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Hydrogen isotope replacement reactions on rhenium
SURFACE
SCIENCE
HYDROGEN
36 (1973) 494-512
ISOTOPE
REPLACEMENT
R. P. H. GASSER,
Phy.Gcal Chemistq
Received
0 North-Holland
Ci. MORRIS
and
Publishing
REACTIONS
Co.
ON RHENIUM
A. K. SZCZEPURA
Luborntory, South Parks Road, Oxftird OXI 392,
9 October
1972; revised
manuscript
received
20 December
England
1972
The existence of a mobile equilibrium at room temperature between part of the hydrogen adsorbed on rhenium and gaseous hydrogen is demonstrated by the easy exchange of isotopes between the adsorbed layer and the gas phase. The adsorbed gas is desorbed as a mixture of homonuclear molecules (of H2 or Da) and of the isotopically mixed species (HD). However, the replacement reactions are not symmetrical; there is a greater proportion of HD in the desorbed gas when deuterium is replaced by hydrogen than in the converse reaction. This kinetic isotope effect is attributed to differences between the zero-point energies of the various hydrogen containing species. Quantatitive agreement between the shapes of the experimentally observed desorption curves and calculated curves is obtained if the zero-point energy of the bond between a surface rhenium atom and deuterium is assigned the value 2.6 kcal mole-‘.
1. Introduction The kinetic concept of the nature of a chemical equilibrium implies that both forward and back reactions take place at significant rates at the prevailing temperature. For many of the reactions at room temperature between a clean metal surface and a surrounding gas this condition is not fulfilled and it is only at elevated temperatures that the reverse reaction, desorption, occurs at a measurable rate. However, when it appears that an equilibrium one conbetween free and adsorbed gas is “mobile” at room temperature venient method of measuring the rate of interchange of absorbate between the gas and surface is to “label” the molecules by using different isotopic species for the initial gas phase and surface moieties. This technique was successfully used to establish the rate at which the adsorption and desorption of carbon monoxide on Ni (I IO) single crystal surfaces took place’). The build up of r4C0 on the 12C0 covered surface when gaseous 14C0 was admitted to the system, or the converse reaction in which “CO replaced adsorbed 14C0, were recorded with a radiochemical counting technique. It had been established earlier that nickel at room temperature does not catalyse the interchange of atoms between carbon monoxide molecules”) and it was concluded therefore that the replacement took place in a single molecular event. 494
HYDROGENISOTOPEREPLACEMENTREACTIONSON
When the substrate
Re
does catalyse the isotope equilibration
495
reaction
under
conditions where replacement is also taking place, a new and interesting situation arises. The replacement reactions of the hydrogen isotopes on tungsten are examples of such systems which have been studied previouslya) and the established activity of rhenium as a catalyst for the HZ/D, equilibration reaction at room temperature gives grounds for supposing that combined replacement and isotopic mixing could be observeda). It was, therefore, decided to investigate these reactions, which have a further interesting feature in that they might show a kinetic isotope effect. Such an effect would arise from the difference in the rates of making and breaking the various bonds to the different isotopic species. No a priori estimate of the magnitude of any such effect was made but rather it was left as a matter for experimental determination. 2. Experimental The experimental conditions were unchanged from the earlier work4) for which the rhenium filament of length 3 1 cm and geometric area 2.47 cm2 was mounted in a Pyrex ultra-high vacuum chamber of volume 1.8 litre. Two bakeable metal valves connected the reaction vessel to two gas storage volumes and a third, similar, valve led to the pumps. Adjustment of this latter valve allowed a convenient rate of flow of gas through the chamber to be selected, whilst adjustment of the inlet valves provided an appropriate equilibrium pressure of the relevant gas. The replacement of adsorbed hydrogen by deuterium was recorded by saturating the filament at room temperature with hydrogen at an equilibrium pressure of about 1 x lop7 torr (1 torr= 133.3 Nmm2), closing the hydrogen inlet valve and pumping out the system for 10 min. Deuterium was then admitted, the inlet valve being adjusted to produce a final pressure between 7 x 10e8 torr and 3.6 x low7 torr. An omegatron radiofrequency mass-spectrometer which formed an integral part of the UHV apparatus was used, after calibration against an ionization gauge equipped with a lanthanum boride coated cathode (to minimize atomization of the gas), for all pressure measurements. The sensitivity of the omegatron was the same for H, as for D, and this sensitivity was also used for HD. During the course of the replacement reaction the omegatron was tuned, in successive experiments which were as nearly similar as possible, to D, (mass 4) HD (mass 3) or H, (mass 2). The whole series of experiments was then repeated with the filament initially saturated by deuterium and with hydrogen as the replacing gas. Before the reactivity of the filament could be calculated it was necessary to determine whether there was a contribution by the other surfaces of the UHV system to the observed effects. To do this the filament was allowed to saturate
496
R. P. H.GASSER,
G. h4ORRlS
AND
A. K.SZCZEPURA
overnight in the residual gas, which was predominantly carbon monoxide and which deactivates it4). One hydrogen isotope was then admitted to give a pressure of about I x iOm7 torr. After saturating ail surfaces in the chamber the inlet valve was shut and the apparatus was pumped out for 10 min. The other isotope was then let in. The pressure of newly-ad~l~itted gas rose rapidly to its equilibrium value, at which time a small background of HD and a miniscule pressure of the initial isotope were observed. These residual pressures can be seen on the experimental traces in fig. I. In calculating the effect of the filament these final pressures have been subtracted from the pressure records. Some similar experiments at elevated filament temperatures were also performed. The equilibrium uptake of hydrogen dilninished with increased temperature and the upper limit of the temperature at which the duration of the reaction was sufficient to allow the various isotope pressures to be usefully recorded was 380 K.
Fig. I.
Partial pressures of HT, HD and DZ during the replacement of adsorbed deuterium by hydrogen.
it was necessary to determine whether the clean rhenium surface made any distincti between the individual isotopes. To do this the initial sticking probability s0 and the maximum uptake O,,, at room temperature and an equilibrium pressure of ca. 1 x 10 -’ torr were calculated from the mass spectrometer records of the pressures during adsorption “). For both isotopes s0 and O,,, were the same at 0.24 and 7+0.5 x lOi4 atom cmm2 respectively. (The error in the uptake is the range of the random scatter; the systematic error due to un~ertaitlties in the gauge sensitivity may be much greater. For the calculations of uptake the manufacturer‘s quoted sensitivity was used.) However, the presence of some reversibly adsorbed gas on the filament was demonstrated by pumping down the reaction chamber for periods of
3, 5, 7 and 10 min and measuring
497
Re
HYDROGENISOTOPEREPLAC‘EMENTREACTIONSON
the amount
of hydrogen
taken
up when
the supply of gas was restored. For a pump-down period between 5 and 10 min a constant amount of gas, equivalent to about 0.9 x 1014 atoms cm-’ of rhenium filament, was required to saturate the filament, though less gas was required at shorter times. These results are in accord with earlier work6). As with a polycrystalline tungsten or molybdenum filament, therefore, a clean rhenium surface makes no distinction between the individual isotopes 7l 8). 3. Results Measurements were made over the pressure range 6 x IO- * torr to 4 x 10e7 torr. A typical series of pressure records at room temperature for the replacement of deuterium by hydrogen is shown, for a final equilibrium pressure of hydrogen near I .2 x IO-’ torr, in fig. 1. A similar series of runs for the reverse reaction but with an equilibrium pressure of deuterium near 2.8 x IO-’ torr is shown in fig. 2. From the many pressure records made (about 35 sets in all), all of which showed the characteristic shapes of the curves in figs. I and 2, it is possible to carry out two groups of calculations.
Time
Fig. 2.
Partial
pressures
(mln)
‘-
of HZ, HD and De during hydrogen by deuterium.
the replacement
of adsorbed
In the first group are the calculations of the total amount of adsorbed gas which can be replaced by the alternate isotope and the distribution of the desorbed isotope between the homonuclear isotope (i.e. H, or DJ and the mixed isotope (i.e. HD). The second group is concerned with the rate of the overall replacement process, both with respect to the pressure of the incoming gas and with respect to the concentrations of the isotopic species on the surface. We shall deal with these in turn.
498
R. P. H. GASSER.
G. MORRIS
AND A. K.SZCZEPURA
4. Quantity and isotopic composition At any instant
during
of replaced gas
the desorption dP -_=c~ dt
dn
~-kP,
dt
where c is a constant which relates the number of molecules in the apparatus to the pressure, P, and k is the pumping constant of the aperture of the valve connecting the reaction chamber to the pumps. k is separately measured from the record of the first order decay of pressure when the gas admission valve is closed rapidly. k varies with the molecular weight of the gas (kccm)) and was normally about 0.7 see-l for H,. Then: t=CC
ndca=
1
t=CC
dn-j
s
t=o
,=
dP+;>
t=o
Apart from the effect of the initial
ic
k(P-P,)dt.
1 i=O
settling down period, which is negligible,
t=v
I
dP=O.
f=O The activity of other surfaces in the U.H.V. chamber was shown to be constant and to give rise to the finite final pressure of HD or replaced X,, i.e. to P,. The contribution of the other surfaces is, therefore, subtracted from the pressure record in the final integral on the R.H.S. of the above equation.
(P
-
P,) dt.
