LANGMUIR KINETICSIN CYCLOALKANE ISOMERIZATION
4555
Tracer Studies of Acid-Catalyzed Reactions. VIII. Langmuir Kinetics in Cycloalkane Isomerization over Silica-Alumina by Joe W. Hightower and W. Keith Hail Carnegie-Mellon University, Mellon Institute, Pittsburgh, Pennsylvania
16616
(Received June 12, 1068)
A series of static, microcatalytic, and steady-state flow experiments, designed to study the kinetics of cyclopropane and methylcyclopropane isomerization to olefins over silica-alumina, has demonstrated that the reactions may be reasonably well explained by a simple steady-state theory involving activation of the adsorbed cycloparaffin to a carbonium ion. The reaction orders varied between zero and first in different reactant pressure regions and increased toward unity as the temperature was increased. I n general, the results could be explained by Langmuir-Hinshelwood kinetics. An isotopic-tracer technique was used to obtain information concerning the relative magnitude of the rate constants k-l and kz which determine the fate of the adsorbed surface complex, L e . , the probability of its being desorbed as an unisomerized reactant or as an isomerized product molecule, respectively. Traditionally (Langmuir-Hinshelwood theory) k-1 has been assumed to be much larger than kz, but for cyclopropane the two rate constants were about equal, and for methylcyclopropane k z was considerably larger than Ll.The treatment was therefore modified to agree with a simple picture in which cyclopropane is hydrogen bonded to an acidic hydrogen atom, becomes activated to a nonclassical carbonium ion, and either isomerizes or returns to the ground state.
Introduction Acids have long been known t o catalyze the isomerization of cyclopropane and alkylcyclopropanes.’ A number of oxides2 are also catalysts for these reactions, and the activity of these solids has been attributed to their acidic nature. We3*4have recently used deuterium tracers to demonstrate that over silica-alumina the isomerization OF both cyclopropane (CP) and methylcyclopropane (RIICP) occurred via intermolecular hydrogen-transfer mechanisms, probably involving metastable (c-CnHZn+1’)surface complexes. These surface species were formed not by direct interaction with BrZnsted sites intrinsically present on the catalyst but by reaction of a substrate molecule with a proton supplied by a carbonaceous “residue” (coke) which was rapidly formed on its freshly pretreated surface. A similar picture, involving a sec-butyl carbonium ion complex, also explained all of the observations for interconversion of the n-butenes over silica-alumina.6-8 Whereas several investigators have clearly shown that the n-butene reactions over such catalysts are first order in reactant, the kinetics of the cyclopropanes have not been firmly established. Roberts2 reported that no simple reaction order was followed during CP isomerization over several oxides. Bassett and Habgood9 used a microcatalytic technique to demonstrate first-order kinetics over a relatively inactive sodium-X zeolite at high temperatures, and Larson, Gerberich, and Halllo suggested that similar behavior occurred over amorphous aluminosilicates at lower temperatures. I n order to gain a clearer insight into the kinetics of C P and MCP isomerization over silica-alumina, these reactions were studied in static, microcatalytic, and
steady-state flow reactors. It is the purpose of this communication to show that the results can be reasonably well explained by a Langmuir-Hinshelwood formulation. A tracer technique was used to evaluate the relative magnitudes of certain rate constants in the Langmuir-Hinshelwood equation which heretofore have not been amenable t o experimental observation.
