November 1954
Subscripts h refers to less volatile component I refers to liquid phase u refers to vapor phase c refers to critical conditions of more volatile component ch refers to critical conditions of less volatile component r refers to reduced conditions relative to the critical point of more volatile component
Superscripts 0 refers to saturation conditions of pure, more volatile component -refers
to average value of quantity below bar LITERATURE CITED
(1)
(2) (3) (4) (5)
2381
INDUSTRIAL AND ENGINEERING CHEMISTRY
Raldwin, R. R., and Daniel, S. G., J . AppZ. Chen~.,2, 161 (1952), J . Inst. Petroleum, 39, 105 (1953). Brunauer, S., Emmett, P. H., and Teller, E., J . Am. Chem. SOC., 60, 309 (1938). Carpenter, J. A,, J . Inst. Petroleum, 12, 288 (1926). Derry, L. D., Evans, E. R., and associates, Ibid., 38, 475 (1952). Dow, D. B., and Calkin, L. P., U. S.Bur. Mines, Rept. Invest. 2732,1926.
(6) Edmister, W. C., Petroleum Re.ner, 27, No. 6, 104 (1948); 28, No, 2, 137 (1949); 28, No. 5, 149 (1949). (7) Fischer, F., and Zerbe, C., Brennstof-Chem.. 4,17 (1923). (8) Frolioh, Per K., Tauch, E. J., and associates, IND.ENG.CHEM., 23, 548 (1931). (9) Gjaldbaek, J. C., Acta Chem. Scand., 6,623 (1952). (10) Hildebrand, J. H., and Gjaldbaek, J. C.. J . Am. Chem. Soc.. 71. 3147 (1949); Hildebrand, J. H., and Scott, R. L., “Solubility of Nonelectrolytes,” 3rd ed., Reinhold, New York, 1950. (11) Hooper, J. H. D., Proc. Ana. PetroZeumInst., III,28, 31 (1948). (12) Horiuti, J., Sei. Papers Inst. Phys. Chenz. Research (Tokyo), 17, 125, 256 (1931). (13) Hougen, 0. A., and Watson, K. M., “Chemical Process Principles,” John Wiles, New York, 1947. J . B i d . Chem., 72, 545 (1927). (14) Kubie, L. S., (15) Lawrence, J. H., Loomis, W. F., and associates, J . Physiol. (London), 105,197 (1946). (16) Markham, A. E., and Kobe, K. A , Chern. Revs., 28, 519 (1941). and Morris, L. C., Oil Gas J . , 38, (17) Schulze, W. A,, Lyon, J. P., 149 (1940). (18) Schweitzer, P. H., and Szebehely, V. G., J . A p p l . Phys., 21, 1218 (1950). RECEIVED for review November 27, 1953.
ACCEPTED May 5 , 19.54.
Measurements of Vapor Diffusion Coefficient c.
c.
