A. J. Kresge and Y. Chiang
822
e Effects on the Ionization of Hydrofluoric Acid'
Department o i Chemistry. iiiinois institute of Technology, Chicago. iilmois 6061 6 (Received October 6, 197%)
Measurements of fluoride ion activities using a selective-ion electrode and hydrogen ion activities using a quinhydrone electrode were performed on dilute hydrofluoric acid and hydrogen fluoride-sodium fluoride buffer solutions in H2O and D20. These determinations lead to pK(H20) = 3.165 rt 0.009, K(H2O)I K(D,O) = 2.05 rt 0.04 for H F = H + 3. F-, and pK(H20) = -0.598 *. 0.010, K(H20)/K(&O) = 1.13 rt. F 3. F- = HFz-. Calculations show that the dominant contribution to each isotope effect comi:s from the twofold change in the moments of inertia of hydrogen fluoride produced by isotopic substitution; zero-point energy effects are small, principally because hydrogen fluoride, being a diatomic molecule, has no bending vibrations.
Hydrogen fluoride is the only diatomic acid available in aqueous solution with which acid catalysis may be studied conveniently. As such, it presents a number of unique opportunities for investigating acid-base catalysis2 and isotope effects.3 In this paper, we determine the solvent isotope effect on the acid ionization (of hydrogen fluoride (eq 1) as well as on the other ionization reaction which it undergoes in aqueous solution: association with fluoride ion to give hydrogen bifluoride (eq 2 ) ~These are quantities without which accurak evaluation of kinetic isotope effects on proton transfer from hydrofluoric acid is not possible. However, the equilibrium isotope effects are of considerable interest in themselves, for they are controlled by the same factors which make the kinetic isotope effect.3 unusual.
HF 3. H 2 0
=
H,OS
+ F-
(1)
HF f F = HF,(2) ydrogen fluoride associates with fluoride ion in additioc to ionizing as an acid is a complication which reduces the accuracy with which the equilibrium constant of either reaction may be determined. In order to compensate for this, a n additional quantity was measured in the present worik; hydrogen ion activities were determined in the usual way with a pH sensitive electrode and fluoride ion activities were measured with a fluoride ion selective-ion electrode. Since hydrogen fluoride attacks glass, a quivrhydrone electrode was substituted for the more usual glass electrode in making the pH determinations. ~ x ~ ~ ~Section i ~ e n t ~ ~ Stock solutions of hydrogen fluoride (Baker, AR), sodium fluoride (Mallinckrodt, AR, dried a t 110" for 24 hr), and hydrogen chloride (Matheson, Reagent) were made from deionized HzO, purified further by distillation from potassium permanganate and sodium hydroxide, or D2Q (Eo-Rad Laboratories, 99.8 atom % deuterium) as received. All solutione were prepared and diluted by weight, and polyethylene vessels (beakers with fitted caps or screw-cap dropping bottles) were used exclusively for all fluoride solutions. Acid concentrations were verified by titration with standard base, and sodium fluoride solutions were checked potentiometrically against fluoride The Journal of Pbysical Chemistry. Vol. 77. No. 6 , 1973
standards (Orion Research, Inc.). Fresh hydrogen fluoride and sodium fluoride stock solutions were prepared daily. Electrode potentials were measured with a Beckman Research pH meter (Model 1019) against an Orion singlejunction reference electrode (Model 90-01) which has a fiber tip and plastic body. The selective-ion electrode was a Beckman lanthanum fluoride membrane assembly (Model 39600), and a length of stiff platinum wire served as the quinhydrone electrode; solutions to be measured were saturated with quinhydrone (Fisher, Reagent). All three electrodes were supported in a snugly fitting Teflon cap specially constructed for the plastic beakers in which the measurements were made, These beakers were clamped in a constant temperature bath operating at 25.0 f 0.01", and a t least 30 min was allowed for their contents to reach bath temperature. Potentials were measured at least in duplicate and were reproducible to 0.1 mV. Both cells were calibrated against reference sodium fluoride or hydrogen chloride solutions immediately before each series of measurements.
