-
e
for &cand-n&
time,
(e)
d o n )
Vapor-Phase Esterification Rates H . F. Hoerig', Don Ramon, 0. L. Kowalka ~
'
E
IOF WI%WNIIIN. l ~ MADISON, WIS.
IIE esterification reaction between organic acidn and alcoholn has been atudied quantitatively in the liquid p h from the standpoint of equilibria and of reaction rates. The reaction in the vapor phsse has not been inveatigated 80 thoroughly, however. The equilibrium constante for the v a p o r - p h reaetion have bean accurately determined (#), and various catalynta have been employed; silica gel apparently has been the moat s u c c d u l (I, 8, 6,6). No data are available to correlate the eEect of maas velocity of the gases and the eEect of temperature on the reaction rate. In thia investigation the esterification reaction between ethyl alcohol and acetic acid in the vapor phsse was studied in a Bow system, operated at stmonpheric pressure, and employing a silica gel catalyst. ESTERIFICATION UNIT
The a paratus consisted, in general, of a calibrated delivery aptem L r the maetantn. a propofiioning pump, vaporiaen,
k n t sdd-..
E. I. du Poot d. Nsmoun & Comp.ny. Io&. BuUdo.
Y.
reaction chamber, Dowthmn heating 8ptem. condenser, and contml panel (Figure 1 The calibrsted delivery w&.m for acetic acid and for e t b k almhol wan constructed of glaes. AU the other unite in the reaction system ware mmtructed of
KAZSM08tainlesssteal. The reactmtm were pumped separately from the calibrated glaae burets by the proportioning pump m order to ad'& the D ~ toDthe desired Bow rate. After the rate wan aet, th, rsao&ti wem pumped fmm storaga mb0 to avoid repeated in of the tla& which nu lied the rmts. Calcium chloride tu& were connected to slf%r inleb of the feed swlem so that
A se&wate vaporizer wan built for each m.iant from a l ' t ~ inch stainless steel nip le, 18 inchas Ion These nip lea were canned on the ends. an8were cast in n,arr%el into two &minum the Ilqtdds at an initial, mntrolled, constant temperature. In addition, a second similarly controlled region wan rovided at the disc6ane end of each vanorher to control the of sumrheat. %e aluminum b1ocb acted BB constan~tempraiure wasvoim of heat, EreFntii +ow, vapo&ation of the resctsnta and consequent co ection o hqud m pools in the vaporiaenr. The superheating section WBB neceseary to obtsin close control of the temperature of the reactants entering the reaction chamber.
8-
I
I The esterification rate of acetic acid with ethyl alcohol in the vapor phose UXM investigated in a flow system using a dica gel catalyst. The mass velocity of the vapor did not affect the constants in the rate equations representing conditions a t spe&fie looations in the bed. I t appears then that m ( u ~t r a d e r in the vapor phase UXM not significant. Furthermore, with temperature increase, these constants were augmented linearly, which indicated that the sunface reoction
Ha):
1943
rate UMII not a controlling factor. The experimental evidence shows that the rate of vapor-phose esterifieotion is controlled by the rate of m ( u ~transfer or diffusion through a condensed phose present in the capillaries of the silica gel. The temperature effect is in agreement with this obserwtion, as ia the magnitude of the activation energy. The second-order reaction rate ordinnrily encountered in liquidphase esterification UXM negligible in the catalyzed reaction.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
575
T
n
h Gdibroled Tuber
VMm Tubes From
In addition, an electrically heated box was Lacad over the tubes which carried the reactants from the super&ater to the raaction chamber, and the degree of su heat was h a U y controlled b adjwtii the temwature in The temwmtnm of n6 un'ta in the vaporbii and nu rheating axtion Were contmlled b thennmtats consisting of &a mda set in holed drilled in the bloch or. in the w e of the box. set in a brass tube closed at one end. *he d i f f m e e in &&ts of SxpaULaion
Ebx.
