JOEW. HIGHTOWER AND W. KEITHHALL
1014
Tracer Studies of Acid-Catalyzed Reactions.
V.
Carbon-14 Kinetic
Studies of n-Butene Isomerization over Alumina and Silica-Alumina Catalysts
by Joe W. Hightower and W. Keith Hall Mellon Institute, Pittsburgh, Pennsylvania
(Received November 18, 1966)
Carbon-14 tracers have been used in a static reactor to examine the kinetics of n-butene isomerization over alumina and silica-alumina. All reactions were first order and all paths interconnecting the various isomers were significant. Relative rate constants were determined for each catalyst at room temperature. The selectivities over both catalysts were temperature dependent, although those of silica-alumina were much less so than those of alumina. The activation energy differences between all paths have been quantitatively determined. Silica-alumina underwent rapid poisoning and this poisoning resulted in apparent selectivity changes when the catalyst-to-charge ratio was large for lowtemperature runs. This apparently resulted from the preferential formation of “residue” from 1-butene. Some of the mechanisms which have been advanced in the literature to explain these isomerization reactions were tested in light of the kinetic results. The data presented are consistent with a common intermediate, possibly a classical carbonium ion, for all paths over silica-alumina. Using this model, together with the activation energy profile, it was possible to account quantitatively for the selectivities and reactivities observed for the three n-butenes. Over alumina it is probable that the various reactions proceed through different surface complexes, perhaps on different sites.
Introduction Several investigators’-6 who have studied n-butene isomerization over oxide catalysts have suggested that the reactions follow first-order kinetics. Haag and Pines have clearly demonstrated that 1-butene isomerization is first order over both sodium dispersed on alumina’ at room temperature and pure alumina2 at 230”. Recently we6 have used C14tracers in a microcatalytic reactor’ to demonstrate the first-order character of n-butene reactions over alumina, fluorided alumina, and silica-alumina at temperatures below 100”. Since there are always some inherent uncertainties about kinetic measurements made using a microcatalytic technique, additional work was undertaken to investigate the kinetics of n-butene isomerization over alumina and silica-alumina in a static reactor. C14 tracers were used in a rather novel way to follow simultaneously the isomerization of both 1-butene and cis-2butene from low conversion to equilibrium. The two sets of results are compared herein. The Journal of PhyaiCal Chemistry
The effect of temperature on selectivity can supply information about possible common transition states in the formation of any two isomers from the third. Measurements of the selectivities over both catalysts have been made a t various temperatures and the activation energy differences between the various paths have been quantitatively determined. While kinetic studies alone (disregarding isotope effects) can lead only to formal reaction schemes, in some cases they may be used to test the credibility of mechanisms which necessarily imply certain kinetic
(1) W. 0. Haag and H. Pines, J . Am. C h a . SOC.,8 2 , 387 (1960). (2) W.0. Haag and H. Pines, ibid., 82, 2488 (1960). (3) 9. Ogasawara and R. J. Cvetanovio, J . Catalysis, 2,45 (1963). (4) D.M. Brouwer, ibid., 1, 22 (1962). (5) J. Wei and C. D. Prater, Advan. Catalysis, 13, 203 (1962). (6) J. W.Hightower, H. R. Gerberich, and W. K. Hall, J . Catalysis, 7,57 (1967). (7) R.J. Kokes, H. Tobin, and P. H. Emmett, J . Am. Chem. SOC., 77, 5860 (1955).
TRACER STUDIESOF ACID-CATALYZED REACTIONS
consequences. The relative rate constants developed here have been used to calculate expected molar radioactivities in the products and these are compared with experimentally determined values. In this way it has been possible t o exclude several possible mechanisms which have been advanced in the literature.