Results Potentials of the two cells were translated into hydrogen and fluoride ion activities with the aid of relationships between E and A ( H + ) or A(F-) obtained from calibration measurements on reference solutions. These calibration curves were determined daily; each was based upon measurements on six to eight solutions of different concentration designed to provide a range of E appropriate to the unknowns being examined a t the time. Concentrations o€ these reference solutions were converted into activities using activity coefficients estimated by the Debye-Huckel formula with a n ion-size parameter of 4.5 A. i n all cases, the relationship between E and log A was accurately linear, and slopes were generally well within 1%of the theoretically expected value. Best, values of the slope and intercept parameters were obtained by least-squares analysis, and these were then used to calculate activities from the potentials of the unknown solutions. Reference solu(1) This research was supported by the National Science Foundation through Grants No. GP 6580 and G P 9253 to the illinois institute of Technqlogy. (2) (a) R. P. Bell, "The Proton in Chemistry," Corneil University Press, ithaca, N. Y., 1959, p 179; ( b ) A. J. Kresge and Y . Chiang, J. Amer. Chem. Soc., 90, 5309 (1968); 84, 2814 (1972). (3) A. J. Kresge and Y. Chiang, J. Amer. Chem. Soc.. 91, 1025 (1969).
HF Ionization Solvent isotope Effects
823
TABLE I: Summary of Experimental Results
-No. of solutions
I 02[H
102[NaF],a
PKi
measured
pKzb
Hz0 5.4-0.58 3.1-0.33 8.7-0.78 7 0.9-0.92 6.0-0.63 2.7-a.z:o 2.1-0.21
8 7 8 8
3.164 f 0.002 3.156 f 0.003 3.166 f 0.003 3.1 57 f 0.001 3.159 f 0.003 3.161 f 0.003 3.167 f 0.005 Av 3.161 f 0.004 3.181 f 0.004 3.169 f 0.004 3.164 f 0.003 3.171 f 0.005 3.1 72 f 0.003 Av 3.171 f 0.006 K 2 = 3.96 f 0.09
a 7 7 10 8.5 5.4 6.4 3.5
53-22 45-18 45-8.7 38-1 2 45-1 0
5 5 7 6 6
K t = (6.85 f 0.11) X
-0.589 -0.605 -0.587 -0.605 -0.606 -0.598
f 0.01 1 f 0.003 f 0.005 zk 0.001 f 0.005 f 0.01 0
-0.541 -0.540 -0.547 -0.548 -0.545 -0.545
I- 0.003
D20
7.8-5.3 6.5 4.6 8.4 4.5
3.474 f 0.002 3.475 f 0.007 3.475 f 0.007 3.476 f 0.006 3.480 f 0.003 Av 3.476 f 0.006 K , = (3.34 f 0.04) X K 2 = 3.50 f 0.03 Kl(HzO)/Kq(D20) = 2.05 f 0.04; K~(HzO)/K~(D~O) = 1.13 f 0.03
44-8.7 47-1 6 50-1 5 49-1 5 49-16
a Stoichiometric concentrations.
5 6 6 6 6
-log A(H+)A(F-)/A(HF)
(3)
pK, = .-log A(HF,-)/A(HF)A(F-)
(4)
r
i 0.003 f 0.003
f 0.001 f 0.004
Error limits are standard deviations.
tions prepared from HzO were used for the work in DzO as well as that in HzO, after it was established that E"(D20) - E"(H20) is constant for both electrodes; the+valueof this quantity was 29.65 rt 0.25 mV for the quinhydrone electrode and -0.31 f 0.04 mV for the fluoride ion electrode. Hydrogen ion and fluoride ion activities evaluated in i,his way were used directly in the expressions for pK1 and pM2 (eq 3 arid 4). They were also converted into hydrogen ion and fluoride ioti concentrations, from which, by simple stoichiometry, the concentrations of the other solute species could be calculated; this led to the other activities needed to evaluate pK1 and pK2. In these calculations the activity coefficient of 13F was taken to be unity, and those for the ionic species were estimated as for the reference solutions, i.e., by the Debye-Huckel formula with a n ionsize parameter of 4.5 A. In this case, however, the ionic strength was not known in advance, and the calculations had to be done in an interative fashion; they were performed on a progrninnnable desk calculator (Wang Model 362). pK,
f 0.002
Measurements in W 2 0 were made on unbuffered solutions prepared from hydrofluoric acid alone and also on solutions with added fluoride ion (Table I). The unbuffered solutions contained little HFz- and were thus of little value in determining pK2; their ionic strengths, however, were very low ( I = 0.0001-0.001 M ) , and estimates of activity coefficichnts could therefore be expected to be very good. Since these solutions gave essentially the same
