J. Phys. Chem. 1981, 85, 35-37
Equation 11explicitly demonstrates the significant loss of information one may expect from the FT NMR perturbation-response experiment that employs large flip angles. For a 90° pulse, one samples at most only four independent linear combinations of multiplet components, and only two of these (the AB and X magnetizations) readily lend themselves to simple interpretations. In many cases, these considerations explain why nonlinear effects resulting from dipolar-dipolar (dipolar-shift anisotropy) interferences have not been seen in many studies where simple calculations suggest that such effects should be significant. It is well understood that interferences give rise to differential recovery rates for individual multiplet components in coupled spin systerns.l3 For the ABX spin system, these multiplet asymmetries are manifest in the modes v: through v;. Therefore, the telltale characteristics of these interferences are hidden whenever large flip angles are employed. However, it is important to realize that this fact does not imply that such effects do not influcence the relaxation behavior of the AB and X longitudinal magnetizations. It (13)L. G.Werbelow, G. Pouzard, and A. Thevand, J. Chim. Phys. Phys.-Chim. Biol., 76,941 (1979).
35
simply means that a straightforward isolation and characterization of these interference effects is complicated whenever Fourier-transform methodologies are used to study the perturbation-response characteristics of nuclear paramagnetism. In systems where interferences between competing relaxation mechanisms are likely, it is apparent that small flip angles should be employed if one wishes to ascertain the strength and the effect of these interferences. Conclusions Detailed expressions have been presented which facilitate the analysis of the longitudinal magnetizations of an ABX spin system relaxed by dipolar and random-field like interactions. Flip angle dependencies of the various magnetizations have also been calculated. It has been assumed that this observing pulse is nonselective. These latter expressions demonstrate that assessment of various interference effects can result only if relatively small flip angles are employed. Acknowledgment. This work has been supported in part by the National Science Foundation (Grant No. CHE80001839) and the Petroleum Research Fund (Grant No. 12326G6).
Reaction of Ethanol Vapor with Alkali-Metal Mirrors E. E.
Qulror
Deparamento de Quimica, Facultad de Clenclas, Unlversldad de Chile, Casllla 653, Santlago, Chile
and D. H. Volman" Department of Chemistty, Unlversw of Californla, Davis, Californla 956 16 (Recelvsd: August 14, 1980; In Final Form: September 25, 1980)
The reaction of variable-compositionethanol-ethanol-d vapor with alkali-metalmirrors, Na, K, Rb, Cs, to yield hydrogen gas was studied. The mass-action expression [HD]2/([H2][D2]) = Q yielded Q = 10.6 f 1.6 at 298 K, well above the equilibrium constant value of 3.26. The rate of hydrogen evolution for the reaction of ethanol with rubidium ethoxide and the adsorption isotherm of ethanol on rubidium were determined. A model for the reaction is the analogous one that we earlier proposed for water: the reaction of metal with ethanol yields the alkali ethoxide and a bound hydrogen atom; these adatoms transfer by quantum-mechanicaltunneling for which the relative probabilities for H and D are (P,/P2)= 8.5, and the minimum transfer energy based on an assumed rectangular barrier is -5.4 kJ mol-l; molecular hydrogen is formed by the reaction of transfer atoms with adatoms.
Introduction In a previous study' we reported results on the reaction of variable-composition, deuterium-enriched water vapor with alkali-metal mirrors. The overall reactions
+
where a + b + c = 2, d + e = 2, and f + g h = 1, yielded D-enriched alkali-metal hydroxides and H-enriched molecular hydrogen. The molecular hydrogen composition conformed to the mass-action expression
Q = [HD12/([Hz1[Dz1)
(2)
appropriate to the reaction Hz + D2 = 2HD
(3) with Q = 12.0 f 2.6, valid for all water compositions and all of the metals used: Li, Na, K, Rb, and Cs. The corresponding value for the equilibrium constant calculated from the Gibbs energy of formation,2 AGPZgs = 1.46 kJ mol-', for HD is K = 3.26. The mechanistic model adopted to explain enrichment was the generation of an adatom3 (eq 4 and 5) with fracHOD(g) + M(s) MOD(s) + M-H(s) (4) HOD(g) + M(s) MOH(s) + M-D(s) (5)
--
~
(1) R. 0. Bremner and D. H. Volman, J.Phys. Chem., 77,1844 (1973). 0022-3654/81/2085-0035$01.OO/O
~~
~
(2) "Selected Values of Chemical Thermodynamic Properties", NBS (US'.)Tech. Note No. 270-3, 12 (1968).