Experimental Section Reactor. In all these static experiments the reactor was a 300-cc spherical Pyrex bulb connected through a stopcock and standard taper to a conventional BETtype gas-handling system. The catalyst was placed at the bottom of a 22-mm 0.d. well which extended 4 in. below the bulb. An oven which fit around the catalyst well could be maintained within *lo of a given temperature by a Thyratron resistance controller. The gas was stirred by convection. Since the reaction conditions were selected so that measurements could be made over periods of days, this was deemed satisfactory. KO attempt was made to protect the catalyst from mercury vapor. Catalysts and Pretreatment. One alumina and two silica-alumina catalysts were examined in these experiments. The (GA-48) aluminas-'0 was prepared from the neutral hydrolysis of redistilled aluminum isopropoxide by the R f K Research and Development Co., Pittsburgh, Pa. Its total metallic impurity level was less than 50 ppm and its surface area was 158 m2/g. X-Ray measurements, made as the catalyst was dehydrated during the final stages of preparation, revealed that it was probably a mixture of 7- and yalumina. The first silica-alumina (DSA-1)'l was a very pure synthetic sample from the same preparation used by Leftin and Hermana12 in their optical photometric studies. The catalyst contained 88% Si02 and 12% AlzOawith less than 50 ppm metallic impurities. Its surface area was 278 m2/g. The second t ilica-alumina (51-46) was a commercial Houdry catalyst containing 13Oj, alumina and having a surface area of 270 m2/g. The major metallic impurity was iro? which amounted to between 0.1 and 0.3 wt %. Before use each catalyst was given a standard pretreatment which consisted of the following steps. First, each x a s outgassed in the reactor at 300" for 2 hr. It was then contacted with 200 mm of O2 and the temperature was raised to 530" for 1 hr. After a 30-min evacuation at 530", another 200-mm charge of 0 2 was admitted and allowed to stand for 2 hr at the same temperature. This was followed by overnight evacuation at 530" to a sticking vacuum in a McLeod gauge.
1015
The catalysts were then cooled to room temperature; in all cases they were white after this treatment. Reactants. The 1-butene and cis- and trans-2-butene (Phillips Research grade) were a t least 99.6% pure. Just before use, each was distilled from -78 to - 195" and outgassed to a sticking vacuum at -195". No impurities were detected by glpc analysis. The 1-b~tene-1-C~~ (4.2 mcuries/mmole) was purchased from Tracerlab and used without dilution following purification by gas chromatography. cis-2-Butenel-C14 was prepared from the radioactive 1-butene by isomerization over a small sample of 1.2% fluorided alumina in a microcatalytic apparatus; this catalyst was chosen because of its high selectivity.6 The radioactive mixtures were prepared by combining about 0.1% of the radioactive material with the purified gases. Tests using a dilution technique revealed no radioactivity in any of the other isomers. Procedure. After each catalyst had been pretreated, it was cooled to -195" and a measured amount of the desired reactant was frozen into the reaction vessel which was then rapidly warmed to reaction temperature. In each radioactive experiment 100 cc of the mixture and 30 mg of catalyst were used and 4-cc samples were periodically withdrawn and subjected to glpc and radioactivity analysis. The 30-ft X 0.25in. chromatographic column contained a 2: 1 ratio of dimethyl sulfolane to hexamethylphosphoramide on firebrick and was thermostated at 0". The separated products were individually trapped and tested for radioactivity in a vacuum-tight Geiger counter previously described;'j all specific activity measurements are given as counts min-l mm-l in the counter. These can be converted to counts min-I mmole-l by multiplying by 8.5 X lo2mm mmole-l. In the experiments designed to study effect of temperature on selectivity, 25 cc of each pure compound was used. Samples were taken every 20 min and conditions were adjusted in such a way that less than 5% conversion occurred in 2 hr. Catalyst samples ranged in weight from 1 to 100 mg. Product ratios were plotted as a function of time at a given temperature (see Figure 8). These were extrapolated to obtain initial selectivities. Reproducibility was tested by (8) W.K.Hall and F. E. Lutinski, J . Catalysis, 2, 518 (1963). (9) W.K.Hall , F. E. Lutinski, and H. R. Gerberich, ibid., 3, 512 (1964). (10) W.K.Hall, H. P. Leftin, F. J. Cheselske, and D. E. O'Reilly, ibid., 2, 508 (1963). (11) W.K.Hall, D. S. MacIver, and H. P. Weber, Ind. Eng. Chem., 52, 421 (1960). (12) H. P. Leftin and E. Hermana, Proc. Intern. Congr. Catalysis, 3rd, Amsterdam, 1963, 2, 1064 (1964).