Experimental Section Catalyst. The Houdry M-46 silica-alumina (12.5% alumina) had a surface area of 270 m2/g and was ground and sieved to 40-60 mesh for all experiments. Pretreatment included slowly heating under vacuum to 530°,followed by calcining in 0 2 and overnight evacuation at the same temperature. The catalysts were preconditioned by treatment with several charges or pulses of reactant a t the desired reaction temperature until the conversion rates became reproducible. (1) C. R. Noller, “Chemistry of Organic Compounds,” W. B. Saunders Co., Philadelphia, Pa., 1957, p 831. (2) R. M. Roberts, J. Phys. Chem., 63, 1400 (1959). (3) H. R. Gerberich, J. W. Hightower, and W. K. Hall, J . Catalysis, 8, 391 (1967). (4) J. W. Hightower and W. K. Hall, J . Am. Chem. Soc., 90, 851 (1968). (5) J. W. Hightower, H. R. Gerberich, and W. K. Hall, J . Catalysis, 7, 57 (1967). (6) J. W. Hightower and W. K. Hall, J. Phys. Chem., 71, 1014 (1967). (7) J. W. Hightower and W. K. Hall, J. Am. Chem. Soc., 89, 778 (1967). (8) J. W. Hightower and W. K. Hall, A m . Inst. Chem. Engrs., Symposium Series, 63, 122 (1967). (9) D. W. Bassett and H. W. Habgood, J. Phys. Chem., 64, 769 (1960). (10) J. G. Larson, H. R. Gerberich, and W. K. Hall, J. A m . Chem. SOC.,87, 1880 (1965).
Volume 78, Number 16 December 1068
JOEW. HIGHTOWER A N D W. KEITHHALL
4556 Gases. Cyclopropane was purchased from Ohio Chemical and Surgical Equipment Co., and MCP was an API standard sample. Perdeuteriocyclopropane and RICP were obtained from Merck Sharp and Dohme of Canada, Ltd. The latter was purified by glpc, and all reactants were twice distilled from -78 to -195" immediately before use. The Airco helium was passed through an activated charcoal trap thermostated at -195". Techniques. The same 1.0-g catalyst sample held in a tubular reactor was used for both the microcatalytic and steady-state flow experiments. The catalyst bed filled loosely a 1-cm i.d. glass tube to a depth of about 2 cm. The temperature was maintained constant within f0.5" by means of a Thyratron regulated-resistance furnace above 100" and with a water bath below 100". In the microcatalytic experiments, pulses of CP could be introduced by manipulation of stopcocks from a 5cm3 doscr into a stream of helium flowing at various rates over the catalyst at 1 atm total pressure. The pulse size was varied by using different pressures of CP in the doscr and then diluting the hydrocarbon with He. Products were collected in a trap thermostated at - 195" before being flashed into another helium stream which carried them into a 30 ft x 0.25 in. propylene carbonate on Chromosorb W glpc column at 0" for analysis. I n the steady-state flow experiments, He-GI' mixtures were passed at a total pressure of 1 atm over the catalyst and through a constant-volume trap at room temperature. After steady-state conditions had been attained, the trap was by-passed and its contents were swept into the analytical glpc column. The partial pressure of the CI' could be varied by means of a needle valve, but the absolute partial pressures could not be measured very accurately in these experiments. However, a measure of the relative partial pressure was obtained from the chromatographic data. Because the trap had a constant volume, the sum of the areas under the product propylene and CP peaks (sensitivities for the two compounds were essentially the same) was directly proportional to the initial pressure of CP; hence, the ratios of the total areas gave the relative initial CP pressures in any two experiments. In the static experiments, 30 mg (for NICP) or 100 mg (for CI') of catalyst was placed in the bottom of a 20-mm 0.d. tube which extended 4 in. below a 250-cm3 spherical reactor; the total reactor volume was about 300 em3. Measured amounts of reactants from a BET vacuum system were frozen into the reactor, which was then warmed rapidly to reaction temperature. Samples amounting to 1-5% of the total mixture were periodically removed for glpc analysis (a silver nitrateethylene glycol o n firebrick column at 0" was used in addition to the propylene carbonate column for complete separation of the MCP products), The same static reactor was used for the tracer exThe Journal of Physical Chemistry
periments, where the reactants were 1: 1 mixtures of perdeuterio and lightweight materials. The separated products were trapped at -195" and subjected to analysis for deuterium content at low ionizing voltages using a 6-in. radius Nuclide mass spectrometer. Under these conditions, fragmentation was less than lo%, and the usual corrections were made for naturally occurring l3C, as well as for fragmentation. Treatment of Data. Static Experiments. Adsorption isotherms (vide infra) of cyclopropane on silica-alumina indicated that the quantity of the reactant adsorbed was negligibly small compared with that in the gas phase of the reactor. For this reason the reaction could be followed accurately by observing concentration changes in the gas phase. To obtain an estimate of the simple reaction order n (of course the reaction might be more accurately described by a more complicated expression but over a limited pressure range n may be relatively constant), the equation
-dP
=
kP"
dt
was transformed into one involving fractional conversion, x, and the initial partial pressure, Po,by substituting P = Po(l- 2). The initial rate of conversion is
Pee),
= kPon
This equation was normalized for a given series of experiments (each at the same temperature using the same reproducible catalyst sample) to the lowest initial partial pressure, Poo,which yielded the fastest initial fractional conversion rate, (dx/dt)oo, as determined from aliquots of the gas phase. I n logarithm form, a linear equation results, viz.
