Ind. Eng. C h e m . Res. 1991, 30, 82-88
82
Venuto, P. B.; Habib, E. T. Catalyst-Feedstock-Engineering Interactions in Fluid Catalytic Cracking. Catal. Rev. Sci. Eng. 1978, 18,1-150. Viner, M. R.; Wojciechowski, B. W. The Chemistry of Catalyst Poisoning and the Time on Stream Theory. Can. J. Chem. Eng. 1982,60,127-135. Voltz, S. E.; Nace, D. M.; Jacob, S. M.; Weekman, V. W., Jr. Application of a Kinetic Model for Catalytic Cracking. 111. Some Effects of Nitrogen Poisoning and Recycle. Ind. Eng. Chem. Process Des. Deo. 1972,11, 261-265. Voorhies, A., Jr. Carbon Formation in Catalytic Cracking. Ind. Eng. Chem. 1945,37, 318-322. Weekman, V. W., Jr. A Model of Catalytic Cracking Conversion in Fixed, Moving and Fluid-bed Reactors. Ind. Eng. Chem. Process Des. Deu. 1968, 7,90-95. Weekman, V. W., Jr. Kinetics and Dynamics of Catalytic Cracking Selectivity in Fixed-Bed Reactors. Ind. Eng. Chem. Process Des. Deu. 1969,8,385-391. Weekman, V. W., Jr.; Nace, D. M. Kinetics of Catalytic Cracking Selectivity in Fixed, Moving and Fluid-Bed Reactors. AIChE J. 1970,16, 397-404. Wilson, J. L.; Den Herder, J. M. Reforming Studies with Molybdena-Alumina Catalyst. Ind. Eng. Chem. 1958,50, 305-308. Winterfield, P. H. Percolation and Conduction Phenomena in Disordered Media. Ph.D. Thesis, University of Minnesota, Minneapolis, 1981. Wojciechowski, B. W. A Theoretical Treatment of Catalyst Decay. Can. J . Chem. Eng. 1968,46,48-52. Yeh, J. J.; Wojciechowski, B. W. Comparison of Catalytic Cracking on L a x and LaY Catalysts. Can. J. Chem. Eng. 1978, 56, 599-602.
Can. J . Chem. Eng. 1978,56,595-598. Pachovsky, R. A.; John, T. M.; Wojciechowski, B. W. Theoretical Interpretation of Gas Oil Selectivity Data on X-Sieve Catalyst. AIChE J. 1973a,19,802-806. Pachovsky, R. A,; Best, D. A.; Wojciechowski, B. W. Applications of the time-on-Stream Theory of Catalyst Decay. Ind. Eng. Chem. Process Des. Deu. 1973b,12,254-261. Paraskos, J. A.; Shah, Y. T.; McKinney, J. D.; Carr, N. L. A Kinematic Model for Catalytic Cracking in a Transfer Line Reactor. Ind. Eng. Chem. Process Des. Deu. 1976,15,165-169. Prater, C. D.; Lago, R. M. The Kinetics of the Cracking of Cumene by Silica-Alumina Catalysts. Ado. Catal. 1956,8,293-339. Pryor, J. N.;Young, G. W. A Kinetic Model of the Catalytic Cracking of Gas Oil Feedstocks. Catalysis on the Energy Scene; Elsevier: Amsterdam, 1984;pp 173-183. Ramser, J. H.; Hill, P. B. Physical Structure of Silica-Alumina Catalysts. Ind. Eng. Chem. 1958,50,117-124. Rudershausen, C. G.; Watson, C. C. Variables Affecting Activity of Molybdena-Alumina Hydroforming Catalyst in Aromatization of Cyclohexane. Chem. Eng. Sci. 1954,3,110-121. Sagara, M.; Masamune, S.; Smith, J. M. Effect of Nonisothermal Operation on Catalyst Fouling. AZChE J. 1967,13, 1226-1229. Sahimi, M.; Tsotsis, T. T. A Percolation Model of Catalyst Deactivation by Site Coverage and Pore Blockage. J . Catal. 1985,96, 552-562. Shah, Y. T.; Huling, G. P.; Paraskos, J. A.; McKinney, J. D. A Kinematic Model for an Adiabatic Transfer Line Catalytic Cracking Reactor. Ind. Eng. Chem. Process Des. Deo. 1977,16, 89-94. Suga, K.; Morita, Y.; Kunugita, E.; Otake, T. Deterioration of Catalysts for the Dehydrogenation of n-Butane due to Diffusion in Particles. Int. Chem. Eng. 1967,7 , 742-748. Szepe, S.; Levenspiel, 0. Catalyst Deactivation. Proceedings of the 4th European Symposium on Chemical Reaction Engineering; Pergamon Press: Oxford, 1970;pp 265-271.