Volume 71,Number 4 March 1967
JOEW. HIGHTOWER AND W. KEITHHALL
1016
evacuating the mixture after several hours reaction and replacing it with a second 25-cc charge of reactant. The reactions were “clean.” Isobutene, n-butane, isobutane, or dimers would have appeared on the glpc chromatograms had they been present in appreciable amounts. Since none of these was detected, skeletal isomerization, saturation, or polymerization could not have been important. A carbonaceous (probably polymeric) “residue” did form on the surface of the silica-alumina catalysts, but it was estimated from earlier results6 that no more than about 1% of the gas in the present experiments was utilized in this way. This could not be displaced into the gas phase a t the temperatures employed. Treatment of Data from Radioactive Experiments. Haag and Pines1 have derived the rate equations for parallel, reversible, first-order reactions among members of a three-component mixture of the type *I 1
\:gt
1-butene
trans-2-butene
cis-2-butene The amount of trans-2-butene formed from 1-butene a t any time is given by the equation
+ d r n 2 - 4n)]
a
exp[-(m - d m 2
-[k1,
P - -(m 2n
a
dmz - 4n
exp [ - ( m
- 4n)t/2]
x
-
- d m 2 - 4n)
1x
+ d m 2 - 4n)t/21 + n
(2)
where x = concentration of trans-2-butene at time t; a = starting concentration of 1-butene; m = ki, kll k,, ICl, kl, k,l; n = kllkCl kllklc kllkct kcikic kilkc1 kilkci klckic klckct kclklc; and p = kllkol kllkCt k ~ & . Analogous expressions can be derived for concentrations of other isomers as a function of time. The rate constants are not all independent, because their product in a clockwise direction must equal the corresponding product in a counterclockwise direction around the three-component mixture, viz.
+
+
+
+ +
+ + +
klckc1k1l
+ +
+ +
+ +
kcl/klc
for forward and reverse reactions between any two
=
0.15
k&, = 0.04 k , , / k , , = 0.26
(4)
Application of these equations to our results involved the implicit assumption that the surface reactions are rate controlling; i.e., adsorption and desorption are relatively fast. If this condition is satisfied, the relative rate constants obtained in the homomorphic description of eq 1 reflect the true reaction sequences which occur on the surface. Experiments justifying this assumption are reported elsewhere.6 The equations were used as follows. Suppose the starting mixture were 1-butene with a trace of radioactive cis-2-butene. Two separate and independent reactions were assumed. The 1-butene reacted as though it were the only species initially present in the system and the product distributions were calculated as a function of time from eq 2 by assuming arbitrary rate constants which satisfied eq 3 and 4. Relative rate constants from our earlier work6 provided a first approximation and a “best fit” of the data was obtained by successive approximations (vide infra). Similarly, the radioactive cis-Bbutene also reacted as though it were the only species present and product distributions were again calculated from eq 2 using the same arbitrary time units and rate constants applied to 1-butene isomerization. This yielded amounts of both nonradioactive and radioactive material for each of the three isomers at various times as both reactions proceeded toward equilibrium. The specific activity of any isomer could then be derived from the number of moles originating from the original radioactive gas which is present in each particular isomer and the total number of moles of that gas. A term, CY,^,^^-^^ which is a function of time, was defined as
+
= kclkltkrc
The J O U Tof ~Physical ~ Chemistry
isomers must be equal to their respective thermodynamic equilibrium constants, e.g., at 23013
ffai
[
]
instantaneous specific activity of any isomer (i) = instantaneous specific activity of initial radioactive isomer (a)
(5)
This parameter can be determined experimentally (13) D. M. Golden, K. W. Egger, and S. W. Benson, J . Am. Chem. Soc., 8 6 , 5416 (1964). (14) W.A. Van Hook and P. H. Emmett, ibid., 84,4410 (1962).
c a t a l y ~ i sdrd, , Amsterdam, 1964,1, 688 (1965j.
TRACER STUDIES OF ACID-CATALYZED REACTIONS
1017
for comparison with values calculated from kinetic models. The 01 values are very sensitive to changes in relative rate conctants and, hence, to mechanism. Treatment of Data from Selectivity vs. Temperature Experiments. The temperature dependence of the cisto trans-2-butene ratio from l-butene isomerization was obtained from a plot of the log of the initial cis/ trans ratios (assumed proportional to k1Jc1,) vs. 1/T. The activation energy difference between the two parallel paths (AE = El, - El,) could then be determined from (iClC/h ,) 1
log
[GmJ
=
&[i
-
&I
6081 c 1
10
(6)
Analogous plots and calculations were made for selectivities of each of the three n-butenes over both alumina and silica-alumina in the temperature region from 0 to loo".
3
< But. =Tirnr
20
! 30
!
.
