J. Phys. Chem. B 1997, 101, 3381-3399
3381
Raman Measurements of the High-Temperature Heats of Vaporization of HF and H2O and of the H-Bond Enthalpies of the Hydronium-Fluoride Complex in the 50 mol % HF-H2O Solution G. E. Walrafen,* W.-H. Yang, Y. C. Chu, and M. S. Hokmabadi Chemistry Department, Howard UniVersity, Washington, D.C. 20059 ReceiVed: October 31, 1996; In Final Form: February 10, 1997X
Heats of vaporization, ∆Hv, of the monomers HF and H2O from 50 mol % aqueous HF were determined to 150 °C (HF to 300 °C) under saturation pressures using Inconel and Monel cells with sapphire windows. Heats were obtained from the temperature dependences of the integrated Raman intensities, as well as the peak heights, of the 3958 and 3652 cm-1 vapor bands from HF and H2O, respectively, ratioed against the 2329 cm-1 band from the N2 internal standard. The Raman ∆Hv for the HF at 20 °C, 9340 ( 220 cal/mol, agrees well with 20 °C calorimetric data, but it decreases to 6600 ( 200 cal/mol at 150 °C. The Raman ∆Hv values for H2O are larger by the ≈∆H of one H-bond; they are 11 800 ( 300 and 9350 ( 350 cal/mol at 25 and 150 °C, respectively. The H-bonded dimer, (HF)2, contributes relatively little to the gas-phase spectrum below ≈150 °C, but its Raman intensity, centered near 3931 cm-1, rises rapidly between 150 and 300 °C. (HF)2 vaporizes first, but its H-bond breaks almost instantaneously in the vapor to give the monomer, except that the dimer finally becomes more favorable at very high saturation pressures. Gaussian deconvolution of the broad, structured, nominal 3600 cm-1 contour from the liquid between -12 and ≈150 °C yielded an H-bond enthalpy of 2.8 ( 0.2 kcal/mol OH‚‚‚F, which falls within the range of 2.5+0.6 -0.1 kcal/mol OH‚‚‚F obtained from Young-Westerdahl analysis involving -∆HINT ) gB ) ∆HvRaman(HF,solution) + ∆HvRaman(H2O,solution) - ∆Hv(HF,pure liquid) - ∆Hv(H2O,pure liquid). The 50 mol % solution is essentially a molten salt composed of very strong H2OH+‚‚‚F- complexes interbonded via peripheral H-bonds having ordinary, ≈2.9 Å, O-F distances. The ∆H of 2.5-2.8 kcal/mol refers to breakage of such peripheral H-bonds, and this breakage produces a pronounced Raman intensity increase near 3590 cm-1 due to dangling, nonH-bonded proton(s), schematically the left protons of H2OH+, or to the (above right of) F-. Three valence vibrations due to the O-H stretches of the H3O+ ion were observed. However, a fourth, very broad, valence vibration from the H+‚‚‚F- stretching of the H2OH+‚‚‚F- complex was also observed, near 2900-3000 cm-1, which results from proton transfer in a double-well potential with a very short, ≈2.4 Å, O-F distance. A detailed energy analysis of the complete vaporization process also suggests that the hydronium-fluoride H-bond, between the H2OH+ and the F- (above), has an unusually large energy, estimated to be at least ≈8 kcal/mol, thus breaking only upon vaporization, or at temperatures above those employed here for solution studies.
I. Introduction Partial molal heats of dissolution of H2O and HCl, as monomers, were determined recently from concentrated aqueous HCl solutions by measurements of the Raman vapor intensities between 20 and ≈110 °C.1 [The partial molal heats of dissolution are equivalent to the heats of vaporization because the solution concentration does not change appreciably in the vaporization process.] Some slight downward concavity was suggested from ln I versus 1/T plots at the highest temperatures (I is the integrated Raman intensity), but this curvature was only slightly outside the scatter of the Raman data. Hence, no serious effort was made to determine the temperature dependence of the ∆Hv values. In this new work our goals are (A) to demonstrate that hightemperature, high-pressure Raman measurements of a vapor, relative to a gaseous internal standard, can yield accurate heats of vaporization and their temperature dependences for corrosive materials, e.g., 50 mol % HF-H2O, and (B) to obtain a complete energy analysis for all steps in the vaporization process for 50 mol % HF-H2O using the measured H-bond ∆H values and liquid structures elucidated by Raman measurements. X
Abstract published in AdVance ACS Abstracts, April 1, 1997.
