Feb., 1953 EXCHANGE O F ISOTOPIC OXYGEN
BETWEEN VANADIUM P E N T O X I D E , O X Y G E N AND W A T E R
rearrangement in photolysis is not unexpected since the photon absorption raises the alkyl molecule to a higher electronic st.ate which is repulsive, eliminating any chance of vibration which might result in the rearrangement. The occurrence of radicals in the pyrolysis of many alkyls has been so well established that a radical split of the alkyl molecule in addition to the rearrangement can hardly be denied. The observed linearity of the Arrhenius plots for methane formation could result from a closeness of the values of the energy of activation for methane production
220
by the rearrangement mechanism and by the radical mechanisms. The observed energies of activation for methane and ethane formation suggest that the rupture of the alkyl molecule is more easily achieved through the rearrangement involving a bending vibration than by radical production involving a stretching vibration. Granting this, qualitative explanations of the observed effects of temperature, of added gases and of surface are easily forthcoming. In the absence of more quantitative data it would serve no useful purpose to elaborate these explanations in detail.
EXCHANGE OF ISOTOPIC OXYGEN BETWEEN VANADIUM PENTOSIDE, GASEOUS OXYGEN AND WATER BY W. C. CAMERON, A. FARKAS AND L. M. LITZ Research Laboratoty, Barrett Division, Allied Chemical & Dye Corporation, Philadelphia, Pennsylvania Received June 17, 1966
.
The exchange of isotopic oxygen atoms waa measured in the systems vanadium pentoxide-oxygen, vanadium pentoxidewater, and vanadium pentoxide-water-oxygen in the temperature range 400-550'. The rate of exchange in the system vz05-0~increased with decreasing particle size of the VZOS. In the case of Alundum-supported VZOS catalysts, the sup ort did not participate in the exchange and the reaction proceeded according to surface reaction-controlled mechanism. !his reaction was of the first order regarding its progress with time, zero order with regard to the oxygen pressure and had an activation energy of 45 kcal. per mole. The kinetics of the oxygen exchange between gaseous oxygen and fresh amorphous V Z Omicrospheres ~ was also controlled by the surface reaction. On heat treatment, the microspheres crystallized and the exchange of oxygen atoms with these microspheres indicated a diffusion-controlled mechanism. The rate of the oxygen exchange in the system water-supported VZOSwas 20 t o 30 times more rapid than the exchange involving gaseous oxygen. The rate of exchange between water and gaseous oxygen in the presence of V206was similar to the rate of exchange in the system V~OS-OZ,indicating that in this instance the latter reaction was rate controlling. It is suggested that in the case of the surface reaction-controlled exchange, the fast diffusion of the oxygen in the bulk of the vanadium pentoxide particles yas due to lattice imperfections caused by the presence of foreign ions or defects. It is shown that the first-order kinetics found for the progress of the exchange reactions in the system supported vanadium pentoxide-oxygen is compatible with an apparent zero order with res ect to the oxygen pressure if the oxygen is strongly adsorbed. It is proposed that the activation process in the exchange oPoxygen atoms involves either the dissociation of the oxygen molecules or the loosening of the vanadium-oxygen bonds.
Vanadium pentoxide is a very extensively-used catalyst in the commercial oxidation of sulfur dioxide, naphthalene and ' other hydrocafbons. The action of this type of catalyst has been ascribed to an alternative reduction and oxidation. According to this mode of action, the oxygen involved in the primary step is derived from the catalyst rather than from the molecular oxygen. Consequently, the validity of this mechanism could be checked by using the isotope tracer technique, provided the exchange of oxygen atoms between the catalyst and molecular oxygen is not fast compared with the rate of oxidation. The present study refers to the investigation of this exchange reaction and related reactions. Its purpose was not only to provide rate data for further tracer studies, but also to obtain information regarding the reactivity of the oxygen atoms of the catalyst. The exchange of oxygen atoms was studied in the systems vanadium pentoxide-oxygen, vanadium pentoxide-mater, and vanadium pentoxide-oxygenwater. While, in these studies, vanadium pentoxide was mostly used in the form of a supported catalyst, some exchange experiments mere also carried out with unsupported vanadium pentoxide (1) C. E. Senseman and 0. A. Nelson, Ind. Eng. Chem., 15, 621 (1923).
in various forms and with the Alundum (silicate bonded alumina) support alone.
Experimental OI8-Enriched Water .-The source for the oxygen isotope of mass 18 was water containing 1.3 to 1.6% 0 ' 8 obtained from the Stuart Oxygen Company of San Francisco, California, through the Atomic Energy Commission. One of the water samples was 0'8-enriched deuterium oxide. 018-EnrichadOxygen .-Gaseous oxygen was produced by electrolyzing approximately 25 ml. of the O's-enriched water to which potassium hydroxide had been added. The apparatus could be completely evacuated and permitted drying of the oxygen produced and the removal of the hydrogen by catalytic oxidation on latinized asbestos. The gas system was so designed that t i e volume of the hydrogen reservoir, plus tubing connections, was slightly larger than twice the volume of the oxygen section. Consequently, in order to prevent the building-up of a pressure on the hydrogen side, an auxiliary electrolytic cell was provided, the current to which was controlled by the mercury manometer. Using the described a paratus, it was possible to fill the oxygen reservoir with 818-enrichedoxygen automatically. Vanadium pentoxide was used in the following forms. Catalyst.-The catalyst was prepared by mixing 6-10 mesh Alundum particles with a hydrochloric acid solution of vanadium oxide, evaporating the solution to dryness and then roasting the dried material.2 The catalyst thus prepared contained 9.5'% of vanadium pentoxide and about 0.1% of vanadium tetroxide. Vanadium Pentoxide Crystals.-This material was crystallized from molten, chemically pure vanadium pentoxide (2) E. B. Punnett, U. 8. Patent 1,978,506.