The composition of the reactants w88 determined by denaity measurements with a calibrated 100.c~. pycnometer. ,AU y tanta uaed were over 99.60 Der oent m.the imnuntv belllp h g n a m n d f t6e liquid
pmdict at 0' C. for the fm &id with &and ium hydmade containing barium hydroxide. A I-oc. pipet waa used to withdraw BII exwt rtion of the sample for titration. and also to withdraw identica!?mrtions which were d u d ashift in the relative positions of the tarm+d pinta 0% weighed in a $awnto pered weighing bottle.* Cam was taken to silica and of the metal tube or block with change m temperature. bring the pipet to 0" before withdrawingthese portions. This motion actuated a m i c d t o h which, in turn, moved a The unit wan operated continuously for each w until periodic mercw swine -&Y .that carried the electric current to the heatsampling of the pmdud gave the m e titration for at leaet three ing elkents. conwcutive samples. After completion of a run the reaction A stainleas steel ipe 2 inchea in diameter and 6 feet in length, chamber wae flushed with nitrogen and a positive pressure of waa the reaction cBamber. Flanges were used to seal the ends, was maintained in the reaction chamber until the unit and the catalvst was 8 u ~ ~ 0 1 tin. dthe tube by a d o r a t e d ~ h t e nitmpn had cooled to mom temperature. This waa done to prevent air restin on th6 lower hr&. To maintain a &tht temperhure from entering the system and oxidizing any alcohol which might over tfe entire length of the reaction chamber, a, jacket was built have remainedon the catalyst. amund the stainleas steel ipe. Dowtherm was crrculated upward To determine whether the wall of the stainless steel catalyst through this jacket and o h a system containing an ironerehsmber bed any catalytic efiact on the reaction, a w was made sion hentar and a silica md &catat. By this mama it was with no catalyst in the chamber. The product showed no meas pwaihle to maintain the temperature of the entire catalyst bed urahle conversion of the reactants beyond experimental error. conatant within '1 C. fromtop to bottom. Thermocouples for tern nrture readings were placed at the top and bottom ofthe Sinca 110 data on equilibrium were available at temperaturea bed and on the outside waU of the jacket equidistant fmm cat.& above 200' C., equilibrium runs were also made at 230' and the ends. 270° C. These were carried out by starting with a mixture of one The vapora from the reaction chamber were condensed and mole of m t i c acid to one mole of ethyl alcohol. The pumping moled rapidly in a c o n d m r Ned with ica and water 80 that syatem waa fvet flushed with the mixture. Using only one feed no further reaction would take plm. The liquid p d u d was line, the mixture was then pumpd through the reaction chamber ' cohoted wntinuoudy in a lage 9n&, and 88111 ea were anth at a rate as slow as possible. Careful analyses of the pmduct drawn for analysis by means of a side arm above tg', Bask. were made,.and when 110 changee in dpis were noted, wllecTo calculate the reaction rate and the equilibrium constant tion of the pmduct wan begun. After all the initial mixttm had for the four-corn nent 8aoetic acid-athyl eloobol-ethyl through the reaction chamber, the pmduct was sent fouowing information was neoeassry: mmeretste-water, k through the s p h and the p r o m repeated. The rep i t i o n of resotante i n ~ u c a dinto reaction chamber, "te of cycling of the produd waa continued until no further change in introduction of reactants mto reaction chamber, cornpositwon of product compositionwan noted. pmduct leaving the system.
d&um
8.
&
-
tE
S76
CY
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vol. 35, No. S
..