value of pK1 as the buffers whose ionic strengths were considerably higher ( I = 0.03-0.01 M ) , it was concluded that activity coefficients were estimated correctly in the latter cases as well. Measurements in D20 were therefore performed in buffer solutions alone. In no case could consistent trends in pK1 or pK2 with ionic strength be detected, and the results were therefore simply averaged rather thap extrapolated to I = 0. Averages for sets of experiments performed on a single day as well as overall averages are presented in Table I. The weighted average value of pK1 obtained here, 3.165 f 0.007, is in good agreement with the early potentiometric work of Broene and De V r i e ~ who , ~ report 3.17, as well as that of Ellis,s who used a conductometric method to get 3.18 f 0.01. Several more recent investigations have used a fluoride ion electrode similar to the one employed here. Baumann's6 result, 3.164 f 0.010, is in excellent agreement with ours, and Vanderborgh!s7 value, as recalculated by Patel, Moreno. and Pate1,s 3.21 f 0.03, IS not significantly different. Patel, Moreno, and Patel themselves report 3.233 f 0.002, in poor agreement with the present work. The value of pK1 obtained here also gives a self-consistent kinetic analysis of rates of hydrolysis of ethyl vinyl ether measured in buffered and unbuffered hydrofluoric acid solutions, and it is in good agreement with the results of indicator experiments carried out in conjunction with that kinetic work.2b The Patel, Moreno, and (4) H H Broene and T J De Vries J Amer Chem Soc 69, 1644 (1947) (5) A J Ellis,J Chem SOC 4300 (1966) (6) E W Baumann, J lnorg Nuci Chem 31, 3155 (1969) (7) N F Vanderborgh Taianta 15, 1009 (19138) ( 8 ) P R Patel. E C Moreno, and J M Pawl, J Res Nati Bur Stand Sect A , 75,205 (1971) The Journal of Physical Chemistry, Voi 77 No 6. 1973
82
A. J. Kresge and Y. Chiang
LE tl: Resullts of Isotope Effect Calculationsa Reaction .-
M
i-IF 4- H20 = W 3 0 + C F1.012 HF C F - := HF21.036 a ( HF) / Q (DF)= 0.04946 a
MI plus LIBR
2.009
1.903
EXC
ZPE
0.985 0.803 0.971 0.663 Q (HF2 -) / Q (DF2 -) = 0.06213
K ( H z 0 )/ K ( D z O )
1.607 1.268
T = 25O.
Patel value, on the other hand, agrees less well with the indicator determinations and gives a n inconsistent kinetic analysis; when the specific rate for catalysis by H F evaluated from the experiments in unbuffered solutions is used to calculate rates for the buffers, values some 10% greater than observed rates are obtained. This discrepancy is well beyond the accuracy of the kinetic method and is, moreover, in a direction opposite to that expected for additional catalysis by the bifuoride ion. The average value of pK2 obtained here, -0.598 f O.OlCl., is in good agreement with all previous reports of this quantity: -0.E19,~-0.53 f 0.06,5 and -0.7 rk 0.2.6 iscussion
Isotope Effect on: the Acid Dissociation of Hydrogen Fluoride, Solvent isotope effects on acid dissociation constants originate for the most part in zero-point energy differences between reactants and products, and, for acids similar in strength to hydrogen fluoride, generally amount to about a factor of 3 fK(HzO)/K(DzO)).gThe effect observed here, 2.05 & 0.04, i s therefore somewhat weaker than could have !been anticipated. It might, moreover, be unusual in another respect, for hydrogen fluoride is a small diatomic molecule and properties other than its zero-point energy could be affected appreciably by isotopic substitution. An order to investigate this point, as well as to attempt t o account for its magnitude, we performed a theoretical calculation of this isotope effect. The calculation w,as carried out in the usual way by formulating the isot,ope effect in terms of ratios of partition functions of isotopically substituted molecules (eq 5 ).IO The partition fianc;:tion ratios for hydronium ion and water are available from a recent semitheoretical determination.ll That for hydrogen fluoride was evaluated using the vibrational frequency measured for HF in € 3 2 0 solution12 and the theoretically expelcted isotalpic shift, i. e., v(DF) = v(HF) ( ~ ~ H ~ ) / ~ ~ ~where F ) ) l~(1tlF) / z , , and p(DF) are the reduced masses of M F and DF', respectively.