W. C.CAMERON, A. PARKAS AND 1,. M. LITZ
230
and was tested in the form of well-developed crystals and after grinding t o -200 mesh powder. Precipitated Vanadium Pentoxide.-This matcrial was obtained by acidifying an aqueous solution of ammonium vanadate solut,ion wit,h nitric acid, drying and outgassing the precipitate. Vanadium Pentoxide Microspheres.3-These were produced by cooling molten ,droplets of vanadium pentoxide suspended in an air stream, then screening. The spheres used in the cxcbnge experiments were 149 to 177 microns in diameter and showed only a weak X-ray diffraction pattern for VZOS. Alundum is a refractory material produced by the Norton Company, Worcester, Massachusetts, and contains 80% a-aliimina bonded with aluminum silicate. Isotopic Analysis Oxygen Gas.-The isotopic composition of the oxygen gas samples was determined using the Consolidated Engineering Corporation Model No. 21-102 mass spectrometer with a special glass inlet system having a volume of approximately 90 cc., and the reverse scan technique. Approximately 0.02 cc. (S.T.P.) of gas was required tor each test. The gas samples were taken from the reaction vessel by sealing off a few centimeters of the sampling tips (capillaries, 3 mm. in diameter). Comparative tests, in which a sample of the gas was taken immediately after the run was completed and again after the reactor had remained overnight a t room temperature, showed no difference in the 0’8 concentration. This indicated that the diffusion into the sampling capillaries was sufficiently fast.
VOl. 57
Water.-Since the direct determination of the abundance ratio of the oxygen isotopes in water by the mass spectrometer offers some difficulties as a consequence of adsorption, the following adaptation of the analytical method for deuterated heavy water4 was used. A small amount of the water to be analyzed was distilled into a small cell provided with a platinum filament, and then ordinary oxygen was admitted. The oxygen was equilibrated with the water catalytically by heating the platinum filament to red heat. Samples of the gas from the cell taken by means of the capillary lock were then analyzed by the mass spectrometer after the water in the samples was removed by a Dry Ice-cooled trap. It was found that in about half an hour complete equilibrium was established, and that the final 0’8 content of the oxygen equilibrated with water of known 0 ’ 8 content agreed exactly with the value calculated from the mole ratio water: oxygen (usually about 50: I).
Procedure and Apparatus
i-
V
Exchange Involving Gaseous Oxygen.-Two types of reaction vessels were used for the study of the exchange reaction between gaseous oxygen and solid oxides. A small “test-tube” apparatus used for orienting experiments consisted of a 15-mm. tube with four sampling tubes attached. The oval shape of the “race-track” apparatus (Fig. 1) was chosen so as to ensure gas circulation by convection when the side containing the solid oxide was heated by a split furnace wound with nichrome wire. Both types of reactor were sealed after the solid had been charged and baked out and the 018-enriched oxygen had been admitted. The “race-track” type reactor was provided with break-off tip8 which permitted several runs to be carried out in the same apparatus without exposing the solid to air. Exchange Involving Water.-For these experiments, the apparatus shown in Fig. 2 was used. The granular, Alun~ s t was charged through tube A dum-supported V Z O catal which was then sealed. $he 018-enriched DsO was placed into tube B, frozen and the whole system was thoroughly evacuated while the catalyst (C) was kept at 425”. Stopcock No. 2 was then closed, the DsO was distilled into tube E cooled with Dry Ice, and finally stopcock No. 1 was closed. The reaction was started by warming tube E, to tube E through the condenser (F) and goose-neck. The temperature of the condenser was 24“ corresponding to a water pressure of 2.5 cm. From time to time, the exchange was stopped, the water distilled back into the analyzer tube B, and equilibrated with oxygen. Samples of this equilibrated oxygen were collected in tube D and analyzed by the mass spectrometer.
-S
C,
I
S I
c I
Fig. 2.-018
J
d
Fig. 1.-018 exchange apparatus: C catalyst; R, breakoff tip for refill; s, seal-off points; ,‘J!‘ sample tubea; W, thermocouple well. (3)
W.F. Rollman, U. R. Pat.ent 2,489,347.
exchange apparatus used for the system ViO5DeO.
Exchange Involving Water and Oxygen.-The experimental arrangement used was similar to that shown in Fig. 1, except that a small U-tube was provided a t the bottom of the reactor for containing the water so as to permit the circulating oxygen to sweep over the water.
Experimental Results Exchange Involving Gaseous Oxygen. Orienting Experiments.-The results of exchange experiments carried out with various samples of vanadium pentoxide and with catalyst support at 500 and 550” in the test-tube apparatus are (4) A. Farkas, Trans. Faraday Soc., 32, 413 (1938).
