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The Journal of Physical Chemistry, Vol. 83, No. 16, 1979
TABLE I Q,(I
samde Bi,O,MoO,
E,,
kcal/
kcall
mol
mol
2.63
E,,
kcall mol
5.65 -2.73
0,
-1
3.81 7.01 -4.33 -1 8.3gb 11.84 -4.88 0.976 16.72 Q' = -R[d lnp,/d(l/T)]. For e * * = 0.016.
Bi,O32MoO, Bi20,3MoO, a
Q, kcall mol 8.38 11.34
in ref 5. In essence the pressure buildup was recorded as a function of time. The pressure reached after 12 h is taken as the equilibrium pressure. The largest part of the enclosed volume was kept at 300 K. The main results are summarized in Table I. The table shows that when Bo 1 the ratio Q/Q' is about 3, while when 8** is comparable to 1- Bo, as it is the case with the 2:3 compound, the ratio &/&'is about 2. The modified Clausius-Clapeyron equation (eq 9') provides similar values for the ratio &/&', namely, 3 for the 2:l and 1:l compounds and 1.8 for the 2:3 compound. The small discrepancies are probably caused by the fact that the equilibrium pressure is not fully reached even after 12 h. An unexpected byproduct of Table I is the negative activation energy obtained for the adsorption coefficients. This can be explained as follows: The interaction potential vs. the reaction coordinate has two wells, separated by a potential barrier. Both wells and the top of the potential barrier have negative energies. The oxygen molecules are adsorbed in the potential well furthest from the surface; then they move over the potential barrier to arrive as oxygen ions at the well nearer the surface. Because the top of the potential barrier has a negative energy, the kinetic energy which the O2 molecules acquire by moving from the zero energy at large distances to the well furthest from the surface overcomes the potential barrier and therefore the apparent activation energy is negative. An alternative explanation must be used if the potential barrier is sufficiently high. In these circumstances one can
-
J. SzydYowski and M. Zielinski
assume that the concentration of the molecules of oxygen in the furthest well is in equilibrium with that in the bulk gas and hence the former concentration is larger than the latter by a Boltzmann factor containing the energy of the furthest well. Since we assume that the top of the potential barrier has a negative energy, the absolute value of the energy of the furthest well is larger than the height of the barrier and, therefore, the apparent activation energy for the adsorption from the bulk is negative.
Conclusion Two methods, a thermodynamic and a kinetic one, are examined concerning the deduction of the isosteric heat of adsorption from experiments at constant volume. They are used to confirm by their comparison the derived thermodynamic equations. Concerning the thermodynamic method, a modified Clausius-Clapeyron equation is derived which accounts for the constraint of the constant volume. Conditions are specified under which the modified form reduces to the traditional one. Concerning the kinetic method, equations are formulated which allow the computation from the pressure buildup in time of the activation energies for desorption and adsorption and hence of the isosteric heat of adsorption. As a byproduct the finding and explanation of negative activation energies for adsorption deserves mention. References and Notes (1) D. B. Dadyburjor, S. S.Jewur, and E. Ruckenstein, Catal. Rev.-Sci. fng., 19, (2), 293 (1979). (2) V. A. Sasonov, V. V. Popovskii, and G. K. Boreskov, Kinet. Katal., 9, 307 (1968). (3) V. A. Sasonov, V. V. Popovskii, and G. B. Boreskov, Kinet. Katal., 9, 312 (1968). (4) C. K. Boreskov, V. V. Popovskii, N. I. Lebedeva, V. A. Sasonov, and T. V. Andrushkevich, Kinet. Katal., 11, 1253 (1970). (5) E. Ruckenstein, R. Krishnan, and K. N. Rai, J. Catal., 45, 270 (1976). Table I in this reference is in error and the results should be reinterpretedalong the lines of the present paper, hence on the basis of a desorption-adsorption mechanism. (6) R. H. Fowler, Proc. Camb. Phil. Soc., 32, 144 (1936).