The result, K(I&O)/K(DzO) = 1.61, is in reasonably good agreement with the experimental value, considering the ill-defined nature of the vibrational band of hydrogen fluoride in aqueous !solution.lZ Use of the gas-phase vibrational frequency, which is known with much greater accuracy,l3 gives a result (K(H2O)/K(DzO) = 2.25) in even better agreement wi1,h experiment, but this would seem to be unjustified in view of the fact that the experimental value refers to aqueous solution. These calculations include medium effects on the transfer of' hydronium ton and water species from € 3 2 0 to DzO (as lthrationnl frequency contributions to Q(H30+)/ The Jciurnai of Physicai Chemistry. Voi. 77. No. 6 1973
Q(D30+) and Q(HzO)/Q(DzO)),but they do not allow for similar effects on hydrogen fluoride or the fluoride ion. Two different estimates of the free energy of transfer of fluoride ion14 both predict a medium effect for this species which contributes a factor of 0.85 to K(HzO)/ K(D20). The medium effect on hydrogen fluoride is more difficult to assess; it is, however, likely to be small. Fortunately, much of the insight which these calculations provide into the nature of this isotope effect does not depend a t all strongly upon medium corrections or the choice of vibrational frequency. Table I1 lists separately the contributions to the overall effect made by the translational (M), rotational (MI plus LEBR), Boltzmann excitation of vibrational levels (EXC), and zero-point energy (ZPE) parts of the partition function ratios. It may be seen that the dominant factor is provided by MI plus LIBR. Much of that, moreover, may be traced to the effect of isotopic substitution on the two principal moments of inertia of hydrogen fluoride; this alone contributes 1.90 to K(HzO)/D(DzO). The librational motions of water and the hydronium ion, which replace free rotation in these species, add another factor of 1.06 to bring the overall rotational contribution up to 2.01. In contrast to this, the zero-point energy effect is small and actually inverse. This is a direct consequence of the fact that hydrogen fluoride has no bending vibrations. Even though its single stretching frequency is high, u(HF) = 3450 cm-l,12 that alone is not enough to offset the difference between the frequency sums for hydronium ion and water, Zu(HaO+) - Zv(Hz0) = 12,320 - 8550 = 3770 cm-1.11 As a result, the product of this reaction ( H 3 0 + ) has nearly 0.5 kea1 more zero-point energy than the total for both reactants (HF and HzO), and the zero-point energy factor in the isotope effect is therefore less than unity. It is of interest to compare this situation with the solvent isotope effect on the acid ionization of a less unusual substrate. A typical carboxylic acid, for example. has one stretching, u(0H) 3000 cm-1, and two bending vibrations, u ( 0 H ) 1400 and 900 ~ m - 1 , ~which 5 are sensitive to isotopic substitution. The sum of these frequencies, 5300 cm-1, is considerably greater than the difference between the sums for hydronium ion and water, 3'770 em-l, (9) P. M. Laughton and R. E. Robertson in "Solute-Solvent Interactions," J. F. Coetzee and C. D. Ritchie, Ed., Marcell Dekker, New York, N. Y., 1469, p 407. (10) L. Melander, Isotope Effects on Reaction Rates," Ronald Press, New York, N. Y., 1960; W. A. Van Hook in "Isotope Effects in Chemical Reactions," C. J. Collins and N. S. Bowman, Ed., Van Nostrand-Reinhold, New York, N . Y., 1970, Chapter 1 (11) R. A. More O'Ferrall, G. W. Koeppl. and A . J. Kresge, J. Amer. Chem. SOC..93,1,9 (1971). (12) H. 11. Hyman, M. Kilpatrick, and J. J. Katz, J. Amer. Chem. SOC.. 79, 3668 (1957). (13) K. Nakamoto, "Infrared Spectra of Inorganic and Coordinatlon Compounds," 2nd ed, Wiley-lnterscience, New York, N. Y., 1970, p 78, (14) C. G. Swain and R. W. Bader, Telrahedron, IO, 182 ('1960); E. M. Arnett and D. R. McKelvey in ref 9, p 407. (15) L. J. Bellamy, "The Infrared Spectra of Complex Molecules," Wiley, New Yark, N. Y., 1960, Chapter 10.