S1089-5647(96)03436-0 CCC: $14.00
Raman intensities were previously measured under constant laser power,1 but this “absolute” method is inadequate for accurate determination of the temperature dependence of the ∆Hv values. Moreover, the absolute method fails entirely if the laser power in the cell is attenuated, as in the present case, by loss of the optical quality of the sapphire window surfaces, i.e., clouding, due to attack by the HF. (The attack of the sapphire windows by the vapor is much less severe than the attack by the 50 mol % HF-H2O solution.) A ratio method was developed which allowed precise vapor intensity data to be obtained with clouded windows. In this method the integrated Raman intensities (or peak heights) from the HF and H2O vapor species were ratioed against the integrated intensity (or peak height) from N2. The N2 in the air, purposely trapped within the cell during closure, acted as an internal reference standard. The intensity ratio method was found to produce a significant reduction in the scatter of the Raman data compared to the previous work.1 Reliable data could be obtained even under conditions of significant window clouding. This improvement in the intensity data allowed us to determine the curvatures of ln I versus 1/T plots (henceforth called van’t Hoff plots), and we were thus able to determine the temperature dependences of the ∆Hv values. © 1997 American Chemical Society
3382 J. Phys. Chem. B, Vol. 101, No. 17, 1997 The data improvement resulting from the intensity ratio method was sufficient to allow for fits of the form ln(R) ) A + B/T + C/T2, where R refers to ratio, e.g., the peak height ratio, RH, or to the integrated intensity ratio, RA. Such fits involve constant curvature in terms of the variable (1/T). Fits of the form ln(R) ) A + B/T + CT + (CC) ln(1/T), corresponding to a quadratic polynomial temperature dependence of ∆H, were also accomplished in conjunction with the critical temperature measured in this work. The HF dimer concentration also had to be taken into account by means of spectral deconvolution at temperatures above 150 °C to obtain enthalpies related to a single, i.e., solution to monomer, vaporization process. Extreme care was exercised in previous work1 to remove temperature gradients in the glass Raman cells. Such gradients were found to produce errors in the intensity data. However, the present Inconel and Monel Raman cells are very massive (≈1900 g) compared to the small glass cells used previously; hence, they cool or heat relatively slowly. Good Raman intensity data could thus be obtained simply by use of heavy insulation around the metal cells (asbestos tape and/or glass wool), plus the added precaution of a surrounding, closed container to eliminate air currents completely. Raman spectra from the HF-H2O liquid phase were also obtained from 2300 to 4000 cm-1 over a wide range of temperatures, ≈-30 to ≈250 °C, and under saturation pressures. A broad, structured Raman contour whose peak occurs below 3600 cm-1 was observed at moderate temperatures, but this contour shifts upward and shows marked sharpening with temperature rise. This finally results in a much narrowed contour having low-frequency skew whose peak occurs near 3590 cm-1 at 250 °C. Gaussian deconvolution of the nominal 3600 cm-1 contour for temperatures from -12 to 150 °C followed by van’t Hoff treatment, i.e., ln(I1/I2) versus 1/T, yielded a constant ∆H value of 2.8 ( 0.2 kcal/mol. (I1 refers to the integrated intensity of the Gaussian component near 3600 cm-1, which increases with temperature rise, and I2 refers to the sum of the integrated intensities of Gaussian components below 3600 cm-1, which decrease with temperature rise and whose temperature dependences were found to be the same.) This ∆H is midway between the Raman O-H‚‚‚O value, 2.6 kcal/mol,2 and the spectroscopic D0 value (from the ground state; not De) for the gas-phase dimer, (HF)2, 3.045 kcal/ mol.3 The shape of the Raman contour due to HF monomers in the vapor was found to be roughly constant from room temperature to about 150 °C. The 3958 cm-1 component from the HF monomer displayed low-frequency asymmetry, but no rotational fine structure was observed because of the 16 cm-1 resolution used. We were forced to use 16 cm-1 resolution to observe the 3958 cm-1 feature, even when an extremely high laser power of 5 W was employed at the sample (4880 Å excitation). Increased low-frequency asymmetry of the 3958 cm-1 Raman feature was observed for temperatures rising between 150 and 303 °C. This asymmetry finally resulted in an overt shoulder near 3920 cm-1 at 303 °C. The 3920 cm-1 feature corresponds to the maximum intensity of the manifold of unresolved O-branch rotational transitions of the free-H stretching mode of the dimer. Gaussian contour deconvolution was conducted, and it clearly indicated that the dimer concentration rises very rapidly between 150 and ≈300 °C. A very weak Raman feature centered near 3872 ( 5 cm-1 was also found to rise in intensity for temperatures above about 150 °C. This feature is thought to refer to the H-bonded F-H stretch of the dimer.
Walrafen et al. The HF dimer is planar and corresponds to the Cs point group. Its structure is of the type F-H‚‚‚F-H, where the H-bonded F-H‚‚‚F linkage is roughly linear, but the free or dangling proton is off of the FHF axis.3 The angle between the F-F line and the F-H line is obtuse. The vibrational frequency of the free-H stretching mode ν1 has been reported to occur near 3931 cm-1, and the vibrational frequency of the H-bonded F-H stretch ν2 occurs near 3868 cm-1.3 A D0 value of 3.045 kcal/mol, obtained from accurate photofragment angular measurements, has been reported for the dissociation of the dimer into monomers.3 This value represents the H-bond energy in the vapor phase, and it is shown to be fairly close to values obtained here from the Raman vapor and liquid data. Finally, we carried out three types of auxiliary measurements: (A) of the total saturation pressure as a function of temperature, (B) of the critical temperature, and (C) of the absolute Raman intensities of N2 in the vapor above the liquid. The