Analysis of the Isotope Effect in the Hydrogen Exchange Reaction between Pyridinium Chloride and Hydrogen Chloride J. SzydYowski" and M. ZieliAski Department of Chemktry, Warsaw University, Zwirki i Wigury 10 I , 02-089 Warsaw, Poland, and Institute of Chemistry, Jagiellonian University, 30-060 Cracaw, Poland (Received December 6, 1978)
Hydrogen isotope exchange between pyridinium chloride and gaseous hydrogen chloride has been studied both experimentally and theoretically over the temperature range of 273-353 K. The experimental fractionation factor obtained shows some dependence on the composition of the substrates. This phenomenon can be accounted for by specific interactions in pyridinium chloride + hydrogen chloride system. The calculated fractionation factor in harmonic approximation and within the framework of quantum statistical theory of isotope effects agrees satisfactorily with the experimental results in these cases when well-defined species of Py(HCl), were formed and the nature of the interactions were well enough known. In other cases some interaction models have been proposed and briefly discussed. Recently a short communication on the equilibrium isotope effect in the tritium exchange reaction between pyridinium chloride (PyHC1) and gaseous hydrogen chloride has been reported.la These preliminary studies *Address correspondence to this author at Warsaw University.
0022-3654/79/2083-2122$01 .OO/O
revealed some interesting features. It thus has been found that pyridinium chloride reacts with gaseous HC1 to form nonstoichiometric compounds Py(HC1),.1*3-5It has been suggested that compound formation might be due to hydrogen bonding between the extra HC1 and the ?r cloud of the pyridinium cation.4 On the other hand, the for@ 1979 American Chemical Society
The Journal of Physical Chernistty, Vol. 83,No. 16, 1979
Hydrogen Exchange between PyHCl and HCI
mation of HC12- anions is known to result from the uptake of HC1 by several related organic chloride salts.6 Our kinetic studies on tritium and 36Clisotope exchange seem to unequivocally confirm the existence of the HC&species.lb These facts suggest the specific interaction between PyHCl and HCl and this seems to be reflected in fractionation factor of hydrogen isotopes and its dependence on the composition. As pyridinium salts play an important role in hydrogen bond theory we have decided to analyze in detail the equilibrium isotope effect accompanying the above exchange reaction both experimentally and theoretically. It is believed that the isotope effect method will be very helpful in the elucidation of the interaction between pyridinium chloride and hydrogen chloride. Experimental Section As it was mentioned some dependence of the overall fractionation factor on composition has been 0bserved.l However, the data reported are averaged values over all compositions studied. Presently we reexamine these results and extend the studies focussing on the composition dependence. Chemicals, procedures, and apparatus are essentially the same as described ear1ier.l For comparison a few experiments with freshly prepared labeled Py(H*Cl), and HC1 were carried out. Under experimental conditions only hydrogen from the NH group in the pyridinium ring exchanges with tritium in HC1.lb Therefore the fractionation factor CY can be defined as the ratio of the specific activity of tritium for condensed and gaseous phases a t equilibrium: 01
= Ae,c/Ae,g
(1)
The specific activity of the condensed phase, A,,, is never determined directly. Instead, from material balance considerations A , , can always be expressed in terms of the initial specific activities Ao,,and AO,g in the condensed and gas phase, respectively
where m and n are the number of moles of HC1 and pyridinium chloride, respectively. Hence
I
(3)
Two methods were used to determine C Y . In the first method when the exchange was carried out in the system PyHCl + H*Cl directly, we must take into account the solvation process leading to pyridinium hydrogen dichloride. Since initially Ao,c= 0, eq 3 is transformed into
Ao,g m Ae,gn+ r
a!=-----
m-r n+r
(4)
where r is the number of moles of HC1 absorbed from the gas phase by pyridinium chloride. In the second method labeled Py(H*Cl), was prepared by exchange reaction with HC1 and the specific activity of tritium in Py(H*Cl), was calculated from the balance, and in the next step it was considered as the initial specific activity in reaction Py(H*Cl), + HC1. In this case, since = 0 at t = 0, eq 3 is transformed to
2123
TABLE I: Experimental Fractionation Factor of Tritium T/K
m/n = 1
m/n > 2
27 3 299 313 323 333 343 353
2.38 i: 0.03 1 . 8 4 + 0.05 1.72 i 0.04 1.58 i: 0.03 1.49 i 0.04 1.40 i 0.03
2.51 i 0.06
333
Py(H*Cl), t HCl 1.47 i: 0.08
1.98 +. 0.05 1.79 i: 0.03 1.65 i 0.02 1.65 i 0.03
TABLE 11: Composition of the Solvate m/n
T/K273
299
313
323
333
343
1 >2
1.90 2.0
1.85 2.0
1.66 2.0
1.64 2.0
1.62 2.0
1.60 2.0
