Owing to the limited amount experimental data and high degree of association, modeling HF has been proven to be a difficult task. While such is the case for pure HF, adding a highly polar and associating compound like water only increases its complexity. Unlike water that associates in the liquid phase and shows limited association in the vapor phase, HF associates in both liquid and vapor phases. These associating pure components in a mixture forms a variety of cross associates, which in turn affects the properties of aqueous mixtures of HF resulting in a highly non-ideal behavior that does not lend itself to traditional modeling techniques. Earlier studies have failed to provide a reasonable description of this binary mixture because of the complex association interactions between these compounds, which were not adequately modeled. In this work, the phase behavior of this mixture is understood by exploring these strong self as well as cross-association interactions that occurs in this system.

Pure HF was modeled using 14 different association schemes that allow the formations of different physically meaningful oligomers with different distribution schemes (1-2, 1-6, 1-2-6 etc), where the 1-2 scheme allows the formation of monomers and dimers and likewise. The parameters for these pure component association schemes were obtained by correlating the experimental vapor pressure and saturated liquid and vapor volumes. These parameters were also used to predict several other pure component properties such as heat of vaporization, constant pressure heat capacity, constant volume heat capacity etc. The dominance of these association patterns and their respective distribution were understood based on their correlative and predictive ability. Based on the percentage absolute average deviation values for various experimental data over a wide range of operating conditions, the 1-6, 1-2-6, 1-2-6-8, 1-2-3-6-9, 1 to 9 (allows all oligomers up to nanomers) and 1 to 12 were considered to be reasonable in comparison with other association schemes. The results also corroborate the earlier spectroscopic studies that reported the dominance of hexamer rings in HF^1,2 460030004400330037003500340037003000300039003600410033003600380035003600310030003000300030003800330032004300460036003500360045003700320036003600300030003400360034003400420045004200460030003000340035004600390042003600300032003000300030003000300030003000340030003000300030003000310037003900300032003000300030003000300030003200340035004200340033003700350037003200370034003600390037003300370033003200430032003000330031003300390033003800330038003200300032003300330031003300350033004200320030003400430036004600360045003600370032004300320030003300310033003900330034003300330032003000320033003300310033003700350044003000300030004300300030003000300030003000 . The association schemes that allow the formation of hexamers were reported to be with better correlative and predictive ability when compared to the ones without it.

The pure component association schemes that were developed for HF were extended to the binary mixture with water. Initially the mixture is considered to show only self-association interactions with no inclusion of the cross association. The effect of the strong interactions between HF and water is studied by including the cross association interactions through various association schemes. The different cross association patterns that are more likely to occur in the solution are obtained from a hybrid meta density functional theory study on this mixture that was performed at a mPW1B95/6-31+G(d,p) level of theory³ 370043003700420035004100430032003000300037003800410033003600380035003600310030003000300030003800330032004300460036003500360045003700320036003600300030003400360034003400420045004200460030003000340035004600390043003600300032003000300030003000300030003000310030003000300030003000300033003300300032003000300030003000300030003100350035004200340032003600310036003200370035003700320036003100360046003200430032003000330032003300300033003000330037003200300032003300330032003300310033003900350044003000300030004300300030003000300030003000 . The phase co-existence properties were correlated using these different association patterns for the pure components and mixtures using one-parameter van der Waal's mixing rule. The results from some of the self-association schemes are shown in Figure 1.  Several mixture properties such as liquid density, heat of vaporization, constant pressure heat capacity are predicted using these mixture association schemes. The significance of these self and cross-association patterns are studied and understood based on the correlative and the predictive ability of the association schemes.

360033003300420045003200460038003000300034003200410033003600380035003600310030003000300030003800330032004300460036003500360045003600320036003200300030003400360034003400420046003000380030003000340037003100370031003000300032003000300030003000300030003000300030003000300030003000300030003000300030003000300030003000   360033003300420033004400360038003000300034003200410033003600380035003600310030003000300030003800330032004300460036003500360045003600320036003200300030003400360034003400420046003200310030003000340037003700410030004200300032003000300030003000300030003000300030003000300030003000300030003000300030003000300030003000  

Figure 1. T-x-y results for HF-H₂O system at 1 atm from various self-association models. The experimental data from Miki et al, Munter et al and Vieweg et al are indicated by empty symbols.

References:

(1) L. A. Curtiss and M. Blander, "Thermodynamic Properties of Gas-Phase Hydrogen-Bonded Complexes", Chem. Rev, 88, 827, (1988)

(2) R. W. Long, J. H. Hildebrand and W. E. Morrell, "The polymerization of gaseous hydrogen and deuterium fluorides", Journal of the American Chemical Society, 65, 182-7, (1943)

(3) B. Baburao, D. P. Visco, Jr. and T. V. Albu, "Association Patterns in (HF)m-(H2O)n (m + n =8 ) clusters", Journal of Physical Chemistry A, submitted, (2007)