*
RESULTS VRg VAIUOUS CATALYSTS
The catelyst waa the standard silica gel mannfactnred by the D a h n chemical Compsny; four lots were prepared from it. The 6rst waa a mixed catalyst in which the particle &ea ranged from No. 3 to No.8 Tyler Standard Sawn (2.4 to 6.7 mm.). The total volume occupied by this c a W waa 3520 cc., of which 51 per cent waa void space. The other three cawere carefully 8ueened to W t e Tyler Standard Screen mesh &ea: (a) through No.3, held on No.4 (4.7 to 6.7 mm. in diameter), (a) through No.4, held on No.6 (3.3 to 4.7 mm.), and (c) t h u g h No.6, held on No.8 (2.36 to 3.3 mm.). With the mired catalyst, four sets of rn were made respeotivelyat150°, 180e,230',and~70'C.usingineachcssea constant mole ratio of resdente of 1:1, but with varyingmas, velocities. The results of these teets are shown in Figure 2. It waa not poasible to inveetigste hperatures higher than WOO C. beeause pyrolynin of the alcohol is known to begin at 300". The 6rst Beriea of NDB waa made at 150", and the resulte obtained are shown aa curve A. The catalyst for this aeries had not been used previously, and the data for ourve A therefore represant the initial activity of the catalyst. UBing the m e catalyst, similar seriee of NDB were made at successively higher tempmtureu. After completion of the lyns at 270" C., it was deeirsble to make nure that the catalyst activity bad remained constant, and a checL run waa made at 150" C. (run 38). The d t e obtsined lay below Line A and indicated that the activity of the catalpt had d d . An attempt waa then made to reactivate the gel by heating it to 300' C. for 15 hours while air waa pBBsed thmugh. After this treatment, a second identical check m at 150' C. waa made (run 39); the resulte duplicated those of run 38 and nbowed that the decrease in activity of the gel waa permanent. Fobwing this a nm was made at 190' C. (run 40)to determine whether the data previously obat this hperatwe could be reproduced. The d t e coincided with the data originaUy obtained at 180' C. It waa concluded, therefore, that the catalyst had teaohed constant activity at sometimesfteathe6rstseriesofrumat150°C. Thedata for 150' C. were then m-mtablished by making two further NDB at that temperature, which with the check rn previously mentioned, d t u t a the data for curve B. The data on B were usad in all of the correlations cited. Complete data for the mixed catalyst- are shown in Table I. The runs with the 8ueened catdynt were conducted in each CBBB at 230" C. with a 1:l mole ratio of redante. For 4net of NDB, 2500 grama of catalyst were used and the volume occupied waa 3380 w. for each of the d=tal* The data are pres3nted in Table 11. CORRELATION OF DATA
since the convereion of ethyl alcohol and acetic acid to ethyl acetate and water does not proceed to completion, it waa neoeg sarg to know the equilibrium conatants for this reaction at all temperatures inwtigated, in order to make an analysin of the data on miction rates. The equilihrium * %Ye
1943
INDUST
constant bssed on fugacities or activities can be expreae8d ea follows:
--
when, K. kl
kr
f
P
P
dibrium constant 3 o c i t y comtmt of forward reaction velocity conatant of revem &ion fugacity of any speciIied component of system
It haa been shown (8) that the partial pnrsaures of the aster, water, and alcohol can be considered equal to their fugacitk at pressures leas than one atmosphere. But for acetic acid vapor such simpli6oation is not tenable, becsw even at 300" C. the amciation of the acid is signiscant and must he considered. Furthermore, Since the equilibrium constants were determined at one atmosphere total pr8enure, the mole fraations of the componente other than acetic acid may be substituted for their reapedive partial pnrsaures in the equation. Thus Quation l h o m e s :
where
N
=
mole fraction of any individual component
chartswere developed from data taken from the International m of Critical Tables to show the relation of the partial p m t i c acid to ite fugacity at various temperatures. These charts were used in dl calclllations. Esaex and Clark (8) determined values for K,, experimentaUy up to 2 M ) O C., and their valuea were 4 at 150' and lWOC. The data of NDB 55 and 56 obtained ea outlined previously were uaed to calculate the equilibrium oonstanta at 230' and 270' C. The valuea of K. and the corresponding valuea of the equilibrinm degree of c o n d o n using a 1:1 mole ratio of reactante follow:
1W 1W
m 270
88.e.3dc.i
dd
a1
18.87 f#, 16.00 11.20 mu.