results of (A) and (B) are given subsequently, whereas (C), the absolute Raman N2 intensity measurements (measurements at constant laser power), were used in error analysis and enthalpy corrections. Experimental procedures are described in section II. Raman intensity data from the vapor are presented via van’t Hoff plots in section III, which also contains a table of ∆Hv values. Raman spectral contributions from (HF)2 in the vapor are described in section IV. Raman measurements of the 50 mol % liquid phase are presented in section V and for high temperatures in section VI. Tests of the heat of vaporization data are presented in section VII. Interpretation follows in section VIII. II. Experimental Procedures Our first high-temperature, high-pressure Raman cell was constructed of Inconel. The cell body was 10 cm long, with an o.d. of 5 cm and an i.d. of 1.8 cm. Three sapphire windows, 2.54 cm in thickness and in diameter, were used. The Teflon window gaskets were completely inert to HF, but they often leaked at elevated temperatures. Gold-plated soft-copper gaskets were thus used for the highest temperatures. Heavy steel window caps, 1.0 or 1.3 cm thick, held the windows against the interal forces. The Inconel cell body was attacked by HF. This produced a thin coating of deposits inside the cell and on the sapphire windows (easily removed with concentrated HCl). A second cell was thus constructed of Monel which more effectively resisted corrosion at temperatures between 150 and 300 °C. H2 was detected spectroscopically when the pristine Monel surface first encountered HF at high temperatures, but we found that the resulting, HF-insoluble, fluoride deposit protected the Monel from further attack. Hence, only the “worked-in” Monel cell was used for Raman intensity measurements. The H2 correlated with the insoluble deposit; i.e., it did not arise from HF dissociation into H2 and F2. Moreover, no evidence of fluorine evolution from the Teflon gaskets was detected. Significant etching of the sapphire windows was encountered at temperatures approaching 300 °C. Therefore, the very hightemperature Raman spectra had to be obtained in 30 min or less. Nevertheless, window etching was never so extensive that any effect of alumina dissolution could be detected in the solution. The horizontal Raman cell was moved up or down to obtain spectra from the vapor or the solution, respectively. Heating of the Inconel and Monel cells was accomplished with heating tape. Heavy insulation (asbestos tape and/or glass wool) was used in all cases. The cell was also placed inside a
H-Bond Enthalpies of the Hydronium-Fluoride Complex closed container to remove any temperature fluctuations due to air currents. Temperatures were measured with a thermocouple in intimate contact with the cell body. A few pressure measurements were made to obtain approximate estimates of the total ∆Hv values from ln P versus 1/T plots. One of the windows of the Inconel cell was replaced by a steel fitting having the same outer dimensions as the sapphire windows. This fitting contained a cylindrical insert of Teflon which acted as a gasket as well as a cylinder. A snugly fitted Teflon piston inside the Teflon cylinder transmitted the force from the gases inside the Raman cell through highpressure tubing filled with water. The high-pressure water, in turn, actuated a high-pressure Bourdon gauge. Calibration of the high-pressure gauge and piston assembly was accomplished by measuring the high-temperature saturation pressures above water in the Inconel cell. Experimental determinations of the critical temperature of the 50 mol % acid solution were also made. These measurements, however, could not be made optically with sapphire windows, because temperatures well in excess of 350 °C were involved. However, advantage was taken of the extremely sharp demarcation line produced on a long thin Monel rod resulting from the much greater corrosion due to the liquid acid, compared to the vapor. All three sapphire windows were replaced by heavy steel cylinders, faced with platinum disks 0.5 mm in thickness. The platinum-faced cylinders were seated against gold-plated softcopper gaskets. An accurately measured (fixed) volume of the 50 mol % acid was added, and the Monel rod was placed, precisely and reproducibly, inside the vertical cell (used horizontally for Raman spectra). The liquid height was observed at a set final temperature by measuring the sharp demarcation line produced by the greatly different amounts of corrosion at the liquid-vapor interface. Such corrosion line measurements were conducted at a series of elevated temperatures until the critical temperature was reached, at which point no demarcation line could be observed. The cell had to be opened to observe the Monel rod for each temperature, after which the rod was cleaned and the cell resealed. Corrosion measurements were also continued above the critical temperature as a check on the method, and several repeat measurements near the critical temperature were conducted. Raman measurements were conducted with a high-power, 10 W, Coherent argon ion laser, designed for optimum power at 4880 Å. This laser was routinely operated at power levels of 5 W or above. A slit width corresponding to a resolution of 16 cm-1 was used for all vapor measurements, but the resolution was increased to 3 cm-1 for measurements of (the much more dense) HF-H2O solutions. It should be emphasized that no attempt was made to work with resolutions higher than 16 cm-1 in our Raman studies of the vapor. High-resolution Raman measurements would yield less accurate HF and H2O intensity data, because of a great decrease in the signal-to-noise ratios.1 The reason for this is that the density of the vapor is roughly 3 orders of magnitude less than that of the solution, and the Raman intensities scale in about the same way. Hence, 16 cm-1 resolution was always used with power levels of 5 W or more at the focus position in the sample. (A resolution of 16 cm-1 corresponds to the largest slit width possible with our Raman instrument.) The low resolution necessarily obscured any O, Q, and S rotational fine structure, but the effects of this structure could be seen as definite shoulders in the broad Raman contours. The allowed transitions for Raman scattering are ∆J ) O, which corresponds to the Q branch, and ∆J ) ( 2, which