The IR spectra of the solid samples of PyHCl and Py(HCl), in Nujol were recorded on Specord 71 IR spectrophotometer equipped with sodium chloride optics. The samples were prepared very carefully to avoid moisture. Results and Discussion The results obtained are presented in Table I. These results can be divided into two groups. In the first group there are fractionation factors for the ratio mln = 1, and in the second one for m l n > 2. The results of the additional experiments on the reverse exchange (Py(H*Cl), HC1 at 333 K) are also presented in Table I. The agreement of the fractionation factors (at 333 K) for both exchange directions seems to prove the real equilibrium of the exchange reaction studied. Before entering on the detailed discussion of the results obtained, a few general points concerning some properties of pyridinium chloride and its behavior in the presence of an excess of gaseous hydrogen chloride should be recalled. As mentioned above, pyridinium chloride appears to act as a Lewis base toward HCLS5 Over the temperature range studied, 273-353 K, we have found compounds (solvates) of PyHCl and HC1 with nonstoichiometric composition but never exceeding the mole ratio of HCkpyridine of 2:l. The compositions of the solvate obtained are given in Table 11. However, the nature of the molecular species remains open. Moreover at about 305 K we observe the melting of the solvate. This phase change can be nicely seen in kinetic studies.lb We note some disagreement as to the melting point of pyridinium hydrogen dichloride. Our findings agree exactly with those of Kilty and Nicholls3 but not with those of Goffman and Harrington4 (Shuppert and Angel15 do not specify the melting point of Py(HCl),). Probably instability of the composition here plays an essential role. However, in further discussion we must allow for this phase transformation. Recently Shuppert and Angel15 on the basis of extensive NMR studies proposed the most consistent model for the interactions in the Py-HCl system. Some of their findings coincide nicely with our 0bservations.l Thus over the temperature range studied and at the mole ratio m / n > 2 the situation seems relatively clear, that is to say, we obtain solvate of the general formula Py(HC1)2. The latter can be thought to consist of the new species HC12- hydrogen bonded with the pyridinium cation PyH+. Following Shuppert and Angell's suggestion5 we accept that a moderate hydrogen bonding still exists between PyH+ and HC12- [PyH+-Cl-HCl] in comparison with very strong hydrogen bonding in PyH+-C-.7,s One would expect the ClHC1- ion to be a much weaker proton acceptor than C1since in the former case the chloride ion can be considered
+
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The Journal of Physical Chemistry, Vol. 83,
No. 16, 1979
already strongly hydrogen bonded by HC1. If m / n C 2, we have a much more complex situation. At m / n = 1, as we actually studied, solvates of nonstoichiometric composition Py(HC1)1,60-1,90 over the range 273-343 K were formed. Under these experimental conditions solvation of PyHCl by HC1 is not complete, and the system may be considered as a solution of PyHCl in Py(HCl)> The molecular structure and the nature of the interactions of each of the above species is the subject of the following discussion. Following the Odinokov's suggestion^,^ we accept that both pyridinium salts can be characterized by the same type of hydrogen bonding, that is, they exist essentially as conjugated H complexes (ionic pairs) PyHf...A- . However, hydrogen bonding in PyH+.-Cl- is much stronger than that in the dichloride salt and the latter can be regarded more ionic. From the hydrogen exchange view point, we distinguish three distinct species: PyH+, HCl2-, and PyHC1. Let us now consider three general exchange reactions: HC12-
+ H*C1 = H*Clp- + HC1
+ H*Cl = Py+H* + HC1 PyHCl + H*C1= PyH*Cl + HC1 Py+H
(1)
x1
+ x2 + x3
PzKz + P3K3
(7) where the weights pi are atom fractions of exchangeable hydrogen in the above substrates defined as = P&l+
xi
Pi P1
=
x1
+ x2 + x3
+ Pz + P3
For m l n > 2, p3 = 0 and then to a!
p1
=1 = p2 and eq 7 simplifies
= YAK1 + Kz)
d,
0.2
I
I"
28
30
32
3L
36
38
10'1 T
Figure 1. Comparison of the experimental and theoretical fractionation factor of triiium exchange between pyridinium chloride and hydrogen chloride: 0 , experimental points for m l n > 2; 0 , experimental points for m l n = 1. Straight lines 1, 2, and 3 correspond to the different calculation models (see text).
The equation for the isotopic reduced partition function ratio, s 2 / s l f , in the harmonic approximation neglecting effects owing to the quantum-mechanical rotation id1
(111)
where xl, x2, and x 3 are the number of moles of HClZ-, Py'H, and PyHC1, respectively. The asterisks denote labeled forms. Equation 6 is the more general form of eq 1. Equation 6 can be written as the weighted average of the equilibrium constants K1, K2,and K3of reactions 1-111, respectively: a!