Y. LEE AND 13. WILIiE Unicersity of California, Berkeley, Calif.
Tw, $4,
HE method used in this study was originated by Stefan 18)and used extensively by other investigators ( 7 , 1 4 , 2 1 ,
22, $5). One of the components, in the liquid state, is placed in the bottom of a vertical tube. With the tube and liquid maintained at constant temperature, the second component, a gas, is passed over the top of the tube a t a rate sufficient to keep the partial pressure of the vapor there a t a value essentially corresponding to the initial composition of the gas-i.e., zero in the case of vapor-free gas. The gas rate must be low enough to prevent turbulence a t the mouth of the tube. The general theory of the method may be presented by considering a tube to he filled with liquid (designated as component A), so that the gas-liquid interface is located at a distance z from the top of the tube, as shown in Figure 1,a. In the steady state the rate of vaporization is given by the well-known equation N A
DPAp = ___ RTpja:
where
Background and general limitations of Equation 1 have been reviewed by W l k e ( 8 6 ) . The equation is specifically applicable only to the diffusion of one gas through a second stagnant gas. I n this case there is a finite hydrodynamic velocity in the tube corresponding to the rate of diffusion of component A. I n the derivation of Equation 1 an average uniform hydrodynamic velocity over the tube cross section is assumed, whereas in viscous flow the velocity distribution should be parabolic. Possible error due to this assumption may warrant special study (15). During diffusion the liquid level falls as vaporization proceeds and z is not constant. Assuming quasi-steady-state conditions, it can be shown that z may be taken as the arithmetic average of
values at the beginning and end of the diffusion period and used in conjunction with the over-all average rate of diffusion to give correct values of D by solution of Equation 1. Thus:
x=- xo GAS -
+2 xe
T X
I
i (b)
Figure 1. Models for Application of Theory
The assumption of quasi-steady-state conditions usually involves negligible error for measurements a t atmospheric pressure-Le., when the relative change in z with time is very small. APPARATUS AND MATERIALS
The apparatus was constructed somewhat aIong lines employed by hlchfurtrie and Keyes (Id), utilizing diffusion tubes of larger
2382
INDUSTRIAL AND ENGINEERING CHEMISTRY
diameter than those of most previous studies. Figures 2 and 3 illust rate the diffusion tube m d holder and Figure 4 is a flow diagram of the entire apparatus. T h e diffusion unit (Figure 2) was made of Iirase t o obtain satisfactory heat conduction into the system from the surrounding constant temperature bath. The upper gas chamber, 8.5 em. in d i a m e t e r , was connected to gas inlet and outlet tubes 1.8 em. in diameter by means of union joints, so that the diffusion tube could be inverted for downward diffusion. S t r a i g h t e n i II g vanes C o n s i s t i n g of t h i n Figure 2. Diffusion Unit copper plates 2 mm. A . Cover B . Gas chamber apart extended from C . Straightening vanes the end of the gas D. Diffusion tube E . Diffusion tube holder mlet tube to the edge F , 0. Union joint of the diffusion tube t o reduce gas disturbance associated wit,h the sudden enlargement of the flow path. T h e diffusion tube was fitted tightly into a holder which screwed into the bottom of the gas chamber. Two holders vcere employed for diffusion tubes 1.75 and 0.94 em. in diameter (Figure 3). Tube diameters were arbitrarily selected, arid other sizes might have been satisfactory. I n general, it is necessary t o have :Llarge enough diameter to obtain a conveniently veighable evaporation lose in a reasonable time wit,hout excessive dist,urbance inside the tube due t,o gas flow. T h e diffusion unit vias connected into the apparatus as irtdicated in Figure 4 .
f
Vol. 46,No. 11
E. I. du Pont de Nemours &. Co. and U.8.Bureau of blines, respectively. Specified purity ~va399.96% or better for h t t i gases.
With valves Va, V 3 , V:, V s , and V i 0 c l o d (see Figure 4 j the whole system was evacuated with the vacuum pump until 29.5inch vacuum (highest obtainable wit,h t.his pump) was indicated by the mercury manometer, CI. Valve V3 was opened and the system was filled with the gas used from the gas cylinder to atmospheric pressure. With valve Va closed, the system was evacuated once more. The system then rvas filled again to about 4 inches of mercury positive pressure and the gas in the system analyzed for oxygen. The procedure of evacuation and filling was repeated until the air content of tmhesystem rvas reduced to 0.1% or less. The condensing units were filled with the proper refrigerant (dry ice and acetone when helium was used; dry ice and carbon tet,rachloride when Freon was used; and liquid nit,rogen for some runs with air). The diffusion tube was filled to a desired level with