whose slope is l / ( n - 1). According to the Langmuir-Hinshelwood hypothesis, the surface reaction of a single reactant can be formulated in terms of an adsorption isotherm11t12depicted in the scheme
Under steady-state conditions, i.e., constant surface coverage e, the number of molecules being adsorbed (klP(1- e)) must equal the number being desorbed as (11) C. N. Hinshelwood, "The Kinetics of Chemical Change," Oxford University Press, London, 1955. (12) K. J. Laidler and I. M. Socquet, J . Phys. Colloid Chem., 54, 519 (1950).
LANGMUIR KINETICS IN CYCLOALKANE ISOMERIZATION reactants (k-,e) plus those reacting to form products (kzO). This assumption results in the equation
klP
e=
k-1
+ kz + k i p
(5)
which becomes the normal Langmuir equation
(6)
KP * = l + K P
where the adsorption equilibrium constant K = kl/ (IC-1 ICz). I n the usual treatment k-1 is assumed to be much larger than kz, and K then becomes the ratio kl/k-1. Note that inhibition by product has been assumed negligible in this treatment. If the rate is proportional to coverage, i.e.
+
-(dP/dt)
(7)
= k2e
the reaction may be expressed in terms of initial fractional conversion rate (&/dt)o and initial pressure Po by the linear equation
4557
I n the Langmuir-Hinshelwood treatment, the normalized initial fractional conversion rates were plotted against Po/Pooto determine the adsorption equilibrium constant K i n eq 9. The extent of adsorption does not alter the definition of the fractional conversion rate determined from the gas phase in the steady-state reactions. Microcatalytic Experiments. Data from the microcatalytic experiments could not be treated in the same way -as data from the static and steady-state flow reactors because a significant fraction of each pulse was adsorbed on the catalyst. This caused pulse broadening and destroyed the simple relationship between fractional conversion and the gas-phase pressure. The Langmuir-Hinshelwood scheme may be applied to the microcatalytic data in the following way. Let V (cm9 be the unfilled volume in a 1 cm long bed containing weight W(g) of catalyst. At low conversions, where the partial pressure of product is negligible compared with reactant, the molar concentration of adsorbed reactant Q (per g) is related to the pressure through the equation Q=-
Again normalizing the results of a single series of experiments to the lowest initial pressure and the fastest initial fractional conversion rate, the equation becomes 1+ -(dZ/dt)o" ____ _ -KPo -_
(dx/dt)o
1
+ KPo"
1
1
+A
K-
RT
-2.303 log (1 .- X) - KPo(1
- Z)
dN -dt
=
kzKt
- KPo
(11)
A straight line should be obtained when the entire left side of eq 11 is plotted against time. Steady-State Flow Experiments. As with the static reactor, the reaction rates in the steady-state flow reactor were reduced to fractional conversion where (dzldt), represents the initial, or differential, reaction rate obtained by plotting x vs. reciprocal flow rate for small values of Z. The reactant partial pressure could be varied over a limited range and the simple reaction order, n, determined from plots according to eq 3.
