Research: Science and Education
The Strength of the Hydrohalic Acids Roland Schmid* and Arzu M. Miah Institute of Inorganic Chemistry, Technical University of Vienna, A-1060 Vienna, Austria; *
[email protected] The strength of an acid HX in water is given by the position of equilibrium between the undissociated and the dissociated forms, HX(aq)
H+(aq) + X ᎑(aq)
(1)
It is important to note that the species on the left is the solvated molecule. In the series of the hydrogen halides this equilibrium can be determined experimentally only for HF. For the others, the concentration of the HX molecules in the solution is too small to measure. In these cases the acid strengths have been estimated from the partial vapor pressure of HX over concentrated aqueous solutions, assuming that Raoult’s law is obeyed. The literature values of pK a so obtained, given in Table 1, appear to be taken from Bell (1). Support of the value for HCl has been provided by Robinson and Bates (2), from the agreement of the value of pK a derived from partial pressure measurements of HCl over solutions dilute with respect to HCl and concentrated with respect to LiCl and those calculated from data for solutions containing HCl alone. Although it was later shown by Myers (3), reinforcing an earlier criticism by Högfeldt (4), that Raoult’s law must be abandoned as a reliable basis for the calculation of acidity, these antiquated values continue to be quoted in recent text books (5–9). Clearly, in the Born–Haber-type cycle shown in Figure 1, the free energy ∆G1° of dehydration of a neutral molecule is the indeterminate quantity, while ∆G 2° is accurately known using the current edition of the CRC handbook, Section 5 (10). From these two quantities, the free energy ∆G ° of ionization, and hence the wanted dissociation constant, can be derived, 2.303RT (pKa) = ∆G ° = ∆G1° + ∆G2°
(2)
For the assessment of ∆G1° two methods have been suggested. Myers assumed that ∆G1° might be similar for homologous series. Therefore he adopted the measured value for HF (Table 1) for the congeners also (3). Pearson suggested that
4
+
H(g) + X(g)
H
(g)
᎑
+ X (g)
∆hydG °(HX) ≈ ∆hydG °(CH3X) be used as an approximation (11). The free energies of solvation of the methyl halides are available (12). However, the more polar the H–X bond the less reasonable is this assumption (note the large difference between ∆hydG °(HF) = ᎑23.4 kJ and ∆hydG °(CH3F) = +7.1 kJ). Thus the applicability of this approximation to the cases of HCl and HBr is highly questionable, although the figure for HCl (+5.9 kJ) is retained in the recent literature (13). Without a detailed analysis, even the sign of the free energy of hydration for HCl and HBr cannot be predicted. The overall solvation energy represents the competition between a positive cavity-formation energy and a negative solvation energy. The latter involves not only the dipole–dipole forces, but also dispersion and induction forces. Dispersion forces result from dipolar interactions between the virtually excited dipole moments of the solute and the solvent. Induction forces are caused by the interaction of the permanent solute dipole with the solvent dipoles induced by the solute and solvent field. There is now evidence that dispersive interactions are also important in highly polar solvents (14), in contrast to the traditional point of view. Table 1. Standard Free Energy Changes and Acidity Constants of HX ∆G1°/kJ mol ᎑1 Calcd
Exptl
∆G2°/ kJ mol ᎑1
HF
+23.5
+23.64
᎑6.12
HCl
+13.4
—
᎑35.92
᎑22.5
᎑3.9
᎑7
HBr
+17.4
—
᎑50.49
᎑33.1
᎑5.8
᎑9
᎑6.1
—
᎑53.42
᎑59.5
᎑10.4
᎑10
HX
HI
pKa ∆G °/ kJ mol ᎑1 This Work 17.52
Lit.
3.1
3.1
NOTE: Based on pathways in Fig. 1.
Table 2. Molecular Properties of Gaseous HX HX
µ /D
σ /Å
HF
1.826
3.148
330
0.80
HCl
1.109
3.339
344.7
2.63
HBr
0.827
3.353
449
3.61
HI
0.448
4.211
288.7
5.45
(ε /k )/K
α /Å 3
3 HX(g) 2
HX
1 HX(aq)
H+(aq) + X᎑(aq)
Figure 1. Thermodynamic cycle for determination of the acid strengths of HX.