Feb., 1953 EXCHANGE OF ISOTOPICOXTWENBETWEEN VANADIUM PENTOXIDE, OXYGENA N D WATER231 TABLE I EXCHANGE OF ISOTOPIC OXYGEN Volume of Reactor 15 cc. Oxygen Pressure 260 mm. Hg 1186-37 1621-553 1621-383 1621-381 6-10 Mesh 1 X 2 X 10 mm. 8/8-'/P" a/8-1/4" None Alundum Alundum Alundum 1.455 1.470 0.946 0 0.217 0.2015 0.205 0.208
-
-
0'
30 60 60 ' 70 90 120 130 150 185 200 245 260 320 1
500
0'8,
%
018,
%
0'8,%
ou, % 1.13 1.13 1.13
1.13 1.13 1.14
1.14 1.09 1.02
1.32 1.14 1.03
1.14
0.53
0.99 .62
1186378 -200 Mesh None 1:363 0.196 018,
*
1.13 1.12
%
018,
%
1.34 1.32 1.27
1.26 1.23 1.07 '
1.27 1.18
0.69
1.03
.40
.45 .40
550
shown in Table I. It will be seen that while no exchange took place with the Alundum support the supported and unsupported vanadium pentoxide sam les showed exchange, the reaction being faster with the smafier size material than with the larger. Supported Vanadium Pentoxide Catalyst. Equilibrium.The extent of the exchange and the approach to the equilibrium are shown in Fie. 3 for a run carried out in the "racetrack" apparatus un'Eler the conditions given. If it is assumed that the Alundum support does not participate in the exchange and that the equilibrium constant for the exchange between VIOsand molecular oxygen is unity, the equilibrium value for the 0 1 8 can be calculated to be 0.33%, which is in complete agreement with the experimental value. I n most experimental runs, the calculated equilibrium value and that found experimentally .did not differ by more than 0.02%. 552% --
1186-45 Powder None I . 396 0.219
.31 .29
0.87 .78
1.10
.36 1.10
-
the value log (z - q)/(a q ) versus time, a straight line should be obtained if equation (1) is valid. As indicated by Fig. 4, the progress of the exchange can indeed be represented by equation ( 1 ) very satisfactorily. The aurve with the breaks (1621-63) corresponds to the data represented in Fig. 3, the breaks in the line being due to the temperature changes. The conditions for experiments no. 1161-21 and 1732-28 are given in Tables I1 and IV.
1732-28
1621- 3
___ 9""
Minutes. Fig. 3.-Exchange between gaseous oxygen and alundumsupported vanadium pentoxide, run no. 1621-63: reactor 1.636 millivolume, 91.9 cc.; 0 2 pressure, 103.9 mm.; VZO~, moles; O?, 0.502 millimole. Progress of the Exchange.-It can be readily shown that the exchange reaction will follow first-order kinetics if the rat.e is controlled by a surface reaction rather than by diffusion into t,he solid. For such a case, the progress of the rsrhangr can be represented by the equation x - q = (a - q)e-kt (1) where a = zo a t t8ime,t = 0, z = concentration of 0 1 8 in gaseous oxygen a t t8ime,t , and q = concentration of 0 1 8 in the gaseous oxygen at equilibrium. Consequently, plotting
>O
Minutes. Fig. 4.-Progress of the exchange between gaseous oxygen and vanadium pentoxide catalysts.
It is interesting to note that the mass spectrographic analysis was su5ciently accurate to permit the measurement of the concentration of the 0'1 isotope. As indicated by the data of Table I1 and Fig. 5, the first-order kinetics held also for the exchange of the 0 1 7 isotope. Although, in this case, some scattering of the points was found as a consequence of the lower concentrations involved, it is evident that the rate of exchange for 0 1 1 and 0'8 are similar. It should be noted that while the first order kinetics were found to be valid for most of the catalysts studied (regarding an exception see comments on microspheres) as far as
232
W. C. CAMERON, A. FARKAS.AND L. M. LITZ
1701.
57
the progress of the exchange was concernrd, the pressure dependence of the rate does not need to correspond necessarily to first order kinetics. I n the subsequent tables, the velocity const.ants k, derived from equation (l),are given, together with the corrected constants k,,, calculated according to formula (13). Temperature Dependence.-The tempcrat,urc dcpendence of the rate of exchange was studied in t,he range 445 to 554' in the manner indicated by Fig. 3. Two series of runs were carried out at pressures of 100 to 300 mm. I n one of these series, a fresh sample of catalyst was used in each run, while in the other series, the same catalyst was used in three consecutive runs. (Details will be discussed under Reaction Order.) The conditions under which these runs were carried out and the first-order rate constants obtained are summarized in Table 111. The rogress of the exchange reaction is I I I Mo 400 so0 shown in Figs. 6 and Minutes. The logarithms of the corrected velocity constants arc lotted against the reciprocal absolute temperature in Fig. 8. Fig. 5.-Exchange of 0lTand OI8 between gaseous oxyen and vanadium pentoxide catalyst a t 500: . , 0lT; t will be observed that, on the whole, the points thus obtained are located on a family of almost parallel lines. The 0'8. only exception is the point corresponding to the rate a t 552' in run no. 1621-69. It is very likely that this discrepTABLE I1 ancy was due to an experimental error in the temperature EXCHANGE OF 0 1 8 AND 0 1 7 WITH SUPPORTED VANADIUMmeasurement If this point is disregarded, the slope of the lines of Fig. 8 PENTOXIDE Run No. 1161-21: reactor volume, 80.4 ml.; oxygen, 0.783 corresponds to activation energy of 42.6 to 46.6 kcal. per mg. atoms; pressure, 89.2 mm.; ViO,, 1.724 millimoles; mole, the average being 45 kcal. per mole. Reaction Order.-The a parent reaction order ( 0 ) of the temperature, 500 exchange was determined {om the results of the runs sum. 0'7, % Progress of run, 0'8,' % marized in Fig. 8. in gas niin utea in gas By comparing the reaction rates obtained with different, 0 1.13 0.100 samples of the same catalyst a t pressures of 95.6 to 321.6 mm. in the series consisting of runs no. 1621-41, -32 and 20 1.10 .097 -46, i t will be seen that a 3.3-fold increase in the pressure 80 0.99 .088 (lp) decreased the rate constant (k)approximately 2.5-fold. 170 .88 .081 Since the rate constant is proportional to ( 0 1)th power of 320 .72 .072 the Dressure 500 .59 .067 k = const. P(0 1) (2) .52 .059 620 these data lead to an apparent order of 0.2. (calcd.) .29 .045 Since, occasionally, it was observed that the rate of exchange for different samples of the same catalyst was not Normal oxygen contains 0.21% O I 8 and 0.04% 0''.