KQmWP 1 KP
+
If one assumes that the reaction rate is proportional to the amount of material adsorbed (i.e., the surface reaction is rate controlling), the rate becomes
slope Poo(intercept)
From its value, 0 may be calculated for any pressure from eq 6. Once K has been evaluated, an integrated form of eq 7 may be used to relate the fractional conversion to time for a single reaction at initial pressure Po, viz.
+
where Qm represents the specific monolayer capacity of the adsorbent and K is the equilibrium constant previously defined. The total number of moles, N , of reactant per l-cm length of bed is then PV N=-+-
where A = KPoo. A plot of (dx/dt)oo/(dx/dt)o vs. Po/Poo should yield a straight line whose slope and intercept may be combined to give a value for K through the equation
KQmP 1 KP
= k2'QW =
k2'KQmWP 1 KP
+
(14)
Equation 13 may be differentiated to yield dN -= dt
V KQmW - K'QmWP Id-? -[RT -+1+ K P (1 + KP)z dt
(15)
which may be combined with eq 14 to give a complex equation relating dP/dt to the other variables. At low conversions where the microcatalytic reactor approximates a differential reactor, P -+ Po and
-(-dP\
=
h'KQm WPO
(16)
which at low pressures (where KPo > 1) reduces to
0-CP, Static 0-CP, Microcolalylic
*-MCP,
Static
0.9
i/
These equations can also be formulated in terms of fractional conversion by setting dz = -d(N/No). Equation 13 gives NO when P = Po. Dividing the corresponding members of eq 14 by those of eq 13 yields the desired relationship, which for the initial conditions reduces to
6)0-[ =
d(NIN0) dt
10-
(1
+
hKQmWPO (19) POV KPoIii?; KQmPoW
+
and which can be inverted and rewritten as
1 _ _ -1 __ - _ (dx/dt)o kz'
0.0
V + kz'KQmWRT
+
where D = (l/kz') (V/kz'KQmWRT) and E = V/k2'QmWRT. For a given catalyst and temperature, D and E will be constants, and the initial rate will be a function only of Po. Within a given series of experiments, then, the initial rates may be normalized to the lowest initial partial pressure, Poo,which corresponds to the fastest initial fractional conversion rate, (dz/dt),,O,
+ EPo D + EPo" D D + EPOO
+
D
Cidr +
p)
+Epoo EPoo Poo
I
0.6
2n
(
A
(21)
(2n - i ) d i (22)
i=n+l
where n is the number of carbon atoms in the molecule, and d , is the fraction of the molecules having i deuterium atoms.
Results The kinetics of cyclopropane isomerization were investigated over silica-alumina by observing the effect of varying the initial partial pressure in static, microThe Journal of Physical Chemistry
I
0.5
n7L
(atoms exchanged)/(molecule) = i=O
I
0.4
103rnm;
0.8
Equation 21 is analogous to eq 9 derived for the static reactor. It must be remembered, however, that Po is the initial partial pressure of the reactant after part of the pulse has been physically adsorbed. Tracer Experiments. In the tracer experiments involving 1: 1 mixtures of perdeuterio and lightweight molecules, the hydrogen atoms exchanged per molecule in the products were calculated' from 11
I
0.3
0.9
(dx/dt)oo - D
(dx/dt)o
I
0.2
Figure 1. Plot showing the effect of initial partial pressure on initial reaction rate during cyclopropane and methylcyclopropane isomerization to olefins over silica-alumina. The slope is related to the simple apparent reaction order, It, through eq 3.
viz.