J. Phys. Chem. B, Vol. 101, No. 17, 1997 3383 corresponds to the O and S branches. Hence, under low resolution there is an intensity maximum in the Raman spectrum at the Q position (as opposed to the infrared spectrum where the ∆J ) O or Q absorption is zero), and the O and S contributions are not resolved. The O and S branches, nevertheless, contribute asymmetry to the HF Raman contour shape. Asymmetry is also seen for the symmetric stretching mode of H2O for analogous reasons. All Raman intensity measurements were made relative to the intensity of the N2 internal standard. However, the volume of the 50 mol % acid increases as the temperature rises, and this increase necessarily compressed the N2 in the vapor (also containing monomer and dimeric HF, H2O, and O2). The gas volume in the Inconel and Monel cells was thus made 2.4 and 2.9-3.0 times larger, respectively, than that of the liquid acid to minimize the effect of the compression on the intensity ratios. Nevertheless, the expansion of the acid at the highest temperatures resulted in a measurable increase in the N2 intensity (hence concentration). This rise in N2 concentration produced errors in the HF and H2O concentrations, determined via the intensity ratios. We thus made a few absolute intensity measurements, at constant laser power, and with clear (unclouded) sapphire windows, to estimate the N2 compression effect. These measurements had to be made very quickly, and then only to 150 °C, to minimize window clouding. They nevertheless indicated a small and roughly linear rise in the N2 concentration amounting to a few percent for the 20-150 °C range. It should be emphasized that intensity measurements relatiVe to the N2 internal standard are possible over a wide range of temperatures and experimentally difficult (window and cell corrosion) conditions and that such relative measurements provide data of good precision. But absolute measurements over the complete range of conditions with our cells are virtually impossible. (Raman cells constructed of platinum and employing diamond windows might allow for absolute intensity measurements.) The Raman instrumentation and the computerized scanning and data collection methods have been described.1,4 Deconvolution of the Raman stretching contours from the HF-H2O solution was accomplished with a Gaussian deconvolution program and with a 100 MHz computer as described recently.5 The HF solution composition was determined from accurate density measurements, using least-squares equations computed from reported density-composition data.6 These results were checked by volumetric analysis. III. Relative Integrated Raman Intensities, and Relative Peak Heights, from HF and H2O Monomers in the High-Temperature Vapor We present the Raman intensity data first, before presenting Raman spectra. Raman spectra from H2O monomers in the gas phase were shown previously under the same experimental conditions used here,1 and Raman spectra from HF [with contributions from (HF)2 at the higher temperatures] are presented in a subsequent section dealing with the dimer. Integrated Raman intensities and peak heights from the 3958 and 3652 cm-1 stretching modes of HF and H2O, respectively, obtained relative to the corresponding two quantities from the 2329 cm-1 stretching mode of N2, are displayed in Figures 1-3. The N2 from the air trapped in the Raman cell, during closure, acted as an internal standard. Figures 1 and 2 involve measurements over the temperature range 23-146 °C. Figure 3 involves data between 23 and 266
3384 J. Phys. Chem. B, Vol. 101, No. 17, 1997
Walrafen et al.
Figure 1. Plots of ln R versus 1/T for vaporization of HF from a 50 mol % aqueous HF-H2O solution. R refers to the Raman intensity from gaseous HF as the monomer, relative to the intensity of the gaseous N2 internal standard. RA refers to the ratio of integrated intensities (A), whereas RH refers to the ratio of peak heights (B). Large circles refer to the Raman data. Small circles and triangles refer to fits of the form ln R ) A + B/T + C/T2 and ln R ) A + B/T + CT + (CC) ln(1/T), respectively.
Figure 2. Plots of ln R versus 1/T for vaporization of H2O from a 50 mol % aqueous HF-H2O solution. Meanings of symbols and point designations were defined in the Figure 1 caption. (A) and (B) refer to integrated intensity ratios and to peak height ratios.
°C. A spectrum was also obtained at 303 °C; intensity data are not plotted. The Raman measurements from 23 to 146 °C were obtained using the Inconel cell with the same sample and N2 internal standard fill. The measurements were extended from 50 to 266 °C by use of the Monel cell. The two sets of raw intensity data were then scaled to each other by using separate second degree least-squares polynomial fits, with a very large region of temperature overlap, ≈100 °C. (The 50 mol % aqueous HF solution was added to the Raman cell, and the remaining volume was occupied initially by air. The ratios of the air to the HF
solution volumes were described above. The initial pressure was 1 atm, but the pressure rose more than 10-fold in the initial experiments to ≈150 °C.) The Raman intensity data of Figures 1-3 were fitted in two ways, designated method A and B. Method A employed a fit of the form ln R ) A + B/T + C/T2. This fit involves constant curvature in terms of the variable 1/T. Method B employed a fit of the form ln R ) A + B/T + CT + (CC) ln(1/T), and it requires use of the measured value of the critical temperature, Tc, where Tc ) 651 ( 3 K. [(CC) is
H-Bond Enthalpies of the Hydronium-Fluoride Complex
J. Phys. Chem. B, Vol. 101, No. 17, 1997 3385
Figure 3. Plots of ln R versus 1/T for vaporization of HF from a 50 mol % aqueous HF-H2O solution. The integrated intensity ratio data (A) and the peak height ratio data (B) include measurements to much higher temperatures, 266 °C, than shown in Figure 1. These data were corrected for (HF)2 contributions as described in the text.