7.
P
b,
.
-
-
Q
TABLM I11 EFFECT OF TEMPERATURE AND PRESSURE ON EXCHANGE OF ISOTOPIC OXYGENWITH SUPPORTED VANADIUM PENTOXIDE. RATECONSTANTS Run number 1621-41 1621-32 1621-46 1621-63 1621-69 1621-66 Reactor volume, ml. 81.0 84.1 86.7 91.9 87.3 89.5 1 .850 2 811 2.934 1.004 0.813 0.912 Oxygen, mg. atoms 302.1 103.9 201.3 321.6 95.6 101 Pressure, mm. 1.31 1.32 1.32 1.32 1.12 1.17 OI8, % 1.636 1.636 1.636 1.588 1.724 1.726 V20s,millimoles 0.47 0.21 0.33 0.21 0.21 0.21 O'*, % Rate constant X lo3,min.-l 445O 0.18 476 0.67 0.26 0.35 0.r4 482 0.48 500 1.16 0.81 505 1.25 , 0.36 520 3.05 530 4.07 1.80 552 6.93 2.1 554 2.48 Rate constant, cor., X lo3, min.-I 0.16 445O 476 0.57 0.21 0.30 0.11 0.48 482 0.64 500 1.00 1.25 0.30 505 2.69 520 1.42 530 3.50 6.93 1.81 552 3.50 2.03 554
Feh., 1853 EXCHANGE OF ISOTOPIC OXYGENBETWEEN VANADIUM PXNTOXIDE, OXYGEN AND WATER233 pressure from 103.9 mm. to 302.1 mm. decreased the velocity constant approximately threefold and that therefore the apparent reaction order is zero. Vanadium Pentoxide Microspheres.Experiments with vanadium pentoxide microspheres were carried out in order to have some data on the oxygcn exchange with unsupported vanadium pentoxide particles of well-defined shape and size. The conditions and results of two runs performed with two samples of fresh V 2 0 ~ microspheres at 554 and 523" are shown in Table IV and Fig, 9. It will be seen that the linear relationship between log (z q ) / ( a - q ) and the reaction time is followed very well, indicating that, again, the surface reaction is the rate-controlling ste 8 n removal of the spheres from the reactor at the conclusion of the run, it was found that they had sintered. Moderate pressure was required to break apart the mass. 200 4w GOO 800 1000 1200 During the run, the spheres had changed Minutes. in color from the initial steel-blue tfo a Fig. 6.-Effect of pressure and temperature on the 0 1 8 exchange between golden color similar to that of powdery gaseous oxygen and vanadium pentoxide catalyst. Fresh catalyst sample used vanadium pentoxide. Microscopic examination showed that, whereas initially in each run. the surface appeared uniformly smooth identical, it was believed that more accurate data on the pres- and shiny, similar to ball bearin s, it had become dull and sure dependence could be obtained by using the same sample appeared to be made up of very !ne crystallites. On some of catalyst in all runs. For this reason, the following ex- of the spheres, a few larger crystals were discernible. Evidently, crystallization accompanied by the sintering of the periments were carried out. particles had occurred during the long time a t the high temuerature of these runs. This conclusion was confirmed by
-
.