(2)
As in a conventional flash filament experiment, the integral is evaluated graphically from the pressure record. With a knowledge of k, c (6.08 x 1Ol9 x x P mol) and the area of the filament the number of molecules of gas evolved per unit area of filament surface can then be calculated. The number of molecules of incident gas required to complete the replacement reaction was obtained from the pressure record of this gas. In this case the amount of gas consumed was calculated from t=%
s
(‘final - f’) dt
r=o
HYDROGEN~SOTOPEREPLACEMENTREACTIONSON
(where the pressures the experimental
are those of the incident
Re
499
gas), i.e. from the area between
curve and the extrapolation
of the final pressure
to zero
time. In the experiment designed to measure the quantity of gas reversibly adsorbed the number of molecules was again calculated from the pressure record by graphical integration. This experiment of course uses the same isotope throughout. The results at room temperature are summarised in table 1. TABLE I No. of atoms of gaseous isotope required (x 1Ol4cm-2)
Reaction
7.3 6.6 0.9 3.5 7.0 2.6 7.8
(1) Re + HZ +ReHa&atd) (2) Re + DZ --f ReDsds(satd) (3) (4) (5) (6) (7)
ReHaas(pump IO min) + ReFh(satd) ReH + t De(g) + ReD + f Hz(g) ReH + Dz(g) + ReD f HD ReD + 4 Ha(g) + ReH + +Dz(g) ReD + Hz(g) --f ReH + HD
The random errors in the uptakes [reactions (l)-(3)] are ca. f 10% and in the replacement reactions (4)-(7) ca. f5”/,. There was no measurable dependence of uptake in the experimental pressure range 6 x 10m8 torr to 4.0 x lo-’ torr. The principal points of interest about these results are: (I) The replacement reactions were unsymmetrical; the ratio (HD/D,),,, That is to say, it was relatively easier was greater than the ratio (HD/HJdes. for HD to desorb from a deuterium-saturated surface than from a hydrogensaturated surface. (2) All of either adsorbed isotope could be replaced quite rapidly even though only ca. 10% of the gas was reversibly adsorbed. An independent evaluation of the self-consistency of the measurements can be made by comparing the total number of gas phase atoms required to replace an isotope [i.e. (4)+(5) or (6)+(7)] estimated from the desorption curves, with the consumption of gas calculated from the replacing-isotope adsorption curve. The two numbers should differ by the amount of gas reversibly adsorbed [reaction (3)], 0.9 x 1014 atoms cm-‘. For deuterium as replacing gas the gas phase consumption was 10.8+ 1 x 1014 atoms cmm2 compared with the desorbed gas sum of 10.5kO.5 x lOI atoms cme2, whilst for hydrogen the equivalent numbers were 10.7+ 1 x 1014 atoms cmm2 and 10.4+0.5x 1014 atoms cm-‘. The agreement is thus satisfactory. 5. The rates of reaction (1) The kinetics
of the replacement
reaction
with respect to the incident
R. P. H.GASSER,
500
G. MORRlS
AND A. K.SZCZEPLJRA
gas were determined in a manner similar to the technique used for flashfilament work. The probability of utilization of an incident molecule by the surface when covered with the other isotope was calculated from the relationship: Probability
= (acid’) (P,,jP
- if,
where cf is a constant which relates the rate of collision to the gas pressure (2.53 x IO” collisions see-’ torr-’ for D2). This probability was then plotted against the fractional uptake of gas. The results are shown in fig. 3 for both hydrogen and deuterium as incident gas. The single curve obtained suggests that the rate of uptake of either gas is directly proportional to the rate of collision, i.e. the reaction has first order kinetics with respect to the incident
Fractional
Fig. 3.
Utilization
probability
consumpt,or,
as function of fractional
consumption
of replacing gas
(*-.f final pressure I% - 3. I5 x 10 i torr, ( ;?) final pressure D2 -- 2.72 x 1Omi tori-,
(\;) final pressure De ~- 1.98x 10m7torr, (0) tinal pressure H:! _~ 1.02x IO i torr, (A) final pressure Hz (7) final pressure He
1.21 ? IO ’ tot-r, 1.98 ‘XIO-’ torr,
gas. The initial uptake probability by the filament after saturation with gas and pumping out for 10 min. was the same for both isotopes, 0.056. This value is close to the initial sticking probability of hydrogen on a pumpedout, hydrogen-covered filament, 0.055. An alternative method of demonstrating the first order kinetics is to plot the number of surface molecules which have desorbed as a function of number of collisions of incident gas as in fig. 4. The single curve for the evolution of hydrogen when deuterium was the replacing gas, or for the converse reaction, shows that both replacement reactions have first order
Re
HYDROGENISOTOPEREPLACEMENTREACTIONSON
kinetics.
The
separation
between
these
two replacement
501
reaction
curves
reflects the difference in the proportions of H, or D, in the desorption products. The isotopic mixing reaction can also be seen to have first order kinetics (H, pressures: 2.0x 10-‘-6.6x 10e8 torr, D, pressures: 3.1 x IO-‘-1.2 x 1OF7 torr, and in the initial stages to proceed at the same rate for both isotopes. At higher collision numbers than the limit of fig. 4 the curves diverge further as the result of the greater evolution of HD by hydrogen as incident gas than by deuterium.
Fig. 4.
Evolution
of adsorbed (G) (Cl) (A) (A)
gas as a function HD displaced by HD displaced by Hz displaced by Dz displaced by
of collisions De, HZ, Dz, HZ.
by replacing
gas
(2) The rate of desorption of any species from the surface was calculated from its partial pressure, using eq. (I), and subtracting the contribution of the walls [i.e. P, as in eq. (2)]. In practice, the inequality dP/dtekP was sufficiently closely followed to allow the reat of evolution to be calculated from the simple relationship: dnjdt
= (k/c) (P - P,).
During the early stages the incident gas is mainly utilised in filling the reversibly-bound sites and desorption is relatively unimportant. After about + min at 1 x IO-’ torr these sites are nearly full and the incident gas is then predominantly consumed by the replacement and isotopic mixing reactions. 6. Discussion
The most important pretation are:
features
of our experiments
which
require
inter-
502
R. P. H.GASSER,
G. MORRIS
AND A. K. SZCZEPURA
(1) The observation that all of the adsorbed gas can be replaced readily even though only ca. lo”/, of it is reversibly adsorbed. (2) The general shape of the desorption curves. (3) The difference between the behaviour of the two isotopes. In the discussion which follows these points are all covered, but in the absence of an agreed mechanism for the equilibration reaction g- 12). it is by no means impossible that an alternative explanation could be devised which would also fit all the facts. We start with a consideration of (1). Hydrogen is usually chemisorbed on transition metals at room temperature and above as atoms and we shall assume that this is so for rhenium. Atomic adsorption requires the breaking of the fairly strong bond in the hydrogen molecule (D, = 103.2 kcal/mole) followed by the formation of two Re-H surface bonds, each of strength x. The overall heat of adsorption then reflects the balance between these two large energies, AEad5 = 2~ - D,. Quite a modest change in x, such as may well occur from one crystal face to another on the polycrystalline surface with which we are dealing, will then have a profound effect on the rate of desorption since this is proportional to exp( - AEJRT) for a non-activated adsorption. This exponential dependence of rate on adsorption energy allows a rough division of the sites on the surface to be made into those from which desorption into the gas phase takes place readily, p’, and the rest, l3, from which desorption is negligible during the course of an experiment, The following reaction scheme for the chemisorbed gas can then be written: gas 2 l3’-state 2 p-state. km, h-2
(Ml)
We now suggest that because movement of an H-atom from a b site to a l3’ site is energetically unfavourable (k, 9 k _ 2) it only takes place when there is a simultaneous motion of an H-atom from a P’-site to a p-site. This concerted reaction is isoenergetic for a single isotope and nearly isoenergetic for the interchange of hydrogen and deuterium. At room temperature, where chemisorbed hydrogen tends to be mobile, the reaction may be expected to take place readily. Using the model we can now formulate the replacement of hydrogen
by deuterium
as follows:
Re-H (b’ + l3) 5
Re-H (p) + H,(g)
2
Re-H (0) + Re-D(l3’) surface movement
Re-D@
+ /!I’) + H,(g)
+ HD(g)
2 ReeD(P) + Re-H(F) +_ Re-H (b) + Re-D (p’)
Re
HYDROGENISOTOPEREPLACEMENTREACTIONSON
An alternative
and simpler mechanism
for the reaction
in which the p as well as the p’ undergoes i.e.