TABLE 1: Heats of Vaporization for 50 mol % HF-H2O Calculated from Two Different Types of Fits; See Text RA(HF)
RH(HF)
low T
high T
low T
high T
T, K
no CC
CC ) 12.78
no CC
CC ) 12.60
no CC
CC ) 15.15
no CC
CC ) 12.44
298.15 323.15 348.15 373.15 398.15 423.15 448.15 473.15
9361 8641 8025 7491 7024 6612
9245 8660 8078 7500 6926 6356
9804 8784 7911 7155 6494 5911 5393 4293
9207 8581 7955 7329 6703 6077 5451 4825
10171 9098 8180 7385 6690 6077
10624 9871 9119 8366 7613 6861
9865 8935 8139 7449 6846 6315 5842 5420
8725 8107 7489 6871 6253 5635 5017 4399
RA(H2O) low T
RH(H2O) low T
T, K
no CC
CC ) 14.38
no CC
CC ) 16.05
298.15 323.15 348.15 373.15 398.15 423.15
11445 10997 10614 10282 9992 9736
11552 11093 10655 10237 9840 9463
12092 11276 10577 9972 9443 8976
11966 11320 10630 9976 9333 8700
used to highlight the ln term coefficient, relative to coefficients from simple powers of T.] More details regarding method B are described subsequently, but the heats of vaporization from method B are compared with those from method A in Table 1. Fits involving method A and method B were employed for all data shown in Figures 1-3, but the differences between these two types of fit were too close in Figures 1A and 3B to be evident from the figures. The differences are evident for Figures 1B, 2A,B, and 3A (barely) where they are shown by 3 and O. IV. Raman Evidence for the Dimer, (HF)2, in the Vapor at Temperatures above ≈150 °C The asymmetric Raman contour shape which results from the HF monomer in the vapor above the 50 mol % HF-H2O solution is Visually constant between room temperature and ≈150 °C. The peak of the monomer contour occurs near 3958
cm-1, but it displays marked low-frequency asymmetry. Accurate simulation of the asymmetric HF contour shape was accomplished (10 bar should begin to favor the dimer, but the highest temperatures in the present work exceed the critical temperature of pure HF. Hence, the enthalpy term more effectively opposes the volume term; i.e., the monomer is favored to higher temperatures in the aqueous solution case. Major contributions from (HF)2 only become evident near 300 °C for the 50 mol % solution. Finally, we emphasize that no evidence for H bonding between H2O and HF [or (HF)2] in the gas phase was uncovered in this work, nor was any evidence found for ionic species in the vapor. E. Energetics: Double-Well Potential and Enthalpy Assymetry. Two questions are of key importance relative to understanding the molecular vaporization mechanism from the 50 mol % HF solution: (1) why are the heats of vaporization for HF and H2O asymmetric, that is, why does the difference between the heats of vaporization, ∆Hv(H2O) - ∆Hv(HF), equal ∆HH-bond for low and high temperatures; (2) why do the heats of vaporization for HF and H2O decline in the specific manner observed here with temperature rise. We initially attempted to understand our heat of vaporization data by examining known energies for bonds of the strongly
Walrafen et al.
Figure 14. Transition-state diagram, schematic. A to B refers to both of the Figure 11 double-well structures; i.e., the double-well is shown schematically by a single minimum, for simplicity. C refers to the stretched O-F distance of 2.84 Å, which refers to an H-bond of normal strength, 1.82 Å. This H-bond restrains a normal HF molecule, H-F distance ≈0.92 Å. ∆Emin refers to the energy difference between the left and the right minima, ≈12 600 cal/mol.
H-bonded hydronium-fluoride complex, relative to the bond energies of the vaporization products, HF and H2O. But we discovered later that a successful analysis required the following: use of a double-well potential and its structures, shown in Figure 11, a transition-state diagram, depicted by Figure 14, plus the above-described enthalpy asymmetry. Our analysis elucidated the above questions, and it also explained another observation as well, namely, that proton motion in the doublewell potential gives rise to the fourth valence vibration, as invoked in the present Gaussian deconvolutions of the Raman stretching contours. Panel A of Figure 11 depicts the strong hydronium-fluoride complex in its O-H+- - -F- state (bold print) for which the O-H bond length for H3O+ is about 1.02 Å and where the H+- - -F- bond length is estimated to be about 1.35 Å. The value of 1.35 Å was used, in conjunction with other distances depicted in Figure 11, because these values yield calculated densities in essential agreement with experiment. Panel B of Figure 11 shows a more nearly neutral O- - -HF state (bold print), where the O- - -H distance is assumed to be about 1.35 Å and where the H-F distance of ≈1 Å is beginning to approach that of the free HF molecule, 0.92 Å. The (A) and (B) structures of Figure 11 refer to potential energy minima in a double-well potential. The energies of these two minima are the same for proton transfer, which may involve jumping over a barrier and/or tunneling through this barrier. Note that we do not show the double-well diagram for proton transfer corresponding to Figure 11. However, we do show a schematic transition-state diagram (Figure 14), but this should not be confused with the double-well potential energy diagram. The thin dashed lines of Figure 11 all refer to distances of roughly 1.82 Å, which we assume to refer to the ordinary or peripheral H-bonds. The heavy dashed lines all refer to short, ≈1.35 Å, H-F distances. [Any “phase” differences in such heavy dashed lines are the result of schematic necessity; compare (A) to (B).] We believe that the very strong ≈1.35 Å H+- - -F- H-bonds must break only upon vaporization (or at high temperatures not employed here for Raman studies of the liquid). Before this breakage occurs, it is likely that the short ≈2.35 Å O-F distance increases to the more normal H-bond O-F distance of about