-
I
0.1
2
0.4 0.3
t
dy
,!!J
0.2
0.1 0.0 0
I I
L
10
20 30 40 50 60 70 80 90 100 110 120 l/Fo (Time in Secs for 2 5 c c Flow in Bubtde Meter)
'
0
Figure 2. First-order plot of microcatalytic conversion of cyclopropane to propylene over silica-alumina for various pulse sizes a t 150'; see eq 23.
catalytic, and steady-state flow reactors. I n Figure 1 the relative initial rates have been plotted against relative initial pressures according to eq 3 to provide an estimate of the simple reaction order, n. Although such a plot is strictly applicable only for the static and steady-state cases, the microcatalytic results were included also. I n this case, the initial pressures were assumed proportional t o the pressure in the doser. The three sets of data for cyclopropane almost superim-
LANGMUIR KINETICS IN CYCLOALKANE ISOMERIZATION
4559
Table I : Effect of Reactant Partial Pressure on Reaction Rate during Cyclopropane and Methylcyclopropane Isomerization over Silica-Alumina (Langmuir Treatment)
Initial pressure, PO,m m
Re1 initial pressure,
27.6 56.1 101.7
1.00
Pressure in doser, mm
PolPo0
Calcd initial pressure, PO,m m
Calcd initial surface coverage, BO = KPo/ (1 $. K P Q )
Re1 initial rates, (dz/dt)o/ (dz/dt)oO
Calcd re1 initial rates, (1
+ KPoO)/ + KPo)
(1
Cyclopropane, Static Reactor, 150'
... ... ... ... ,..
... ...
... ...
...
53 106 40 212 53 159 40 80
...
1.00 0.79 0.53
Cyclopropane, Microcatalytic Reactor, 150' 103 ,.. ... 250 ... ... 507 ... ... 749 *.. ...
1.00 0.61 0.47 0.36
Cyclopropane, Flow Reactor, 150 O 6.8 0.13 ... 18.6 0.28 ... ... 24.1 0.34 59.7 0.56 ... 65.8 0.58 ... 80.7 0.63 ...
1.00 0.56 0.50 0.35 0.32 0.28
0.58 0.53 0.36 0.34 0.30
0.75 0.51
0.89 0.61
0.36 0.75 0.40 0.97 0.61
0.38 0.89 0.47
...
1.00
2.43 4.92 7.27 1.00
2.73 3.54 8.78 9.68 11.87
#
.
.
...
...
Methylcyclopropane, Static Reactor, 50' ... ... 0.45 ... ... 0.62 ... *.. 0.39 ... ... 0.77 ... ... 0.45 .,. ... 0.71 ... ... 0.39 ... *.. 0.56
1.33 2.65 1.00 5.30 1.33 3.98 1.oo
2.00
posed and gave a reaction order of about 0.5 at 150". The reaction order tended to increase toward unity at higher temperatures and to decrease as the temperature was lowered below 150". A plot of data from static MCP isomerization a t 50" is also included in Figure 1; for it n cv 0.4. I n Figure 2 the results from the microcatalytic isomerization experiments have been plotted according to the first-order Bassett and Habgood equationa 7-70
/
1
1.oo
0.37 0.54 0.68
...
2.03 3.68
\
for various pressures of cyclopropane in the 5.0-cma doser; k is the reaction rate constant, K' an adsorption equilibrium constant, R the gas constant, and W the weight of catalyst. Had the kinetics been first order, all curves in Figure 2 would have superimposed; obviously, this was not the case. Furthermore, the curves deviated from linearity a t high contact time in a direction consistent with the reactions being less than first order. It is thus apparent that the equation of Bassett and Habgooda cannot be used to fit our results. After the first four to six pulses, the combined areas under propylene and cyclopropane peaks were propor-
1.oo
0.72 0.50
... ...