liquid, stoppered, and weighed. With valves Vd and V Qclosed, t'he cover of the diffusion unit was opened, the diffusion tube was quickly irisert,ed into the holder, and the stopper was removed. With the cover replaced, the diffusion unit was immersed in the bath. The electric heater, D, was turned on. With valves V?,V l O , and V g opened the system was flushed with the gas for 10 minutes a t the desired flow rate. Valves T'2 and VB were t'hen rlosed. Valves V,, V,, and V swere opened while the blower was turned on. Va was adjusted to 010tain the desired flow rate. The time, flow rate, temperature oC t,he bath, atmospheric preesure, manometer Cz reading (about 3 inches of mercury positive pressure n-as maintained to prevent leakage into the system), diffusion length, and initial weight of the tube were recorded. The temperature of the gas passing through the condensing unit, S,was recorded every 2 hours. At the end of a run, the blower was turned off, valves V,, lis, V 6 ,and T i s were closed, and the diffusion tube was taken out, stoppered, and weighed. The t'ube TI same gas when meigheti hefore and aft
Gas from a caylinder connected to the surge titnlc \vas supplied t o the syst,eni as required to maintain the total pressure a t the diffusion tube constant and slightly above the prevailing atmospheric lesrel. A blower provided continuous recirculation of gas in t,he system. The diffusion unit was immersed in an oil bath maintained a t 25' =t0.02" C. An electric heater p l y e d in the line leading t o the unit brought, the gas t o within 1 C. of the bath temperature. The gas then passed through a 40-foot coil of l/s-inch copper tubing immersed in the oil bath which brought the gas entering the diffusion unit to the bath temperat'ure. Rate of gas flow was measured with an orifice meter and controlled manually with a bypass valve a t the blower. T o prevent saturation with vapdr, the gas leaving the diffusion tube was passed through a condensing coil immersed in a large Deivar flask containing a suitable refrigerant,. I n experiments with air, gas recirculation and condensation of vapor were not employed; air entering the syst,eni \\-as dried in a calcium chloride tower and discharged t o t'he room after leaving the diffusion unit. To eliminate vibration, the blower and stirring motor for the oil bath were mounted independently on the concrete floor of the laboratory. -4 vacuum pump Iyas emploved to evacuate the entire apparat,us prior to charging the .. syitem with gas. Liquids used included water, benzene, nitrobenzene, ether, and absolute alcohol. Benzene and nitrobenzene n-ere redistilled. Boiling points, and in some cases freezing points, mere measured for all materials and found to agree well n-ith accepted values in the literature. High purity Freon 12 and helium were used as received from
Figure 3.
Difftwfon Tube Assembly
When the diffusing vapor !vat4 lighter than the gas componerit for example, water vapor and Freon 12-the diffusion tube lvab filled to a desired levcl with cotton saturated with the liquid. A disk of blotting paper of proper size was placed on top of the cotton to provide a smooth surface. After the tube had been placed in the holder, the whole diffusion unit waR turned upside down and the run conducted as described above. When air was used, the procedure waa similar, except t h a t the air was supplied directly from the room and was discharged into the room again after it swept over t h e diffusion tube. The con-
November 1954
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
densing unit was disconiiected in this case, but the air was dried with calcium chloride before it entered the apparatus. The water content of the outcoming air rvas measured a t various timcs and utilized in the subsequent calculations. For experiments using gases other than air, the purity of the gas in the system was measured by determining oxygen a t the end of each run. I n all c a s ~ scontamination of the gas hy air was less than 1% a t thc end of the run, making the average air content of the gas al\Tays 0.5% or less. EVALUATION OF METHOD
2383
molecules was observed by Clusius and Waldman (5). This behavior represents a reversal of the phenomenon of t,hermal diffusion. I n the present experiments, described above, the effert was evidenced by lower ternperaturcs a t the thermocouples 0.4 and 0.8 cm. above the interface than that indicated by the thermocouple a t the liquid surface or by the thermometer a t the upper end of the diffusion tube. Typical data are given in the righthand column of Table I. For even the most.extreme system studied, ethyl ether, the effect was not sigriificontly large, never exceeding 0.1' C. B y means of equations developed by Waldmann (28-24) the temperature 0.4 cm. above the liquid was calculated for the present case of ether vaporization and found t o agree with the measured values within the accuracy of the experiment.