H-Bond Enthalpies of the Hydronium-Fluoride Complex 2.84 Å. This means that the O-H distance goes from the 1.02 to 1.35 Å, double-well states, depicted for simplicity by the single minimum of the Figure 14 schematic (left), to the normal H-bond O-H distance, ≈1.8-1.9 Å, the right minimum of Figure 14. This second minimum may be viewed as an HF molecule whose proton is hydrogen-bonded via one lone electron pair of a water molecule. The HF molecule is then free to escape, only if the normal H-bonds (to its left and right sides) break. The energy difference between the minima shown in Figure 4 is ∆Emin. We believe that ∆Emin ) 12 600 cal/mol, from (AA) - ∆HH-bond(max, YW) ) (AA) - 2636 cal/mol. We subsequently use 12 600 cal/mol to calculate the energy of breaking the strong hydronium-fluoride H-bond, and we treat the energy of breaking the normal H-bond separately. This normal H-bond has not yet broken in the depiction shown by the right minimum of Figure 14. To explain the observed heats of vaporization in relation to Figures 11 and 14, it is essential to begin by invoking the enthalpy asymmetry, ∆Hv(H2O) - ∆Hv(HF) ) ∆HH-bond, at high as well as low temperatures. From Table 3 it is evident that N ) 1 at 265 °C. We do not have heats of vaporization for both HF and H2O at this high temperature, but we do have both heats of vaporization near 150 °C. Therefore, we assume that N ) 1 at 150 °C solely for purposes of our initial illustration. An N value of 1 implies that all H-bonds bonds on the periphery of the Figure 11 structure are broken, but the strong central H+- - -F- H-bond remains intact. When this central H-bond ultimately breaks, it yields an HF molecule whose proton is H-bonded to the lone electron pair of a water molecule, as described above. This H-bond of ordinary length, O-F distance 2.84 Å, is what gives the needed counting, namely, N ) 1. Any other counting has been found to disagree with experiment. We next assume that the ∆Emin value of 12 600 cal/mol at 150 °C is partitioned equally between the escaping HF and H2O molecules, and we then include the above-described enthalpy asymmetry to deal with the fact that the heat of vaporization of H2O is larger than that from HF. Under these assumptions the heat of vaporization of H2O equals ∆Emin/2 + ∆HH-bond, or 6300 + 2800 ) 9100 cal/mol, whereas that for HF is only ∆Emin/2, or 6300 cal/mol. The average experimental values from Table 1 are about 9218 cal/mol for H2O and 6230 cal/mol for HF, at 150 °C; i.e., the agreement is satisfactory (too good as shown next). A more rigorous approach, however, would be to use the N value of 1.62 calculated from the YW equation and apportion an additional 0.31∆HH-bond to both the HF and the H2O. This yields a heat of vaporization of 7170 cal/mol for HF and 9970 cal/mol for H2O if the van’t Hoff H-bond enthalpy of 2800 cal/ mol is used. If the YW value of 2500 cal/mol is used, one obtains 7075 cal/mol for the heat of vaporization of HF and 9575 cal/mol for H2O. The implication is that the 12 600 cal/ mol value may decrease at the highest temperatures, because the calculated values are higher than the experimental values. Certainly, a decrease in all enthalpy terms is to be expected because the heat of vaporization must reach zero at the critical point, but experimental error in the N value or the 12 600 cal/ mol value, or both, cannot be excluded. Now consider the temperature of 44 °C where N ) 3, according to Table 3, and also consider that N ) 3 corresponds to one H-bond to the right of the F- of Figure 11A and only one H-bond to left of the hydronium ion. When this structure breaks to yield H2O and HF in the vapor, we calculate that ∆Hv-
J. Phys. Chem. B, Vol. 101, No. 17, 1997 3397 (HF) ) 6300 + 2800 ) 9100 cal/mol, which agrees fairly well with the experimental 44 °C value of 8980 ( 400 cal/mol. We also calculate that ∆Hv(H2O) ) 6300 + 2 × 2800 ) 11 900 cal/mol, where 2∆HH-bond encompasses the asymmetry described above plus the value of 2800 cal/mol for the H-bond to the left of the hydronium ion. Again, fair agreement with the experimental value of 11 300 ( 160 cal/mol is obtained. We used the van’t Hoff value of 2800 cal/mol for the H-bond enthalpy in the aforementioned case, but even better agreement is obtained if we use the Young-Westerdahl value of 2500 cal/ mol for the H-bond enthalpy. The Young-Westerdahl approach gives 8800 calculated versus 8980 cal/mol observed, and 11 300 calculated versus 11 300 cal/mol observed, respectively, for HF and H2O. The better agreement obtained at the low temperature of 44 °C suggests that the value of 12 600 cal/mol is more nearly correct at low as opposed to high temperatures, where it may be too high. N ) 2 at 110 °C according to Table 3. We will assume that there is a statistical half H-bond to the fluoride ion and a statistical half H-bond to the hydronium ion. This means that ∆Hv(HF) ) 6300 + 1400 ) 7700 cal/mol and that ∆Hv(H2O) ) 6300 + 2800 + 1400 ) 10 500 cal/mol, or if the YoungWesterdahl H-bond enthalpy is employed, the values are 7550 and 10 085 cal/mol, respectively. The corresponding experimental values are 7200 ( 170 and 9930 ( 190 cal/mol, in fair agreement. Again, a decline in the value of 12 600 cal/mol is suggested. We emphasize again that the central (2.35 Å, O-F) H-bond shown in Figure 11A is the linchpin of the asymmetry assumption. This central H-bond always counts as N ) 1, which with two other H-bonds gives the required N ) 3, or three H-bonds in the 44 °C case; the required N ) 2, or two H-bonds in the 110 °C case, and N ) 1, of course, for the initial 150 °C illustration. The ordinary H-bond which ultimately results from breakdown of this strong, central H-bond is thought to have a bond energy in the 2.5-2.8 kcal/mol range, like the peripheral H-bond energies. The central ≈1.35 Å H+- - -F- H-bond energy (Figure 11A) is estimated below as 15.7 ( 8.11 kcal/mol, and this unusual strength explains why it remains largely unbroken in the liquid to fairly high temperatures, as opposed to peripheral H-bonds whose energies are only about 2.5-2.8 kcal/mol. Nevertheless, the central H-bond unquestionably breaks in the vaporization process as evidenced by the appearance of H2O and HF molecules in the vapor. The heats of vaporization for HF and H2O must both go to zero at the critical point of the 50 mol % solution, that is, at about 378 °C, and thus the ∆Emin value of 12 600 cal/mol also must go to zero at the critical point. The inference is that the hydronium-fluoride complex no longer exists at such high temperatures and that the solution may only involve H2O and HF molecules or aggregates involving these molecules. Such a situation might explain why the observed critical temperature is near the critical temperature of pure water. (The critical temperature of HF is not involved here because the critical temperature of 378 °C for exceeds the HF critical point, 188 °C; see Figure 13.) Thus far, we have answered question 2 by assuming an enthalpy asymmetry in addition to the empirical ∆Emin value of 12 600 cal/mol, but we postponed question 1 which asks why the H-bond breakage enthalpy is included with the heat of vaporization of H2O, instead of with the heat of vaporization of HF. Question 1 is extremely difficult; what follows is at least a rational interpretation based on known facts.