1.00
1.00
1.oo
0.72
tional to the pressure in the doser and equal to the cyclopropane area in the blank determination for each pressure. Since the data of Figure 2 were taken on "lined-out" catalysts, the observed deviations from the first-order law could not be attributed to a pressuredependent process, e.g., polymerization of product olefin. The straight lines drawn tangent to the curves at low conversion in Figure 2 represent the initial rates, (&/d&,, which were normalized before recording in column 6, Table I. All of the data for both CP and MCP have been plotted in Figure 3 according to the normalized Langmuir-Hinshelwood equations (eq 9 and 21), and the results are summarized in Table I. From the slope and intercepts of these plots, together with the absolute value of Poo, the adsorption equilibrium constant K could be calculated by eq 10. Since only in the static experiments were the absolute values of the initial pressure known, only in those cases could K be determined explicitly. For cyclopropane at 150", K = 0.0212 mm-'; for MCP at 50") K = 0.0157 mm-l. However, since K is assumed to be a function only of the temperature according to Langmuir-Hinshelwood formulation, the value calculated in the static cyclopropane experiments should hold for the steady-state Vohme 7.8, Number 13 December 1968
JOE W. HIGHTOWER AND W. KEITHHALL
4560
IOOO/
3,'
TOK
312 3,3
3,4
3,5 3,6 3,7 ]:3 20
20 -18
~3~
-g 0
\
J
1.6
z
Pressure (torr)
P,/P8
Figure 3. Langmuir-Hinshelwood piot relating initial reaction rate to initial partial pressure during cyclopropane and methylcyclopropane isomerization to olefins over silica-alumina; see eq 9 and 21.
Figure 5. Adsorption of cyclopropane on silica-alumina. Isosteric heat is 5.5 kcal/mol.
Time (Hours)
o o o k o Y o
Per 40Cent 5on Conversion 6; 70
Figure 6. Exchange concentration curves for coisomerization of methylcyclopropane-d& over silica-alumina.
0
10
20
40 50 Time (Hours)
30
60
70
Figure 4. Langmuir-Hinshelwood and first-order plots contrasting fit of time-dependent data from cyclopropane and methylcyclopropane isomerization to olefins over silica-alumina; shaded areas indicate deviation from linearity on first-order plots.
flow experiments a t the same temperature as well. With this assumption the absolute values for the initial pressures can be calculated; these results are shown in column 4, Table I. The highest calculated initial partial pressure (80.7 mm) in the flow experiThe Journal of Physical Chemistry
ment was in approximate agreement with a crude measurement which indicated about a 10:l helium-cyclopropane reactant mixture; this would correspond to an initial partial pressure of about 76 mm. The initial surface coverage, 00, may also be calculated from K and the Po values may be calculated from eq 6; the values are given in column 5 , Table I. The same isomerization data (from a static reactor) have been plotted for both reactants in Figure 4 in accordance with both time-dependent eq 11 and the first-order law. Linear curves were obtained with both reactants for the Langmuir-Hinshelwood model, but significant deviations from linearity were observed when the same data were plotted on a strictly first-order basis. In another experiment the Langmuir-Hinshelwood plot for cyclopropane at 150" showed a small deviation from linearity above 80% conversion. The volume of cyclopropane adsorbed on the catalyst was determined from the isotherms shown in Figure
LANGMUIR KINETICSIN CYCLOALKANE ISOMERIZATION 5. The isosteric heat of adsorption at 0.5 cm3 (NTP)/g was 5.2 f 0.3 kcal/mol; Hall, Lutinski, and Gerberich13 obtained a heat of adsorption of 5.5 kcal/mol from the variation of the chromatographic retention time with temperature in the same temperature region. Extrapolation of the data to 150" indicates that a pressure of over 200 mm would be required to cause 0.5-cm3 adsorption on 1 g of catalyst. It was reported earlier that an irreversible "residue" amounting to about 1 cm3 (NTP)/g formed on the surface under reaction conditions.'O This would not, however, affect the pressure dependence. The intercepts near 0.5 of the exchange concentration curves in Figure 6 indicate that the RICP isomerization reactions all involved an intermolecular exchange of one hydrogen a t ~ m . ~ ?Similar ~ J data for C P are presented in ref 10. Intermolecular scrambling among reactant molecules accompanied isomerization, but this process was much more extensive for C P than for ?t!tCP.