&.
0.848 0.807
C.788
0.798
W
.
4. T
2:.
L
e
e
4
6
6
The eateri6cation motion in the liquid phsse is a clasSicsl example of a 88cond-der &ble reaction, and there is no evidence to indicate that the vapor-phase catalytio resotion proceeds in any merent fsshion. If the ratscontmllingstep in the hetemgenenus vapor-phase reaction is the actual rate of reaction, the experimental data ahodd fit the aecondder r e d b l e reaction equation developed for a flow pmeeas, and a conatant for the readion rate &odd be obtained which is d e c t e d by chsnges in space veldty. Equation 3 is the differential form of the equation for a swond-order mverible resetan: dA/d k d B W D (3) where A fugacityof acetic wid B fugacity of ethyl alcohol C fuPaaitvofwater D = fu&,it~ofethylseaQts
---
I
-
-
-
=time
Thia equation was expanded for application to a flow proand integrate3graphically, using the data obtained at 230' C. with the mixed cstalyat. A value for h was found which varied significantly with mass v e l d t y and indicated that the ratecontrolling step in the esteri6cation was not the actual rate of reaction. Supporting evidence for this conclusion ia found in the obearvations that the cablpt Sotivity gter its iuitial d decrease remained unchanged thmughout the investigation, and that during eaperimental runs as much as 12 hours of operation w m required to reaab oonetant oonversion. Theza phenomena point toward mass transfer as the controllingfsdor in the rata of reaction rather than limitation by chemid rate of combination. If the velocity of reaction at the c a W o Burface is large enough, the rate of formation of the pmduct may be controlled pMcipaUy by the rate of difluaion of the reactanta from the gas stream to the c a w muface or the rate of ditiu%on of the 578
I2
10
I4
It)
I.
I
PO
pmducta from the catalyst surfaee to the gas atrenm. Where the van der Waals type of condensation on a catalyst surface is poesible, it esn logically be concluded not only that a gse film resistance existe,but also that a condensed pbaee may be pHePmt in the capillaries of the gel and that d8usion through it may mntml the formation of product. Maxwell and Stefan (8) derivd an expression for the diffusion of two components of a binary gss mixture where the net movement of the mixture is m.This m y be applied to a catalytic reaction, such as the esterifcation reaction, Since no ahange in volume occnm and the moles of reactants diEusing to the catslytic surface are equal to the moles of product diffusing fromthe surface into the gss stream. Since four components were actually pregent, the equation is not rigorously applicable to the &cation reaction, but is a d c i e n t l y good approximation and wgs uaed because of the complexity of an exact equation for the system:
where N. A
D,
I$
v.1,
yu
--
dh'./dA
-
-
( D J 4 ) bi I/-)P
(4)
moles of component a diffusingpast any point in 61m runittime area oP"cm section for diffusion mmss m e w ured at right angles to direction o?diffusion ditlusivity -61mthicknasa = mole freotiona of component a at terminal points of flrn
The equation is valid for both reactants and producta if due
conaideration is given to the sign of dNe. In enginwring calcdationa this equation is uauaUy e x p d in terms of a net transfer coefficient,grouping both terms D, and B, into a single tmm K,called thB " d c i e n t of mum t r d e r " .
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vd. 33,No. 5
INUUSTHldL REACTION HATES
T.m-
Bun -tu., No *C. 4160 a* 160 7im 8. I60 0. 160 10. 160 11. 160
lz. 18.
im
6a
160 190
sa
17 19
m ai
aa
18
ha.
0.68.5 4.om
0 . a
a.m
1.m 1.061 6.81
ssa
160
b
HAo'in Roduot M h A r . M&&.