503
can also be envisaged,
direct exchange
with the gas phase,
The first order kinetics with respect to the replacing gas suggest that the reaction is collision controlled but do not allow us to distinguish between the two mechanisms (Ml) and (M2). However, this latter mechanism was thought to be unlikely on a tungsten surface and would, indeed, lead to a high initial rate of desorption of the homonuclear molecule, in contrast with the observed zero rate. This consideration effectively rules out mechanism (M2). When discussing the rates of the reactions it is convenient to take together the consideration of the shapes of the curves and of the differences between the characteristics of the isotopes, points (2) and (3) above, together. In seeking to interpret the results we have chosen to relate them to quantities which are either known from independent experimental observation or, where this is not possible, to quantities about whose order of magnitude informed conjectures can be made. This procedure has the advantage that it avoids any postulate about the detailed atomic configuration of the transition states of the various reactions. Since the mechanisms of the reactions are not known any such postulates would necessarily be speculative. The quantities involved are (1) the zero point energies (ZPE) of the several isotope species of hydrogen, (2) the ZPE of hydrogen or deuterium bonded to rhenium and (3) the equilibrium constant for the reaction H, + D,$2HD. Of these quantities (1) and (3) are known and a better than order-of-magnitude estimate of (2) can be made. However, the use of energies which relate to reactant or product molecules alone and which do not include the (unknown) transition states carries with it the implicit assumption that whatever the atomic arrangements of the transition states may be they reflect the energies of the participating molecules, Although the theory evolved after the experiments had been completed it
504
R. P. H.GASSER,
C.MORRlS
AND A. K.SZCZEPURA
may be clearer to reverse the order in the discussion and start with the basic postulates, develop the equations which describe the behaviour of the reactions at room temperature and then compare these results with the experiments. Postulate I: Equilibration
on the surface
is rapid.
This implies
that the
reaction Re-H (f3) + Re-D (p’) --f Re-D (p) + Re-H (p’) takes place rapidly compared with interchange between the B’-state and the gas, i.e. k, % k_, . Theconsequence ofthis postulate is that in an experiment in which say, deuterium replaces hydrogen the ratio of hydrogen to deuterium atoms in the B’-state is at all times the same as the ratio in the p-state, even though initially the b-state contains exclusively hydrogen atoms whilst the deuterium adsorbs only into the p/-state. This statistical distribution between the B and the p’-states can be achieved by the concerted movement of atoms already suggested in the discussion of point (I). Postulate 2: Adsorbed isotopes desorb in proportions governed by the gas-phase equilibrium constant. By this we mean that when gas desorbs from a surface on which both hydrogen and deuterium are adsorbed, the proportions of the molecules H,, H D and D, are governed principally by the equilibrium constant K for the gas-phase reaction H, + D,+2
HD;
K=3.26 at room temperature’“). Thus, for example, when an incoming, replacing hydrogen molecule collides with a surface on which there are equal numbers of hydrogen and deuterium atoms, equilibrium considerations lead to the conclusion that the desorbed molecules of interest, D, and HD, should come off in the ratio of I to 1.8. This postulate carries the implication that the velocity constants for the desorption of all isotopic hydrogen molecules are the same. However, as discussed below, the influence of the zero point energy changes for the particular reactions taking place may introduce an extra term into the desorption rate equation. In order to use this postulate to calculate the expected gas phase composition at any stage during the replacement reactions it is necessary to know the instantaneous surface concentrations of hydrogen and deuterium. As an example of how these concentrations are obtained and of how the calculation is carried out, the replacement of hydrogen by deuterium will be considered. The total area under the desorption curves of H, and HD is used to calculate the surface concentration of hydrogen when the deuterium was first admitted. At any time thereafter during the desorption the amount of hydrogen removed from the surface (as H, and HD) is calculated from the
HYDROGEN
ISOTOPE
REPLACEMENT
REACTIONS
ON
Re
505
desorption curves of H, and of HD. The remaining hydrogen is then obtained by difference. The coverage of deuterium at any time is calculated from the area of the deuterium adsorption curve from t =0 to the chosen time, less a correction for the deuterium contained in the desorbed HD. The way in which the surface concentrations of hydrogen and deuterium change during the experiments illustrated in fig. 2 are shown in fig. 5.
Fig. 5.
Surface concentrations of hydrogen (:I) and of deuterium (0) during replacement of hydrogen by deuterium.
Postulate 3: The rate at which an isotopic
species desorbs depends upon the Zero Point Energy change of the reaction during which it is formed. The Zero Point Energies (ZPE) concerned are those of the gaseous molecules H,, HD and D, and the surface species Re-H and Re-D. No experimental data exist for calculating the surface ZPE and in the absence of a rigorous mathematical expression for the potential energy curve of hydrogen bonded to rhenium, we shall use the Morse potential the ZPE of Re-H and Re-D. The Morse equation is U(Y - r,) = D, {I - exp[-
for the estimation
of
/?(r - r,)]}‘,
where D, is the dissociation energy of the bond from the minimum P.E. curve and /I is a constant. The term values for the vibrational levels are then
of the energy
This equation is similar to the term value equation for the anharmonic oscillator when cubic and higher terms are omitted. For the ensuing discus-
506
R.
P. H.GASSER,
G. MORRIS
sion we can neglect the anharmonicity G(r)
AND
A. K.SZCZEPURA
effect and use the simple expression
= (u + +) hv
to obtain the ZPE of the surface species Re-H and Re-D. The vibration frequencies of the molecules H,, HD and D, are known from spectroscopic studies 14) and from these frequencies the calculated ZPE are: H,, 6.23 kcal mole-‘; HD, 5.39 kcal mole-’ and D,, 4.41 kcal mole-‘. For the species Re-H and Re-D the reduced masses are close to I and 2 respectively so that the simple vibration energy level expression yields ZPE (Re-H) since for the simple harmonic
= J2 ZPE (Re-D),
oscillator v = (I /27r) (k/p)“,
where k is the force constant
and the reduced
/f = (111, x m2)/(n1r
mass, p, is defined as + n1J.
Whilst we cannot calculate the magnitudes of these two ZPE we can conjecture that they may be slightly more than half the ZPE of H, (Re-H) or D, (Re-D). This conjecture is based on the considerations that the strength of the surface bond is probably a little greater than half the dissociation energy of the hydrogen or deuterium molecule (exothermic adsorption) and that for similarly shaped P.E. curves the dissociation energies and force constants vary in parallel. Now for hydrogen p=+ and ZPE,, p= I and ZPERe_H=JkRe_H/4rr. If =(1/4+/2 k,, whilst for Re-H, >+k,, the ZPE of Re-H is slightly greater than half ZPE of H,. then kRe--H Similarly, for the deuterium containing moieties. In this discussion our concern is entirely with the relative rates of desorption, either H,/HD or D,/HD, and the effect of ZPE changes on these ratios. It is a matter for experimental observation to determine the inherent probability of reaction taking place, i.e. of the rate constant k,. Postulate 4: Desorption from the surface is associated with the collision of a gas phase molecule. This requirement follows from the observation that the overall rate of reaction is first order in the pressure of the replacing gas and was discussed above. A collision is then a necessary but by no means a sufficient condition for desorption to occur. It is only when there are signiicant numbers in the p’-state that measurable desorption can take place when an impact occurs. The consequences of postulates (l)-(4) can be summarised: Rate of desorption
= k, x Rate of collision of replacing gas x Equilibrium concentration of desorbing x exp[ - (ZPE change)/RT].
gas (1)
Re
HYDROGENISOTOPEREPLACEMENTREACTIONSON
In order to make a comparison selected two groups
between
of experiments
theory
for detailed
507
and experiment
analysis.
Within
we have
each group
the pressures of the replacing gas were as closely similar as could be obtained. These are the results shown in fig. 1 in which the pressure of H, was 1.3+ f0.08 x 10e7 torr and fig. 2 in which the pressure of D, was 2.74 f0.14 x of the relative rates of evolution of H, or D, x lo-7 torr. The calculation and HD then makes use of eq. (1) in the form: Rate of evolution of X, ~_____.._ Rate of evolution of HD Equilibrium
concentration Equilibrium
Consider
X, x exp [ - A (ZPE)/RT] concentration
HD
first the pair of reactions: 2Re-H+D,+2Re-D+H,, Re-H
A schematic
representation
(1)
+ D, + Re-D
+ HD .
of the ZPE changes
Re-H
Hz HD
ReH
Re-D
Dz
ReD
Reaction In reaction A (ZPE)I
(1)
(1)
(2)
for the two reactions
is:
9 1
(2)
(2)
(1) the change in ZPE is: = ZPE (Hz) + 2ZPE (Re-D) = 6.23 - 4.41 - 2 ((J2
- ZPE (D2) - 2ZPE (Re-H)
- 1) ZPE (Re-D))
= 1.82 - 0.82 ZPE (Re-D) . In reaction A (ZPE),
(2) the change = ZPE (HD)
in ZPE is: + ZPE (Re-D)
= 5.39 - 4.41 - ((J2
- ZPE ( D2) - ZPE (Re-H)
- 1) ZPE(Re-D)}
= 0.98 - 0.41 ZPE (Re-D)
.