200
400
6M)
BM)
Minutes. Fig. 7.-Effect of pressure and temperature on the 0'" exchange between gaseous oxygen and vanadium pentoxide catalyst. All runs made with same sample of catalyst. The first exchange run (no. 1621-63) was carried out at a pressure of 103.9 mm. in the temperature range of 482 to 552". At the conclusion of this run, the reaction vessel was attached to the vacuum line by the break-off tip, the oxygen was pumped, and fresh 018-enriched oxygen was admitted to a pressure of 302.1 mm. Then the reactor was sealed and the second run (no. 1621-66) was carried out. After similar manipulations, the third run (no. 1621-69) was performed at 201.3 mm. I n evaluating the results obtained (see Table I11 and Fig. 7), the initial 0 1 8 content of the solid catalyst a t the beginning of each run has to be taken into account. These initial 0 1 8 concentrations based on the total oxygen content are 0.21, 0.33 and 0.47 for the first, second and third run, respectively. The rise is, of course, due to the exchange reaction that had occurred in the previous run. If the series of run no. 1621-69 is disregarded for reasons stated above, it will be found that increasing the oxygen
Fig. 8.-Temperature dependence of rate constants for the exchange between gaseous oxygen and vanadium pentoxide catalyst: runs no. 162141, -32 and 4 6 carried out on different catalyst samples at 95.6, 101 and 321.6 mm., respectively; runs no. 1621-63, -69 and -66 carried out on the same catalyst sample at 103.9, 201.3 and 302.1 mm., respectively. When, in the subsequent run, the exchange experiment was repeated with the spheres, used in Run No. 1732-34, under the conditions given in Table IV, the data shown in Fig. 9 were obtained. I t will be seen that, in this case, firstorder kinetics are not strictly followed and that the rate at the start was somewhat larger than with the fresh spheres, but slowed down appreciably as the experiment progressed. This curvature may be associated with diffusion becoming rate-controlling as the bed sintered and the vanadium pentoxide became more crystalline. The higher initial rate was probably due to increased surface area produced when
234
W. C.
CAMERON,
A.
PARKAS AND
r,.
M.
TABLE IV 0'' EXCHANGE BETWEEN ENRICHED OXYGEN AND VANADIUM PENTOXIDE MICROSPHERES Run Number
1732-28 1732-34 Fresh Fresh Weight, g. 0.400 0.400 Oxygen content, mg. atoms 11.00. 11.00 Ole, % ' of total oxygen 0.21 0.21 Oxygen gas , Volume, cc. 117.4 116.6 Pressure, mm. 213.2 199.4 mg. atoms 2.66 2.566 01*,% of total oxygen 1.34 1.33 Exchange, temperature, "C. 554 523 Fresh spheres heated 45 hours a t 420°, 18 hours a t 590'. in oxygen.
VZOSspheres
the smooth-surfaced vanadium pentoxide spheres crystallized with the accompanying roughing of the surface.
1732-36 From no. 1732-34 0.400 11.00 0.46
VOl. 57
JJTZ
OF
149-177 DLAMETER
1732-38 Heat treated" 0.400 11.00 0.21
111.3 129.4 206.7 212.2 2,68 2.91 1.33 1.32 523 523 Spheres from run no. 1732-38 heated
1732-42 Heat treatedb 0.400 11.oo 0.29 121.5 212.4 2.722 1.32 523 to 520' for 300 hours
of the sample tubes, the run was repeated using the same apparatus and the same spheres after the spheres had been thoroughly evacuated and kept in contact with normal oxygen a t 520" for 12 days. The purpose of this latter treatment was to redistribute the 0l8content of the spheres picked up in run no. 1732-38, and to remove some of it. Assuming that subatantiall complete equilibrium had been estahished, the 0 1 8 content of the spheres was calculated to be 0.29%. The conditions of the exchange run no. 1732-42 are given in Table IV and the results are shown graphically in Fig. 10. For sake of comparison, the results of runs no. 1732-34, 1732-36 and 1732-38 are also represented in this figure. The deviation from firstorder kinetics in the case of run no. 1732-42 is clearly indicated by the curvature of the plot log (z - p)/ ( a - p) vs. time. This curvature is in the direction expected for a diffuxion controlled exchange. From a comparison of the plots shown, the following conclusions may 4w 800 I2 w 1600 2000 24w 2800 be drawn: a, fresh microspheres obey Minutes. first-order kinetics; b, heated microFig. 9.-018 exchange between gaseous oxygen and vanadium pentoxide microspheres. spheres do not obey first-order kinetics; e, the more the spheres are I n order to ascertain the effect of the heat treatment and heated, the greater the deviation from first-order kinetics. crystallization on the character of the 0 ' 8 exchange with the Exchange Involving Water .-Using the Alundum-supvanadium pentoxide microspheres, the following run was ported vanadium pentoxide catalyst, the first experiment carried out. The s heres were heated to 420' for 45 {ours and to 590' for 18 hours, screened to the proper size, and then charged into the exchange apparatus. Here they were baked out in vacuo a t 400" for 0 two hours prior to the exchange run. It was observed that, as a consequence of this latter treatment, the orange color of the heattreated VZOS spheres changed to blue. This was evidently due to loss of oxygen, since reheating the spheres at 400" in the presence of oxygen caused the orange color to + return. ,+ The conditions and results of the exchange run No. 1732-38 %regiven in Table IV and Fig. 10. I t is read0 ily Been that the plot log "-p us. a-!7 time shows a marked curvature indicating that the diffusion process inside the spheres is not sufficiently fast to keep pace with the first-order surface exchange reaction. Minutes. Since this r;n was prematurely Fig. 10.-01* exchange between gaseous oxygen and vanadium pentoxide microterminated because of a leak in one spheres; effect of prolonged heat treatment.
,
2
.
PENTOXIDE, OXYGENAND WATRR235 Feh., 1953 EXCHANGE OF ISOTOPIC OXYGEN BETWEE:N VANADIUM was carried out a t 388" but had to be discontinued because of a leak. The second run was started a t 424". The data relating to these ratc constants calculated on Ohc basis of formula ( 1 ) are given in Table V. The final 0 1 8 content, found in the water a t t.he conclusion of run no. 1732-18 was somewhat lower than the calculated value of 0.98%. This may have been caused partly by the manipulation of the water during the run required for the isotopic analysis.