Et0H 0.988
1w
190
1w
1w 1w 1w
10.01
14.67
6.70
9.811
14.68 17.60 26.10 94.11
SM)
a70 Made b+me the o*t& EpuilianUm
2. 186 0.612 0.1~1
0.W
0.018 0. iaa
0.866
1.07 0.W
1.18
o.am
0.1m
9.79
o.ow
0 . ~ 6 0.108 0.048 0.08s 0.0~1
14.80
o.ia7 0.176 0.061
3.m 2.m
0.018 0.006.
0.u
0.m 4.486
].am a.oa
1.06
7.04 a.04
6.30 9.m
13.26 1.708
0.0118
14.68 17.70
1.60
0.137
8
1.817
a .78
2.76
a .a8 IS
4.29 4.89 6.n 6.69
0 .M 8 81 8 6a 6 49
4 80
a
e 09 6 .I6 a 09 8 .as 7.os
1.91 ~~~~
4.25
6.70 6.40 6.88
8.09
7 61
....
84.w
94.04 h$mohd-&
--
-
-
dN./dA K (VU 1.4 mole fractionof wmpownt a in gaa stnsm mole fraction of a at equilibrium
(6)
In the application of the exprimental data to Equation 6, all calculations were based on acetic acid as the difiuaing componept, and fugacities ware used in plsce of mole fmetions. Hence @?&A equals the moles of acetic acid diflusing to the catalyst per unit time per unit area of transfer d a c e . "bin quantity is numerically equal to the mole
-
of ethyl acetate diffusing from the catalyet surface to the &as atream, which is equal to the moles of ethyl acetate pmduced per unit time per unit area. The area of trader may be taken as the area of the catalyd d w , which for any given cab lyst is proportional to the volume of the catalyst. Integration of Quation 6 over the volume of the catalyst gives:
Nn wbereNr
--
YW-
vu
-
hour
%p &e*
2
59 60
61 82 6a
1
w
w l ~ o f & i o n ~ ~ sllbmintl3 l a n d 2 refer to terminal pinta of chambsr
VI
Run No.
67 68
(6)
moles of product f o d per
TULE11. DATA NIB CATAL~TSOF D ~ m SIZE m AT 230' C.
a
KV*
MASS TRANSFER COBPFICIENT
At 150' C. with the mixed catalyst, a value of K wan found which was UnSfIected by ohangea in,mass velocity. At higber temperatK decraaeed slightly with in nma velocity but reached a inconstant value at the higher rates of flow. The YBIII~~ ob. tgined for K with the catalyet of different &ea ahowed the m e tendency to reaoha cooatant value. The fact that the mase trader ccm5cient in not infiuenced by mass velocity at high rate of flow ia dgni6cant. If the controlling reaistanoe to difluion were a gas film on the outside of the @ particles, the transfer ooaftioient would inmarkedly with inin mase velocity. The a h c e of any mch &ect shown that the rate of diffusion through such a gsa film is not the controlling factor in the apparent d o n rate, but rather that the major resistsnOe to W o n is in either a &as plwa or a condenmi plwa preaent in the capilhies of the catalmt. Because the t a m p e r a t u ~of~ the investigation were below the pseudo oritical tempeostures of w w w of the -tion Systean, and becaw Of the highly pomua structure of the cstalyet, the BsBumption that the v ~ n dm W& eyPe of condensation occurs ia reasonable (7). The magnitude of this &rption of reactants and pmducta by silica gel ia indicated by the fact that, after operation at
-hi%;--
If the film is considered to have a definite tbiclmess, and a sharp change in concentration occurs at the film and the main &as ntream interface, garis equal to the concantration of component a in the main gas stream. Also, in the w a of a catalytic reaction where mch reaction takes place at the c a b lyst d a c e , and the reaction reaches an equilibrium, y. approaches the concentration of component a at equilibrium. At one atmoqhere total p m , the pressure term equals unity. Rewriting, where y,. y,
Very close agreement wan obtained by Equation 7 with values of K d e u lated by graphical integration, and Quation 7 was therefore used to correlate the entire eorperimentsl data. Figure 3 shows the relation of the nma trader ooefhcient to mase velmity for the mixed catalyst at various temperatww, and for a constant temperature of Moo C. with catalyata of differant &ea.