Then for ZPE(Re-D) > $ZPE(D,) it follows that A(ZPE), co.01 kcal mole-l and A(ZPE), co.08 kcal mole-‘. Thus A(ZPE), -A(ZPE), is negative [i.e. reaction (1) is favoured over reaction (2)], and becomes more negative as ZPE(Re-D) increases. It follows that the larger is ZPE(Re-D) the more favoured reaction (1) becomes relative to reaction (2). Thus a correct assign-
508
R.P.H.GASSER,
ment of a greater gas, can be made. to assign a value value which will
G.MORRLS
AND
A.K.SZCZEPURA
rate of evolution of H, than of HD, when D, is the incident To put the results on a quantitative footing it is necessary to ZPE(Re-D). At this stage it is appropriate to choose a both produce as good a fit as possible, and be physically
reasonable. ZPE(Re-D)=2.36 kcal mole-’ =2.2 kcal mole-‘]. We now have: Rate of desorption
Hz
Rate of desorption
HD
fulfils these criteria [cf. f ZPE( D2)
Equilibrium cont. H, ~~ -~~ --exp = Equilibrium cont. HD Then A (ZPE),
= I .82 - 0.82 x 2.36 = - 0. I2 kcal mole-’
A(ZPE),
= 0.98 - 0.41 x 2.36 = -t 0.01 kcal mole-’
,
Thus R HZ
R HD For this pair of reactions R,, = k,[H,]
_
I321 exp
CHDI
(I 30/RT)
(3)
we can write exp(l30jRT),
R,,
= k,[HD],
so that if a value of k, is chosen which brings the rate of desorption of HD near its peak into as close agreement as possible with the experimental value we can calculate the overall shape of the HD desorption curve. When choosing k, we are in effect adjusting the scale of the theoretical curve to match the experimental observations. Once k, has been selected, eq. (3) allows the partial pressure of desorbed H, to be predicted at any chosen time during the reaction. The calculated pressures at I min intervals are shown in fig. 6a and are in highly satisfactory agreement with the experimental observations corrected for background exchange. When replacing gas is first admitted, the background is indeterminate and the corrected curve is shown as a broken line in this region. To illustrate in more detail how theory and experiment are compared, the calculations of the ratio of rates of evolution at r=2 min will be carried out. From fig. 5 the surface concentrations of hydrogen and deuterium are 3.3 x 1014 atoms cm-’ and 4.36 x 1014 atoms cm-‘. Using K = 3.26 for the reaction H, + D, = 2HD, the expected gas-phase equilibrium concentration of H, is equivalent to 0.74 x 1014 mol cn1C2 and of HD is 1.81 x 1014 mol cme2. Hence R,J&,u
= (0.74/1.81)
exp(130jl.98
x 296) = 0.51
Re
HYDROGENISOTOPEREPLACEMENTREACT~ONSON
509
(b)
0.5
0.4
0.:
0.2
0.1
0
1-
2
4 6 Tlme(min)
,
8
2
I
4 Time
I
I
6 8 (min)
I
I
10
12
Cd)
2
4 6 8 Time (min)
10
1:
Fig. 6. Comparison of calculated partial pressures of desorbed hydrogen isotopes (circles) with experimental results corrected for background contributions (full lines). Initial backgrounds of HD are uncertain (broken lines). (0) desorbed HD; (0) desorbed HZ or Dz. (a) Replacing gas Dz; final pressure 2.7 x lO-7 torr, room temp.; (b) Replacing gas Hz; final pressure I .2 x 10e7 torr, room temp.; (c) Replacing gas Dz; final pressure 9.8 x IO-* torr, 380 K; (d) Replacing gas Hz; final pressure 5.3 x lo-* tort-, 380 K.
510
R.P.H.GASSER,
Experimentally
G.MORRlS
AND
A.K.SZCZEPURA
the ratio of the rates of evolution
of the gases is given by
(RHJRHDL~ = (PH,Ih,J x J4
Y
where the factor V/S allows for the difference between the molecular velocities of H, and HD and, therefore, for the more rapid pump away of H,. Substitution of the experimental partial pressures, Pflz = 3.1 x lo- * torr and P nn=7.3 x 10e8 torr in the equation yields (R&r&p, We now turn to a consideration 2 Re-D
= 0.52.
of the two reactions: + H, + 2 Re-H + D, ,
(4)
Re-D+H,+Re-H+HD. This time the ZPE changes
are:
Re-H tt
Re-D (4)
(5)
t
H2
H2
HD
HD
Dz
Dz
(4)
(5)
Re-H t
Re-D
(5)
Thus A(ZPE),
= ZPE(D,)
+ 2ZPE(Re-H)
= 0.82 ZPE (Re-D)
- ZPE(H,)
- 2ZPE(Re-D)
- ZPE(H,)
- ZPE(Re-D)
- I .82,
and A(ZPE),
= ZPE(HD)
+ ZPE(Re-H)
= 5.39 - 6.23 -I- ((,,!2 - I) ZPE(Re-D)] = 0.41 ZPE (Re-D)
- 0.84.
Provided then that ZPE(Re-D)>2.39 kcal mole-’ we have that A(ZPE),>A(ZPE), and reaction (4) becomes endothermic relative to reaction 5. This results in a more ready desorption of HD than of D, by incident hydrogen, again in accordance with the experimental observations. We can now make a second estimate of ZPE(Re-D) designed to produce as good a fit as possible to the results of reactions (4) and (5). The appropriate value of ZPE(Re-D) is 2.82 kcal mole-r; ..
A (ZPE),
= 0.82 x 2.82 - 1.82 = 2.31 - I .82 = 0.49 kcal mole-
’,
HYDR~GENI~~~~~EREPLACEMENTREACTIONS~N
Re
511
and = 0.41 x 2.82 - 0.84 = 1.16 - 0.84 = 0.32 kcal mole-’
A (ZPE), The relative RD,~&D
rates of desorption =
of deuterium
.
and HD are then:
~CW/[HDl~ ev I- [A@‘EL - AW’%IIRTI
= ([D,]/[HD]}
exp [ - (490 - 320)/RT]
= {[D,]/[HD]}
exp (-
170/RT).
The rates of desorption calculated from the last equation corrected for the difference in molecular velocities and with the assignment of the appropriate scaling factor once again yield points for comparison with experiment. The fit between theory and experiment, although less good for this pair of reactions than for reactions (1) and (2) is still satisfactory, fig. 6b. Furthermore, the average value of the zero point energy of the Re-D bond obtained from the two experiments, 2.6 kcal mole-’ is entirely reasonable for a fairly strongly bonded surface species (compare, for example, ZPE of DC1 = 3.0 kcal mole-l). One further deduction can be made from the results, namely the difference between the heats of adsorption of hydrogen and deuterium on rhenium. This difference is numerically equal to either A(ZPE), or A(ZPE), [since reaction (3) is the reverse of reaction (l)]. Substitution of ZPE(Re-D) ~2.6 kcal mole-’ gives the energy difference as 0.2 kcal mole-‘, with deuterium having the larger heat of adsorption. This energy is equal to the difference in the activation energies for desorption since the adsorption process is non-activated. It is closely similar to the quoted3) difference between the activation energies for the desorption of hydrogen and deuterium from tungsten, 0.3 kcal mole-‘.
7. Results at 380 K The desorption curves at 380 K are very similar to the room temperature curves in shape and can be analysed similarly. The equilibrium coverage of hydrogen at 380 K was 5.4kO.5 x 1014 atom cm-‘. The rates of the various reactions showed remarkably little variation with temperature. When deuterium was the replacing gas the rate of reaction increased by only about 10% between room temperature and 380 K and for hydrogen the rate increased by about 50%. This latter increase corresponds to an activation energy for this replacement reaction, apart from the ZPE change, of about 1 kcal mole-‘. This is a much smaller temperature dependence of rate than was observed for the similar reaction on tungsten for which an activation energy of about 5 kcal mole-’ was calculated. The analysis of the curves
512
a. P. H.GASSER,
G. MORRIS
AND A. K.SZCZEPURA
follows the same procedure as for the room temperature results except that the equilibrium constant for the hydrogen isotope equilibrium at 380 K (3.46) was used. With calculated and experimental rates adjusted, as before, for the HD-producing reaction of each pair, there is again excellent agreement between the results then calculated for the desorption of either H, or D, and the observed pressure records, as figs. 6c and 6d show. In choosing to interpret the results of these experiments by what is essentially a phenomenalistic approach we have been able to account not only for the general shapes of the desorption curves but also rather successfully for the detailed behaviour of the various isotopic species. In so doing only one variable parameter has been introduced (ZPE of Re-D) apart from a scaling factor. Although for so complex a system this is by no means the only possible approach, it does have the virtues of simplicity and success.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
A. D. Crowell and L. D. Matthews, Surface Sci. 7 (1967) 79. J. T. Yates, Jr., J. Phys. Chem. 68 (1964) 1245. P. W. Tamm and L. D. Schmidt, J. Chem. Phys. 52 (I 970) 1150. C. Boon, R. P. H. Gasser and H. Tovey, Surface Sci. 19 (1970) 255. P. A. Redhead, Trans. Faraday Sot. 57 (1961) 641. K. F. Poulter and J. A. Pryde, Brit. J. Appl. Phys. (2) 1 (1968) 169. R. P. H. Gasser, T. N. Morton, J. M. Overton and A. K. Szczepura, Surface Sci. 28 (1971) 574. B. Bergsnov-Hansen and R. A. Pasternak, J. Chem. Phys. 45 (1966) 1199. R. P. H. Gasser, Chem. Sot. Specialist Periodical Reports, Surface and Defect Properties of Solids 1 (1972) 205. G. C. Bond, Catulysi.s by Mrrals (Academic Press, New York, 1962). D. D. Eley and P. R. Norton, Discussions Faraday Sot. 41 (1966) 135. J.J. F. Scholten and J. A. Konvalinka, J. Catalysis 5 (1966) 1. H. C. Urey and D. Rittenberg. J. Chem. Phys. 1 (1933) 137. G. Herzberg, Mohrlur Spccfra und Molecular Strucfwe (Van Nostrand, New York, 1950).