Before the final procedure was adopted, several effects which might cause experimental error were investigated. TEMPERATURE OF LIQUIDSURFACE. Latent heat must be supplied t o the gas-liquid interface as vaporization proceeds. Heat is supplied mainly through the metal walls of the diffusion tube Trom the surrounding bath into the liquid and then through the liquid into the interface. As the temperature is lowered in the interface, free convection is induced. There is an additional contribution to the heat transfer process by conduction through the gas phase. To explore the magnitude of temperature lowering in the interface, a tube 1 . i 5 cm. in diameter and 17 cm. long was constructed with thermocouple.; of thin copper-advance wire Figure 4. Flow Diagram of iipparatus placed in the center of the tube a t I . Gas blower J . Heating coil distances of 4.6, 5.0, and 6.4 cm. from K . Diffusion unit the open end. The tube was filled with liquid to a depth sufficient to immerse F. Draftgage G . Orifice meter all the thermocouples, and placed in If. Thermostat the apparatus in the manner described. T h e thermocouples were read at, various time intervals as evaporation into air circulated over t,he tube ESTABLISHMENT OF STEADY STATE. I t is of interest to determine the time required t o establish conditions sufficiently caused the liquid surface to recede below each couple in turn. From the rate of evaporation the time required for the interface close to the steady state so that Equation 1 may be used with to coincide with each thermocouple could be calculated. negligible error. Although a rigorous solution of this problem Because of their high vapor pressures and resulting rapid would be extremely complicatrd, an approximate result may be rates of vaporization, benzene, acetone, and ethyl ether were obtained. selected in addition to nater for study in this manner. Table I gives the average lorering of interfacial temperature based on Assume the gas in the diffusion tube (Figure 1, a ) to be initially saturated with vapor a t partial pressure p,. Assume further several determinations on carh liquid, along with rates of vaporithat p , is so small that the diffusion process may be represented zation and over-all average heat transfer coefficients between the satisfactorily b y Fick's second law: interface and the surrounding bath. The heat transfer coefficients are larger than might be espcct,ed for free convection between liquids and plane solid surfaces. However, conditions for heat transfer :nay be more Cavorahle in' the present case where the liquid is bounded by gas. Interfacial temperature lowering was negligible in the experiments with water, which possesses a relatively high thermal conductivity and othcr properties favorable for heat transfer. TABLE I. COOLING EFFECT IK DIFFUSION I t is bclieved that these results indicate the order of magnitude Av. Heat ~ ~ . - . effect which might be expected in an apparatus of this type, and Transfer AT,.." Coefficient that the interfacial temperature may be assumed equal to the VaporizaLowering of Bulk Liquib Temp. Interfacial Dift,ion Rate, t o Interface, Change by bath temperature for most liquids, with negligible error in the Temp., fusing G . Mole/ B.t.u./Ik, Mixing resulting dift'usion coefficient. B y use of two or more diffusion Vapor Hr.-Sq. Cm. Tb - Ts, C. F . , Sa. F t . Ts - To, C;. path lengths in the measurements and extrapolation to infinite Ether 3 . 7 X 10-3 0.17 i 0.02 300 0.10 Acetone 1 . 3 8 X IO - 3 0 , l O i0,02 200 0.06 path length as described below, any error resulting from this Benzene 0 . 4 4 X 10-3 0.07 =t0.02 100 0.05 assumption is greatly reduced. Therefore, in subsequent phases Water 0 . 3 0 X 10-3 Undetectable ... ... of the present work the liquid was assumed to vaporize a t the a Tb. Temperature of bath. Ta. Temperature of liquid suzface temperature of the bath surrounding the diffusion tube. 5 om. from mouth of tube. To. Temperature of gas 0.4 cm. above licluid: All experiments a t 25' C., atmospheric pressure. REVERSEDTHERXALDIFFUSIONEFFECT. A temperature change associated with the spontaneous mixing of dissimilar
i
~
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
2384 I .c
a.:
WTROSEhZENE-
0.E 8
x
!t
.