Discussion The results plotted in Figures 1 and 2 show that isomerizations of both CP and RSCP to olefins over sib ica-alumina have apparent orders significantly less than unity. Furthermore, the apparent orders were not unique but are functions of temperature and pressure. These are characteristics of Langmuir-Hinshelwood behavior, and the reasonably straight lines in Figures 3 and 4 indicate that both the initial pressure and the time-dependen t requirements of that theory are fairly well satisfied by the data. The deviations from linearity which appear in Figure 3 are outside experimental error, however, and may reflect variation in the heat of adsorption with surface coverage or effects of lateral intermolecular interactions on the surface, both being conditions which would violate Langmuir assumptions. The data have been treated according to the simple Langmuir-Hinshelwood model, which assumes each adsorbed molecule may either react on or desorb from the surface. The product distributions for MCP isomerization reported ear lie^,^ together with the present tracer results and those for CP,'O suggest that B of eq 4 does not refer to the total adsorbed substrate but to a metastable (O-CnHen+l+) surface species, which is formed by interaction of a reactant molecule with a proton donated by a polymeric surface " r e ~ i d u e . " ~ , ~ The heat of adsorption measured in Figure 5 (5.2 kcal/mol) is about equal to the heat of liquefaction of cyclopropane, suggesting that most of the adsorption is physical. I n the microcatalytic experiments, a sizable fraction of each pulse was adsorbed on the catalyst. From the data of Figure 5, it is estimated that about 1 cm3 was adsorbed when the cyclopropane pressure was 400 mm at 150". Even if there were no spreading of the pulse between the doser and the reactor, the Povalue used in eq 21 would be about 3001, smaller than
4561
that originally measured in the doser. In principle, one could calculate the effective initial pressures after physical adsorption by applying the slope and intercept of the microcatalytic data in Figure 3 to eq 21; however, this would only be possible if the monolayer capacity Qm of the catalyst and the free volume V in the reactor bed were known accurately, viz. Po0
=
KQ,WRT
+ V(
KV
slope intercept
)
(24)
Furthermore, such a value would be only a crude estimate in a microcatalytic system because of the Gaussian shape of the pulse.14 Therefore, we have simply assumed the pressure over the catalyst is proportional to the pressure in the doser. This physical adsorption may be a type of hydrogen bonding similar to that which Liengme and Hall15 observed in the interaction of ethylene with hydroxyl groups in zeolites. They showed that the system has characteristics of physical adsorption and suggested a mechanism by which the hydrogen-bonded complex could be thermally activated to a carbonium ion. The present data may be explained in the same way. This picture is strengthened by the recent work of Joris, Schleyer, and Gleiter,16 who showed that cyclopropanes act as proton acceptors in hydrogen bonding. If B is the carbonium ion, eq 5 should be replaced by, e.g. +E+ ki
ka
c-Ci"(g)
c-CaHs(ads) - H + k-I ka
kd
>CHaCHsCHz
c-C~H,+
(25)
According to this scheme, adsorption and desorption are very fast compared with carbonium ion formation. A simple steady-state treatment based on this model yields results which are formally identical with those already derived, i.e. -dP/dt
= kz(c-CaH.i+) = k'KP/(l
+ KP)
(26) where k' = klk2/(k-1 k2) and K = k,/kd. The chief difference is that values of K (and values of Bo and Po derived therefrom) may be taken as realistic estimates of the surface properties. Moreover, the selectivity (k2lk-l) will not be the ratio of molecules which react to those which desorb. Rather, it will be the ratio of the metastable nonclassical carbonium ions of the type suggested by Baird and Aboderin17 which de-
+
w.
(13) K. Hall, F. E. Lutinski, and H. R. Gerberich, J. Catalysis, 3, 512 (1964). (14) W. A. Blanton, C. H. Byers, and R. P. Merrill, paper given a t the 154th National Meeting of the American Chemical Society, Chicago, Ill., Sept 1967. (15) B. V. Liengme and W. K. Hall, Trans. Faraday SOC.,62, 3229 (1966). (16) L. Joris, P. van R. Schleyer, and R. Gleiter, J . Am. Chem. SOC., 90,327 (1968).