SCIENCE
HYDROGEN
36 (1973) 494-512
ISOTOPE
REPLACEMENT
R. P. H. GASSER,
Phy.Gcal Chemistq
Received
0 North-Holland
Ci. MORRIS
and
Publishing
REACTIONS
Co.
ON RHENIUM
A. K. SZCZEPURA
Luborntory, South Parks Road, Oxftird OXI 392,
9 October
1972; revised
manuscript
received
20 December
England
1972
The existence of a mobile equilibrium at room temperature between part of the hydrogen adsorbed on rhenium and gaseous hydrogen is demonstrated by the easy exchange of isotopes between the adsorbed layer and the gas phase. The adsorbed gas is desorbed as a mixture of homonuclear molecules (of H2 or Da) and of the isotopically mixed species (HD). However, the replacement reactions are not symmetrical; there is a greater proportion of HD in the desorbed gas when deuterium is replaced by hydrogen than in the converse reaction. This kinetic isotope effect is attributed to differences between the zero-point energies of the various hydrogen containing species. Quantatitive agreement between the shapes of the experimentally observed desorption curves and calculated curves is obtained if the zero-point energy of the bond between a surface rhenium atom and deuterium is assigned the value 2.6 kcal mole-‘.
1. Introduction The kinetic concept of the nature of a chemical equilibrium implies that both forward and back reactions take place at significant rates at the prevailing temperature. For many of the reactions at room temperature between a clean metal surface and a surrounding gas this condition is not fulfilled and it is only at elevated temperatures that the reverse reaction, desorption, occurs at a measurable rate. However, when it appears that an equilibrium one conbetween free and adsorbed gas is “mobile” at room temperature venient method of measuring the rate of interchange of absorbate between the gas and surface is to “label” the molecules by using different isotopic species for the initial gas phase and surface moieties. This technique was successfully used to establish the rate at which the adsorption and desorption of carbon monoxide on Ni (I IO) single crystal surfaces took place’). The build up of r4C0 on the 12C0 covered surface when gaseous 14C0 was admitted to the system, or the converse reaction in which “CO replaced adsorbed 14C0, were recorded with a radiochemical counting technique. It had been established earlier that nickel at room temperature does not catalyse the interchange of atoms between carbon monoxide molecules”) and it was concluded therefore that the replacement took place in a single molecular event. 494
HYDROGENISOTOPEREPLACEMENTREACTIONSON
When the substrate
Re
does catalyse the isotope equilibration
495
reaction
under
conditions where replacement is also taking place, a new and interesting situation arises. The replacement reactions of the hydrogen isotopes on tungsten are examples of such systems which have been studied previouslya) and the established activity of rhenium as a catalyst for the HZ/D, equilibration reaction at room temperature gives grounds for supposing that combined replacement and isotopic mixing could be observeda). It was, therefore, decided to investigate these reactions, which have a further interesting feature in that they might show a kinetic isotope effect. Such an effect would arise from the difference in the rates of making and breaking the various bonds to the different isotopic species. No a priori estimate of the magnitude of any such effect was made but rather it was left as a matter for experimental determination. 2. Experimental The experimental conditions were unchanged from the earlier work4) for which the rhenium filament of length 3 1 cm and geometric area 2.47 cm2 was mounted in a Pyrex ultra-high vacuum chamber of volume 1.8 litre. Two bakeable metal valves connected the reaction vessel to two gas storage volumes and a third, similar, valve led to the pumps. Adjustment of this latter valve allowed a convenient rate of flow of gas through the chamber to be selected, whilst adjustment of the inlet valves provided an appropriate equilibrium pressure of the relevant gas. The replacement of adsorbed hydrogen by deuterium was recorded by saturating the filament at room temperature with hydrogen at an equilibrium pressure of about 1 x lop7 torr (1 torr= 133.3 Nmm2), closing the hydrogen inlet valve and pumping out the system for 10 min. Deuterium was then admitted, the inlet valve being adjusted to produce a final pressure between 7 x 10e8 torr and 3.6 x low7 torr. An omegatron radiofrequency mass-spectrometer which formed an integral part of the UHV apparatus was used, after calibration against an ionization gauge equipped with a lanthanum boride coated cathode (to minimize atomization of the gas), for all pressure measurements. The sensitivity of the omegatron was the same for H, as for D, and this sensitivity was also used for HD. During the course of the replacement reaction the omegatron was tuned, in successive experiments which were as nearly similar as possible, to D, (mass 4) HD (mass 3) or H, (mass 2). The whole series of experiments was then repeated with the filament initially saturated by deuterium and with hydrogen as the replacing gas. Before the reactivity of the filament could be calculated it was necessary to determine whether there was a contribution by the other surfaces of the UHV system to the observed effects. To do this the filament was allowed to saturate
496
R. P. H.GASSER,
G. h4ORRlS
AND
A. K.SZCZEPURA
overnight in the residual gas, which was predominantly carbon monoxide and which deactivates it4). One hydrogen isotope was then admitted to give a pressure of about I x iOm7 torr. After saturating ail surfaces in the chamber the inlet valve was shut and the apparatus was pumped out for 10 min. The other isotope was then let in. The pressure of newly-ad~l~itted gas rose rapidly to its equilibrium value, at which time a small background of HD and a miniscule pressure of the initial isotope were observed. These residual pressures can be seen on the experimental traces in fig. I. In calculating the effect of the filament these final pressures have been subtracted from the pressure records. Some similar experiments at elevated filament temperatures were also performed. The equilibrium uptake of hydrogen dilninished with increased temperature and the upper limit of the temperature at which the duration of the reaction was sufficient to allow the various isotope pressures to be usefully recorded was 380 K.
Fig. I.
Partial pressures of HT, HD and DZ during the replacement of adsorbed deuterium by hydrogen.
it was necessary to determine whether the clean rhenium surface made any distincti between the individual isotopes. To do this the initial sticking probability s0 and the maximum uptake O,,, at room temperature and an equilibrium pressure of ca. 1 x 10 -’ torr were calculated from the mass spectrometer records of the pressures during adsorption “). For both isotopes s0 and O,,, were the same at 0.24 and 7+0.5 x lOi4 atom cmm2 respectively. (The error in the uptake is the range of the random scatter; the systematic error due to un~ertaitlties in the gauge sensitivity may be much greater. For the calculations of uptake the manufacturer‘s quoted sensitivity was used.) However, the presence of some reversibly adsorbed gas on the filament was demonstrated by pumping down the reaction chamber for periods of
3, 5, 7 and 10 min and measuring
497
Re
HYDROGENISOTOPEREPLAC‘EMENTREACTIONSON
the amount
of hydrogen
taken
up when
the supply of gas was restored. For a pump-down period between 5 and 10 min a constant amount of gas, equivalent to about 0.9 x 1014 atoms cm-’ of rhenium filament, was required to saturate the filament, though less gas was required at shorter times. These results are in accord with earlier work6). As with a polycrystalline tungsten or molybdenum filament, therefore, a clean rhenium surface makes no distinction between the individual isotopes 7l 8). 3. Results Measurements were made over the pressure range 6 x IO- * torr to 4 x 10e7 torr. A typical series of pressure records at room temperature for the replacement of deuterium by hydrogen is shown, for a final equilibrium pressure of hydrogen near I .2 x IO-’ torr, in fig. 1. A similar series of runs for the reverse reaction but with an equilibrium pressure of deuterium near 2.8 x IO-’ torr is shown in fig. 2. From the many pressure records made (about 35 sets in all), all of which showed the characteristic shapes of the curves in figs. I and 2, it is possible to carry out two groups of calculations.
Time
Fig. 2.
Partial
pressures
(mln)
‘-
of HZ, HD and De during hydrogen by deuterium.
the replacement
of adsorbed
In the first group are the calculations of the total amount of adsorbed gas which can be replaced by the alternate isotope and the distribution of the desorbed isotope between the homonuclear isotope (i.e. H, or DJ and the mixed isotope (i.e. HD). The second group is concerned with the rate of the overall replacement process, both with respect to the pressure of the incoming gas and with respect to the concentrations of the isotopic species on the surface. We shall deal with these in turn.
498
R. P. H. GASSER.
G. MORRIS
AND A. K.SZCZEPURA
4. Quantity and isotopic composition At any instant
during
of replaced gas
the desorption dP -_=c~ dt
dn
~-kP,
dt
where c is a constant which relates the number of molecules in the apparatus to the pressure, P, and k is the pumping constant of the aperture of the valve connecting the reaction chamber to the pumps. k is separately measured from the record of the first order decay of pressure when the gas admission valve is closed rapidly. k varies with the molecular weight of the gas (kccm)) and was normally about 0.7 see-l for H,. Then: t=CC
ndca=
1
t=CC
dn-j
s
t=o
,=
dP+;>
t=o
Apart from the effect of the initial
ic
k(P-P,)dt.
1 i=O
settling down period, which is negligible,
t=v
I
dP=O.
f=O The activity of other surfaces in the U.H.V. chamber was shown to be constant and to give rise to the finite final pressure of HD or replaced X,, i.e. to P,. The contribution of the other surfaces is, therefore, subtracted from the pressure record in the final integral on the R.H.S. of the above equation.
(P
-
P,) dt.