0 1981 American Chemical Society
38
The Journal of Physical Chemistry, Vol. 85, No. 1, 1981
Quiroz and Volman
IO
20
40
30
50
60
MIN
HYDROGEN, 0 ATOM FRACTION
Flgure 1. Composition of molecular hydrogen as a function of atom fraction D in the gas at 298 K: (0)Na; (0) K; (A) Rb; (V)Cs. Curve calculated from 0 = 10.6.
tionation thus occurring only through the reaction of HOD on the metal surface. The value of Q was explicible on the assumption that the adatoms transferred by quantummechanical tunneling, in which the probability for H would be considerably greater than for D, and reacted with adatoms to give molecular hydrogen. It is expected that the model should apply for any compound having an active hydrogen, and a study with such a compound would provide additional evidence for the validity of the model. Ethanol was chosen as it meets the criterion of having an active hydrogen; further, as the only solid product of the reaction is the metal ethoxide, the complexity of isotope fractionation on the surface is precluded. Experimental Section The experimental methods and materials used were analogous to those described previously. Alkali-metal mirrors were formed by distillation onto the walls of the reaction chamber, a cylindical Pyrex tube, 6 mm in diameter and 20 cm long. Sodium and potassium mirror surfaces were generated from the pure metal (Mallickrodt); rubidium and cesium surfaces were formed from the metal resulting from thermal decomposition of the corresponding azide (Eastman Organic Chemicals). Solutions of ethanol were prepared from anyhrous ethanol-cl (Stohler Isotope Chemicals) and absolute ethanol (Commercial Solvents Corp.). Liquid solutions were flash evaporated into the reaction chamber, and the molecular hydrogen formed was collected and analyzed by mass spectrometry. In addition to reaction experiments, we also determined the adsorption isotherm for ethanol on rubidium ethoxide. The adsorption apparatus and method is described in an earlier publi~ation.~For the present experiments, the adsorption chamber consisted of the reaction vessel. Results In our previous work with water vapor, consistent resulta were obtained provided the metal was in excess. This was (3) A. Gelb and S. K. Kim, J . Chern. Phys., 55, 4935 (1971). (4)F. A. Bettelhein, C. Sterling, and D. H. Volman, J.Phys. Chem., 63,1373 (1959).
Figure 2. Evolution of hydrogen from rubidium mirrors reacting with ethanol at 298 K. -1
l
I
I
I
I
I
I
I
I
.I
.2
3
.4
5
6
7
8
9
I
ETHANOL, P/Po
Figure 3. Adsorption isotherm, 298 K, of ethanol on rubidium ethoxide.
also observed when using ethanol. Consequently, we used 2.6 X mol of ethanol and -1.5 X lod3mol of metal in all experiments. With this amount of ethanol the pressure of ethanol in the reaction vessel could not exceed 6.4 torr,well below the vapor pressure of ethanol, 59.8 torr at 298 K. The results obtained are shown in Figure 1. The mass-action expression, eq 2, for all compositions with all of the metals gives Q = 10.6 f 1.6 at 298 K. The curves were constructed from values calculated from the Q values. The reaction with sodium and potassium was rapid, too fast to be measured in our apparatus; the reaction with rubidium and cesium was slow, requiring some 1-2 h for completion. However, in all cases the reaction proceeded to quantitative evolution of hydrogen as determined by comparing the amount of ethanol used with the amount of hydrogen produced. Results obtained for hydrogen evolution with time for ethanol with rubidium are shown in Figure 2. During the period of evolution of hydrogen, no ethanol was found either in the gas phase or evolved. Obviously ethanol was bound to the surface which was at this stage a mixture of alkali metal and the alkali-metal ethoxide. An isotherm from the absorption of ethanol on a rubidium ethoxide surface is shown in Figure 3. To obtain this isotherm we deposited a rubidium mirror in the reaction vessel; the mirror was exposed to an excess of ethanol vapor until it was all converted to the ethoxide; the hydrogen formed during this process was measured, and thus the amount of rubidium deposited and hence the amount of
Reaction of Ethanol Vapor and Alkali-Metal Mirrors
ethoxide surface was determined; the system was evacuated while excess ethanol was removed by flame brushing the adsorption chamber.
