WHY IS HYDROFLUORIC ACID A WEAK ACID?' An Answer Based on a Correlation of Free Energies with Electronegativities LINUS PAULING California Institute of Technology, Pasadena, California
OCCASIONALLY a student asks why hydrofluoric acid is a weak acid. He may point out that hydriodic acid, hydrobromic acid, and hydrochloric acid are strong acids, and that hydrofluoric acid contains fluorine, which is a more strongly electronegative atom than the other halogens, and which might accordingly be expected to have a greater tendency to go to the anionic form, F-. In fact, however, the ionization constant of hydrofluoric acid is only 6.7 X lo-', whereas those of the other hydrohalogenic acids are much greater than one. We may answer this question by considering the factors that determine the free energies of the hydro~en halogenide molecules and of the haLgenide ions. Let us consider first the free energy of formation of hydrogen ion, H f , and halogenide ion, X-, in aqueous solution a t unit activitv. d . Values " , from Hde) - ,.,, and X -d~.., of A F O for the reactions
of these ions (plus hydrogen ion) in aqueous solution is plotted against the electronegativity of the atoms. It is seen that the points lie nearly exactly on a straight line, the equation of which is AFo = -34.7 I(
- 2.1) kcsl./mole
We conclude that the free energy of formation of the halogenide ions is a linear function of the electronegativity of the halogen. Although this had uot been predicted, i t is, I think, not unreasonable. Now let us consider the free energy of formation of hydrogen halogenide molecules, HF, HCI, HBr, and HI, in aqueous solution. Values of AFVor the reactions
are given in the table. The value for hydrogen fluoride is an exnerimental one.2 The values for the other three hvdroaen halogenides are the values of AF" for the formation of the gaseous molecules with an estimated correction for the free energy of solution. It seems are given in the table. These values have been ob- likely that the correction for the free energy of solution tained from those given by Latimer2by correction from of hydrogen chloride, hydrogen bromide, and hydrogen the standard state to the gaseous state of the halogen. iodide to form the unionized molecules in aqueous soluWe may well expect that for a series of closely similar tion is very close to zero. The standard free energy of atoms, the halogen atoms, the free energy of formation solution of phosphine is 2.6 kcal./mole, and that of of the negative halogenide ion in aqueous solution would hydrogen sulfide is 1.4 kcal./mole, and we might feel depend in a simple way on the electronegativity of the justified in extrapolatiug from these two molecules to a t o m . V h e values of the electronegativity of fluorine, hydrogen chloride, obtaining a value close to zero. The chlorine, bromine, and iodine are 4.0, 3.0, 2.8, and 2.5, free energies of solution of arsine and hydrogen selenide respectively. In the fimre the free enerm of formation are 2.8 and 1.4 kcal./mole, respectively, and also Contribution No. 2032 from the Gates and Crellin Labora- suggest extrapolation to the value zero for hydrogen tories of Chemistry, California Institute of Technology, Pasadens, bromide. The value for stibine is 2.8, the same as that Californin.~ - -..~ .. arsine, and we accordingly accept zero for hydrogen ' LATIMER,W. M., "Oxidation Potentials," 2nd ed., Prentice- for iodide also. Hall, h e . , Neu.York, 1952. The calculated values of the standard free energy of PAULIN~, L., J. Am. Chem. Soc., 54, 3570 (1932). formation of nndissociated hydrogen halogenide molecules in aqueous solution are plotted as open circles in Standard F ~ E n e r g i e of s Formation at 2S'C. of Hydrogen ~t is seen that the values for hydrogen ioIons Plus Halogenide Ions end of Hydrogen Halogenide the figure. Molecules in houaaua Sdutian dide. hvdroeen bromide. and hvdroeen chloride lie Y","
Hydrogen fluoride Hydrogen chloride Hydrogen bromide Hydrogen iodide
-66.08
"."
bnal 1. ~.. ~ 1 . .u-.,,
-31.35 -24.95 -14.67
I
T n
.
-70.41
,
"."A..