D
0
z
i
0 0 8 6 8 s q cm 8 min
a,
0 0 0 0
2
04
/sec
Ne/Ne
I
z
AIR
10 c m
0413
3266 5868 7535 0 8521 0 9484 0 9893
3 4
5 7
10 15
0 9992
02
0
5 IO TIME 0 , MINUTES
0
Figure 5 .
15
Time to Reach Steady State
It is convenient to define a variable, c =
c, so that Cquation 4 PS
become8
Vol. 46, No. 11
Figure 5 shows the result obtained in the application of Equation 8 t o the case of diffusion of nitrobenzene vapor int,o air in :I tube with 5 0 = 10 em.: and D = 0.0868 sq. em. per second. This corresponds t o the system in the present) experiments requiring the longest time to approach steady state. The vaporization rate reaches 99.92% of the steady state rate in 15 minutes. It may therefore be concluded that for t'he present measurements, usually of 10 hours or more duration, the assumption of steadj-state diffusion was satisfactory. I n the experiments with helium and Freon 12 the system wai; flushed with vapor-free gas for 10 minutes prior t o starting circulation with the blower. Although the gas composition during this flushing period was slightly different than during the r w t of the run, the error introduced by neglecting this difference was too small to justify correction. CORRECTION FOR EKDEFFECTS.Because of surface tension forces the liquid surface in the tube will be curved, general1)concave downward, and therefore t'he effective length of diffusion path will be somewhat Phorter than that which would be measured a t the center line of the tube or calculated from the volume of liquid in the tube. As gas flows across the open end of the tube, any developnierii of turbulence or eddies will increase the rate of diffusion through the space in the vicinity of the end. This may be viewed 3s est,ending the region of vapor-free gas (or unaltered gas composition) doFn into the tube and thereby reducing the effective diffusion path length. By studying a given system at the same experimental conditions with two or more different lengths of diffusion path, the above end effects niay be evaluated. Assume the effective average diffupion path (Figure 1,b) in any experiment to be given b>-:
x
= T o - I&
- ax, = Z a
Then the rate of evaporation may be esp
- Ax
(9)
ed by the equation.:
This equation must satisfy the boundary conditions: c = 1 a t z = T Ofor all 8 c = 1 a t 0 = 0 for all z
\\-here
c=Oatz=Olorall8>0 Integration of Equation 5 is presented by Carslaw (a) l'oi the analogous problem of heat conduction. and may he w i t t e n for diffusion as follows:
n, D
= apparent, diffusion co(>fficient,,based on apparcnt diffusion path, x a = true diffusion coefficient, haaed on effective dir-
fusion path, 2: Fquating the middle and right-hand memhws of IfSa
Converted t o 760 mm.. 25' C.
Y
-22 -22 -22
RESULTS FOR
System Air-bensene Air-ethyl alcohol rlir-nitrobenzene Air-water Freon 12-benzene Freon 12-ethyl alcohol Freon 12-water Helium-benzene Helium-ethyl alcohol Helium-nitrobenzene Helium-water
Air,a Expt
FINAL
2385
I1
AIR RATE
:
0 20 C F M
D AX
:
0 260 sq c m i s e c
I
0.05
:
1 . 1 3 cm.
I
I
I
I
0.10
0.15
0.20
0.25
I/X,
0.30
, cm:'
Figure 6. Diffusion of Water-Air Attempts were made to separate Ax into compoiients due to surface tension and air flow. Methods employed for this purpose involved elimination of the surface tension effect bv vaDorizing the liquid from a saturated cotton plug having a fiat upper surface and attempting to find gas flow rates for which the effect of eddy formation was negligible. For the systems investigated with the diffusion tube 1.75 cm. in diameter, A r , T$as estimated a t 0.1 to 0.2 cm. and A r e ranged from essentiallv zero to 1.3 cm. No general correlation of these factors could be obtained. For vaporization of various liquids into the same gas, 112, appeared to be larger for systems of low vapor pressure. Existence of an interfacial resistance has been suggested as a possible factor inI
RESULTS
Apparent difiusion coefficients, adjusted to 760-mm. pressure, and other pertinent data for all the systems, are given for a range of apparent diffusion path lengths in Table 11. Also presented are values of true diffusion coefficients based upon these measurements, summarized in Table 111. Diffusion occurred a t 25" C.
