mathrm{ideal\; gas})+99{\text{H}}_2\text{O}(\text{l})=2(\text{HF}·50{\text{H}}_2\text{O})(\text{l})$$ (20)

using the same flame calorimeter. The difference of the enthalpies of reactions (19) and (20) is Δ_fH_m^ο(OF₂(ideal gas)) + Δ_fH_m^ο(H₂O(l)). The value Δ_fH_m^ο(OF₂(ideal gas)) = (24.5 ± 1.6) kJ·mol⁻¹ derived from these results is in an excellent agreement (<0.6 kJ·mol⁻¹ difference) with the high-level ab initio predictions.^86,87 Since the point 1.47 kJ·mol⁻¹ significantly deviates from most results (Figure 2), we believe that these measurements have a systematic error. The observed consistency between the experimental and predicted values for OF₂(ideal gas) can be explained by cancellation of this systematic error when the difference between the enthalpies of reactions (19) and (20) was used to obtain Δ_fH_m^ο(OF₂(ideal gas)).

Removing these two potential outliers results in the average of (0.27 ± 0.23) kJ·mol⁻¹ that we recommend for further use. Formally, it implies that the currently recommended Δ_fH^ο_m(l) should be shifted by this value, yielding the recommended Δ_fH^ο_m(HF(l)) = −(303.28 ± 0.23) kJ·mol⁻¹.

The data at infinite dilution deviate by ~1 kJ·mol⁻¹ from the recommendations of Johnson et al., which exceeds the combined uncertainty from these two sources. However, if the enthalpy increment ΔH^ο_m = −(10.16 ± 0.10) kJ·mol⁻¹ between HF(·5500H₂O) and HF(·∞H₂O) is used, the value Δ_fH^ο_m(F⁻(aq)) = −(334.82 ± 0.25) kJ·mol⁻¹ can be obtained, which is in good agreement with the experimental data.^9,36,37 The consistency of three experimental values obtained with different techniques indicates that the enthalpy increment derived by Johnson et al.⁴ is too negative by 0.6 kJ·mol⁻¹. The experimental data points from that work are presented in Figure 3. The experiments were planned in such a way that, in the final solution, m(NaF) + m(NaOH) = 0.1 mol·kg⁻¹. The point marked with a cross is a statistical outlier. The remaining seven points show a clear dependence on the final molality of NaF. The value extrapolated to m(NaF) = 0 mol·kg⁻¹, ΔH = −(87.37 ± 0.10) kJ·mol⁻¹, corresponds to Δ_fH^ο_m(F⁻(aq)) = −334.81 kJ·mol⁻¹, which is in an excellent agreement with the value above. In the original paper,⁴ all experimental values were averaged. The description of experimental procedures given in Ref. 4 does not provide a clear indication of a potential source of the problem. One of the possibilities, for example, is that the average power in the main periods of the calorimetric experiments was 3.5 W at the maximum m(NaF), while the maximum power of the electrical heater used for calibration of the LKB 8700 calorimeter is only 0.5 W. Thus, the conditions in the experiments significantly differed from those in the calibration. The other possibility is that the enthalpy correction for dilution to zero molalities significantly deviates from zero. This hypothesis was used by both Johnson et al.⁴ and Vanderzee and Rodenburg.⁹ We are not aware of any experimental data that could be used to support or reject it.

Figure 3.

Experimental enthalpies of HF(l) neutralization with 0.1 mol·dm⁻³ NaOH⁴ as a function of the final molality of NaF: green circles and yellow cross are experimental data points, dashed line is the linear least-squares fit for the green circles.

At this point, we can only suggest using the results of Johnson et al.⁴ shifted by 0.27 kJ·mol⁻¹ for w(HF) > 2·10⁻⁴ and by 0.83 kJ·mol⁻¹ for w(HF) = 0 as the provisional reference values. The new recommended values are listed in Table 2, and the deviations of the experimental values from these recommendations are presented in Figure 4.

Table 2.

Recommended enthalpies of formation of HF(aq)