TABLE VI1 CUMPARISON O F EXCHANGE RAT88 System VZOS-OZ 1621-46 Run no. Reactants, mg. atoms 0 vzos 7.939 0 2 2.9 DzO Temperature, " C . 476 500 k x 103,niin.-' 0 . 2 6 0.81
V1Os-D1O VZOS-O~-DZO 1732-18
1732-7
23.4
8.1
..
3.6 28.7 488 530 555 0 . 3 2 1.25 2 . 4 7
28.7 530 488 1.80 1 0 . 3
TABLE V EXCHANGEBETWEEN SUPPORTEDVANADIUM PENTOXIDE AND ~ ' ~ - E X R I C H WATER ED the Ols contmentm of the gas was determined by the mass specRun No. 1732-14 1732-18 trometer. The conditions and results of these runs are summarized in Table VI. Charge The equilibrium 0 I 8 concentration observed a t the con9.006 9.0307 clusion of the reaction, 1.15%, mas slightly snialler t'han the . Catalyst, g. yalue of 1.20%calculat,ed from the composit,ionand amount 23.42 23.35 Oxygen in VZO,, mg. atJomx(cnlcd.) the react,ants. It is believed that this discrepancy is 0.5764 0.5764 of DzO, g. probably due to a slightly higher VzOj content of the par28.73 28.73 Oxygen in DzO, mg. atoms ticular sample of catalyst used than that, found for the whole batch. Time, Temp., Run 0'8in Dz0, IC, % min. - 1 no. min. O C . The calculat,ion of the rate const,ants in this instance is complicated by the fact that this exchange consists of two 1732-14 0 388 0.0005 consecutive and simultaneous reactions 120 388 1.56 Q2O*(g) V Z O ~ S ) DzO(g) V?Ob*(s) (3) 1732-18 0 424 '"O .0034 130 424 oP(g) f v206*(s) 02*(g) vZob(s) (4) 1.36 130 488 .0103 The asterisk denotes the presence of the 0 ' 8 isotope. A full 286 488 1.01 discussion of the kinetics of these reactions is given in the 1,426 488 0.92 next section. If it is assumed that reaction (3) is rapid a,(calcd.) 0.98 compared with reaction (4)-an assumption justified by the of Table VII-one will expect the progress of the reacA comparison of these rate constants with the rate con- data tion to follow first-order kinetics according to equation (1). stant8sfor t8heexchange with gaseous oxygen shows that the The progress of the exchange run is shown in Fig. 11 which exchange with wat,er is some 20 to 30 times more rapid (see represents log (z - q)/(ra - q ) plotted against the time. Table VII). It will be seen that satisfactory straight lines are obtained Exchange Involving Water and Oxygen.-The reactants for each temperature. in these runs were granular Alundum-supported VZO~, The velocity constants derived from these data are sum0'8-enriched deuterium oxide, and normal oxygen. marized in Table VII. I t is significant to observe that they The exchange experiments were carried out a t 388, 424, are very close to the constants derived for the exchange re488, 530 and 555". Samples of gas were taken from time to action between the vanadium pentoxide catalyst and gaseous t,ime by sealing parts of the capillary sampling tubes, and oxygen. TABLE VI Discussion OXYUEN EXCHANGE BETWEEN SUPPORTED VANADIUM Kinetics of the Exchange.-In isotopic exchange PENTOXIDE, OXYGEN GAS AND O~B-ENRICHED WATER(RUN reactions involving a solid and a gas, one has to disNO. 1732-7) tinguish between two processes (a) surface reaction Charge: oxygen gas: pressure, 32.2 cm.; volume, 104 cc.; and (b) diffusion in the solid. The kinetics of the oxygen, 3.60 total mg. atoms. Catalyst: weight, 3.116 g. oxygen, 8.10 total mg. atoms (calcd.). D.0: weight, exchange reaction depends on the relative rates of 0.5764 g.; Ole content, 1.60 mole per ccnt.; oxygen, 28.73 these two processes. total mg. atoms Surface Reaction Rate Controlling of Exchange
OXYDEN
'
+
1
+ +
1
Time, min.
0
150 150 330 330 515 600
600 650 700 750 750 780 830 930 1030 1130 2320 3750 9400
Progress of Piin Temp., OC.
388 388 424 424 488 488 488 530 530 530 530 555 555 555 555 555 555 555 555 555
018,
%
0.21 .21
..
.21
..
.27 .2R
.. .36 .40 .45
..
.47 .55 .70 .78 .86 1.10 1.15 1.15
with Gaseous Oxygen.-If it is assumed that the diffusion of oxygen (in the form of molecules, atoms or ions) in the solid is much faster than the exchange reaction on the surface, the rate of exchange is given by
-E !! dl
=% f!
v
[k,x(l
- y)
- kz[(l - z ) y l
(5)
where c is the concentration of oxygen in the gas phase, x and y are the fraction of 0 ' 8 atoms in the gas and solid phases, respectively, A is available surfac,e area of the solid, V is the volume of the reaction vessel, and k , and kz, the velocity constants for the forward and backward reactions, respectively. The latter constants are dependent on the pressure, t = time in minutes, Since k l may be set equal ICz, equation (5) reduces to dx
- z =Avkl (x - y) If we let n = gram atoms of oxygen in the solid,
W. C. CAMERON, A. FARICAS AND L. M. LITZ
236
Vol. 57
.