(2)
As in a conventional flash filament experiment, the integral is evaluated graphically from the pressure record. With a knowledge of k, c (6.08 x 1Ol9 x x P mol) and the area of the filament the number of molecules of gas evolved per unit area of filament surface can then be calculated. The number of molecules of incident gas required to complete the replacement reaction was obtained from the pressure record of this gas. In this case the amount of gas consumed was calculated from t=%
s
(‘final - f’) dt
r=o
HYDROGEN~SOTOPEREPLACEMENTREACTIONSON
(where the pressures the experimental
are those of the incident
Re
499
gas), i.e. from the area between
curve and the extrapolation
of the final pressure
to zero
time. In the experiment designed to measure the quantity of gas reversibly adsorbed the number of molecules was again calculated from the pressure record by graphical integration. This experiment of course uses the same isotope throughout. The results at room temperature are summarised in table 1. TABLE I No. of atoms of gaseous isotope required (x 1Ol4cm-2)
Reaction
7.3 6.6 0.9 3.5 7.0 2.6 7.8
(1) Re + HZ +ReHa&atd) (2) Re + DZ --f ReDsds(satd) (3) (4) (5) (6) (7)
ReHaas(pump IO min) + ReFh(satd) ReH + t De(g) + ReD + f Hz(g) ReH + Dz(g) + ReD f HD ReD + 4 Ha(g) + ReH + +Dz(g) ReD + Hz(g) --f ReH + HD
The random errors in the uptakes [reactions (l)-(3)] are ca. f 10% and in the replacement reactions (4)-(7) ca. f5”/,. There was no measurable dependence of uptake in the experimental pressure range 6 x 10m8 torr to 4.0 x lo-’ torr. The principal points of interest about these results are: (I) The replacement reactions were unsymmetrical; the ratio (HD/D,),,, That is to say, it was relatively easier was greater than the ratio (HD/HJdes. for HD to desorb from a deuterium-saturated surface than from a hydrogensaturated surface. (2) All of either adsorbed isotope could be replaced quite rapidly even though only ca. 10% of the gas was reversibly adsorbed. An independent evaluation of the self-consistency of the measurements can be made by comparing the total number of gas phase atoms required to replace an isotope [i.e. (4)+(5) or (6)+(7)] estimated from the desorption curves, with the consumption of gas calculated from the replacing-isotope adsorption curve. The two numbers should differ by the amount of gas reversibly adsorbed [reaction (3)], 0.9 x 1014 atoms cm-‘. For deuterium as replacing gas the gas phase consumption was 10.8+ 1 x 1014 atoms cmm2 compared with the desorbed gas sum of 10.5kO.5 x lOI atoms cme2, whilst for hydrogen the equivalent numbers were 10.7+ 1 x 1014 atoms cmm2 and 10.4+0.5x 1014 atoms cm-‘. The agreement is thus satisfactory. 5. The rates of reaction (1) The kinetics
of the replacement
reaction
with respect to the incident
R. P. H.GASSER,
500
G. MORRlS
AND A. K.SZCZEPLJRA
gas were determined in a manner similar to the technique used for flashfilament work. The probability of utilization of an incident molecule by the surface when covered with the other isotope was calculated from the relationship: Probability
= (acid’) (P,,jP
- if,
where cf is a constant which relates the rate of collision to the gas pressure (2.53 x IO” collisions see-’ torr-’ for D2). This probability was then plotted against the fractional uptake of gas. The results are shown in fig. 3 for both hydrogen and deuterium as incident gas. The single curve obtained suggests that the rate of uptake of either gas is directly proportional to the rate of collision, i.e. the reaction has first order kinetics with respect to the incident
Fractional
Fig. 3.
Utilization
probability
consumpt,or,
as function of fractional
consumption
of replacing gas
(*-.f final pressure I% - 3. I5 x 10 i torr, ( ;?) final pressure D2 -- 2.72 x 1Omi tori-,
(\;) final pressure De ~- 1.98x 10m7torr, (0) tinal pressure H:! _~ 1.02x IO i torr, (A) final pressure Hz (7) final pressure He
1.21 ? IO ’ tot-r, 1.98 ‘XIO-’ torr,
gas. The initial uptake probability by the filament after saturation with gas and pumping out for 10 min. was the same for both isotopes, 0.056. This value is close to the initial sticking probability of hydrogen on a pumpedout, hydrogen-covered filament, 0.055. An alternative method of demonstrating the first order kinetics is to plot the number of surface molecules which have desorbed as a function of number of collisions of incident gas as in fig. 4. The single curve for the evolution of hydrogen when deuterium was the replacing gas, or for the converse reaction, shows that both replacement reactions have first order
Re
HYDROGENISOTOPEREPLACEMENTREACTIONSON
kinetics.
The
separation
between
these
two replacement
501
reaction
curves
reflects the difference in the proportions of H, or D, in the desorption products. The isotopic mixing reaction can also be seen to have first order kinetics (H, pressures: 2.0x 10-‘-6.6x 10e8 torr, D, pressures: 3.1 x IO-‘-1.2 x 1OF7 torr, and in the initial stages to proceed at the same rate for both isotopes. At higher collision numbers than the limit of fig. 4 the curves diverge further as the result of the greater evolution of HD by hydrogen as incident gas than by deuterium.
Fig. 4.
Evolution
of adsorbed (G) (Cl) (A) (A)
gas as a function HD displaced by HD displaced by Hz displaced by Dz displaced by
of collisions De, HZ, Dz, HZ.
by replacing
gas
(2) The rate of desorption of any species from the surface was calculated from its partial pressure, using eq. (I), and subtracting the contribution of the walls [i.e. P, as in eq. (2)]. In practice, the inequality dP/dtekP was sufficiently closely followed to allow the reat of evolution to be calculated from the simple relationship: dnjdt
= (k/c) (P - P,).
During the early stages the incident gas is mainly utilised in filling the reversibly-bound sites and desorption is relatively unimportant. After about + min at 1 x IO-’ torr these sites are nearly full and the incident gas is then predominantly consumed by the replacement and isotopic mixing reactions. 6. Discussion
The most important pretation are:
features
of our experiments
which
require
inter-
502
R. P. H.GASSER,
G. MORRIS
AND A. K. SZCZEPURA
(1) The observation that all of the adsorbed gas can be replaced readily even though only ca. lo”/, of it is reversibly adsorbed. (2) The general shape of the desorption curves. (3) The difference between the behaviour of the two isotopes. In the discussion which follows these points are all covered, but in the absence of an agreed mechanism for the equilibration reaction g- 12). it is by no means impossible that an alternative explanation could be devised which would also fit all the facts. We start with a consideration of (1). Hydrogen is usually chemisorbed on transition metals at room temperature and above as atoms and we shall assume that this is so for rhenium. Atomic adsorption requires the breaking of the fairly strong bond in the hydrogen molecule (D, = 103.2 kcal/mole) followed by the formation of two Re-H surface bonds, each of strength x. The overall heat of adsorption then reflects the balance between these two large energies, AEad5 = 2~ - D,. Quite a modest change in x, such as may well occur from one crystal face to another on the polycrystalline surface with which we are dealing, will then have a profound effect on the rate of desorption since this is proportional to exp( - AEJRT) for a non-activated adsorption. This exponential dependence of rate on adsorption energy allows a rough division of the sites on the surface to be made into those from which desorption into the gas phase takes place readily, p’, and the rest, l3, from which desorption is negligible during the course of an experiment, The following reaction scheme for the chemisorbed gas can then be written: gas 2 l3’-state 2 p-state. km, h-2
(Ml)
We now suggest that because movement of an H-atom from a b site to a l3’ site is energetically unfavourable (k, 9 k _ 2) it only takes place when there is a simultaneous motion of an H-atom from a P’-site to a p-site. This concerted reaction is isoenergetic for a single isotope and nearly isoenergetic for the interchange of hydrogen and deuterium. At room temperature, where chemisorbed hydrogen tends to be mobile, the reaction may be expected to take place readily. Using the model we can now formulate the replacement of hydrogen
by deuterium
as follows:
Re-H (b’ + l3) 5
Re-H (p) + H,(g)
2
Re-H (0) + Re-D(l3’) surface movement
Re-D@
+ /!I’) + H,(g)
+ HD(g)
2 ReeD(P) + Re-H(F) +_ Re-H (b) + Re-D (p’)
Re
HYDROGENISOTOPEREPLACEMENTREACTIONSON
An alternative
and simpler mechanism
for the reaction
in which the p as well as the p’ undergoes i.e.