I
l
l
40
50
60
70
80
iM"e,lO" P"CC"1
Figure 1. a-Value plot for products of &-%butene isomerization Over synthetic s&a-alumina, DSA-1, a t 23'. Points are experimental; calculated lines based on two
Results The six relative rate constants (kl, defined as unity) for the n-butene interconversion reactions, together with representative values taken from the literature, are given in Table I. Values from the present work were obtained from plots of a: vs. conversion in which arbitrary rate constants (consistent with eq 3 and 4) were varied until the calculated lines gave good agreement with experimental points. (The k t j derived in this way are refinements of previously determined values; comparison can be made in Table I.) Such plots are shown in Figure 1A for cis-Zbutene (1butene-C1*) isomerization over DSA-1 and in Figure 2 for l-butene (cis-2-butene-C14) isomerization over GA-48. Similar results were obtained Over M-46 silica-alumina. The conversion in each case was based on that of the nonradioactive component and was defined as the sum of the mole fractions of the two nonradioactive product isomers. By this definition it was only possible for the cis-2-butene and l-butene to undergo 80.0 and 96.9% conversion, respectively, a t equilibrium. The corresponding compositional data have been plotted in triangular form for the same two systems in Figures 3 and 4. Over silica-alumina the line and experimental points originating from the cis-Qbutene corner were based on conversion of the nonradioactive material, while those from the l-butene corner were based on the radioactive component, the two sets of kinetics being determined simultaneously in the same experiment. The solid lines were calculated with eq 2 using the same parameters which best fit the points in Figures 1 and 2. The satisfactory "fit" of both sets of data demonstrates that both isomers are obeying the
(0
20
30
40 50 60 Conversion, Percent
70
80
90
I00
FiD"e 2. a-Value plot for products of l-butene (cis-%butene-C14)isomerization over alumina, GA-48, at 23".
same first-order law, Le., that the large excess of cis-2butene is not interfering with the reaction of the "trace" amount of butene-1. The radioactive and nonradioactive isomers were reversed in the case of alumina in Figure 4. The dashed lines drawn from the corners representing the two reactants are tangent to the composition curves (solid lines) a t low conversion and their intercepts on the opposite sides correspond , k,l/k,,). The to the initial selectivities ( k ~ , / k ~and third selectivity (kcl/kcc) was then fixed by a line through the truns-Zbutene corner and the intercept of the other two tangents, a necessary consequence of the rate constant restrictions given in eq 3 and 4. It was instructive to plot the data according to a first-order equation which, although based on an incorrect model, delineated poisoning effects and indicated the reactions were generally first order on a time Volume 71,Number 4
March 1967
JOEW. HIGHTOWER AND W. KEITHHALL
1018
Table I : Relative Rate Constants for n-Butene Isomerization over Alumina and Silica-Alumina Temp, Catalyst
Methoda
DSA-1
ST
DSA-1 DSA-1 M-46 M-46
S
S ST
Ketjen MS3-A Esso SA WRG-SA (11% A) WRG-SA (13% A ) GA-48 GA-48 Alcoa q - A l ~ 0pellets ~ q-AI2Oapowder Na-AhOa Equil Equil Methods:
ST
MT M,F Circ Circ M
ST MT Circ
F F S
.... I
.
.
. -Selectivities-
Relative rate constantsC
OC
Ref
kl,
kcl
kit
ktl
kat
ktc
klc/klt
kcdkcl
kdkn
23 85 150 23 50 150 75 35 24 23 50 300 230 230 30 50 150
b 12 12 b 6 4 21 21 6 b 6 21 2 2 1 13
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
0.15
1.10 0.59 0.78 1.00 0.95 0.88 0.94 0.63 1.00 0.16 0.49 0.77 0.42, 0.23 0.25 3.35 2.16
0.04
0.14
0.04
0.91 1.70 1.29 1.00 1.05 1.13 1.06 1.59 1.00 6.25 2.04 1.30 2.38 4.35 4.00 0.30 0.46
0.93
1.00
13
0.29 0.15 0.24 0.29 0.23 0.18 0.15 0.15 0.21 0.63 0.51 0.51 0.16 0.21 0.36
...
...
0.15
...
0.04
0.16 0.31 0.29 0.26 0.22 0.26 0.67 1.05
0.04 0.09 0.19 0.09 0.06 0.07 0.17 0.30
0.51 0.51 0.12 3.44 2.24
0.26 0.26 0.04 1.02 1.00.
0.06 0.17 0.07 0.03 0.05 0.01 0.03 0.30 0.11 0.06 0.01 0.21 0.35
...
...
...
...
.
I
.
...
...
1.07 1.29 1.00 1.13 1.22 1.73 4.47 5.00 >200 1.00 1.00 0.75 16.40 6.22
1.00 1.50 1.12 1.28 2.00 1.40 17.00 10.00
>zoo
2.36 4.34 4.00 4.86 2.86
= static tracer; S = static; MT = microcatalytic tracer; M = microcatalytic; F = flow; Circ = circulation.