1.0
(11)
The fractionation factor, defined usually as the ratio of atom fractions of exchangeable hydrogen in the condensed phase divided by the ratio of the atom fraction of the label in the gas phase, is related to the mole fractions of the exchanging species in the above reactions by a!=
J. SzydYowski and M. Zielinski
(8)
The theoretical basis for the evaluation of the equilibrium constants for the isotope exchange reaction was established by Bigeleisen and Mayer.l' Following Bigeleisen the equilibrium constant for the isotope exchange reaction A,H + H*C1 = A,H* + HC1 can be expressed in terms of the reduced partition function ratio K L= (sZ/sf)A,H/(s2/slflHCl (9) AiH denotes the molecular species HC12-, PyH+, and PyHCl participating in reactions 1-111 with the corresponding equilibrium constants K1, K,, and K3, respectively.
where u = hcw/kT, w is the normal-mode vibrational frequency in cm-l, c, k , h, and T have their usual meaning, s is the symmetry number, and the subscripts 1 and 2 refer to the light and heavy isotopic species, respectively. The products and sums are taken over all normal mode vibrational frequencies of the molecule. Thus the reduced partition function ratio can be easily calculated by using the spectroscopic data of isotopic molecules. Let us consider mln > 2. The overall fractionation factor is defined by eq 8. The equilibrium constant K1 has been experimentally determined and also calculated by the method outlined above, using the best available vibrational force field of the valence force type.1° Presently we accept these values. The vibrational spectra of various pyridinium salts were extensively studied7 but we know little about the Py+H-ClHCl- system. Analyzing the vibrational data of pyridinium salts7we find relative invariance of all but one vibrational frequency. It appears that only the NH stretching frequency v, is very sensitive to the counterion. Goffman and H a r r i n g t ~ n ,while ~ studying the solid spectrum of Py(HCl),, observed the disappearance of the band at 2450 cm-' (v, for PyHC1) but they gave no information about the new position of this band. From our measurements it appears that this band seems to be shifted toward higher wave numbers; the center of gravity is placed at about 3060 cm-l and deuterated compound at about 2300 cm-l. Uncertainties are, however, large as the band is very broad and complicated. Under these reservations K 2 can be calculated by using the spectroscopic data reported by Cook7 and Foglizzo and Novak8 and vs determined by ourselves. Since the experiments were carried out with tritium and calculations considered deuterated molecules, we use the known relation12J3In (YH/T = 1.44 In aHiDto compare the experimental and theoretical results. As can be seen in Figure 1 the theoretical values (straight line 1)agree fairly well with the experimental results. The discrepancies seem to result mainly from the uncertainties of the vibrational data, in particular of NH the stretching frequency v,. Going over to the second case when mln 2 we meet more complex situation. The overall fractionation factor
The Journal of Physical Chemistry, VoL 83, No. 16, 1979
Hydrogen Exchange between PyHCl and HCI
is determined by the three processes described by reactions 1-111. We assume three different species PyH', HC12-, and PyHCl at appropriate mole ratios to be present. The calculations of K1 and K2 were discussed above. pi can be easily calculated on the basis of the data of Table 11. In the first approximation K3 can be calculated accepting the vibrational data of Foglizzo and Novaks and Cook7and introducing some assumption as to the nature of the molecular interactions involved. Shuppert and Angel15 propose among others two models for the interactions of molecular species presented in the solution which lead to the dimers (PyHCl), and PyH+-ClHPy. It seems that the former already exists as a dominant form in the crystalline state as can be deduced from crystallographic studies.14 Therefore we assume that the vibrational data reportedsB8 concern the dimer structure. Calculations of cy by means of a slightly modified eq 7 allowing for dimer cy
=
PIKl
+ PZK2 + 1/2P3K3
(11)