Received f o r review February 9, 1990 Revised manuscript received July 6 , 1990 Accepted July 31, 1990
Influence of Mass Transfer and Chemical Reaction on the Kinetics of Grignard Reagent Formation for the Example of the Reaction of Bromocyclopentane with a Rotating Disk of Magnesium Walter W. Hammerschmidt and Werner Richarz* Department of Industrial and Engineering Chemistry, Swiss Federal Institute of Technology ( E T H ) , 8092 Zurich, Switzerland
Kinetic data for the reaction of bromocyclopentane with a rotating disk of magnesium show that a t a temperature of 25 "C the overall rate constant (k,,) is strongly influenced by mass transfer a t Reynolds numbers as high as 825000 (6300 rpm). Only at temperatures below -5 "C and high rotating speeds of the magnesium disk is the k,, value hardly influenced by mass transfer and the reaction rate limited by chemical reaction. By decreasing the temperature a t a constant rotating speed of the magnesium disk, the activation energy changes from 21 to 51 kJ/mol. From extrapolation of these data, the value of the chemical reaction constant (k,) is 55 X 10"'s-1 a t 25 "C for a disk with a surface area of 12.6 cm2. With an extended model, it was possible to describe the concentrations of Grignard reagent and side products in the reactor. The selectivity to the Grignard reagent of the reaction is strongly influenced by the number of revolutions/minute and temperature. The mass-transfer relations on rough disks could be determined by an electrochemical test reaction. The mass-transfer coefficients (12,) varied a t 25 "C from 3.5 X to 40 X 10"' s-l with increasing rpm. From it, and k, values, a value of the chemical reaction rate constant (k,)of 52 X lo4 s-l is calculated, which is in good agreement with the values obtained from Grignard experiments. 1. Introduction
Many scientists have investigated the mechanism of Grignard reagentformation(e,g.,G ~ and~~ & ~ ~ 1927; Kharash and Reinmuth, 1954; Ruchardt and Trautwein, 1962; Bodewit2 et al,, 1973; Walborsky and Aronoff, 1973; Lawrence and Whitesides, 1980; Ashby and *To whom all correspondence should be addressed. 0888-5885/91/2630-0082$02.50/0
Oswald, 1988). It has been shown that alkyl radicals are formed during the formation of Grignard reagent (Boentire reaction is dewitz ~ ~et al., 1972), b but the~ ~ mechanism , still not known (e.g., Garst and swift, 1989; Wdbomky and Rachon, 1989; de Boer et al., 1988). Kinetic data for the formation Of Grignard reagents are rarely reported especially with regard to well-defined mass-transfer regimes. Some works have been carried out with turnings of mag nesium without a calculable mass transfer, so that only
0 1991 American Chemical Society
R-X
t
Mg,
-
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 83 R-X'
*Mgf
t
4 OR t
R-R
X-Mg;
R(H)
+
-
R-MgX
R(-H)
Figure 1. Simplified reaction pathway for the formation of Grignard reagent and byproducts during the Grignard reaction. RX is bromocyclopentane, R' is cyclopentyl radical, RMgX is (bromocyclopentyl)magnesium, R(H) is cyclopentane, R(-H) is cyclopentene, and R-R is bicyclopentyl; indices s, surface.