-22.8 -13.1 - 2.0
for hydrogen fluoride lies below the valie for the ions. This means that the ions are more stable than the undissociated molecules for the heavier halogenides, and less stable for hydrogen fluoride. A curve that approximates roughly the values for the
VOLUME 33, NO. 1, JANUARY 1956
acter to a greater amount than the fluoride ion is stabilized by its electron affinity, etc. From the values given in the table (the vertical separation of the full circles and open circles in the figure) we can calculate the equilibrium constants of the The value 2.1 that appears subtracted from x, the hydrogen halideswith use of the equation APo = -RT In electronegativity of the halogen, is the electronegativity K. The calculated values are uncertain because of of hydrogen. This equation, involving the square of a uncertainty in our estimate of the standard free energy difference in the electronega,tivities, was introduced of solution of the undissociated molecules. The values over 20 years ago to express the heat of formation of of the acid constants obtained in this way are 2 X lo6 hydrogen halogenide molecules and other molecules for HCI, 5 X lo8for HBr, and 2 X lo9for HI.& These containing single bonds between unlike atoms from acids are accordingly very strong acids. elementary molecules containing single bonds.3 The I t need not surprise us that the acid strengths inexpression is of course only a rough approximation and crease rapidly in the sequence HF, HC1, HBr, HI. The the experimental points do not lie exactly on the dashed same increase is observed also for the sequence H1O, line in the figure. Nevertheless, it is important t o reHzS, HnSe, and H,Te. If the activity of water is taken member that there is a sound theoretical reason for as its molal concentration, its first acid constant is 2 X expecting the enthalpy of formation of compounds in- 10-l6. The first acid constants of H2S,HSe, and H,Te volving single bonds with hydrogen, for example, when are 1.1 X lo-', 1.7 X and 2.3 X respectively. plotted as a function of the electronegativity of the We see that these four very weak acids have a total atom bonded t o hydrogen, to he represented by a pa- span of their first acid constants of loi3; hydrogen rabola,with its maximumat x = 2.1,theelectronegativity telluride is lox3times as strong an acid as water. Simof hydrogen. The dashed curve in the figure represents ilarly, the hydrogen halogenides have a span of 1018, one side of this parabola. We may expect that the free hydrogen iodide being l0I3 times as strong as hydrogen energy of formation of the hydrogen halogenides in fluoride. The intermediate acids in each series occupy aqueous solution will depend .on the electronegativity similar positions. of the halogen atoms in a way not greatly different from The energy of stabilization of covalent bonds by parthe enthalpy of formation of the hydrogen halogenides, tial ionic character is accordingly so great for the bonds and accordingly the parabolic curve, represented by the between hydrogen and the most electronegative atoms, dashed line, is the expected approximation. fluorine and oxygen, as to overcome the anion-forming We can now understand why hydroflnoric acid is a t,endency of these atoms and t o cause hydrogen fluoride weaker acid than the other hydrohalogenic acids. The and water to be much weaker acids than the hydrogen stabilization energy of the halogenide ions is a linear comaounds of their heavier congeners. function of the difference of the electronegativity from Since this paper was written, s, rather similar evaluation of the that of hydrogen, and these ions become the more stable, the more the electronegativity of the halogen differs acid strengths of the hydrogen halogenides has been published, J. C., T~ans.Favadav Soe., 51, 743 (1955). by MCCOUBREY, from that of hydrogen. I n consequence, the standard The values of K calculated by McCoubrey for HCI, HBr, and free energy of formation of hydrogen ion and fluoride HI are 107, log,and 3 X lo9,respectively. ion in aqueous solution is about twice that of hydrogen ion and chloride ion. On the other hand, the free energy of formation of a hydrogen halogenide is a quadratic function of the difference in the electronegativity of the halogen and hydrogen. When this difference is small, the free energy of formation of the molecule is very small, and it increases rapidly with increase in the difference. We mould expect that the standard free energy of formation of undissociated hydrogen fluoride would be four times that of hydrogen chloride, and it is in fact over three times as great. I n consequence, the two curves, the dashed curve and the straight line, cross for a value of the electronegativity that lies hetween that of chlorine and that of fluorine. The undissociated hydrogen chloride molecule is stabilized by its partial ionic character to a smaller amount than the Standed €--energy Cheng. for ths Reaction of Gassous Hydrochloride ion is stabilized by its electron affinity, heat of The g.n and H.1og.n Molacules t o Form Hydrwe" Helogenid. Molecular hydrat,ion, etc., whereas the undissociated hydrogen in A g ~ e o - solution (Open Circles) and Hydr-n Ion Plva Hdogenide Ion in Aqueous Solution (Fillad Circles). fluoride molecule is stabilized by its partial ionic charundissociated molecules is shown as a dashed curve in the figure. This curve is a parabola, with equation