_
11.0
12 -D:0.0855
*\'-\\\
E
---
IO
10.5 -
\bih . iu ;10.0 -
.0
n
A
0.13CFM l a i r ) A X :0.48 cm.
\
:
1.43 cm.
I
8
-
\\
\
\
\
-
0
-
9.5-
oA A
9.0
I
I
Cm. : e x t r a p o l a t e d )
0
\-
0.17 C F M
AX
0.0962 s q
-
\
>
0
:
I
I
w-----
\
-
9 -
D
-
-9-
\
u
3
I
sq,cm /sec lextropoloted)
\
I I -
Y)
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
2386
-
0 \. 1 '5 ~'i ~ i a ~ r ) AX -008cm. 020CFM A X : 0 59 CT. I I
Air fluencing the apparent values of Axe (15). Further study would appear necessary to explain the observed behavior and t o develop relations for predicting the magnitude of these effects.
A \ I
Vol. 46, No. 11 1373' K . Results of the seven studies agreeing most closely suggest the value 0.257 sq. cm. per second ae the probablc best average diffusion coefficient a t 25" C. and 760 mm. The result for naterair obmiricd in thie work agrees very satisfactorily with t,he various results of other
paths, as in this work, introduces greater possibility for experimental error because of the great influence of the Ax correction. However, the attendant reduction in time required for the measurements may justify the procedure when utmost precision is not necessary.
DI scus SIOK
I n order to establish the accuracy of the present method, the result of the water-air system \vas compated with the available data. For purpose of comparison, all values weie corrected to 25' C. and 760 mni. by determining the temperature coefficient if the data were reported a t more than one temperature, or by calculating the temperature correction from the equations of Hirschfelder, Bird, and Spotz (6) if the data were reported a t one temperature only. These results are summarized in Table IV. Data by Ackermann, Houdaille, and Summerhays have been omitted in computing the average of values in Table IV because they seemed obviously in error. The studv b y Schirmer is of particular interest for its coverage of temperatures up to near the boiling point. Failure to evaluate end effects may cause Schirmer's results to be slightly hlgh, even though relatively long diffusion tubes n ere used. Kilbanora, Poerantsev, and FrankKammeritskii (8) have reported data over the range 373" to
OF DATAo s TVATER-AIR SYSTEM TABLE IT'. COMPARISOS
Reported Values D ,Sq. D at cm./sec. a t 23' C . , C. 700 inin. 760 iniii. 8 0 239 15 0 216 0 257 18 0 218
-
T,
Investigator Guglielnio (10)
0,203
0,242
Suininerliays ( i f , 19)
16 1
0.282
0.817
LeBlanc a n d Wuppermann ( 1 9 )
I2
0.288 0.3313
0 238
16.6
0.244 0.3i7 0,238 0.237
lIoudaille (10)
67
T i a u t r (20)
99.2
23.9
Gilliland ( 6 ) Kimgton and Wall (9)
21.8
Kinkelmann ( 8 7 )
D
=
0.221
>lache ( I S )
D
=
0,217
Aokermann ( 1 )
D
= 0.314
Schirmer ( 1 6 )
D
=
0.230
...
0 ij7 0.257 0.21il
(2F5)1'ss (gj)'"' (2%)''b1
Average of above resultsa This work Excluding Houdaille, Scliirmer, Summerhays, and Ackermann.
0 256 0.273
0.270
0 265
0
0 2551 0
I
I
I
0 5
I O
15
TUBE DIAMETER,
Figure 9.
