R. Thomas Myers
The Strength of the Hydrohalic Acids
Kent State University Kent, Ohio 44242
, The hydrohalic acids show some unique features. H F is a weak acid, and the others are all strong. The order of strength is generally given as HI > HBr > HC1 >> HF, which is contrary to a naive expectation based on electronegativity of the halogens. The first three are even sometimes assumed to have essentially infinite ionization constants (in water), although the presence of HCl(g) above hydrochloric acid solutions contradicts this. I t is impossible to determine experimentally the ionization constants of the first three (above), because the concentration of H X molecules in the solution is too small to measure. Therefore some assumption or assumptions must be made in order to calculate the ionization constant. I t is i m ~ o r t a n tthat anv assum~tionsmade lead to data which are consistent with known facts, and these data must agree with chemical intuition. The hvdroeen halides offer a unique example for which all of t h e various factors involved in acid strengths may be separated out, quantified, and comparisons made. This is therefore an excellent example for our students. When speaking of the strength of an acid it is necessary to state which base i t is being reacted with. Commonly this hase is water, and that is the one we will be using. The strength of the acid is therefore given by the size of the equilihrium constant for the following reaction
I t is important to note that the species on the left is the solvated molecule. Born-Haber Cycle
In trying to understand the equilibrium process above it is common to break the reaction into several parts, and use a Born-Haber cycle to evaluate their contributions. (In fact when we say we "understand" a reaction i t frequently means that we are aware of and have evaluated the iarious steps in this cycle.)
Table 1. Enthalpy of Hydration of Hydrogen-Banding Molecules Ikcsllmolel HCOOH CH,COOH
Table 2.
HF HCI
-11.20
-12.79
NH, CH,NH, ICH.).CHNH,
-
8.17 -11.28 -12.47
CH,OH -10.82 C2HsOH -12.7
Born-Hsber Data for H F and HCI
AH,
AH,
AH,
AH,
AH,
AH
11.7 (12.5)
135.8 103.2
231.5 227.2
-268.6 -268.6
-113.4 -79.6
-3.00 (-5.4)
Table 3. Free Energy of Hydration of Gaseous HydrogenBonding Molecules Ikcallrnole)
tion ( I ) of gaseous hydrogen-bonding molecules of a homologous series, Table 1, then the fact emerges that the enthalpies of hydration are quite close to each other, becoming slightly more negative as size increases. For H F the value is -11.7 kcallmole, so for HC1 one would expect approximately -12.5, with an accuracy of *1 kcallmole. Another difficulty is that the enthalpy of aqueous ions is relative to H+, arbitrarily taken to he zero. However, various theoretical calculations are now dependable enough t o assign (2) absolute enthalpies of hydration of gaseous ions. Those of interest are: H', -268.6; F-, -113.4; C1-, -79.6; Br-, -71.5; I-, -64.8. We are now in position to tabulate the data for H F and HC1. One can of course see that the hond energy (AHn) for H F is much higher than for HCI, but the energy regained by solvation of F- is much greater than for C1-. In fact the sum of AH2 and A H 5 is almost exactly equal for these two substances. HF 135.8 - 113.4 = 22.4 HCI 103.2 - 79.6 = 23.6
+
+
+
+
AH = AH, AHz AH3 AH4 AHs. A H 3 includes the electron affinity of the halogen along with the ionization energy of hydrogen, but the latter is constant for the series, as is also the solvation energy of HC(g), so the latter two can he neglected in comparisons. The very low acid strength of HF, as compared to HC1 is frequently attributed to the high hond energy of HF. We will see if one is justified in coming to this conclusion. This can be accomplished by tabulating the individual enthalpy changes. Immediately, we are blocked, because AH1, the negative of the enthalpy of hydration of the H X molecule, is not available for HCI. But there is a good way to approximate this quantity. If one compares the enthalpy' of hydra-