are represented by line (2) in Figure 1. Unfortunately we observe a jump in the temperature range 299-313 K though the experimental points could be described by a continuous line. It is worth noting that in the same range the melting point of the solvate has been found.'J Therefore we suspect that the jump on line (2) is caused by structural changes on phase transformation. It is then very likely that in liquid (T > 305 K) an equilibrium such as (PyHC1)2 @ 2PyHC1 exists instead of one dominant form. Moreover we can expect some small changes15in v, frequency on the transfer from the crystalline state to the liquid. If one assumes, however, that the monomer is the dominant form and uses the available data for pyridinium chloride7i8 one obtains straight line (3) in Figure 1. The discrepancies between the theoretical and experimental values are apparent but no jump is observed. As can be seen in Figure 1the experimental results lie between the two theoretical lines actually describing two extreme cases. At the present state, however, there is no way to carry out exact calculations due to the lack of information on the system studied. The other dimer PyH'41HPy cannot also be considered as a dominant form. The calculations carried out with various vibrational data gave a results far too low to be taken into account. These results seem justified as PyH' is still sufficiently strongly hydrogen bonded with ClHCl- and the competition of neutral PyHCl molecules with negative ClHC1- ions must be unsuccessful. The discrepancies between calculated and experimental results are caused first of all by the uncertainties in the vibrational data in particular in the NH stretching frequency v,. Indeed, it appears that the choice of a single value along the manifold for VNtH...Cl- absorption was often subjective and arbitrary and there is doubt whether the
2125
value listed should be considered as significant within less than *50 cm-l. Moreover the discrepancies can result from the harmonic approximation used. In general anharmonicity corrections are small but the exceptions in hydrogen bonded systems are already noted.16 The inherent approximations and simplifications do not warrant a detailed evaluation of the isotope effect. This has to await a normal coordinate analysis of various pyridinium salts based on a common anharmonic force field for all isotopic species. However, even in its preliminary form, the preceding discussion reveals that the isotope effect appears to be sensitive to the structure and hydrogen bonded systems involved. Thus it can be seen that the pyridinium cation in pyridinium hydrogen dichloride salt is still moderately or even strongly hydrogen bonded with the HC12-ion. The calculations of isotope effect under the assumption of free Py+H (data taken from Arnett and Chawla's paper15result in a serious discrepancy between theoretical and experimental values. At some compositions we propose specific forms of interactions. Thus, contrary to Shuppert and Angell,5 the PyH+ClHPy dimer does not seem to be a dominant form. Instead, the equilibrium (PyHC1)2 + 2PyHC1 is proposed. As the temperature decreases the straight lines describing the temperature dependence of the isotope effect for the two cases studied, Le., m f n > 2 and m f n C 2, seem to coincide. This would suggest that at still lower temperatures only one molecular form exists, that is, pyridinium hydrogen dichloride. This finding confirms the results of vapor pressure measurements on the pyridine-HC1 system by Kilty and N i ~ h o l l s . ~ Although some correlations between the strength of hydrogen bond and the magnitude of the isotope effect can be seen, the results obtained are by far insufficient to generalize these observations and further studies are desired. References and Notes (1) (a) J. SzydYowski and M. ZieliAski, Radiochem. Radioanal. Lett., 8, 291 (1971); (b) J. SzydYowski, Thesis, Warsaw University, 1971. (2) J. SzydYowski, Radiochem. Radioanal. Lett., 14, 155 (1973). (3) P. A. Kilty and D. Nicholls, Chem. Ind., 1123 (1963). (4) M. Goffman and G. W. Harrington, J. Phys. Chem., 67, 1877 (1963). (5) J. W. Shuppert and C. A. Angell, J . Chem. Phys., 67, 3050 (1977), and references therein. (6) J. C. Evans and G. Y-S.Lo, J . Phys. Chem., 70, 11 (1966). (7) D. Cook, Can. J. Chem., 39, 2009 (1961). (8) R. Foglizzo and A. Novak, J. Chim. Phys., 66, 1539 (1969). (9) S. E. Odinokov, A. A. Mashkowsky, V. P. Glazunov, A. V. Iogansen, and B. V. Rassadin, Specfrochim. Acta, Part A , 32, 1355 (1976). (10) J. SzydYowski, 2. Naturforsch. A , 30, 38 (1975). (11) J. Bigeleisen and M. G. Mayer, J. Phys. Chem., 15, 261 (1947). (12) J. Bigeleisenin "Triiium in the Physical and Biological Sciences", Vol. 1, IAEA, Vienna, 1962, p 161 (13) R. E. Weston, Jr., 2.Naturforsch. A , 28, 177 (1973). (14) C. Rerat, Acta Crysta//ogr., 15, 427 (1962). (15) E. M. Arnett and B. Chawla, J . Am. Chem. Soc., 100, 214 (1978). (16) E. U. Monse, 2. Naturforsch. A , 28, 174 (1973).