oa 8 .46 8 ,411
2.a
0.m
io.7a
0.166
1.m
3.w
osea
-
i.ia
a.ua
1.4n 18.80
nal conditions in the ohambbr was attampted. An avarage driving force was doulated for the entire ohambbr using the logarithmic mean aversges for bW v), determined fmm the end conditions. Expressed mathematically,
I:&
1.m 11.410
10.8a
0.~41 0.087
10.06
i.ia
0.740 1.W
4.76 4.76
0.048
111.~4 ia.78 6.U 6.88
a.t.26 1.4%
0.037 0.W 0.090 0.016 0.048
1.08 0.688
1.-
0.091
1.100 6.71
.... .. .. .. .. .. ..
4.sa 9.m
0.080
i.aw
-E.,uta, .tm.
0.348 1.1M 1.24 1.20
2.m
0.048
0.844 11.84
M*AZ
o.ua
0.008 0.W
4.048
K anm m&
Eth Rod"0t
min -ntr
1 . w 1.w 11.88 11.98 1a.m 1a.M 8.96 8.93 16.70 m.oa 2.47 a.sa 1.711 1.70 7.40 7.aa 6.70 6.79 7.84 7.14
160
40 a s 3 8 0 ed' m a 7 3 8 0 88 180 %Q 180 m m ai 180 84 a70 as a70 a70 ed SSb Wb
b
6.70 6.n 10.01 10.49 2.4~ a.a
160 160
88 a9
m
M&&
69
.
-. I,
B*
-
7s
R..Ot.nt. MOWHI: HAo EtOH 6.77 6.79 7.7a 7.73 10.11 10.11 18.80 1a.69 18.6a 18.66 6.79 6.96 7.77 7.88 10.26 10.39 13.77 13.78 18.81 18.95 . 6.18 6.18 7.66 7.68 In n. 10.06 ii:G 14.10 18.80 18.68 ~~
1
piaun a.
HiOin
HAoin
0.074
2.19 8.68
~m&b, M u o t Molas/Hr Mol-/&.
o.iw 0.1ao 0.18 0.a4 0.10
0.18 0.16
0.21
o.ao
0.08 0.10 0.14 0.19
o.as
INDUSTRIAL AND ENGINEERING CHEMISTRY
5.72 8.98 n.a9 1.99 3.18 6.09 8.08 1a.M a.07 4.83 6.M
10.m 14.60
EtAa R Prdduot G-m& Y0l-A;. 8r..Iiter,atm 8.68 4.06
4.39 4.82
5.33 3.80 4.B
5.16
5.71 6.31 3.11 3.32 3.61 a.63 3.79
6.77
6.40
5.18 6.18 6.40 ~~
~~
6.78 6.92
6.75 6.W 6.76
Loa 8.94
3.82 3.61
.61 .. 8
si3
160" C., 161 cc. of condensed vapor8 were desorbed by aW0 grama of catalyst by continued hesting of the catalyst at
300" c. in8 Sk€%Ul
Of
nitrOgEU.
At the mggwtion of Henry Eyring of Princeton Universiity, the obseaved activation energy for Musion wed deternlined from the equation, mrbersD.
