J. Phys. Chem. 1981, 85, 2529-2530
almost as strong as in formic acid or trifluoroacetic acid mixtures, a split of the methylene quartets was not observable any more. Further, the downfield shift of the acidic proton becomes somewhat less pronounced than with the stronger acids. The NMR data for the acidic proton in propionic acid + triethylamine have been measured by different groups under different experimental conditions; they are very sensitive with respect to the purity of the acid. The composition dependence of S for the acidic proton as well as for the methylene protons adjacent to nitrogen does not change significantly when triethylamine is replaced by tri-n-propylamine or tri-n-butylamine. However, a drastic change is observed when the tertiary amines are replaced by the primary n-propylamine. This is shown in Figure 12. It is evident that the acid-amine hydrogen bond is less polar. On the other hand, the methylene protons at equimolar composition are more affected than in the systems with tertiary amines. If we compare this behavior with either the conductivity data or the KV curve of propionic acid + butylamine, it seems again hard to believe that ionization is so strong that
2529
ionized aggregates do account for all of the conductivity. Acknowledgment. We are grateful to the Deutsche Forschungsgemeinschaft for support of the density measurements and to the Deutsche Forschungsgemeinschaft and the Office of Cultural Relations of the Hungarian People’s Republic for facilitating the cooperation between Ruhr-Universitat Bochum and Veszpremi Vegyipari Egyetem. Supplementary Material Available: Tables containing the following: (i) values of excess volumes at various mole fractions of amine ( x 2 ) for the systems formic, trifluoroacetic, propionic, and trimethylacetic acids + triethylamine, propionic acid + di-n-butylamine, and propionic acid + n-butylamine, all at 293.15 and 313.15 K; (ii) electrolytic conductivities of formic, acetic, and propionic acids + triethylamine and propionic acid tri-n-butylamine at 293.15 and 313.15 K, of propionic acid di-nbutylamine at 293.15 and 318.15 K, and of trifluoroacetic acid + triethylamine and propionic acid + n-butylamine at 293.15 K (9 pages). Ordering information is available on any current masthead page.
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Vapor-Pressure Lowering of Anhydrous Hydrogen Fluoride by an Involatile Solute Peter McTlgue Department of Physical Chemistty, Universw of Melbourne, Parkvllle, 3052, Australia (Received: March 17, 198 1)
The extent of the lowering of the vapor pressure of anhydrous hydrogen fluoride (AHF) by an involatile solute is “abnormally” large because of the high degree of association in HF vapor. Existing experimental data are used to illustrate this previously unnoted effect.
The activity of a solvent in a solution at some fixed temperature is given by a =f
/f
(1)
where f and f are the fugacities of the solvent vapor in equilibrium with the solution and the pure solvent, respectively. The vapors of most common solvents behave nearly ideally, and (1)may then be replaced to a fair approximation by a = P/P‘
(2)
where p and p’ are the pressures exerted by the solution and the pure solvent, respectively. If, on the other hand, the solvent vapor is highly associated, a satisfactory approximation to the solvent activity would be
main gas-phase equilibria have been identified as 2HF = (HF), 6HF = (HF), Janzen and Bartel13have analyzed all existing data to 1968 and have prepared tables of the mole fraction of monomeric HF at various total HF pressures up to the saturation vapor pressure, from -36 to 24 “C. From (3), then, the €IF activity of any solution will be given by UHF
= PHF/PHF*
(4)
(3) where pmand pm*are the partial pressures of monomer present in the vapor of the solution and the pure solvent, respectively. Many investigations have shown that AHF is virtually unique among ligands in having a vapor that is highly associated even at quite low The
where pm and pm’ are the monomer partial pressures over the solution and pure solvent, respectively. Figure 1shows a plot of UHF calculated in this way, as a function of total HF pressure at 0 “C, using Janzen and Bartell’s tables and the moxt recent4svalue of p’, the saturation vapor pressure of AHF at 0 “C. The data of Figure 1 can be used to calculate the expected total vapor pressures of HF above solutions of both dissociated and undissociated involatile solutes at 0 “C.