qualitative data have resulted (e.g., Horak et al., 1975). Only a few papers have dealt with discrimination between mass transfer and chemical reaction control (Rogers et al., 1980a; Root et al., 1981; Hasler and Richarz, 1989). We describe a technique to measure the absolute kinetic data (mass-transfer coefficients, chemical reaction rate constants, and activation energy) for the reaction of bromocyclopentane with a rotating disk of magnesium in diethyl ether over a wide range of Reynolds number. The disappearance of substrate and formation of Grignard reagent and byproducts can be described for the chosen measuring system. 2. Evaluation of Kinetic Data
A simplified reaction scheme for the formation of Grignard reagent and its byproducts from alkyl halides with a radical pathway is illustrated in Figure 1. The rate-limiting step is the abstraction of an electron from magnesium (Rogers et al., 1980b; Lindsell, 1982; Sergeev et al., 1983). All the other reactions are much faster due to the radical nature of these reactions. For our own reaction conditions (substrate is bromocyclopentane, concentrations below 0.15 mol/L, and temperatures below 30 "C), the following assumptions are possible. A Wurtz-type side reaction between bromocyclopentane and (bromocyclopenty1)magnesiumcan be neglected (Anteunis and van Schoote, 1963; Bodewitz et al., 1975; Zakharkin et al., 1965; Tuulmets et al., 1985; Hammerschmidt, 1990). Therefore, the formation of the byproducts is explained by disproportion and recombination reactions between alkyl radicals. The Schlenk equilibrium (Schlenk and Schlenk, 1929) PRMgX MgR2 + MgX2 (1) K = ([MgX2][MgR2])/[RMgXI2 = 0.002 (2) is on the side of the Grignard reagent for the chosen system and can be neglected (Smith and Becker, 1966). For the consumption of the substrate, the following model is assumed. The first step is the diffusion of the substrate through a liquid layer to the magnesium surface, where (second step) the chemical reaction between bromocyclopentane and metallic magnesium takes place. The kinetic equations for the model are for a steady-state situation (processes in series) as follows: (l/AMg)(aRx/dt) = -~',,,(cRx - CRX,JV~ (3) (1/AMs) (wRX/dt) = -k : c ~ xv, ~ b
(4)
(m~x / dt) = -k bvC~x vb l / k O v= l / k , + l / k ,
(5)
( 1/AMg)
(6) where v b is the volume of the reactor (L), AMs is the surface of magnesium (cm2), t is time (s), NRX is the number of moles of substrate (mol), k', is the chemical
reaction rate constant (cm-2.s-1),k 6, is the mass-transfer coefficient (cm-2.s-1), k 6, is the overall rate constant (cm-2.s-1), cRX is the bulk concentration of substrate (mol/L), and cRxs is the surface concentration of substrate (mol/L). k,, is k6,AMs in s-l, k, is k',,,AMg in s-l, and k, is k'dM& in s-'. By using this model, the overall rate constant k,, is measurable by Grignard reaction. For Grignard experiments with a hig'i mass transfer, the chemical rate constant can be determined directly because in eq 6 the term l/k, can be neglected and therefore k,, = k,. The extended kinetic model for the description of the concentration of all substances in the reaction mixture based on Figure 1 consists of the following stoichiometric equations RX Mg, R' + 'MgX, rate constant k,, [s-l] (7) R' + 'MgX, RMgX rate constant kgri [s-l] (8)
-
+
2R'
-
-
R(H) + R(-H)
2R'
-
RR
rate constant ken [L-mol-'d] (9) rate constant kbi [ L . m ~ l - ~ d(10) ]
and rate equations dCRx/dt = -k,,,C~x
(11)
dcR./dt = ~ O V C R X- kgriCR. - k,n(cR,)2 - kbi(CR.)'
(12)
dCRMgX/dt = kgriCR.
(13)
dCR(-H)/dt = (1/2)ken(CR,)'
(14)
dCRR/dt =
(15)
(1/2)kbi(CR.)'