116
Table 3. Standard Free Energy Changes for the Born–Haber-Type Cycle of Figure 1
5
Free Energy Change/ kJ mol ᎑1 ∆G1°
∆G3°
∆G4°
∆G5°
∆G °
HF
23.64
541.0
989.6
᎑1536.7
+17.52
HCl
13.4
403.9
968.8
᎑1408.6
᎑22.5
HBr
17.4
339.0
992.7
᎑1382.2
᎑33.1
HI
᎑6.1
271.7
1022.1
᎑1347.3
᎑59.5
Journal of Chemical Education • Vol. 78 No. 1 January 2001 • JChemEd.chem.wisc.edu
Research: Science and Education
Fortunately, these fundamental solvation terms are becoming amenable to an adequate treatment. Here we utilize the scheme developed in a previous paper (15). Accordingly, the solvent is modeled by spherical hard molecules of spherical polarizability, centered dipole moment, and central dispersion potential. The parameters used for the gaseous HX molecules, namely the dipole moment, the effective radius, the Lennard– Jones (LJ) energy, and the polarizability, are summarized in Table 2. Unfortunately, the values of σ and ε/k, taken from ref 16, do not show a smooth trend in the HX series, and this feature is reflected in the values of ∆G1° in Table 1. Notwithstanding this shortcoming, the overall trend seems reasonable. In the case of HF, the calculation can be checked against experiment. The exact coincidence shown in Table 1 is surely fortuitous, however. The calculated value represents ∆A(T,V ), which is related to ∆G (T,P) via ∆G = ∆A + P∆V. Fortunately, when water at ambient conditions is the solvent, the volume change arguably is negligible (13). Another independent check involves the rather nonpolar HI, for which our calculated value compares favorably with the experimental hydration free energy of MeI, which is +4.69 kJ. This correspondence seems plausible, since it can be assumed that the increase in the cavity formation energy in going from HI to MeI tends to be compensated by the increased dispersion forces due to the higher polarizability of MeI. In contrast to Pearson’s hypothesis, the hydration free energies for neutral HCl and HBr are clearly negative. Likewise, the indirect approach via the Hammett acidity function (4 ) underestimates the solubility of the two acids. It should be mentioned that our values of the free energies of hydration for HF and HCl are similar to those based on a self-consistent reaction field model of solvation (17). For our scheme, the calculation of the dispersion solvation component is not straightforward because the particles have different LJ energy and different size. The commonly applied combining rules appear to be adequate only if solute and solvent molecules are similar in size. Thus, in ref 15 we introduced empirical coefficients to get agreement between calculated and experimental solvation energies for selected inert gases and nonpolar large solutes. This empirical scaling was used in the present calculations. Although it is to be expected that the methods for calculating the various solvation components, and particularly that of dispersions, will be improved further, we believe that our present suggestions for the values of ∆G1° are reasonable. As another point of concern, the impact of quadrupolar solvation should also be investigated in more detail (18). On the other hand, the fact that a hydrogen-bonding solvent is dealt with (i.e., where specific solvent effects not yet amenable to adequate treatment are involved) should not worry us too much. There are reasons to believe that solvent reorganization is locked into exact enthalpy–entropy compensation (19). Therefore, the structural peculiarities of the water solvent can be expected to be of minor importance for the hydration free energies (15). The hydrogen halides offer an example in which the various factors involved in acid strengths may be separated.
This is accomplished by tabulating the individual free-energy changes according to Figure 1, as shown in Table 3. Such an analysis is already available (3), but we present the updated figures. The necessary thermodynamic data are taken from ref 10, except for the ionic gas-phase entropies, which are taken from Krestov (20). The ∆G5° values were calculated from the difference, ∆G5° = ∆G2° – ∆G3° – ∆G4°. The very low acid strength of HF relative to HCl is frequently attributed to the high bond energy of HF. However, inspection of Table 3 reveals that no single factor is predominant. In particular, the extensive compensation of the free energy of bond breaking (∆G3°) and hydration (∆G5°) is noteworthy, as the sum ∆G3° + ∆G5° gradually becomes more negative in going down the series. It is concluded that HCl is a much stronger acid than HF because of the higher electron affinity of Cl (50%), the lower solubility of HCl (25%), and a more negative sum ∆G3° + ∆G5° (25%), relative to the fluorine analog. Literature Cited 1. Bell, R. P. The Proton in Chemistry, 2nd ed.; Cornell University Press: Ithaca, NY, 1973; pp 87–91. 2. Robinson, R. A.; Bates, R. G. Anal. Chem. 1971, 43, 969. 3. Myers, R. T. J. Chem. Educ. 1976, 53, 17. 4. Högfeldt, E. J. Inorg. Nucl. Chem. 1961, 17, 302. 5. Shriver, D. F.; Atkins, P. W. Inorganic Chemistry, 3rd ed.; Oxford University Press: Oxford, 1999; p 146. 6. Holleman, A. F.; Wiberg, E. Lehrbuch der Anorganischen Chemie, 101th ed.; Walter de Gruyter: Berlin, 1995; p 238. 7. Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements; Pergamon: Oxford, 1984; p 59. 8. Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry: Principles of Structure and Reactivity, 4th ed.; HarperCollins: New York, 1993; p 349. 9. Atkins, P. Physical Chemistry, 5th ed.; Freeman: New York, 1994; p C18. 10. Handbook of Chemistry and Physics, 79th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1998; Chapter 5. 11. Pearson, R. G. J. Am. Chem. Soc. 1986, 108, 6109. 12. Swain, C. G.; Thornton, E. R. J. Am. Chem. Soc. 1962, 84, 822. 13. Balbuena, P. B.; Johnston, K. P.; Rossky, P. J. J. Phys. Chem. 1996, 100, 2706. 14. Matyushov, D. V.; Schmid, R.; Ladanyi, B. M. J. Phys. Chem. B 1997, 101, 1035. 15. Matyushov, D. V.; Schmid, R. J. Chem. Phys. 1996, 105, 4729. 16. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases & Liquids, 4th ed.; McGraw-Hill: New York, 1987; pp 733 ff. 17. Chipot, C.; Gorb, L. G.; Rivail, J. L. J. Phys. Chem. 1994, 98, 1601. 18. Matyushov, D. V.; Voth. J. Chem. Phys. 1999, 110, 3630. 19. Grunwald, E.; Steel, C. J. Am. Chem. Soc. 1995, 117, 5687. 20. Krestov, G. A. Thermodynamics of Solvation: Solution and Dissolution; Ions and Solvents; Structure and Energetics; Ellis Horwood: New York, 1991; p 39 ff.
JChemEd.chem.wisc.edu • Vol. 78 No. 1 January 2001 • Journal of Chemical Education
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