' Results of static tracer experiments reported in this paper.
'Some rate constants calculated from selectivity observed and K,, (see
ref 13).
Figure 4. Mole fraction of products of 1-butene (cis-2-butene-C14) isomerization over alumina, GA-48, a t 23'. Circles and squares are for the same (successive) times.
Figure 3. Mole fraction of products of cis-2-butene (1-buteneCl4) isomerization over silica-dumina, DSA-1, at 23". Circles and squares are for the same (successive) times.
as well as on a conversion basis. Figures 5 and 6 contain data for three static experiments. The calculations were based on the nonradioactive component (cis-Zbutene for silica-alumina and 1-butene for alumina). The data were plotted according to -In ( X ,
- X ) = kt - In X e
(7)
where X and X , refer to conversions a t time t and a t equilibrium, respectively. This equation holds rigorously for a reactant going to a single product, the reaction being first order in both directions; it has the adThe Journal of Physical Chemistry
vantage over the exact equations of being linear and therefore useful for data testing. Product distributions calculated using real rate constants in the exact equations were shown to follow this equation through a t least 70% conversion. The experimental data for alumina also fitted over the first 70% conversion and the zero-time intercept passed through log X,, indicating poisoning was not affecting the kinetics during the run. Both silica-alumina catalysts showed signs of poisoning, but these were manifested in different ways. Over M-46 (Figure 5 ) the first-order plot was fairly linear
TRACER STUDIES OF ACID-CATALYZED REACTIONS
1019
T
0.7
1.6
I
1.4
I 200
100
I
I
300
400
Time (Hours)
Figure 5. First-order plot for disappearance of cis-%butene over silica-alumina, DSA-1 and M-46, at 23".
I
11.6fC 1
cis -
^_I
I.LiU.CI Tron
I -
M-46
GA-48
Figure 7. Activation energy profile for n-butene interconversion reactions over alumina and silica-alumina. Thermodynamic stabilities's are for 23".
L 10 io
io
io
io
$0 Time (Hours)
o;
EL
o,'
1
Figure 6. First-order plot for disappearance of 1-butene over alumina, GA-48, at 23".
through 50% conversion, but its zero-time intercept was significantly below log Xe, indicating a rapid initial poisoning. On the other hand, the first-order plot for DSA-1 passed through log X,, but its slope decreased continuously for the first 100 hr before becoming linear. This is characteristic of a slow, timedependent poisoning. Figure 7 shows the activation energy profiles for the various n-butene isomerization reaction paths over alumina and silica-alumina. Each AE value was determined from the slope of an Arrhenius plot according to eq 6 and each plot contained from five to two points in the temperature region 0-100". The product ratios were extrapolations of low-conversion data to zero conversion (e.!g., see Figure 8). Duplicate experiments for each isomer showed a maximum AE deviation of 0.2 kcal/'mole. A significant test of the accuracy of these values lies in the circular agreement obtained for both catalysts. For example, the activation energy profile (Figure 7) can be established from data from
-
o'21 0.1
I
20
40
60
80
100
120
0
Time [Minutes)
Figure 8. Apparent changes in 1-buteneltrans-2-butene ratios obtained from cis-2-butene isomerization over M-46 silica-alumina in a static reactor as the catalyst is poisoned.