Discussion Adsorption and Rate of Reaction. Figure 2 shows that some 70% of the molecular hydrogen is produced before 11 min. At this stage the mole ratio of the unreacted alkali metal to metal ethoxide would be greater than 7:l. As unreacted ethanol is not retrievable at this time by pumping on the system, the ethanol must be tightly bound to the surface, either metal or metal ethoxide. SCF calculations have lead to the conclusion that alkali-metal atoms and water can form neutral molecular complexes; it seems reasonable to expect similar behavior with ethanol. The interaction-energy calculation for Na-OH, is 21.8 kJ; for Na-OHC2H5 it would probably be much less. It is not likely that such a complex would not release ethanol on vacuum pumping. Therefore, the ethanol should be strongly bound to the ethoxide surface. The adsorption isotherm is consistent with this observation; at the lowest measured pressure, 0.01 torr or a relative pressure of 2 X the number of moles of adsorbed ethanol is over one-half the number of moles of ethoxide surface. After the period of relatively rapid evolution of hydrogen, the rate of production of hydrogen follows first-order kinetics as indicated by the logarithmic plot in Figure 2. This is expected if the mechanism is a transfer (desorption) of ethanol from the ethoxide surface to the metal surface. Model for the Value of Q. As the value of Q obtained for ethanol, 10.6 f 1.6 for all of the metals at all compositions, is within experimental error in agreement with that previously found for water, 12.0 f 2.6, it is likely that the mechanism for water and for ethanol reaction is the same. It would be surprising if they, or the mechanisms for other active hydrogen species, were different. Perhaps the chief virtue of this study is that it provides assurance that the experimental results are indeed the same or very nearly so. As we assume a common mechanism and as the reasoning which led to the adopted mechanism is given previously,' we shall not repeat it in detail. (5) M. Trenary, H. F. Schaeffer 111, and P. Kollman, J. Am. Chem. SOC.,99,3885 (1977).
The Journal of Physical Chemistry, Vol. 85, No. 1, 1081 37
Obviously the chemical reaction leading to a hydrogen adatom differs in that OC2H5 substitutes for OH. Equations 4 and 5 for ethanol are C,H,OH(g) + M(s) CZH50M M-H(s) (6) CaHSOD(g) + M(s) C2H50M + M-D(s) (7)
-+
+
For molecular hydrogen formed by quantum tunneling of atoms which react with adatoms
where Pl and Pzare the tunneling probabilities of H and D. As shown earlier, eq 8 will represent the mass-action value Q for molecular hydrogen produced during time intervals during which [M-H] and [M-D] may be considered constant. Experimentally, hydrogen is formed from a succession of steady states, and the summation of products gives Qz < Q. Thus the experimental value of Q is a minimum value. With this limitation the calculated value of Pl/Pzcorresponding to Q = 10.6 is 8.5. For water we found Pl/P2= 9.9; on the basis of a rectangular barrier with a thickness of 5 nm, this gave a barrier height (energy) of 6.0 kJ mol-l. The corresponding calculated value for ethanol is 5.4 kJ mol-l. For reasons given above, these are minimum values. The only other study of the reaction of an active hydrogen molecule with an alkali metal was reported by Horiuti and Szabo over 45 yr ago.6 They reported that Polanyi had suggested that tunneling would be involved. It is, perhaps, surprising that hydrogen-atom tunneling can compete with Arrhenius kinetics at 298 K. Nevertheless, calculation indicates that it can. For a rectangular barrier the temperature at which tunneling is predominant as given by Goldanskii' is
T = [hV1/2]/[kBd(2m)1/2] (9) For T = 300 K, V = 7.6 kJ mol-l if d = 5 nm. This value of V is somewhat higher than the values calculated from our Pl/Pzvalues, but these are minimum values. Hence, a tunneling mechanism seems to be reasonable. (6)J. Horiuti and A. L. Szabo, Nature (London),133, 327 (1934). (7)V. Goldanskii, Annu. Reu. Phys. Chem., 27, 85 (1976).