where c, is the concentration of component x and the rate constants are defined in the stoichiometric equations. Because mixing between the liquids below and above the disks during the Grignard experiments was observed, an extension of the equations was necessary. The change of concentrations in the liquid above the disk could been described with a linear change of concentrations with time. Figure 2 shows the mass balance sheet for the used reactor dcRX/dt = -kovcRX + F R X / v b
(16)
dcR./dt = ~ O V C R X - kgr$R. - ken(CR,)' - kbi(CR.)' dCRMgX/dt = kgriCR. - FRMgX/
(17) (18)
vb
dCR(-H)/dt = (1/2)ke11(cR.)~ - FR(-H)/
vb
dcRR/dt = (1/2)kbi(cR.)2 - FRR/v b
(19) (20)
where F, is the mole stream of component x (mol/s). A regression program (SIMUSOLVE, Dow Chemical) was used to fit the data with the kinetic model. Because k,,, k, and kbi are highly correlated, these rate constants could be estimated only relatively. Therefore, a value for kbi was selected arbitrarily. A steady-state approximation for the radical concentration reduced eqs 16-20 to four equations with four parameters, but the system is not determinate. The mass-transfer characteristics for a smooth rotating disk are determined from theory (Levich, 1962) in the laminar flow range (eq 21) and experimentally in the transition region (Dossenbach, 1973) and turbulent flow range (Cornet et al., 1969) (eq 22). The mass-transport relations are usually given by the dimensionless equations ShL = 0.62Re0.5S~0.33
(21)
ShT = 0.0198Re05S~0.33
(22)
84 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991
n
upper reactor part
--I I I I I I I I I I I I I I
II
. "I
dt
I
g l reactor, ~ volume v b
........................ balance region
I I I I I I I I I I I I I I I I I I I
Figure 2. Mass balance over the reactor.
The dimensionless groups are defined as follows: Sherwood number (Sh) = k,r/D, where 12, = k,V/A; Reynolds number (Re) = 2rwr2/o; Schmidt number (Sc) = u / D ; r is the radius of the disk (m), D is the diffusion coefficient (m2/s);u is the kinematic viscosity (m2/s);w is the number of revolutions per second (s-l); V is the volume of the reactor (m3); A is the disk surface area (m2);k, is the mass-transfer coefficient (s-l); and k, is the rate constant (m/s). For small values of the Schmidt number, Liu and Steward (1972) have calculated a corrective term for eq 21 0.62S~O.~~ = S~O.~~/(1.61173 + (0.4803/(S~O.~~ - 0.444870))) (23) During the Grignard reaction, the magnesium is dissolved by reaction and the disk becomes more rough. For rough disks, the change from laminar to turbulent flow (critical Reynolds number (Re,))decreases to lower values of Reynolds number and the mass transport to a rough disk is greater than to a smooth one (Cornet et al., 1969). Therefore, the Sherwood relations have to be determined experimentally for the disks. The exponent of the Schmidt number remains constant (=0.33) (Dossenbach, 1973),and the Sherwood equation can be reduced to Sh = aReaSc0.33 (24) Because electrochemical reduction of alkaline K3Fe111(CN)6 to K,Fe11(CN)6is fully mass transport limited (Selman and Tobias, 1978), the hydrodynamic flow behavior a t the disks is measurable with this test reaction. Electrochemical reaction rates can be determined by measuring the current through the cell. For electrochemical reaction, the Schmidt number is defined as Sh = Ir/rr2zFDcowhere I is the current (A), F is the Faraday constant (96500 A.s/mol), z is the charge-transfer number, ir = 3.141 59, r is the radius of the disk (m), D is the diffusion coefficient (m2/s),and co is the concentration of the Fe"' salt (mol/m3). After determination of parameters a and (Y in eq 24, it is possible with adequate values of D and
I
A
I I
I1 I
N2
Figure 3. Apparatus for the Grignard reaction of bromocyclopentane with a rotating disk of magnesium. u for the Grignard medium to calculate the Sherwood number of the Grignard experiments. Calculating k, from the Sherwood number and k,, from the Grignard experiment allows us to determine k, values with eq 6. 