two of the three isomers, e.g., 1-butene and cis-2-butene. It can be checked by determining the temperature dependence of the selectivity from the third, Le., truns2-butene. Comparison of AB values always agreed within 0.2 kcal/mole. Volume 71,Number 4
March 1967
1020
The relative stabilities of the three isomers in the figure were taken from values reported by Benson and co-workers.13 The absolute activation energy for 1butene isomerization has been r e p 0 r t e d ~ ~ 6 ~to 1 ~lie ~~7 between 8 and 20 kcal/mole over similar catalysts; our results indicated a value of about 12 kcal/mole in both cases. The n-butene selectivities over alumina were much more sensitive to temperature changes than those over silica-alumina. Also, the energy profiles for the two catalysts differed in kind. For example, in cis isomerization over silica-alumina the selectivity kcl/kct increased with temperature, whereas it decreased over alumina. The AI2 for 1-butene isomerization over alumina (1.8 kcalimole) was in the same direction as that reported by A4menomiya and Cvetanovic18 (2.9 kcal/mole) for a chromia-alumina catalyst. However, the temperature independence of kl,/kl, for DSA-1 is in disagreement with the 1.3-kcal/mole activation energy difference reported by Leftin and Hermana.12 Their experiments were repeated using finely ground particles of the same catalyst preparation. Between 0 and loo”, as was observed with AI-46, the 1-butene selectivities showed no temperature dependence. The values obtained by Leftin and Hermana may have been disguised by diffusion due to their larger partide size, higher temperature, and faster reaction rates. Extrapolation of their data to 23” would predict a cisitruns ratio of 2.9; the ratio we observed a t 23” was 0.91. Yo selectivity changes as a result of poisoning were found with alumina. Second and third charges admitted with a 1-min evacuation between each gave selectivities identical with those of the first charge under similar conditions. Over silica-alumina, however, selective poisoning was observed. I n these cases when a 2-butene charge was admitted to a freshly activated catalyst, the initial reaction gave abnormally low 1- to 2-butene ratios, as may be seen in Figure 8. Additional charges gave the expected ratios and these ratios could be reproduced with subsequent charges (Figure 8). The low initial ratio was probably due to the preferential formation of (‘residue” from 1butene, as was observed in the microcatalytic C14 experiments.6 Because of this, the initial ratios used in eq 6 to cdculate activation energy differences were in all cases those obtained after the catalyst had been “prepoisoned” with one charge of the starting 2-butene. Such selectivity changes were not observed for 1-butene isomerization.
Discussion Good agreement between the calculated lines and experimental points in Figures 1-4 justifies the asThe Journal of Physical Chemistry
JOEW. HIGHTOWER AND W. KEITHHALL
sumption of two independent, first-order sets of reactions-one involving the radioactive component, the other the nonradioactive isomer. Plots such as those in Figures 1 and 2 are extremely sensitive to relative rate constants chosen and even a small change in rate constant ratios during the reaction would make it impossible to fit the data with precision. These avalue plots are significant because they demonstrate the existence of all reaction paths over both catalysts. Had all of the trans been formed from the cis isomer through intermediate 1-butene over silica-alumina,12 the experimental a! value us. conversion data of Figure 1 could not have been fitted with a calculated curve. There is insufficient freedom available for adjusting parameters. By definition, k1, = 1 and kcl is then fixed by eq 4; similarly k l , / k l , is derived from the initial cisltrans ratio; consequently kll is fixed by this condition and by eq 4. Hence, nearly the same rate parameters must be used as in the calculation based on eq 1, except that kct and IC,, are assumed to be negligible. Curves calculated on this basis are shown in Figure 1B. The experimental points which are fitted by the curves of Figure 1A are shown for comparison. Note the zero-conversion intercept of unity for this mechanism as compared with the zero intercept for the calculation based on eq 1. This is because if all of the trans isomer is formed via (the radioactive) 1-butene, the specific radioactivity of the trans can never be less than that of the 1-butene. If direct cis-trans interconversion is permitted, a zero intercept results because most of the initial trans product is formed from the 1000-fold excess of cis-2-butene. Similar reasoning applies to the exclusive formation of trans from 1-butene through an intermediate cis isomer over alumina (Figure 2). The available data show that all reaction paths interconnecting the three n-butenes exist and contribute appreciably to the product ratios6 Thus any mechanism which necessarily implies that rate constants connecting any two isomers are zero12J9,20 cannot be solely responsible for the results. The relative insensitivity of silica-alumina selectivities to degree or nature of poisoning, source of catalyst, silica to alumina ratio, or temperature is consistent with a mechanism which involves one common intermediate for all reactions. The only such complex considered in the literature, which will provide a direct (17) S. Ogasawara and R. J. Cvetanovic, J . Catalysis, 2 , 45 (1963). (18) Y . Amenomiya and R. J. Cvetanovic, Can. J . Chem., 40, 2130 (1962).
(19) P. J. Lucchesi, D. L. Baeder, and P. J. Longwell, J . Am. Chem.
Soc., 81, 3235 (1959).
(20) J. Turkevich and R. K. Smith, J . Chem. Phys., 1 6 , 4 6 6 (1948).