503
can also be envisaged,
direct exchange
with the gas phase,
The first order kinetics with respect to the replacing gas suggest that the reaction is collision controlled but do not allow us to distinguish between the two mechanisms (Ml) and (M2). However, this latter mechanism was thought to be unlikely on a tungsten surface and would, indeed, lead to a high initial rate of desorption of the homonuclear molecule, in contrast with the observed zero rate. This consideration effectively rules out mechanism (M2). When discussing the rates of the reactions it is convenient to take together the consideration of the shapes of the curves and of the differences between the characteristics of the isotopes, points (2) and (3) above, together. In seeking to interpret the results we have chosen to relate them to quantities which are either known from independent experimental observation or, where this is not possible, to quantities about whose order of magnitude informed conjectures can be made. This procedure has the advantage that it avoids any postulate about the detailed atomic configuration of the transition states of the various reactions. Since the mechanisms of the reactions are not known any such postulates would necessarily be speculative. The quantities involved are (1) the zero point energies (ZPE) of the several isotope species of hydrogen, (2) the ZPE of hydrogen or deuterium bonded to rhenium and (3) the equilibrium constant for the reaction H, + D,$2HD. Of these quantities (1) and (3) are known and a better than order-of-magnitude estimate of (2) can be made. However, the use of energies which relate to reactant or product molecules alone and which do not include the (unknown) transition states carries with it the implicit assumption that whatever the atomic arrangements of the transition states may be they reflect the energies of the participating molecules, Although the theory evolved after the experiments had been completed it
504
R. P. H.GASSER,
C.MORRlS
AND A. K.SZCZEPURA
may be clearer to reverse the order in the discussion and start with the basic postulates, develop the equations which describe the behaviour of the reactions at room temperature and then compare these results with the experiments. Postulate I: Equilibration
on the surface
is rapid.
This implies
that the
reaction Re-H (f3) + Re-D (p’) --f Re-D (p) + Re-H (p’) takes place rapidly compared with interchange between the B’-state and the gas, i.e. k, % k_, . Theconsequence ofthis postulate is that in an experiment in which say, deuterium replaces hydrogen the ratio of hydrogen to deuterium atoms in the B’-state is at all times the same as the ratio in the p-state, even though initially the b-state contains exclusively hydrogen atoms whilst the deuterium adsorbs only into the p/-state. This statistical distribution between the B and the p’-states can be achieved by the concerted movement of atoms already suggested in the discussion of point (I). Postulate 2: Adsorbed isotopes desorb in proportions governed by the gas-phase equilibrium constant. By this we mean that when gas desorbs from a surface on which both hydrogen and deuterium are adsorbed, the proportions of the molecules H,, H D and D, are governed principally by the equilibrium constant K for the gas-phase reaction H, + D,+2
HD;
K=3.26 at room temperature’“). Thus, for example, when an incoming, replacing hydrogen molecule collides with a surface on which there are equal numbers of hydrogen and deuterium atoms, equilibrium considerations lead to the conclusion that the desorbed molecules of interest, D, and HD, should come off in the ratio of I to 1.8. This postulate carries the implication that the velocity constants for the desorption of all isotopic hydrogen molecules are the same. However, as discussed below, the influence of the zero point energy changes for the particular reactions taking place may introduce an extra term into the desorption rate equation. In order to use this postulate to calculate the expected gas phase composition at any stage during the replacement reactions it is necessary to know the instantaneous surface concentrations of hydrogen and deuterium. As an example of how these concentrations are obtained and of how the calculation is carried out, the replacement of hydrogen by deuterium will be considered. The total area under the desorption curves of H, and HD is used to calculate the surface concentration of hydrogen when the deuterium was first admitted. At any time thereafter during the desorption the amount of hydrogen removed from the surface (as H, and HD) is calculated from the
HYDROGEN
ISOTOPE
REPLACEMENT
REACTIONS
ON
Re
505
desorption curves of H, and of HD. The remaining hydrogen is then obtained by difference. The coverage of deuterium at any time is calculated from the area of the deuterium adsorption curve from t =0 to the chosen time, less a correction for the deuterium contained in the desorbed HD. The way in which the surface concentrations of hydrogen and deuterium change during the experiments illustrated in fig. 2 are shown in fig. 5.
Fig. 5.
Surface concentrations of hydrogen (:I) and of deuterium (0) during replacement of hydrogen by deuterium.
Postulate 3: The rate at which an isotopic
species desorbs depends upon the Zero Point Energy change of the reaction during which it is formed. The Zero Point Energies (ZPE) concerned are those of the gaseous molecules H,, HD and D, and the surface species Re-H and Re-D. No experimental data exist for calculating the surface ZPE and in the absence of a rigorous mathematical expression for the potential energy curve of hydrogen bonded to rhenium, we shall use the Morse potential the ZPE of Re-H and Re-D. The Morse equation is U(Y - r,) = D, {I - exp[-
for the estimation
of
/?(r - r,)]}‘,
where D, is the dissociation energy of the bond from the minimum P.E. curve and /I is a constant. The term values for the vibrational levels are then
of the energy
This equation is similar to the term value equation for the anharmonic oscillator when cubic and higher terms are omitted. For the ensuing discus-
506
R.
P. H.GASSER,
G. MORRIS
sion we can neglect the anharmonicity G(r)
AND
A. K.SZCZEPURA
effect and use the simple expression
= (u + +) hv
to obtain the ZPE of the surface species Re-H and Re-D. The vibration frequencies of the molecules H,, HD and D, are known from spectroscopic studies 14) and from these frequencies the calculated ZPE are: H,, 6.23 kcal mole-‘; HD, 5.39 kcal mole-’ and D,, 4.41 kcal mole-‘. For the species Re-H and Re-D the reduced masses are close to I and 2 respectively so that the simple vibration energy level expression yields ZPE (Re-H) since for the simple harmonic
= J2 ZPE (Re-D),
oscillator v = (I /27r) (k/p)“,
where k is the force constant
and the reduced
/f = (111, x m2)/(n1r
mass, p, is defined as + n1J.
Whilst we cannot calculate the magnitudes of these two ZPE we can conjecture that they may be slightly more than half the ZPE of H, (Re-H) or D, (Re-D). This conjecture is based on the considerations that the strength of the surface bond is probably a little greater than half the dissociation energy of the hydrogen or deuterium molecule (exothermic adsorption) and that for similarly shaped P.E. curves the dissociation energies and force constants vary in parallel. Now for hydrogen p=+ and ZPE,, p= I and ZPERe_H=JkRe_H/4rr. If =(1/4+/2 k,, whilst for Re-H, >+k,, the ZPE of Re-H is slightly greater than half ZPE of H,. then kRe--H Similarly, for the deuterium containing moieties. In this discussion our concern is entirely with the relative rates of desorption, either H,/HD or D,/HD, and the effect of ZPE changes on these ratios. It is a matter for experimental observation to determine the inherent probability of reaction taking place, i.e. of the rate constant k,. Postulate 4: Desorption from the surface is associated with the collision of a gas phase molecule. This requirement follows from the observation that the overall rate of reaction is first order in the pressure of the replacing gas and was discussed above. A collision is then a necessary but by no means a sufficient condition for desorption to occur. It is only when there are signiicant numbers in the p’-state that measurable desorption can take place when an impact occurs. The consequences of postulates (l)-(4) can be summarised: Rate of desorption
= k, x Rate of collision of replacing gas x Equilibrium concentration of desorbing x exp[ - (ZPE change)/RT].
gas (1)
Re
HYDROGENISOTOPEREPLACEMENTREACTIONSON
In order to make a comparison selected two groups
between
of experiments
theory
for detailed
507
and experiment
analysis.
Within
we have
each group
the pressures of the replacing gas were as closely similar as could be obtained. These are the results shown in fig. 1 in which the pressure of H, was 1.3+ f0.08 x 10e7 torr and fig. 2 in which the pressure of D, was 2.74 f0.14 x of the relative rates of evolution of H, or D, x lo-7 torr. The calculation and HD then makes use of eq. (1) in the form: Rate of evolution of X, ~_____.._ Rate of evolution of HD Equilibrium
concentration Equilibrium
Consider
X, x exp [ - A (ZPE)/RT] concentration
HD
first the pair of reactions: 2Re-H+D,+2Re-D+H,, Re-H
A schematic
representation
(1)
+ D, + Re-D
+ HD .
of the ZPE changes
Re-H
Hz HD
ReH
Re-D
Dz
ReD
Reaction In reaction A (ZPE)I
(1)
(1)
(2)
for the two reactions
is:
9 1
(2)
(2)
(1) the change in ZPE is: = ZPE (Hz) + 2ZPE (Re-D) = 6.23 - 4.41 - 2 ((J2
- ZPE (D2) - 2ZPE (Re-H)
- 1) ZPE (Re-D))
= 1.82 - 0.82 ZPE (Re-D) . In reaction A (ZPE),
(2) the change = ZPE (HD)
in ZPE is: + ZPE (Re-D)
= 5.39 - 4.41 - ((J2
- ZPE ( D2) - ZPE (Re-H)
- 1) ZPE(Re-D)}
= 0.98 - 0.41 ZPE (Re-D)
.