Because of the cancellation of these two factors, the quantity which makes the difference is the smaller A H 3 (which includes electron affinity of halogen) for HF. One can just as well say that HC1 is a stronger acid than H F because the electron affinity of C1 is greater than F, although all factors contribute to the result. In any event the enthalpy of ionization of both acids is rather negative, and from this view.point both should he rather strong acids. Free Energy Calculations
As stated in the beginning, what is needed is the size of the ionization constant of reaction (1).This can be obtained only from free energy data, so the previous calculation utilizing enthalpy changes is only suggestive, and by no means conclusive. We are in luck when we examine the free energy change for the process of removing the H X from water. Table 3 gives the free energy of hydration of molecules (homologous series) which form hydrogen bonds 'All thermodynamic data are taken from Technical Note 270, ref. (I),unless stated otherwise. Volume 53, Number 1. January 1976 1 17
with water. By a felicitous conjoining of enthalpy and entropy changes, the free energy of hydration is almost independent of size, for homologous series. For HF(g) the standard free energy of hydration to HF(aq) is -5.65, so for the congeners we can choose -5.6 kcallmole, and be confident of rather accurate figures. There is additional evidence. The standard free energy of solution of the non-polar inert gases is nearly constant, the figures being 4.6, 3.9, 3.6, and 3.2, for He, Ne, Ar, Kr, Xe, respectively. Even more cbnvincing, because both electronegativity and size differences are involved, are data for CH3F and CH3Cl. For these compounds the standard free energies of solution (3) of gaseous molecules are +1.7 and +1.4, respectively. If the data are significant to two figures, then one sees that the value for CH3C1 is more negative than for CHsF, even though the latter is more polar. (Although the dipole moments are essentiallv eoual. the bond leneth in CHlF is considerablv smaller; so the actual charge involved is higher.) Finally, in Table 3. one sees that even for CH-OH and CH2NHn. " -. of similar size but different electronegativity, the free energies of solution are very close. In addition to the standard free energy of the aqueous molecules. we also need standard free enemies of formation of the gaseous ions. These are available frim enthalpies ( 1 ) and straightforward statist:cal mechanical ralrularions of entropy (4-5). The results are given in Table 4. These data are used to calculate the standard free energy changes in a Born-Haher-type cycle. In the case of the hydration of the gaseous ions, these are again referred to an arbitrarily assigned entropy of zero for H+(aq). However, there are those ( 6 )who think that the actual entropy of H+(aq) is close to zero. Therefore if we use the absolute enthalpies of hydration and the standard entropy of hydration, then "absolute" free enereies of hvdration can be calculated. These. and the other data, are tabulated in Table 5, along with the calculated ionization constant for reaction (1). . .. AGO = RTlnK,. We are finally in position to compare and understand the differences in the strength of the hydrohalic acids in aqueous solution. Comparing the free energy of bond breaking (AGzO)and the free energy of hydration of X-
Table 4. Standard Entropies and Free Energies of Formation of Gaseous Ions at 298-K
s" I.")
AGP
4.99
electron
Ht
0 362.57 ~ 6 6 . 3 ~ -60.3
26.01 34.78 36.64
F-
CIBrF
39.06 40.54
1-
60.6
-53.45
Table 5. Standard Free Energy Changer far a Born-Haber-Typ Cycle for the Hydrogen Halides
AG,"
AG,"
AG:
AG."
AG."