TRACER STUDIES O F ACID-CAT-4LYZED REACTIONS
H
I
H
k,cb
c\ ,/j
/3
H a
\
Hb
Figure 9. Classical 2-butyl carbonium ion intermediate for n-butene isomerization over silica-alumina.
pathway between all of the isomers, is the classical sec-butyl carbonium ion.21 It was found possible to modify an earlier based on this ion, in view of the new information, so as to predict uniquely the observed selectivities and the relative reactivities of the three isomers as well. Consider the structure of the carbonium ion shown in Figure 9. The C1, C2-H, and C3 atoms all lie in a plane presumed to he parallel to the surface. Owing to steric interaction, the methyl group extends away from the catalyst and free rotation about the bond is greatly inhibited. However, rotation about the C1-C2 bond may occur. This ion could be formed from 1-butene by proton addition to C1 and a 2-butene product would result from loss of either hydrogen atom on Cs. However, these two H atoms (labeled a and bj are geometrically different, for, should the H, atom be lost, the methyl group would tend to fall into a cis configuration, whereas, if HI, were lost, trans-2butene would be the product. Since the two C3-H bonds are energetically similar, one would expect them to be broken with equal probabilities a t all temperatures. As can be seen in Table I, selectivities (klc/klt) near unity are generally reported for 1-butene isomerization over silica-alumina and these values were independent of temperature (Figure 7 ) . On the other hand, the 1- to 2-butene product ratios obtained from isomerization of either 2-butene cannot be satisfactorily explained in this way. The same carbonium ion can be formed from either 2-butene by proton addition to the C3 position, but statistical product formation would favor 1-butene by odds of 3 to 1 (since there are three hydrogen atoms on Cl). However, the C1-H primary bonds which must be broken in forming 1-butene may be stronger than the C3-H secondary bonds whose loss results in a 2-butene. If the 800-call mole (Figure 7) higher activation energy barrier to reach the 1-butene reflects this difference in
1021
bond strength, it may be used in the Boltzman equation to calculate the relative probability of barrier crossage in the two directions; this reduces the odds by 1 to 4 a t room temperature. A combination of the statistical model (3: 1) and energetic argument (1 :4) results in a 1- to 2-butene product ratio of 0.75; values ranging from 0.5 to 1.1 are commonly reported (Table 1)* If the sec-butyl carbonium ion acts as a common intermediate for the isomerization reactions over silica-alumina, the homomorphic eq 1 must be rewritten as cis-2-butene
\ t -k
trans-Zbutene Moreover, the activation energy profile of Figure 7 must be recast as shown in Figure 10. The 2-butyl carbonium ion is a high-energy state; it is unstable with respect to any of the three isomers. It is not, however, identical with the transition states because, were this the case, there would be no temperature dependence of the selectivity for any of the isomers. The transition state therefore corresponds to the top of the energy barrier between a particular isomer and the carbonium ion. The data of Figure 7 show that the barrier for 1-butene is higher by about 0.8 kcal/ mole than for either of the other two isomers. I n view of the arguments made above concerning the temperature-independent cisltrans ratios, it may be supposed that the tops of the barriers between the carbonium ion and cis- and trans-2-butene1 respectively, are of about the same height, E. Present data do not define this height, but, it may be that the potential well created by the three barriers is fairly deep. Accordingly, the carbonium ion would be a metastable state. The kinetics may now be formulated. Since all of the reactions are first order, equations for the initial disappearance of each species (neglecting back reactions) become
- d(1-butene) dt
= (klo
+ kdP1 &e - E’R
=
+ Al,e-E’RT)P1 ~
(21) N. F. Foster 4274 (1960). (22)
~~
and R. J. Cvetanovic, J . Am. Chem.
~
Soc., 8 2 ,
H. R.Gerberich and W. K. Hall, J . Catalysis, 5 , 99 (1966).
Volume 71,Number 4 March 1967
JOEW. HIGHTOWER AND W. KEITHHALL
1022
- -d(cis) - -
(kcl
dt
mi
+ k,,)P, =
c t O . 8 kcallmole
- -d(trans) dt
(ktl
+
k l P 1
=
where the f:ictor 3 represents the statistical weighting factor due to the three equivalent H atoms on the 1carbon atom which could be lost in formation of 1butene. The relative reactivities are the ratios of the initial rates of disappearance of the three isomers under conditions of equal temperature and pressure, i.e., (klc hi): ( k , ~ k 1 )( k:, l k J . Experimental values for this ratio may be obtained from Table I and compared with values calculated from the righthand members of eq 9, if it is assumed that all of the preexponential factors are equal after the statistical weighting factor, 3, has been factored, e.g.