Then for ZPE(Re-D) > $ZPE(D,) it follows that A(ZPE), co.01 kcal mole-l and A(ZPE), co.08 kcal mole-‘. Thus A(ZPE), -A(ZPE), is negative [i.e. reaction (1) is favoured over reaction (2)], and becomes more negative as ZPE(Re-D) increases. It follows that the larger is ZPE(Re-D) the more favoured reaction (1) becomes relative to reaction (2). Thus a correct assign-
508
R.P.H.GASSER,
ment of a greater gas, can be made. to assign a value value which will
G.MORRLS
AND
A.K.SZCZEPURA
rate of evolution of H, than of HD, when D, is the incident To put the results on a quantitative footing it is necessary to ZPE(Re-D). At this stage it is appropriate to choose a both produce as good a fit as possible, and be physically
reasonable. ZPE(Re-D)=2.36 kcal mole-’ =2.2 kcal mole-‘]. We now have: Rate of desorption
Hz
Rate of desorption
HD
fulfils these criteria [cf. f ZPE( D2)
Equilibrium cont. H, ~~ -~~ --exp = Equilibrium cont. HD Then A (ZPE),
= I .82 - 0.82 x 2.36 = - 0. I2 kcal mole-’
A(ZPE),
= 0.98 - 0.41 x 2.36 = -t 0.01 kcal mole-’
,
Thus R HZ
R HD For this pair of reactions R,, = k,[H,]
_
I321 exp
CHDI
(I 30/RT)
(3)
we can write exp(l30jRT),
R,,
= k,[HD],
so that if a value of k, is chosen which brings the rate of desorption of HD near its peak into as close agreement as possible with the experimental value we can calculate the overall shape of the HD desorption curve. When choosing k, we are in effect adjusting the scale of the theoretical curve to match the experimental observations. Once k, has been selected, eq. (3) allows the partial pressure of desorbed H, to be predicted at any chosen time during the reaction. The calculated pressures at I min intervals are shown in fig. 6a and are in highly satisfactory agreement with the experimental observations corrected for background exchange. When replacing gas is first admitted, the background is indeterminate and the corrected curve is shown as a broken line in this region. To illustrate in more detail how theory and experiment are compared, the calculations of the ratio of rates of evolution at r=2 min will be carried out. From fig. 5 the surface concentrations of hydrogen and deuterium are 3.3 x 1014 atoms cm-’ and 4.36 x 1014 atoms cm-‘. Using K = 3.26 for the reaction H, + D, = 2HD, the expected gas-phase equilibrium concentration of H, is equivalent to 0.74 x 1014 mol cn1C2 and of HD is 1.81 x 1014 mol cme2. Hence R,J&,u
= (0.74/1.81)
exp(130jl.98
x 296) = 0.51
Re
HYDROGENISOTOPEREPLACEMENTREACT~ONSON
509
(b)
0.5
0.4
0.:
0.2
0.1
0
1-
2
4 6 Tlme(min)
,
8
2
I
4 Time
I
I
6 8 (min)
I
I
10
12
Cd)
2
4 6 8 Time (min)
10
1:
Fig. 6. Comparison of calculated partial pressures of desorbed hydrogen isotopes (circles) with experimental results corrected for background contributions (full lines). Initial backgrounds of HD are uncertain (broken lines). (0) desorbed HD; (0) desorbed HZ or Dz. (a) Replacing gas Dz; final pressure 2.7 x lO-7 torr, room temp.; (b) Replacing gas Hz; final pressure I .2 x 10e7 torr, room temp.; (c) Replacing gas Dz; final pressure 9.8 x IO-* torr, 380 K; (d) Replacing gas Hz; final pressure 5.3 x lo-* tort-, 380 K.
510
R.P.H.GASSER,
Experimentally
G.MORRlS
AND
A.K.SZCZEPURA
the ratio of the rates of evolution
of the gases is given by
(RHJRHDL~ = (PH,Ih,J x J4
Y
where the factor V/S allows for the difference between the molecular velocities of H, and HD and, therefore, for the more rapid pump away of H,. Substitution of the experimental partial pressures, Pflz = 3.1 x lo- * torr and P nn=7.3 x 10e8 torr in the equation yields (R&r&p, We now turn to a consideration 2 Re-D
= 0.52.
of the two reactions: + H, + 2 Re-H + D, ,
(4)
Re-D+H,+Re-H+HD. This time the ZPE changes
are:
Re-H tt
Re-D (4)
(5)
t
H2
H2
HD
HD
Dz
Dz
(4)
(5)
Re-H t
Re-D
(5)
Thus A(ZPE),
= ZPE(D,)
+ 2ZPE(Re-H)
= 0.82 ZPE (Re-D)
- ZPE(H,)
- 2ZPE(Re-D)
- ZPE(H,)
- ZPE(Re-D)
- I .82,
and A(ZPE),
= ZPE(HD)
+ ZPE(Re-H)
= 5.39 - 6.23 -I- ((,,!2 - I) ZPE(Re-D)] = 0.41 ZPE (Re-D)
- 0.84.
Provided then that ZPE(Re-D)>2.39 kcal mole-’ we have that A(ZPE),>A(ZPE), and reaction (4) becomes endothermic relative to reaction 5. This results in a more ready desorption of HD than of D, by incident hydrogen, again in accordance with the experimental observations. We can now make a second estimate of ZPE(Re-D) designed to produce as good a fit as possible to the results of reactions (4) and (5). The appropriate value of ZPE(Re-D) is 2.82 kcal mole-r; ..
A (ZPE),
= 0.82 x 2.82 - 1.82 = 2.31 - I .82 = 0.49 kcal mole-
’,
HYDR~GENI~~~~~EREPLACEMENTREACTIONS~N
Re
511
and = 0.41 x 2.82 - 0.84 = 1.16 - 0.84 = 0.32 kcal mole-’
A (ZPE), The relative RD,~&D
rates of desorption =
of deuterium
.
and HD are then:
~CW/[HDl~ ev I- [A@‘EL - AW’%IIRTI
= ([D,]/[HD]}
exp [ - (490 - 320)/RT]
= {[D,]/[HD]}
exp (-
170/RT).
The rates of desorption calculated from the last equation corrected for the difference in molecular velocities and with the assignment of the appropriate scaling factor once again yield points for comparison with experiment. The fit between theory and experiment, although less good for this pair of reactions than for reactions (1) and (2) is still satisfactory, fig. 6b. Furthermore, the average value of the zero point energy of the Re-D bond obtained from the two experiments, 2.6 kcal mole-’ is entirely reasonable for a fairly strongly bonded surface species (compare, for example, ZPE of DC1 = 3.0 kcal mole-l). One further deduction can be made from the results, namely the difference between the heats of adsorption of hydrogen and deuterium on rhenium. This difference is numerically equal to either A(ZPE), or A(ZPE), [since reaction (3) is the reverse of reaction (l)]. Substitution of ZPE(Re-D) ~2.6 kcal mole-’ gives the energy difference as 0.2 kcal mole-‘, with deuterium having the larger heat of adsorption. This energy is equal to the difference in the activation energies for desorption since the adsorption process is non-activated. It is closely similar to the quoted3) difference between the activation energies for the desorption of hydrogen and deuterium from tungsten, 0.3 kcal mole-‘.
7. Results at 380 K The desorption curves at 380 K are very similar to the room temperature curves in shape and can be analysed similarly. The equilibrium coverage of hydrogen at 380 K was 5.4kO.5 x 1014 atom cm-‘. The rates of the various reactions showed remarkably little variation with temperature. When deuterium was the replacing gas the rate of reaction increased by only about 10% between room temperature and 380 K and for hydrogen the rate increased by about 50%. This latter increase corresponds to an activation energy for this replacement reaction, apart from the ZPE change, of about 1 kcal mole-‘. This is a much smaller temperature dependence of rate than was observed for the similar reaction on tungsten for which an activation energy of about 5 kcal mole-’ was calculated. The analysis of the curves
512
a. P. H.GASSER,
G. MORRIS
AND A. K.SZCZEPURA
follows the same procedure as for the room temperature results except that the equilibrium constant for the hydrogen isotope equilibrium at 380 K (3.46) was used. With calculated and experimental rates adjusted, as before, for the HD-producing reaction of each pair, there is again excellent agreement between the results then calculated for the desorption of either H, or D, and the observed pressure records, as figs. 6c and 6d show. In choosing to interpret the results of these experiments by what is essentially a phenomenalistic approach we have been able to account not only for the general shapes of the desorption curves but also rather successfully for the detailed behaviour of the various isotopic species. In so doing only one variable parameter has been introduced (ZPE of Re-D) apart from a scaling factor. Although for so complex a system this is by no means the only possible approach, it does have the virtues of simplicity and success.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
A. D. Crowell and L. D. Matthews, Surface Sci. 7 (1967) 79. J. T. Yates, Jr., J. Phys. Chem. 68 (1964) 1245. P. W. Tamm and L. D. Schmidt, J. Chem. Phys. 52 (I 970) 1150. C. Boon, R. P. H. Gasser and H. Tovey, Surface Sci. 19 (1970) 255. P. A. Redhead, Trans. Faraday Sot. 57 (1961) 641. K. F. Poulter and J. A. Pryde, Brit. J. Appl. Phys. (2) 1 (1968) 169. R. P. H. Gasser, T. N. Morton, J. M. Overton and A. K. Szczepura, Surface Sci. 28 (1971) 574. B. Bergsnov-Hansen and R. A. Pasternak, J. Chem. Phys. 45 (1966) 1199. R. P. H. Gasser, Chem. Sot. Specialist Periodical Reports, Surface and Defect Properties of Solids 1 (1972) 205. G. C. Bond, Catulysi.s by Mrrals (Academic Press, New York, 1962). D. D. Eley and P. R. Norton, Discussions Faraday Sot. 41 (1966) 135. J.J. F. Scholten and J. A. Konvalinka, J. Catalysis 5 (1966) 1. H. C. Urey and D. Rittenberg. J. Chem. Phys. 1 (1933) 137. G. Herzberg, Mohrlur Spccfra und Molecular Strucfwe (Van Nostrand, New York, 1950).