Volume 72, Number 13 December 1988
4562 compose to the olefin to those which return to the ground state without isomerization. This ratio can be estimated in coisomerization experiments of the type shown in Figure 6. With NCP, the scrambling of isotopes into the unreacted substrate was slow compared with isomerization; hence kz/k-l >> 1 and k' FZ kl. With CP, these processes proceeded a t a comparable rate;4,10hence kzllc-1 = 1 and k' = k1/2. The metastable carbonium ion has been pictured4 as lying in a relatively shallow potential well near the top of the reaction coordinate. The selectivity thus depends upon the relative heights of the barriers between the carbonium ion and the olefin and between the ion and the reactant. With RICP, the latter is the highest so that the activation energy for the isomerization reaction may be identified with that for carbonium ion formation. With CP, it has been ~ h o w n that ~~'~ the activation energy for isotope scrambling is very nearly equal to that for isomerization (19 kcal/mol), suggesting the same conclusion but with the reservation that the two barriers have nearly the same height. I n the present work we have shown that our kinetic results conformed reasonably well to a simple Langmuir-Hinshelwood treatment. There is, however, an apparent discrepancy between the kinetic results and the physical adsorption data of Figure 5 . Since the physical adsorption is much less than a monolayer under all reaction and adsorption conditions, it is possible to apply the monolayer Langmuir equation (eq 6) to the adsorption isotherms to obtain a value of KV, at each temperature. In eq 6, 0 = V/V,, where V , is the monolayer capacity in cm3 (NTP)/g. V , should be relatively insensitive to temperature and is probably about 20 cm3/g (assuming each CP molecule covers 25 Bz) or 15 cm3/g (if CP molecules adsorb on surface hydroxyl groups whose concentration is 1.5 X cm2 I*). Extrapolation of the K values obtained from the adsorption data in the 0-100" temperature range to 150" yields 2-3 X mm-1 which is two orders of magnitude lower than that obtained from the kinetic data. This means that the e values in Table I, which represent the coverage of active sites, are considerably larger than the e values calculated for physical ad-
The Journal of Physical Chemistry
JOEW. HIGHTOWER AND W. KEITHHALL sorption on the entire surface under comparable conditions. Hence, the hydrocarbon must be selectively adsorbed on a small portion of the surface, perhaps on Brgjnsted sites of sufficient acidity to effect proton transfer by thermal excitation and thereby catalyze the reaction. The apparent kinetic and adsorption inconsistency could be resolved if these sites were the -1 X 1013/cm2"residues" reported by Larson, et al.,"J which act as sites for the reaction. For example, if the coverage at 150" and 100 mm is 0.68 (Table I), then the total adsorption on these sites should be about 1 cm3 (NTP)/g. The value estimated for these conditions from data of Figure 5 is about 0.25 cm3 (NTP)/$. It must also be pointed out that the same kinetics can be equally well treated on the basis of a Freundlich isotherm
-dP
= kpll'
dt
from which eq 3 can be written with n = l / r . Figure 1 represents both treatments, and the r values calculated from the slope are 1.9 for CP and 2.5 for MCP. As with n, r is not unique but decreases toward unity with increasing temperature. Although both the Freundlich and Langmuir-Hinshelwood theories reasonably well fit the kinetic data, neither gives perfect agreement, but both offer an improvement in the fit of the data. We prefer the Langmuir-Hinshelwood development because it provides a mechanism to account for the tracer data. These findings demonstrate the utility of isotopic tracers in determining reaction mechanisms. Acknowledgment. This work was sponsored by the Gulf Research & Development Co. as part of the research program of the lLIultiple Fellowship on Petroleum. The authors are grateful to Dr. H. W. Habgood for suggesting the theoretical treatment for the microcatalytic results. (17) R. L. Baird and A. A. Aboderin, J . Am. Chem. Soc., 86, 252, 2300 (1964). (18) W.K.Hall and F. E. Lutinski, J . Catalysis, 2, 518 (1963).