3398 J. Phys. Chem. B, Vol. 101, No. 17, 1997 We begin with a qualitative treatment of the double-well structures and their energies (Figure 11). This treatment employs gas-phase BE values, i.e., D0 values of HF, OH+, and OH: 135 100,3 117 380,22 and 101 200 cal/mol,23 respectively. The BE for the O-H bonds in the free H3O+ ion is about 128 700 cal/mol,9,21 but the strong interaction with the F- must certainly lower this value, e.g., 101 200 to 117 380 cal/mol for OH and OH+. We next assume that the central HsF in Figure 11B has a BE approaching 135 100 cal/mol and then use the condition that the double-well minima have the same energy, hence,
BE(A)(OsH) + BE(A)(H+- - -F-) ) BE(B)(O- - -H) + BE(B)(HsF) (5)
Walrafen et al. TABLE 4 RA(HF), low T ln R ) A + B/T + C/T2 A ) 3.737 32, B ) -28.0839, C ) -698 013.4 RA(HF), low T ln R ) A/T + B + CT + (CC) ln(1/T) A ) -8321.12, B ) 96.0427, C ) 1.591 59 × 10-3 CC ) 12.78, Tc ) 651 K RA(H2O), low T ln R ) A + B/T + C/T2 A ) 10.3975, B ) -2848.95, C ) -433 796 RA(H2O), low T ln R ) A/T + B + CT + (CC) ln(1/T) A ) -9364.61, B ) 106.819, C ) 8.276 09 × 10-3 CC ) 14.38, Tc ) 651 K
which upon substitution of values in cal/mol for OH and OH+ gives
RA(HF), high T ln R ) A + B/T + C/T2 A ) 1.191 68, B ) 1698.49, C ) -988 623.8
[101200 to 117380] + BE(A)(H+- - -F-) ≈
RA(HF), high T ln R ) A/T + B + CT + (CC) ln(1/T) A ) 8389.17, B ) 95.7296, C ) 9.515 93 × 10-7 CC ) 12.60, Tc ) 651 K
[BE(B)(O- - -H) + δ] + [135000 - δ] (6) where δ is a quantity which approaches zero when the HF molecule whose bond distance is 0.92 Å is formed, as opposed to the stretched HsF configuration shown in Figure 11. We next assume that the central (B) configuration of Figure 11 goes to the (C) configuration of Figure 14, which means that the O-F distance increases from ≈2.35 to 2.84 Å. The (C) configuration of Figure 14 can be approximated by letting δ ≈ 0 and by using the YW ∆HH-bond value of 2500 cal/mol for [BE(B)(O- - -H)]. From the equality, eq 5, we obtain
[101200 to 117380] + [BE(A)(H+- - -F-)] + 12600 ≈ 135100 + 2500 (7) The energy ∆Emin ) 12 600 cal/mol is presumably the amount needed to move from the left minimum of Figure 14 to the right minimum, i.e., to stretch the O-F distance from 2.35 to 2.84 Å, along with concomitant changes in bonding. Equation 7 gives an enormous range, from 7620 to 23 600 cal/mol, for the strong central hydronium-fluoride H-bond, i.e., [BE(A)(H+- - -F-)] ) 15 710 ( 7990 cal/mol. However, because the proton is more likely to form an O-H+ type of bond to the F-, it is likely that the correct value lies toward the lower end of this range; compare 128 700 cal/mol for the O-H bond of hydronium ion to 117 380 cal/mol for OH+. Nevertheless, even the average value of 15.7 kcal/mol is not totally unreasonable when compared to the related difluoride (FHF)- anion. The difluoride anion has a proton-centered or symmetric structure whose F-F distance is ≈2.26-2.32 Å.24 The calculated H-bond energy for the difluoride ion is 60 200 cal/ mol,25 making it the strongest H-bond known. We next deal with the enthalpy asymmetry in which the normal H-bond energy needed to release H2O to the gas phase is thought to go entirely into the vaporization of H2O as follows. Evidence was described in this work indicating that HF vaporizes first as the dimer and that the dimer then breaks up almost immediately in the vapor, except for high temperatures where the saturation pressure is high. But no evidence was found here whatever for the vaporization of H2O as the dimer. We believe, therefore, that the enthalpy asymmetry results because the energy of breaking the normal H-bond, which arises from the strong central H-bond, goes entirely into the energy of releasing the H2O and that the H2O is released slightly before the HF is released. Moreover, we believe that the release of the HF is slowed, slightly, because it reacts with other HF molecules to form the dimer (HF)2 in solution and that the dimer
RH(HF), low T ln R ) A + B/T + C/T2 A ) 0.844 322, B ) 1855.77, C ) -1 039 579 ln R ) A/T + B + CT + (CC) ln(1/T) A ) -9862.90, B ) 115.824, C ) -3.521 61 × 10-3 CC ) 15.15, Tc ) 651 K
TABLE 5: Parameters of Two- and Three-Gaussian Fits of Raman Spectra from the Vapor above the 50 mol % HF-H2O Solutiona
t ) 76 °C 2 3 t ) 107 °C 1 2 3 t ) 131 °C 1 2 3 t ) 166 °C 1 2 3 t ) 220 °C 1 2 3 t ) 262 °C 1 2 3 t ) 303 °C 1 2 3
center, cm-1
height
width, cm-1
% of total contour area
3946 3959
52.6 140.1
22 13
38.8 61.2
3922 3945 3958
28.5 201.0 682.7
29 21 14
5.6 29.8 64.6
3922 3945 3958
52.5 422.6 1338.9
20 18 14
4.0 27.8 68.2
3922 3945 3958
226.4 1082.5 2576.8
20 21 14
7.2 35.7 57.1
3922 3947 3958
382.8 1509.3 1638.1
25 25 15
13.5 52.9 33.6
3918 3940 3954
761.3 1884.4 2459.0
19 26 18
13.1 45.5 41.4
3918 3941 3958
470.9 934.1 826.1
27 24 23
23.5 41.8 34.7
a Height values are not intercomparable between temperatures. They are useful only for relative comparisons at a given temperature.