(1)Simons, J.; Hildebrand, J. H. J.Am. Chem. SOC.1924,46, 2183. (2)Janzen, J.; Bartell, L. S. J. Chem. Phys. 1969,50, 3611. (3)Janzen, J.; Bartell, L. 5. U.S. Atomic Energy Commission IS-1940, 1968,and references cited therein.
(4) Sheft, I.;Perkins, A. J.; Hyman, H. J. Inorg. Nucl. Chem. 1976,35, 3677. (5) See, e.g. Robinson, R. A,; Stokes, R. H. “Electrolyte Solutions”; Butterworths: London, 1959; 2nd ed, p 34.
a = Pm/Pm’
0022-3654/8 1/2085-2529$01.25/0
0 1981 American Chemical Society
2530
McTigue
The Journal of Physical Chemistty, Vol. 85, No. 17, 1981
PlmmHg
P/mmHg
360
3 60
\ 350
'\\\\
350
\
3Q
340
330
330
320
320 \
310
099
098
0 97
'\\\ 0,96
0.95
310
0.2
a,
Figure 1. Total HF vapor pressure vs. AHF activity in liquid at 0 O C . aw has been calculated as pmIpHF'(s!e text) from tables given by Janzen and Bartell.3 We have taken p = 360.22 mmHg4 at 0 O C .
The simplest way of estimating the HF activity is to assume that Raoult's law is obeyed, i.e. UHF = X H F (5) where xHFis the mole fraction of HF in the solution. This gives U H F e x H F = (1 + umMHF)-' (6) where MHF is the molar mass of HF, m is the solute molality, and u is the number of particles produced in solution per "formula" of solute. The full lines in Figure 2 were obtained by using (6) to calculate U H F for the cases v = 1 and v = 2, and converting the activities to HF vapor pressures by using Figure 1. At low ionic strengths, Debye-Huckel theory6 can be used to give more accurate predictions of U H F but, on the scale of Figure 1, no significant difference is apparent between the more accurate calculations and those based on (6). However, on this same scale, the effects of association in the vapor appear very large. Thus, the vapor pressure calculated from (6), on the assumption that the vapor is unussociated,is given by the dotted lines in Figure 2. Also included are the experimental data of O'Donnell and Peel.6 Because of the relative simplicity of the ap-
0.4
0.6
o.e
1.0
1.2
m/ mol k$ Figure 2. Total HF vapor pressure vs. solute molality at 0 O C : (-) calculated by using eq 6 and Figure 1, for v = 1 and v = 2 as indicated, (. -) calculated by using eq 6 and assuming that HF vapor is unassociated for u = 1 and u = 2 Indicated. The points show the experimentaldata of ODonnell and Peeke (0)NaF; (+) 2,edinitrotoluene; ( 0 ) 2,4dinitrofluorobenzene.
--
paratus they used, the errors in the measurements they report are a little greater than the expected deviations from ideality. However, within these error limits agreement between theory and experiment is excellent for both a 1:l electrolyte, and two nonelectrolytes. The data thus provide further evidence that NaF is a strong electrolyte in AHF, in agreement with earlier cryoscopic7and conductimetrice measurements. Alternatively, accepting that NaF is indeed a strong electrolyte in AHF, the data support the conclusions of Janzen and Bartell about the degree of complexity of HF vapor at 0 "C. It is apparent that, in the future, vapor-pressure measurements will be a useful source of precise thermodynamic information about solutes in AHF over a wide range of temperatures.
Acknowledgment. Thanks are due to Professor T, A. O'Donnell for helpful discussion. (6) O'Donnell, T. A,; Peel, T. F. J . Inorg. Nucl. Chern. 1978,40,381. (7) Gillespie, R. J.; Humphreys, D. A. J. Chern. SOC.A. 1970, 2311. (8) Brownstein, M. PhD. Thesis, McMaster University, 1970.