3. Experimental Section (a) Grignard Experiments. Materials. Magnesium disks with a diameter of 4 cm were made from polycrystalline magnesium of ordinary quality (99.9% Mg, 0.08% Fe, 0.01 % Mn, determined by AAS). Bromocyclopentane (Fluka, purum) was used with a quality >99.8% and was purified by vacuum distillation if necessary. The solvent (diethyl ether) used was dried by storing over activated molecular sieves (4 A) for a t least 24 h, distilling over sodium hydride dispersion (Fluka, 5560% in oil, pract.) and storing over activated molecular sieves at least 24 h again. Grignard experiments could been carried out only if the water content was C20 ppm. The water content was determined with a Karl Fischer coulometer 652 (Metrohm AG). Apparatus. The experiments were carried out by using the apparatus shown in Figure 3. The bottom part of the apparatus was a double-walled glass flask. The upper part was manufactured aluminum with a cooling chamber and the inside covered with a Teflon layer. The magnesium disks had a diameter of 4.0 cm and were imbedded in a poly(viny1idene fluoride) (PVDF) cone with epoxy resin. All experiments were carried out under nitrogen atmosphere. Procedure for Obtaining Grignard Reaction Kinetics. One-thousand milliliters of an etheric solution (1% cyclohexane added as internal standard) of 0.15 mol/L bromocyclopentane was filled in the apparatus. The last gas bubbles were removed through the sample tube, and the apparatus was thermostated at the required temperature. The Grignard reaction was started by scratching the disk periodically with a piece of corundum. Normally the reaction began immediately, which was visible by appearance of turbidness. After 10 min, the required value of the number of revolutions was fixed and the experiment was started. After approximately 30% bromocyclopentane was consumed, the first sample pair was taken out from the apparatus and quenched with water in a closed sample flask. One sample was taken from the upper part of the reactor through the input for the substrate solution (17);
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 85 the other sample originated from the glass reactor taken through the sample tube (8). Periodically sample pairs were taken in the range of 30-70% conversion of bromocyclopentane; therefore, only 1mm of the magnesium disk was dissolved by reaction. Analysis. The etheric phase of the samples was analyzed by temperature-programmed gas chromatography (Hewlett-Packard HP5880A with FI detector and automatic sampler HP7671A). The column material used was 25% methylsilicone SE 30 on Chromosorb W (30/60 mesh). Detector signals were calibrated over the entire concentration range for the internal standard cyclohexane (Fluka, purum). Identified substances were cyclopentene, cyclopentane, cyclopentanol, bromocyclopentane, and bicyclopentyl. New calibrated columns gave a mass balance (eq 25) with an accuracy better than 1%. The subZ = CRX,O = CR(-H) + CRH + CROH + CRX + ~ C R R (25) stances originated from the disproportion reaction (cyclopentene and cyclopentane), recombination reaction (bicyclopentyl),unreacted substrate (bromocyclopentane), and reaction of Grignard reagent with water (cyclopentane) and oxygen (cyclopentanol). Because of tailing in the cyclopentanolpeak, the concentration of cyclopentanolwas calculated from the mass balance. The concentrations of cyclopentene, bromocyclopentane, and bicyclopentyl were obtained directly by gas chromatography. The Grignard reagent concentration was determined indirectly as the hydrolyzed part (cyclopentane)and the part of the reaction with oxygen by hydrolyzing procedure (cyclopentanol) as follows: CRMgX = cRX,O - 2CR(-H) - cRX - 2CRR (26)
(b) Electrochemical Experiments. Materials. The electrochemical reduction was carried out with a solution of 0.01 mol/L potassium hexacyanoferrate(II1) (Merck, 99 % p.a.), 0.02 mol/L potassium hexacyanoferrate(I1) (Merck, 99% p.a.1, and 0.5 mol/L sodium hydroxide (Merck, 99% p.a.). The water used was deionized and distilled. All experiments were carried out under helium atmosphere. Apparatus. The apparatus for electrochemical experiments was similar to that used for Grignard experiments with the following modifications. The upper part was manufactured from poly(viny1 chloride) (PVC) without a cooling chamber, and the activation arrangement was displaced by a wire of platinum as the reference electrode. The current from rotating disks was shunt with a sliding contact on the top of the axle. The moving force from the motor was transmitted on the axle u t the side. Procedure for Measurements of the Hydrodynamic Flow Behavior of Rough Disks. Because magnesium is unstable in aqueous medium, nickel replicates of the magnesium disks were made by producing a silicone rubber (Silicosehl RTVllO + KA-1, Chemia Brugg AG) negative, coating the negative with a thin film of high-conductive silver lacquer (L200, Demetron), and electrodepositing