A B R
T
-
D, A #-#/RT diffusivity awnstant o h 4 activation energy = gasconatant ahlutetemperature
-=
(8)
-
lince transfer coe5cient K is proportional to the M d v i t y , dues of In K were plotted agsinst 1/T, and valuea of E m e o h b i n d from the dope of the Line at vnriow operStiner emperat.um6 (Figum 5). E was found to vary Bignificsntly vith temperature: Temp.. * 0. 1.50 180
5. K5.S.L 8.42 1.82 1.28 0.65
280 270
Since the thicknw of a layer present in the capillaries would be independent of msds velocity, only the value of the diffueivity would afiect the magnitude of the t d e r c d c i e n t . A t higher mea velocities the d u e of the transfer c d c i e n t tended to become constant M the maas velocity wed i n c d . The value of dihivity would be expcted to show the 8ame tendency. The diUwion equation used to correlste the experimental data wed developed for point conditions in the catalyst bed, usu+ng a constant d u e of Mwivity. However, the StokeeEmatein equation for Mwivity of liquids (4) prediediotsthat the Musivityis i n d y proportional to the viscosity. At low mass velocitiw, hi& percentage conversion is achieved and the relative maw8 of the eomponenta of the system vary widely from top to bottom of the catalyat bed. Conseguently, the viscosity and the diffusivity ale0 vary. At higher ratea of flow, the perc8nt.w conversion decrcmw and the diflusivity approaches oonstsncy over the length of the bed, giving constant values for the maas t d e r c0e.fficient. The Musivity of gasm is independent of concentm tion as reported by G i l a n d Q,and the m p t i o n of a gas p h in the capiuaries thus does not explain the devintim of the mass trnnder coe5icient with mass velocity. Variation of transfer d c i e n t K at low maas velocitka may slso be augmented by experimentalerrore. At low m s ~ l velocities, where equilibrium conversion b appronobed at the lower end of the catalyat bed, the driving force for di5wion between the catdyat d m and the main gas stream is d e c d , and any apcirimentalerror or enur in the value of the degrw of convernion at equilibrium destroys tbe accuracy of the logarithmic mean d u e of the driving force. The relation between values of maas transfer coe5cieot K and the temperature further supporte the belief that the ratecontrolling step in the apparent rate of reaction b the rate of diEwion through a condeneed pbaae. When mass transfer coe5icient K, calculated from data at bigb maas velocities (after K had resched a constant value), was plotted absolute temperature, a hear function was found to enst (Figure4). Gilliland reporta that variation of gas daumvitv with temperature is proportional to the 3/2 power of absolute temperature (3). If the actual reaction rate were the cootrolling factor, a much p t e r variation with temperature would be expected. However, the Stokee-Emteh equation predicte that, except for changes in viscosity of the system with temperature, a linear proportionality doe6 e& between the diflusivity of liquids and the absolute temperature. 580
F i y n 5. Colcubtion of 0bnrc.d Enarm of Aotimtion for DWIuion
l'he d u e s obtained were of the correct order of mwnihde 1or Mwion through liquids. The faat that E does m y with temperature also suppork a ditlusion hypothesis, ainae ;be activation energy of a ohemiod pmcsss b m W y indb d e n t of t e m ~ t u r over e mall temperature ranges.
Theasaistsnce of F. C. Wood snd R. 0. Taeoker in aitruction of the appmtw and in the -tal program, md the grant of funds from the WisconSin Alumni Reaearoh Foundation for equipment 1v8gratefully acknowledged. ~
m
B
(1) E b and Sahuyler, J . Am. C h . SOO.. 4 6 6 4 (19%). (a) EezuandClsrk.Ibid.,54, lZSO-l3M,(193~). (3) Gilliland, h. ENQ.C m . , 26. Bsl-5 (1934). (4) Gluultons. Laidler, and EWng, "Theory of R.te Rmead'. let 4..Chap. 9, New York, M&m~-Ell Book Do., 1941. (6) -by and Swarm. IND. ENa. CHUI., 32,1607-14 (1940). (6) Mailhe and W o n , BuU. em.ddni.. 29,101 (1989). In "CstaLvsis". ,., Rnhwnh. Tivlnr. .-.. and 5-oe. . . 1st ad.. Chap. 1, New York. D. Van Noatrand Cb.. 1837. (8) Wdker. Lewis, MoAdsms, snd Oiland. "Rin0iples of Chemical Engineering". 3rd ed., Chap. 14, New York, Mdirsr-Hill Baok Co., 1937. ~~~
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
Vol. 35, No. 5
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