AG"
Ki
*
HCI 96.6 - 72.7 = 23.9 HBr 81.06 - 66.0 = 15.0s HI 64.97 - 60.6 = 4.37 We find that the free energy changes are distinctly different, even for H F and HCI. A negative enthalpy change for the ionization of H F has now become a positive free energy change. The chief contribution to this change from negative to positive is the very large negative entropy of hydration of F- (-38.1 eu versus -23.1 for HCI). One could say, without too much exaggeration, that H F is a weak acid because of entropy effects, although all of the factors contribute to the acid strength of the hydrohalic acids. The comhination of all factors causes H F to he a weak acid, HCl to be a strong acid, and HBr and HI to he very strong, with about equal ionization constants for the latter two. Comparison with Other Calculations I t was stated a t the outset that some assumption(s) are needed in order to compare HF, HCI, HBr, and HI. I t was also stated that these assum~tiousmust be self-consistent. and must lead to data whici fit other chemical knowledge and our chemical intuition. Other calculations do not satisfy these criteria. (Some of what I give here is the Bell, ref. (7), with more complete citations.) The calculations of McCoubrey (8) are sometimes uncritically accepted, without probing the strange chemical logic involved. He assumes that the enthalpy of hydration 18 1
Journal of Chemical Education
of HC1 will be the average for Ar and CHaCl, giving -4.0 kcallmole. Now CHsCl is of course polar, but it is larger than HCI, and cannot form hydrogen bonds with the water: one cannot expect HCI to behave like Ar and CHzCI upon dissolution in water. The error of the calculation can he seen by applying the logic to HF, using Ne and CH3F (3). The result is (-2.9 - 4.3i12 = -3.6 kcallmole, as compared to an experimental value of -11.7. These data were not available to McCouhrey, but they show that his procedure for estimating energy of hydration is untenable. Another assumption made (cf. references in Bell), is that Raoult's law is oheyed by the H X molecules in solution. If no other information at all is available this is justified, provided that it leads to reasonable figures. I t does not, as we shall see. Using Raoult's law the ionization constant of HCI is calculated to be about 1 X lo7. Using this figure the standard free energy change for reaction (1) is -9.55 kcallmole, and the standard free energy of formation of HCl(aq) is -21.8 kcallmole. This leads to a standard free energy of solution of HCllg) of +1.0 kcallmole. All other substances which form hydrogen bonds with water have large standard negative2 free energy of solution. That H X molecules should form hydrogen bonds with water is expected, because they all form strong hydrogen bonds with ethers and ketones, for example (9). We must therefore abandon Raoult's law as a reliable basis for calculations. Is there any experimental precedent for not assuming an ideal solution of H X in water? There are two cases which are pertinent. The first is for the solution of hydrazine in water. The standard free energy of solution of NzHd(g) in water (1 m) is -7.47 kcallmole. This corresponds to a mole fraction of 0.01768. If we assume an ideal solution and correct to a mole fraction of one (hypothetical pure liquid hydrazine with the same properties as the solution) we get -5.08. The actual free energy of solution of NzH4(g) in NzHd1) is -2.40 kcallmole. If Raoult's law is to be obeyed then the equilibrium constant, P(gss)lCjiquid,must remain the same. For this to occur then AG" = -RTlnK,, must remain constant. It does not. The second example is much more pertinent: the dissolution of H F in water. The AGO for solution of monomeric HF(g) in water is -5.65 kcall mole. The equilibrium constant for HF(aq) F? HF(g) is therefore 7 X 10W atmlm. If the solution were 1 X 10-4 rn then the pressure of HF(g) would be 7 X 10-9 atm. Using Raoult's law we calculate that the pressure a t this concentration (mole fraction 1.7 X 10-9 should be 1.21 atm X 1.8 X 10W = 2.2 X atm. A solution of H F in water deThe free energy of solution of the hydrogen halides must be negative; the real question is how much. The previous discussion, centered around Table 3, gives good evidence for believing that AG,' is about the same for all HX.
viates widely from Raoult's law, so HCl is also expected to
-- -
Literature CHed
rleviat* .-- -.
Hogfeldt (10). using an indirect a ~ ~ r o a via c h the Hammett acidity fu~ction;calculates an ionization constant for HCI which agrees essentially with the present one. Summary All hut one of the ~reviouscalculations of the acid strengths of the hydrogen halides are based on untenable hypotheses, or lead to contradicting data, such as a positive standard free energy of solution of the very polar hydrogen halides in water. The present paper presents an assumption, as a basis of the calculation, which is more in line with our chemical knowledge. The present calculated ionization constants for HCl, HBr, and HI are lower than previous figures by a factor of about lo5, although the order of the Ki's remains the same. The (relatively) low value of K; for HC1 explains the rather high pressure of HCI ahove its aqueous solutions.
(1) Wagman, D. D., e t al., "Selected Values of Chemical Thermodynamic Propenies." Tech. Note 270, U S Go*. Printing Office,196b1971. (2) Myers, R. T.. Ohio J. Science. 68.12%7 (19681. and Thornton, J. Amsr. Chsm Soc, 64, 8 2 2 4 (1962): Gleu. D. N., (3) Swain, C. 0.. and Moelwn-Huzhes. E. A,. Disc Forodov Sm.. 15.150-61.1953. (The entmov data ~ r t h ~ i ~ t&'to t e . b e k ~ t e to d oncatmbaphcm.) 1 0 Vasil'eu, V. P.. Zolotareu, E. K.,and Yatsimimk