nickel at 50 "C with a nickel-plating solution (composition for 1-L solution: 330 g of nickel sulfamate dihydrate (Fluka, purum pea.),9.3 g of nickel chloride hexahydrate (Fluka, purum p.a.), 50 g of boric acid (Fluka, puriss p.a.1, and 1.0 g of sodium lauryl sulfate (Fluka, puriss); finally the nickel disks were electroplated with a platinum layer (0.6 gm, platinum solution J, Degussa). The nickel disks, supplied with a wire that was the length of the hollow axle, were imbedded in a PVDF cone with epoxy resin. The electrical supply was connected and the nickel disks were degreased cathodically with an alkaline solution. After the disk was degreased, the apparatus was put together, hex-
acyanoferrate solution was filled in, and the last gas bubbles were taken out through the sample tube. The anode was made of nickel, whereby the anodic surface was 15 times greater than the cathodic surface. The electrochemical cell was powered by a potentiostat (AMEL 549); the reduction potential was -800 mV (three electrode system). Determination of the function Sh = f ( R e )was performed at four temperatures (35.0, 28.6,22.2, and 15.9 "C), each at 60 different speeds from 6@00 rpm to 100 rpm. Measurements and control of parameters were performed with a personal computer (Olivetti M24, data aquisition hardware Burr-Brown PCI 20000). Each Sherwood number has been determined 10 times. 4. Results and Discussion Physical Data for the Grignard Experiments. The diffusion coefficient was determined by the diaphragma method (Stokes, 1950; Janz and Mayer, 1966) with 0.6 M etheric solutions of bromocyclopentane. For the temperature range from -5 to 30 "C, the temperature dependency is D(79 = 127.2 X exp(-8414/RT) (27) (Hammerschmidt, 1990) where the temperature (T) is in K, R is the ideal gas law constant = 8.3144 J/(mol.K), and D is the diffusion coefficient in mz/s. The kinematic viscosity was measured with a capillaric viscosimeter for 0.15 M bromocyclopentane solutions in the range from -30 to 30 "C (Hammerschmidt, 1990). The temperature dependency is u(T) = 0.3976 X exp(5163/RT) (28) where u is the kinematic viscosity in m2/s, R is the ideal gas law constant = 8.3144 J/(mol.K), and T i s the temperature in K. Physical Data for the Electrochemical Experiments. The viscosity of the solution (0.5 M NaOH, 0.01 0.02 M K4Fe11(CN)6)and the diffusion M K3Fe111(CN)6, coefficient were determined with a rotating disk system in the temperature range from 15 to 35 "C (Bourne et al., 1985) as follows D(T) = 3.8180 X 10.191 X 10-lZT+ 14.983 X 10-14T2 (29) u ( T )= 1.7728 X lo* - 4.1820 X 10-8T + 3.9022 X 10-'OT2 (30) where D is in m2/s, u is in m2/s, and T is in "C. Grignard Experiments. Influence of the Rotating Speed of the Disk. Figure 4 shows the calculated kinetic data for the consumption of the substrate during the Grignard reaction. The measured temperatures were 25.0, -5.0, -7.5, -10.0, and -12.5 "C, and the rotating speed changed between 250 and 6300 rpm. No experiments could be carried out at temperatures below -14 "C. The temperature precision for each experiment was better than k0.3 "C, and the rotating speed varied f1.5%. Each experiment has a T value (=parameter estimation/standard deviation) for k,, of greater than 60, mostly between 150 and 250. A t 25.0 "C and 6300 rpm, the accuracy of five experiments is better than 4%. Even at the highest speed, at 25 "C the reaction rate is influenced by the number of revolutions of the disk. Extrapolation of the data at 25 "C to higher speeds with 1/kOv= l / y ~ O+. ~l / k , gives a value of 72 X lo4 s-l for k,. At temperatures below -5 "C and rotatings speeds at about 3000 rpm, the k, values are hardly influenced by the number of revolutions and
+
86 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991
"
a
!3!
1
10104
1 4
00
9
-7.6
00
-82
1,
0
1
0
m45006ooo7Mo E b e r of revolutions Ir.um.1
Iwr,
Figure 4. Dependence of the overall rate constant k,, of the Grignard reaction of bromocyclopentane on the rotating speed a t different temperatures, ( 0 )T = 25.0 O C , (+) T = -5.0 O C , (*) T = -7.5 "c, (0)2' = -10.0 "C, ( X ) T = -12.5 "C. -5.8
1,
4.4
I
-7.0
3
-7.6 -82 -8.8
1
.
'
I
1
'
'
'
'
'
,
'
'
-8.8 0.0032
0.0034
0.0036
0.0038
lltemperature
a
0 . w
Figure 6. Arrhenius law for the Grignard reaction of bromocyclopentane at a rotating speed of 6300 rpm. The obtained Arrhenius straight lines are for low temperatures 1.168 X lo8 exp(-47800 J. mol-'/RT) and for high temperatures 36.26 exp(-24100 J.mol-'/RT).