Exchange in the System V206-02-Dz0.In the intithematical treatment of the kinetics of the isotopic oxygen exchange reaction in a three-component system such, as V2O6-O2-DzO given below, the following R ;" U O8 simplifying assumptions were made: a. M The mixing in the gaseous phases is sufficiently rapid to ensure uniform concentration. b. The diffusion of 0 atoms in the crystal lattice is rapid so that there is no concentrchon gradient in the solid. c. The exchange of 0 atoms occurs only between . 200 400 600 1000 water and V205,and between molecular Minutes. oxygen and Vz06according to a first-ordet Fig. 11.-0~* exchange involving water, gnseou8 osygen, and va- equation, the respective rate constants nadium pentoxide run no. 1732-7. being k l and k11. m = gram atoms of oxygen in gas phase, 20 = If we us; the symbols given in Table VIII, we a and yo = b for t = 0, we find IO
;"I-
Y =
am
=
A k1 ( x
(7)
n
- a?&nzm)
0 content, mg. 0'8 fraction, at t = 0
=
at t
n
$ kl (m-+-!)n
(3
'I
TABLE VIIL
+ hn - xm
and
- dx at
c
- am-'
wi
+ nhn)
(8)
Vanadium pentoxide
m
n
r
a
b Y
c
X
obtain ma
mx
Introducing
Oxygen
Water
.
Z
+ nb + rc = f + ny + rz = f
(14) (15)
or y = - - & r" - - x + mn n
the fraction of 0 ' s in equilibrium, equnt.ion (9) is transformed to
fn
The reaction rates are given by dz/dt k'(y dx/dt = k " ( y
- Z) - X)
(17) (18)
By sithstitiiting the value of y given by (16) into (17) and (18),we obtain
which leads on integration to
+
Since, for a given experiment, the value of A ( m n ) / V n is constant,, a straight line should be obtained on plotting the logarithmic function against time if the described kinetics is followed. It can be readily shown that precisely the same equation results if the gaseous phase is water rather than oxygen. It has been shown in the experimental part that all the results obtained with various samples of vanadium pentoxide cataIyst (with the exception of the heat-treated microspheres) are compatible with equation (11). For convenience, one may lump the constants on the right hand side of equation (1I) and write:
The solutions of these equations have the form x
+
(21) (22)
where
is the equilibrium concentration of 01*,G1 and GZ and constants depending on the boundary conditions Si,?=
nhere k: for a given catalyst depends only on the (m n ) / V ratio, since A is proportional to m. In order to allow for the variation of the (m n ) / V ratio, the actual velocity constants were n = 10 mg. corrected for V = 100 ml. and m atoms, so that
+ GleSlf + G2es?L =q +G (SI ;- A)eSll + (8, - A)eszt z = q
51
[A
+ I? zk d ( A + E)'
- 4(AE
-
U B ) ] (24)
and A , B, U and E are symbols which represent the following terms
+
A = -(kl(n v)h) B = - (klm/n) U = - (kIlr/n) E = - ( k l l (n m ) / n )
+
+
+
of
(25) (26) (27) (28)
If, in the case treated, the initial concentration 0 ' 8 in one or two of the reactants is the natura1
*
Feb., 1963 EXCHANGE OF ISOTOPIC OXYGENBETWEEN VANADIUM PENTOXIDE, OXYGENAND WATER237 concentration of 01*(0.2173, it is convenient to use the excess concentrations 21
- 0.0021 - 0.0021 - 0.0021
= z
2/' = y 2' = I
If, for example, a j"1
=
b
=
0.0021
= rc1 = r(c rcl
q = --
m+n+r
- 0,0021)
+ 0.0021
If we wish to apply these equations to the results of run no. 1732-7, we need to know k1 and IC". In the following equations (21) and (22) are evaluated (a) fork" = k1 = 1 and (b) for kl1 = I , k1 = 10 with m = 3.6, n = 8.1, T .= 28.73, zo = 0.016, .co = 0.0021 and q = 0.012. For case (a)
+ 0.155e-t + 0.245e-4.Qst + 0.233e-t + 0.243e-4.08t
(29) (30)
+ 0.102e-1Jg1+ 0.298e-4b.75t + 1.014ec1Jgt+ 0.024e-"6.7bt
(31) (32)
1002 = 1.2 lOOz = 1.2
For case (b) 1002 = 1.2 lOOz = 1.2
The values for log (1.20 - 100 z/O.99) are plotted against the time in Fig. 12. It will be seen that, while the plot for case (a) gives a curve in the beginning of the exchange reaction, the plot for case (b) is a practically straight line. This is due to the fact that even for relatively small values of t, the second exponential term in the formula can be neglected because of the large factor in the exponent. Since the data of run no. 1732-7 plotted in the manner of Fig. 11 gave a straight line over a given temperature range, it can be concluded that the exchange water-VzOs was indeed faster than the exchange Vz06-oxygen. Diffusion in the Solid Rate of Exchange Controlling.-If the diffusion in the solid is slow compared to the exchange reaction on the surface, the progress of the over-all exchange reaction will follow the same law as the flow of heat between a wellstirred fluid and a solid immersed in it. Using the formula derived for a sphere of the radius R in contact with a fluid6and the nomenclature used for the exchange reaction, we obtain
(33)
where u,(v
=
1,2,3,.. . ) are bhe roots of the equation tan Ita =
3nRa mR2a2
+
-___-
3n
(34)
aiicl 1< is tlie diffusion coefficient.for the solid.