+
+
+
d( 1-butene)/ dt :d(trans)/dt = 2:,-xit/RT[3
IrOrS
Figure 10. Energy profile showing common intermediate in isomerization of n-butenes over silica-alumina values of Xlc and XIT at 23" are 1.6 and 2.8 kcal/mole, respectively.ls
Table I1 : Comparison of True and Calculated Equilibrium Constants Based on a Carbonium Ion Intermediate over Silica-Alumina a t 23"
+ e 0 . 8 / R T ] = 21.7
-Entropy
1.0:0.15:0.040 = 1.0:0.24
f
0.06:0.046
f 0.011
The uncertainties in the calculated ratios are those quoted by Golden, Egger, and BensonI3 for their enthalpy differences ( A I c and A l l ) . The reasonably good agreement of our experimental data with values calculated from the model suggests that equating all of the Ai, is a fair approximation. A corollary is that the same number and kinds of active sites are operative for all reactions. Selectivity ratios can be calculated in a similar way and the results agree exactly with those derived above, from the consideration of Figure 9, e.g.
kCl/k,, = 3ACle- (E+Xlc) / R T / A
cle
- (ESXlc - 0 . 8 ) / R T 3e-0.8/RT
(10)
The same expressions may be combined in a different way to yield the thermodynamic equilibrium constants, e.g. K e s ( l , t )=
k 11
-- =
kr 8
A comparison of values calculated from the model with those taken from the literature is given in Table 11. The Journal of Physical Chemistry
1-Butene trans 1-Butene cis cis trans
~
a
factor"From model
K e g from lit.1*
ref 13
0 . 0 3 f 0.01
0.04
4.7f 1 . 0
3
0.21 f 0.07
0.15 f 0.01
2 . 3 f0 . 3
3
0 . 1 4 h 0.05
0.26f 0.01
1.8f 0.2
1
Keq celcd
The resulting comparison of experimental ratios to calculated ratios (for 1-butene and cis- and trans-2butene) is
From
from model
eAsijlRT =
nAc,/Ajt where n = 3 or 1.
The discrepancies may reflect differences in the A,, which were equated to effect the comparison. This cancellation also removed the factors which reduce the entropy differences as the temperature increases. Considering the simplicity of the model, the agreement between the calculated and the thermodynamic values is probably within the approximations made and is deemed satisfactory. This leaves little doubt that the isomerization reactions over silica-alumina proceed by a carbonium ion mechanism. If a carbonium ion intermediate is involved in these reactions, it is fair to ask the origin of the protons in view of the evidence23of their sparsity. This question is dealt with in another paperlZ4but suffice it (23) H. R. Gerberich, J. G. Larson, and W. K. Hall, J . Catalysis, 4, 523 (1965). (24) J. W. Hightower and W. K. Hall, J . A m . Chem. SOC., 89, 778 (1967).
TRACER STUDIES OF ACID-CATALYZED REACTIONS
to say here that we have evidence which indicates that the required protons are furnished by the adsorbed residue and thae the reaction does not involve the catalyst hydroxyls directly. The situation is more complicated over alumina. Whereas over silica-alumina the selectivities reported by a number of investigators using different catalysts and techniques were all comparable, a cursory examination of the rate constants for alumina in Table I reveals that the reported selectivities vary widely. From this apparently chaotic condition, however, some pertinent conclusions can be drawn. The selectivities are apparently all sensitive functions of the nature of the catalyst surface which, in turn, is dependent on the method of preparation, pretreatment, poisons, and reaction temperature. Using cis-2-butene as reactant, Irans-2-butene/l-butene ratios much greater than unity were frequently found, in spite of the fact that the highest barrier lies between cisand trans-2-butene. Hence, it must be concluded that the statistical energetic arguments which were advanced to explain the selectivities observed with silica-alumina cannot be used with alumina. It is
1023
probable that different sites function in the several reaction paths. Gerberich and have demonstrated that in a microcatalytic reactor both the over-all catalytic activity and cisltrans ratios increased with evacuation temperature; i.e., the two varied inversely with water content. This suggests that butene isomerization over alumina does not involve catalyst protons. Moreover, the selectivity differences between the microcatalytic (2.04) and static (6.25) experiments were probably due to a larger water content in the former because of poorer outgassing of the larger sample. Again this illustrates the different surface requirements for the different reaction paths and reinforces the belief that they occur on different sites. Amenomiya and Cvetanovicl* reached a similar conclusion over chromia-alumina. Acknowledgment. This work was sponsored by the Gulf Research and Development Co. as part of the research program of the Multiple Fellowship on Petroleum. Thanks are due to Mr. F. M. Allen for assistance with some of the experiments and to Drs. H. R. Gerberich and M. Manes for helpful discussions.
Volume 71,Number
4 March
1967