1-1
\
1
I -
0
2 o o o 4 o O 0 6 o o o ~
number of revolutions [r.D.al
Figure 7. Influence of rotating speed on the selectivity of the Grignard reaction at 25 "C, conversion = 90%, cRx = 0.15 mol/L, (+) snip (*) Sbi, (0) Table I. Activation Energies ( E A )for t h e k,, Values at Different Rotating Speeds E,, kJ/mol u,rpm T>O"C TCOOC 1000 33.0 2000 49.4 2500 18.7 37.5 3000 50.9 4000 54.0 5000 51.8 6300 24.2 47.8
the temperature dependency relative to the recombination reaction kbi with an activation energy of 50 kJ/mol.
ken = 3.37
X
1014exp(-48160 J.mol-'/RT)
kgri = 1.79 X 1O'O exp(-53330 J.mol-'/RT) kbi = 5.73 X loi4 eXp(-50000 J.mol-'/RT) The activation energy of the disproportion reaction is 1.8 kJ/mol smaller than the activation energy for the recombination reaction. Therefore, increasing temperature prefers recombination reaction. Selectivity. The selectivity was calculated for an ideal reactor, assuming no mixing between the upper and lower parts of the reactor. A further assumption is that the Grignard reaction started immediately without an induction period. Figure 7 and Figure 8 show respectively the influence of number of revolutions and the influence of
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 87 Table 11. Calculated Chemical Reaction Rate Constants (k,)at 25 OC from Grignard Experiments (k,) (Conditions w, Re) and Measured Mass-Transport Coefficients (k,) (Sherwood Relations SJI = aReeSco.s3 for the Disks) u,rpm Re a Ly k,, s-* k,,, s-l k,, 1.12 x 10-4 1.64 x 10-4 3.54 x 10-4 250 32 800 0.161 0.71 2.35 X lo-' 4.49 x 104 0.77 4.93 x IO-' 400 52 500 0.081 6.72 X IO-' 5.35 x 10-4 2.98 X lo-' 0.67 500 65 600 0.249 6.24 x 10-4 4.08 X lo-' 11.80 X lo-' 0.65 78 800 0.279 600 5.83 X lo-' 18.26 X IO-' 0.74 8.56 x 10-4 0.117 1000 131000 7.46 x 10-4 6.99 X lo4 110.82 X IO-' 1250 0.69 164 100 0.142 55.18 X lo4 8.43 X IO-' 9.95 x 10-4 1500 0.64 197 000 0.286 8.24 x 10-4 63.56 X IO-' 0.67 0.180 9.47 x 10-4 1750 230 000 10.78 X lo-' 27.94 X lo-' 0.73 0.124 17.55 X lo-' 2500 328 300 14.07 X lo-' 18.78 X 56.10 X IO-' 3250 0.70 0.153 526 800 15.18 X lo-' 58.86 X lo-' 0.74 20.34 X 3750 0.099 492 400 16.63 X lo-' 42.71 X IO-' 0.80 27.27 X 4250 0.055 558 000 24.14 X 17.39 X lo-' 62.19 X lo-' 4500 0.73 0.107 590 900 19.01 x 10-4 65.41 X lo-' 0.73 26.80 X 5000 0.116 656 600 19.46 X IO-' 38.30 X lo-' 6000 0.79 0.065 788 000 39.56 X lo-' ~
c""""'"""''"""'"""'~
were used. Table I1 shows the obtained values for a and a of the Sherwood relation. From the Reynolds exponent a and factor a, the mass-transport parameters were calculated for the Reynolds number of the Grignard experiment. The Schmidt number was calculated to be 74.7 from eqs 27 and 28. The correction term (eq 23) for this Schmidt number is 0.92. Therefore, the Sherwood relation for the Grignard experiment is Sh = 0 . 9 2 ~ R e * S c=~ 0.92~Re*(74.7~.~~) .~~ (31) For Reynolds numbers of about 200 000, where there is turbulent flow for a smooth disk, it is possible to calculate " 1 a mean value for k, A mean value of 52.3 X lo4 s-l results 250 260 270 280 290 300 310 with a standard deviation of 13.0 X lo4 s-*. For Reynolds temperature Ir