20
in
Upwwrd Diffusion of Water Vapor into i i r
Diffusion coefficients for nater-air used as a basis for the values reported in Table 111 were obtained by downward diffusion from saturated cotton, as previously described. Additional esperiments were made for upward diffusion with tubes 1.75 and 0.94 cm. in diameter to evaluate the extent to which mass transfer by free convection might affect the results. These data are shown graphically in Figure 9. Ipossible error of about 4% is indicated with the tube of large diameter. However, for upward diffusion of water vapor into Freon, a system Kith density differences more favorable to development of free convection, very- large errors were obtained with the 1.i5-cm. tube. It is therefore recommended that downward diffusion be used wherever the vapor is lighter than the gas. Alternatively, as suggested by Figure 9, several tube diameters might he used to permit extrapolation to zero tube diamet'er where free convection could not occur, tilthough the correct method of extrapolation has not been e ~ tsblished. I n view of the relatively large end-effcrt corrections rcquired in the present experiments t'he data cannot be regarded as highly precise. However, the values are believed sufficicntly accurate to be useful as a source of data for possible engineering applicatioils involving diffusion of these substances.
0.269
0.257 0.260
.
,
. 0.260 '
KORIERCEATWRE
p/p. L) = diffusion coefficient, sq. em. per second D , = apparent diffusion coefficient, sq. em. per second MA = molecular r e i g h t of diffusing vapor
c
=
November 1954
INDUSTRIAL AND ENGINEERING CHEMISTRY
vaporization rate, gram mole per sq. em. per second
IVa
=
h~
= vaporization rate a t time 8, gram mole per sq. cm. per
2387
Fairbanks, D. F., and Wilke, C. R., IND.ENG.CHEM.,42, 471 (1950).
second p = partial pressure of diffusing vapor p / = log mean partial pressure of nondiffusing gas pa = partial pressure of vapor in the circulating gas, mm. Hg or atmospheres p , = liquid vapor pressure a t the surface temperature, mm. Hg or atmospheres P = total pressure, mm. H g or atmospheres Q = gas circulation rate, cu. feet per minute I2 = gas constant, cc. (atniosphcre)(grams mole)(” K.) S = cross section of diffusion tube, sq. cm. t, = temperature of gas leaving condenser, C. 2’ = temperature, O K. IT’a = grams of liquid evaporated in time, 8 = effective diffusion path length, em. z za = apparent diffusion path length, em. = value of x a t zero time 2o Z R = value of x a t time e
Gilliland. E. R.. Ihid..26. 683 11934). Hirsohfelder, J. O., Bird,‘ R. B., and Spots, E. L., J . Chem.
tension Ax, = effective change in diffusion path length due to eddies or turbulence Ar = A r , Ax, e = total diffusion time, seconds
Stefan, J., Wien. Ber., (11) 68, 385 (1873).
AP = Ps - Po Ax, = effective change in diffusion path length due to surface
+
LITERATURE CITED (1) Ackermann, Ing. Archiv, 5, 134 (1934). (2) Carslaw, “Introduction to the hIathernatica1 Theory of the Conductance of Heat in Solids,” Kcw York, Dover Publication, 1945. (3) Clusius, K., and Waldniann, L., r~-uturwissenscha~ten, 30, 711 (1945).
Phys., 16, 968 (1948).
International Critical Tables, Vol. 5, p , 62, New York, McGrawHill Book Co., 1929. Kilbanora, Poerantsev, and Frank-Kammeritskii, J . Tech. Phys. U.S.S.R., 12, 14 (1942). Kirnpton, D. D., and Wall, F. T., J . Phvs. Chem., 56, 719 (1952).
Landolt-Bornstein, “Physikalische Chemische Tabellen,” Yol. I, pp. 250-1, Julius Springer, Berlin, 1923. Ibid., I11 Erg. Bd., p. 240, 1935. LeBlanc, M., and Wuppermann, G., 2. p h y s i k . Chem., 91, 1943 (1916).
Mache, H., Wien. Ber., (Ira), 119, 1399 (1910). Mohlurtrie, R. L., and Keyes, F. G., J . Am. Chem. SOC.,70, 3755 (1948).
Sage, B. H., private communication, 1953. Schirmer, R., Verfahrenstechnik Beih. Z . Ver. deut. Ing., 1938, 170-7.