is finally ejected from the liquid surface, where it very quickly breaks up into monomers in the gas phase. Note that the formation of the dimer in the liquid, and its immediate breakup to the monomer upon entry into the vapor, does not appear in any of our energy calculations and moreover would not involve a net energy change.
H-Bond Enthalpies of the Hydronium-Fluoride Complex Finally, a theoretical calculation of the ∆Emin value of 12 600 cal/mol, which is believed to relate mainly to the stretching of the O-F length from ≈2.35 to 2.84 Å, plus the bonding readjustments, was not attempted here because it would greatly exceed the scope of this work. Appendix Coefficients used in two types of fits of ln R are given in Table 4. Parameters employed in the Gaussian deconvolution of the spectra shown in Figure 4 are presented in Table 5. References and Notes (1) Walrafen, G. E.; Yang, W.-H.; Chu, Y. C.; Hokmabadi, M. S.; Carlon, H. R. J. Phys. Chem. 1994, 98, 4169. (2) Walrafen, G. E.; Fisher, M. R.; Hokmabadi, M. S.; Yang, W.-H. J. Chem. Phys. 1986, 85, 6970. (3) Pine, A. S.; Lafferty, W. J. J. Chem. Phys. 1983, 78, 2154. Pine, A. S.; Lafferty, W. J.; Howard, B. J. J. Chem. Phys. 1984, 81, 2939. Pine, A. S.; Howard, B. J. J. Chem. Phys. 1986, 84, 590. Dayton, D. C.; Jucks, K. W.; Miller, R. E. J. Chem. Phys. 1989, 90, 2631. (4) Walrafen, G. E.; Abebe, M.; Mauer, F. A.; Block, S.; Munro, R. J. Chem. Phys. 1982, 77, 2166. (5) Walrafen, G. E.; Yang, W.-H.; Chu, Y. C.; Hokmabadi, M. S. J. Phys. Chem. 1996, 100, 1381. (6) Landolt-Bo¨ rnstein Physikalisch-Chemische Tabellen, Bo¨rnstein, R., Roth, W. A., Eds.; Julius Springer Verlag: Berlin, 1912.
J. Phys. Chem. B, Vol. 101, No. 17, 1997 3399 (7) Herzberg, G. Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945. (8) Walrafen, G. E.; Chu, Y. C. J. Phys. Chem. 1992, 96, 9127. (9) Gigue`re, P. A. J. Chem. Educ. 1979, 56, 571. (10) Walrafen, G. E.; Hokmabadi, M. S.; Yang, W.-H. J. Chem. Phys. 1986, 85, 6964. (11) Newton, M. D.; Ehrenson, S. J. Am. Chem. Soc. 1971, 93, 4971. (12) Roth, W. A. Z. Elektrochem. 1944, 50, 107. (13) Lide, D. R., Ed. J. Phys. Chem. Ref. Data 1985, 14, 1015; JANAF Thermochemical Tables, 3rd ed., Part II, Cr-Zr. (14) Triolo, R.; Narten, A. H. J. Chem. Phys. 1975, 63, 3624. (15) Haar, L.; Gallagher, J. S.; Kell, G. S. NBS/NRC Steam Tables Hemisphere: New York, 1984. Franck, E. U.; Spalthoff, W. Z. Elektrochem. 1957, 61, 348. (16) Johnson, G. K.; Smith, P. N.; Hubbard, W. N. J. Chem. Thermodyn. 1973, 5, 793. (17) Walrafen, G. E.; Chu, Y. C. J. Phys. Chem. 1995, 99, 10635. (18) Walrafen, G. E. J. Chem. Phys. 1962, 36, 1035; 1964, 40, 3249; 1966, 44, 1546; 1967, 47, 114. (19) Walrafen, G. E.; Fisher, M. R.; Hokmabadi, M. S.; Yang, W.-H. J. Chem. Phys. 1986, 85, 6970. (20) Handbook of Chemistry and Physics, 67th ed.; Weast, R. D., Ed.; CRC Press: Boca Raton, FL, 1985-1986. (21) Hepler, L. G.; Woolley, E. M. In WatersA ComprehensiVe Treatise; Franks, F., Ed.; Plenum: New York, 1973, Vol. 3, Chapter 3. (22) Klotz, I. M.; Rosenberg, R. M. Chemical Thermodynamics, 5th ed.; Wiley: New York, 1994; p 52. (23) Herzberg, G. Molecular Spectra and Molecular Structure. I. Diatomic Molecules; Van Nostrand: New York, 1945. (24) Pauling, L. The Nature of the Chemical Bond; Cornell University Press: Ithaca, NY, 1948; p 297. (25) Dixon, H. P.; Jenkins, H. D. B.; Waddington, T. C. J. Chem. Phys. 1972, 57, 4388.