HF Ionization Solvent Isotope Effects
825
uncertainty about its direction. Halide ions have medium effects which increase with increasing ion size, with fluoride ion being the only member of the series showing an inverse effect; this suggests that the effect on hydrogen bifluoride might be in the normal direction. Methyl fluoride, on the other hand, although also larger than fluoride ion, has an inverse medium effect;l8 this suggests that the effect on hydrogen bifluoride could be inverse. Here again, however, medium effects do not alter the major conclusions which can be drawn from these calculations. As Table I1 shows, the rotational parts of the partition function ratios once more make the largest contribution to the isotope effect. This time, moreover, the entire MI plus LIBR factor of 1.90 comes from the moments of inertia of hydrogen fluoride, for the only other isotopically substituted species involved, bifluoride ion, is a linear symmetrical moleculel9 whose principal moments of inertia are not affected by isotropic substitution. The zero-point energy effect is again inverse and relatively weak, once more because hydrogen fluoride has no bending vibrations. It is interesting that this factor would have been even more strongly inverse, perhaps enough to make the overall isotope effect less than unity, were it not for the fact that one of the four normal vibrations of hydrogen bifluoride (the symmetrical stretch) is not isotopically sensitive. The inverse nature of the ZPE factor is of K(H,O)/K(D,c)) = (&(HFz-)/Q(DFz-))/(Q(I-IF)/Q(DF)) significance in connection with kinetic isotope effects on (6) proton transfer from hydrogen fluoride, which are also unusually weak, a phenomenon ascribed to strong bending vibrational frequency of H F measured in aqueous solution. vibrations in the transition state which are uncompensatAqueous solution vibrational frequencies were also used to ed for in the diatomic proton donor.3 The present reaction evaluate &(HFp--)/Q(DF2-). In this case, values for DF2is in fact closely analogous to the kinetic situation, for the as well as HF2- are available,16 but, for the sake of consistwo degenerate bending vibrations of hydrogen bifluoride, tency with the hydrogen fluoride calculation, experimental u(HF) = 1206 cm-1, here provide more than half of the numbers for HF2- only were used. Frequencies for DF2product zero-point energy. were calculated from these using the theoretically expected Hindered Rotation of Hydrogen Fluoride Species. Both isotopic shift, which again was equal to the square root of a referee and Professor R. P. Bell (personal communicathe ratio of the reduced masses of the two rn0lecules.~7The tion) have pointed out that hydrogen fluoride will be byDFz- frequerrcies obtained in this way were actually in good agreement with the experimentally observed values, and drogen bonded in aqueous solution, and that its rotations use of the latter would have raised K(H20)/K(D20)by only will thus be hindered rather than free. It would therefore 5%. be more appropriate to replace the moment o f inertia factors in the present calculations by zero-point energy and The calculated isotope effect, Y((H2O)/K(DzO) = 1.27, Boltzmann excitation contributions from librational vibrais in even better agreement with the experimental value, 1.13 f 0.03, than was the case for the acid ionization tions. The necessary frequencies, unfortunately, are not reaction. This time, however, use of the gas-phase freknown, but our work on water and hydronium ion species11 suggests that. such a substitution would, if anyquency for H F shifts the result away from the observed thing, reinforce the conclusion that the isotope effects revalue by a considerable amount, K(H20)/K(D20j = 1.78, ported here are largely rotational (or librational) in origin. and that tends :o reinforce the idea that solution frequencies are more appropriate than gas-phase values for calcu(16) L. H.Jones and R. A. Penneman, J. Chem. Phys., 22,281 (1954). lating solution isotope effects. (17) G. Herzberg, "Molecular Spectra and Molecular Structure." Van No medium thffects are included in these calculations. Nostrand, New York, N. Y., 1945, p 145. (18) C. G. Swain and E. R. Thornton, J . Amer. Chem Soc.. 84, 822 The effect on fluoride ion, evaluated as before, would raise (1962). K(HzO)/K(DzO) by 1/0.85. That on hydrogen bifluoride (19) W. C . Hamilton and J. A. lbers, "Hydrogen Bonding in Solids,'' W. A. Benjamin, New York, N. Y., 1968, p 108. is much more difficult to estimate, and there is even some
and that makes the isotopically sensitive zero-point energy of the reaction product in this case some 2.2 kcal less than the total for the reactants. This contributes a factor of approximately 3.0 to K(H20)/K(D20). It is likely, moreover, that this will be the only significant contribution to this isotope effect, for the moments of inertia of the carboxylic acid will be relatively insensitive to isotopic substitution, and M and EXC will probably contribute little as well. Other weak polyatomic acids will behave similarily, i.e., will receive minor to negligible contributions from M, MI plus LIBR, and EXC to solvent isotope effects on their acid ionization equilibria, which leaves zero-point energy effects as the only important factor. 'The isotope effect on the ionization of hydrogen fluoride is therefore extraordinary in being principally rotational and not vibrational (ZPEj in origin. lsotope Effect on the Association of Hydrogen Fluoride with Fluoride ion. The properties of hydrogen fluoride which make the isotope effect on its acid ionization exceptional also influence the effect on its association with fluoride ion, Agarn, this becomes apparent when a theoretical calculation of the isotope effect is carried out. This calculation was performed an the basis of eq 6 using the value of Q(HF)/Q(DF) obtained as described above from the
The Journal of Physical Chemistry. Voi. 77. No. 6 1973