In tlie follolving, we shall evaluate these formulas for mln = 0.247, the value for run no. 1732-42. If, for sake of convenience, we write kl/P = u
RCY,=
~r
(35) (36)
we find for the above value of m / n (37) (5) H. S. Carslaw and J. C. Jaeger, "Conduction of Heat in Solids," Ciarendon Press, Oxford, 1948.
Time. Fig. l2.--l'rogress of the 0l8esclinngo involving water, gaseous oxygen and vanitdiuiii pcritoxide according to eyuations (30) and (32).
and tan w =
3w
3
+0.247~~
The numerical evaluation of equation (37) yields the values given in Table IX. TABLE 1X EVALUATION OF EQUATION (37) U
0.001 .002 .005
.OlO .020
a - q
0.6133 .5109 .3674 .262 1 .1788
1
+ log=*a - q 0.7877 .7083 .5651 .4185 .2524
In order to be able to compare the progress of the exchange reaction calculated for a diffusion controlled mechanism with the experimental data obtained in run no. 1732-42 (see Fig. lo), we have to know the diffusion coefficient K . In the absence of an experimental value for K , we shall assume the point for y = 0.001 of Table IX coincides with the point for t = 650 minutes of run no. 1732-42. The calculated curve thus obtained is shown in Fig. 13 together with the experimental curve. It will be seen that the agreement between the two curves is satisfactory, indicating that in run no. 1732-42 the exchange rate was indeed controlled by diffusion in the solid. Since the average radius of the spherical particles ( R = 0.0163 cm.) is known, one can calculate the diffusion coefficient K = 4.1 X 10-lo cm.2/min. Mechanism of the Exchange Reaction.-It is a striking result of the present study that, in most instances, the exchange reaction was controlled by the surface reaction and that the diffusion of the oxygen in the bulk of the vanadium pentoxide was fast compared with the surface reaction. The fast diffusion occurred both on supported vanadium pentoxide and on the microspheres in their original amorphous state. It is believed that this high diffusion rate was made possible by lattice imperfections caused by the presence of foreign ions or other lattice defects. This view is compatible with the
238
W. C. CAMERON, A. FARKAS AND L. M. LITL
Vol. 57
the progress of the exchange reaction will always be observed when the rate-controlling step is the actual interchange of isotopic atoms or ions.6 The zero order with regard to the oxygen pressure can be ascribed to the strong absorption of the oxygen on the surface of the solid as a consequence of which the concentration of the oxygen in the adsorbed layer remains independent of the oxygen pressure. The next point that needs consideration is the significance of the activation energy found for the exchange Vz0502.In view of the relatively high value of 45 kcal. per mole, Minutes. it is possible that the activaFig. 13.-Progress of the 0l8exchange between gaseous oxygen and vanadium tion process involves either pentoxide microspheres in run no. 1732-42; comparison of experimental data with the dissociation of the oxygen data calculated from diffusion-controlled kinetics. molecules on the surface of the observation that, on heat treatment of the vana- solid, or of the loosening of the vanadium-oxygen dium pentoxide microspheres, the surface reaction- bonds in the vanadium pentoxide. In the system vanadium pentoxide-water, the controlled kinetics changed into diffusion-controlled kinetics as a consequence of crystallization and exchange reaction may involve a transfer of the hydrogen ions from the water molecules to one of heating of lattice defects. It has been mentioned that the vanadium the oxygen ions in the vanadium pentoxide lattice pentoxide particles lost some oxygen and turned as is indicated by the scheme' dark when they were baked out in vucuo. It has H2 H2 occasionally been observed that the 0l8content of 0 o*o 0 o*o r the oxygen brought into contact with freshly evacuI l l -v-v-v+ ated vanadium pentoxide dropped suddenly indicating rapid initial exchange (see Figs. 3, 6 and 7). It is also possible that part of the rapid exchange It is probable that this rapid exchange took place in this system may be due to the preservation of on the highly defective sites of the vaiiadiiim defects formed by baking in vacuo since, in this pentoxide particles. Of course, these defective instance, no reoxidation can take place as in the sites soon disappeared when, on contact with presence of oxygen. This possibility could be oxygen, reoxidation occurred, whereupon the tested experimentally by studying the dependence rapid exchange ceased. of the rate of exchange on the concentration of At the first glance, one may find a contradiction crystal defects. between the first-order kinetics found for the Acknowledgment.-The authors are indebted to progress of the surface reaction and the apparent Mr. R. W. Law for help in the mass spectrographic zero order derived from the dependence of the determination of the oxygen isotopes. exchange rate on the oxygen pressure. Actually, (6) R.B. Duffield and M. Calvin, J. A m . Chem. Soe., 68,557 (1946) there is no contradiction. First-order kinetics for (7) G. A. Mills and 9. G . Hindln, ibid., 72, 5549 (1950).
9
p
-+-+--$-
.