Ibid., 98, 1418 (1889). Summerhays, W. E., Proc. Phys. SOC.(London),42, 218 (1930). Trautr, M., and Mulier, W., Ann. Physik, 414, 332 (1935). Trautr, M., and Ries, W., Ibid., 8 , 163 (1931). Vaillant, P., J . p h y s . radium, 1,877 (1911). Waldmann, L., Naturwissenschuften, 32, 222 (1944). Waidmann, L., 2. Physik, 123, 28-50 (1944). Ibid., 124, 1-29, 30-51 (1947). Wilke, C. R., Chem. Eng. Prop., 46, 95 (1950). Winkelmann, A,, -4nn. Physik, 22, 1, 154 (1884).
RECEIVED for review January 19, 1953.
ACCEPTEI) June 1, 1954.
Vapor-Liquid Equilibria of AlphaPinene-Beta-Pinene System WOODSON C. TUCKER, JR., AND J. ERSKINE HAWKINS Department of Chemistry, University of Florida, Gainesville, Fla.
A
NUMBER of workers have determined the boiling point
of a-pinene, several have worked with @-pinene,and some have worked with gum turpentine, which is primarily a mixture of these two compounds ( I , 3, 7 , 13, 1 7 ) . However, there has been little work done on the system composed of prepared mixtures of these two compounds. Fuguitt, Stallcup, and Hawkins ( 4 ) studied the vapor-liquid equilibrium of the system composed of these two pure compounds in the pressure range 15 to 80 mm. of mercury. The present work comprises a study of the vapor-liquid equilibrium of this system over the pressure range 20 to 750 mm. of mercury and over the complete range of composition. The third paper in this series on the physical and thermodynamic properties of terpenes was recently published (8). EXPERIMENTAL
MATERIALS.The a-pinene and the @-pinenewere obtained by careful fractionation of commercially prepared a-pinene and P-pinene. This fractionation was carried out in columns of the Lecky and Ewe11 type ( l a ) . These columns were approximately 2.5 meters long and 2.5 em. in inside diameter. The columns were wound with Xichrome wire, and the entire assembly was enclosed in a large glass tube. The Nichrome wire winding was connected through a variable transformer which permitted control of the heat so that no flooding occurred in the column. The columns were fitted with a magnetically controlled head and were operated a t a reflux ratio of slightly greater than 100 to 1. The purity of the distillate was checked by means of refractive
index. When the refractive indev reached the proper value (a-pinene, 1.4634; P-pinene, 1.4768) and remained constant the distillate was collected for future use. These materials were stored by sealing in large glass ampoules a t atmospheric pressure after the oxygen had been carefully blown out with nitrogen. It was later found that this method was not satisfactory in the case of @-pinene. Consequently, the @-pinenewas redistilled and sealed in large glass ampoules under nitrogen a t approximately 10 mm. of mercury pressure after the pressure had been repeatedly pumped down to about 5 mm. and then raised to atmospheric with nitrogen. The mixtures were prepared as needed by mixing measured volumes of the two pure compounds. APPARATUS.After a careful study of the various methods and apparatus used for the study of vapor-liquid equilibria, the apparatus described by Jones, Schoenborn, and Colburn (11)was selected. (This apparatus is frequently referred to in the literature as the Colburn apparatus.) The apparatus was modified so that quantities of material as small as 40 ml. could be used. Also, the three-way stopcock and connecting tube from the open end of the U-tube t o the flash vaporizer were omitted, and the condenser was raised several inches farther above the flash vaporizer. This last modification was necessitated by the fact that the condensed vapors stood higher in the open end of the U-tube during operation a t low pressures. As a check on the data, the apparatus designed by Gillespie ( 5 ) mas modified and used. The modifications included enclosing the tube from the pot to the separation chamber and the separation chamber itself in a vacuum jacket; insertion of a three-way stopcock in the liquid return line just below the separation chamber for removal of the liquid sample; and use of an external heater with a small spot heater enclosed