n(H2O) / n(HF)	m(HF) / mol·kg−1	w(HF)	ΔfHοm / kJ·mol −1	ΔfHοm / kJ·mol −1 from Ref. 4 a
∞	0	0	−334.82	−335.65 (−335.35b)
500000	0.0001110	0.000002221	−333.15
100000	0.0005551	0.00001111	−330.23
50000	0.001110	0.00002221	−328.68
20000	0.002775	0.00005553	−326.76
10000	0.005551	0.0001111	−325.53
7500	0.007401	0.0001481	−325.09
5500	0.01009	0.0002019	−324.66	−324.93
5000	0.01110	0.0002221	−324.51	−324.78
4000	0.01388	0.0002776	−324.22	−324.49
3000	0.01850	0.0003701	−323.91	−324.18
2500	0.02220	0.0004441	−323.71	−323.98
2000	0.02775	0.0005551	−323.47	−323.74
1500	0.03701	0.0007399	−323.14	−323.41
1300	0.04270	0.0008537	−322.99	−323.26
1100	0.05046	0.001009	−322.86	−323.13
1000	0.05551	0.001110	−322.79	−323.06
900	0.06168	0.001233	−322.72	−322.99
800	0.06939	0.001387	−322.65	−322.92
750	0.07401	0.001479	−322.62	−322.89
700	0.07930	0.001584	−322.58	−322.85
650	0.08540	0.001706	−322.55	−322.82
600	0.09252	0.001848	−322.51	−322.78
550	0.1009	0.002015	−322.47	−322.74
500	0.1110	0.002217	−322.43	−322.70
450	0.1234	0.002462	−322.39	−322.66
400	0.1388	0.002769	−322.34	−322.61
350	0.1586	0.003164	−322.29	−322.56
300	0.1850	0.003689	−322.25	−322.52
250	0.2220	0.004423	−322.20	−322.47
200	0.2775	0.005523	−322.16	−322.43
175	0.3172	0.006307	−322.14	−322.41
150	0.3701	0.007351	−322.12	−322.39
125	0.4441	0.008808	−322.11	−322.38
100	0.5551	0.01099	−322.09	−322.36
90	0.6168	0.01219	−322.08	−322.35
80	0.6939	0.01369	−322.07	−322.34
70	0.7930	0.01562	−322.06	−322.33
60	0.9252	0.01818	−322.04	−322.31
50	1.110	0.02173	−322.03	−322.30
40	1.388	0.02702	−322.00	−322.27
30	1.850	0.03570	−321.97	−322.24
25	2.220	0.04254	−321.94	−322.21
20	2.775	0.05261	−321.91	−322.18
15	3.701	0.06894	−321.86	−322.13
10	5.551	0.09997	−321.76	−322.03
8	6.939	0.1219	−321.68	−321.95
7	7.930	0.1369	−321.62	−321.89
6	9.252	0.1562	−321.53	−321.80
5	11.10	0.1818	−321.40	−321.67
4	13.88	0.2173	−321.17	−321.44
3.5	15.86	0.2409	−321.00	−321.27
3	18.50	0.2702	−320.77	−321.04
2.5	22.20	0.3076	−320.44	−320.71
2.25	24.67	0.3305	−320.21	−320.48
2	27.75	0.3571	−319.94	−320.21
1.8	30.84	0.3816	−319.66	−319.93
1.6	34.69	0.4098	−319.32	−319.59
1.5	37.01	0.4255	−319.11	−319.38
1.4	39.65	0.4424	−318.87	−319.14
1.3	42.70	0.4607	−318.61	−318.88
1.2	46.26	0.4807	−318.29	−318.56
1.1	50.46	0.5024	−317.92	−318.19
1	55.51	0.5262	−317.35	−317.62
0	∞	1.0000	−303.28	−303.55
gas			−272.72	−273.30b

^aThe recommendations of ATcT for the liquid phase can be obtained by adding 1.15 kJ·mol⁻¹ to the recommendations of Johnson et al.;⁴ for the gas phase, the ATcT value is identical to the one suggested in this work;

^bCODATA value.

Figure 4.

Deviation of the standard enthalpies of formation of aqueous HF at T = 298.15 K from the recommendations of this work (red line): green line, Johnson et al.;⁴ blue line, ATcT recommendation;²⁰ dashed lines, limits of the 95 % confidence interval; yellow circles, experimental results at w(HF) > 0 used for averaging; green squares, experimental results at w(HF) = 0.

Comprehensive analysis presented here conclusively demonstrates that the discussed problem cannot be fully resolved based on the presently available experimental data. Further experimental work is needed to advance. The suggested experiments include but not limited to:

• determination of the enthalpy of neutralization of HF(l) and HF(aq) to derive Δ_fH^ο_m(F⁻(aq));

• pVT or any other measurements near T = 298 K, which would improve the existing value of Δ_vapH^ο_m to the monomeric ideal gas;

• determination of the enthalpy of solution of LiHF₂ in water or HF to verify the results by Cox and Harrop³⁸;

• measurements of the enthalpies of dilution of HF(aq) and HF(l) to cover the concentration ranges not considered by the measurements of Johnson et al.⁴;

• determination of the enthalpy of dilution of the aqueous NaF + NaOH.

Conclusions

Comprehensive analysis of the available data is performed to derive the enthalpies of formation of HF(aq). The new spectroscopic Δ_fH^ο_m(HF(ideal gas))¹⁹ as well as the computational data,^86,87 and calorimetric results^63,65,74 not used previously in addition to the data analyzed before^4,5,9 allowed us to improve the existing recommendations with regard to the enthalpy of formation of HF in the liquid, aqueous, and gas phases. The gas-phase value, Δ_fH^ο_m(HF(ideal gas)) = −(272.72 ± 0.05) kJ·mol⁻¹, is based on accurate spectroscopic results. The values for the liquid and the aqueous phase at n(H₂O)/n(HF) < 5500 (w(HF) > 2·10⁻⁴) are obtained by a relatively small (0.27 kJ·mol⁻¹) shift of the values by Johnson et al.⁴, which have also been adopted by CODATA.⁵ The enthalpy of formation at infinite dilution, Δ_fH^ο_m(F⁻(aq)) = −(334.82 ± 0.25) kJ·mol⁻¹, deviates from the results of Johnson et al.⁴ and CODATA recommendations⁵ by 0.83 kJ·mol⁻¹ and 0.53 kJ·mol⁻¹, respectively. Such a significant revision is grounded on the derivation from three independent sources and favored over the value based on the enthalpy of neutralization of HF(l).⁴ More experimental data is needed to further improve these recommendations.