July, 1955
LIQUID-V-4POR E Q U I L I B R I U M I N
MICROSCOPIC CAPILL.4RIES
(307
LIQUID-VAPOR EQUILIBRIURX IN MICROSCOPIC CAPILLARIES. 11. NON-AQUEOUS SYSTEMS BY M. FOLMAN AND J . L. SHERESHEFSKY' Contribution from the Physical Chei,iistry Laboratory, I s m e l Instilute of Technology, Huifa, Israel R e c e i i e d J a n u a r y 2 8 , 19.53
The lowei,itig of the vapor pressure of toluene and isopropyl alcoliol oirei' coiicave Rucf:wes was inensui,ed in capillniies 0.8 t803.0 p i i i radius. The determination was based on the principle of equilibrium betweeti the liquid contained in a coneshaped capillary nnd the vapor of the same liquid over a solution of :L noli-volatile solute. The results obtained point out the inapplicnbility of Kelvin's i.elation to capillnries of the order concerned. Moveover, it seems that the polarity of the liquid influences the extent of the deviation from the ec~untion. These devintions are explained on hisis of nssumption of Ioiig range foiws.
The vapor pressure loweriilg over curved surfaces is given by Kelvin's relation? P Po
111 -
2uJ1 dRTr
& --- -
\\.lere Po is the vapor pressure over a plane surface; P the vapor pressure over a cur\*ed swface of t,atlius of curvature r ; d the density; d l the molecaiilnr weight; the surface tension; R the gas coiistniit, aut1 T the absolute temperature. The positi1.e aiid iiegati1.e signs apply t80 convex and roncai.e surfaces, respectively. For convex surfaces (1) has been verified for radii of rurvat'ure of several microiis, for water droplets by Goodris and Iiuliko\ra,3 for droplets of dibutyl phthalate by Shereshefsky and Stec*kler,4 by Lya1ikoi.j for mercury droplets and by La Mer aiitl Grueii,6 for dioct'jrl pllthalat,e ant1 oleic acid di,oplets less than a micron i l l diameter. For concave surfaces the esperimental results are considerably different from the calculat8etl. Shereshefsky7 fomid t'hat the lowering of the 1-apor pressiire i t 1 capillaries of 4.05 p radius is twentythree fold. On t8he othey hand, Thoma4 working with capillaries of tenths of a millimeter radius obtained re.sults i i i agreement wit'h KelI-iii's relat'ioii. Receiitdy Shereshefsky a,iid in capillaries 3 to 10 p in radius, obtained lowerings of the vapor pressure of wat'ei. 50 to 80 times t'hat calculated. The present, work was uiidertakeu v.it81i the vie\\. of t,estiiig the applicability of t8he Kelyiii relation ill c a e s of concave surfaces of organic liquids, and t'o observe the influence of polarity on the abnormal effects found by Shereshefsky. (T
and a noti-volatile solute. The liquid column in a capillary of this shape, when brought in contncnt with the vapor of the solution, will either increase or decrease in height, depending on the relat,ive vapor pressures of the two parts of the system. I n a full capillary, the liquid will evaporate, n.nd the radius of the meniscus will decrease until the vapor pt'ewure over the meniscus will equal the vapor pressure of the solution. ..liter this point is reached, coiitinued contact of tlie two parts of the system will not affe,ct the position and radius of the meniscus. The lntter inn>' lie obtained from the relation r cos 8 = r' (2)
where r and r' are the radii of the meniscus and capillary, respectively, and 8 is the contact angle. The vapor pressures of the solutions a t the concentrat'ions involved i n these experiments y e r e calculated with adequate accuracy from Raoult's law. 2 . Apparatus.-The apparatus consisted of a high vncuuni systcm, thermostat,, vessel containing the capillaries and the solution, a vessel for weighing the solvent, :tn :ii~fingemerit for the purification and storage of the solvrnt nnd n inirroscopt,-rathetometer wit'h a source of light. The capi1l:~iieswere prepared from 0.5 mni. Pyres c:q)illibry tubing. The t,ubing was cleaned with hot concentratd nitric :&rid aiid rinsed Tith redistilled water for sever:il hours. The drawing of the cone-shaped capillaries \vas carried out in a cross flame produced by two microburners by a twisting motion in two steps. Suitable portions were theii selected for calibration and use. The calibration was made oii n niicroscope wit.h a screw micrometer eyepiece of tcirfolrl magnification and an objective with R 44-fold ningnification. The micrometer eyepiece was previously c d b r a t e d against a stage micromet,er consisting of a glass j11:itr \\.ith an engraved line one m m . in length and divided into one hundred equal parts. The cal)illnry diameter was measured :tt 0.5-nim. iiitei,vals stnrting from the open end. The light used came from a microscope Inmp provided with n blue filter. The precision of the nieasurements TWS 0.1 for radii of 0.7 p and larger. I n order to eliminate c:ipillaries with an elliptical cross scction, three ca1ibr:itions were made at different positions after the rot:ition of cnch capillary around its axis. Owing to the fact tliat the walls of the capillary act as lenses, it was Experimental necessary to introduce a corwction in order to obtain the 1. Method.-Similar to t,lie niethod of Shei,eshoflzliy leal radius. It, can be shown th:Lt if the thickuess of t,he and Carter,g the measurements were based on tlie equi- capillary wall is at least ten timet; greater than the inner librium estnblished between the liquid in a cone-~haped rndius, the r e d radius may be obtained by dividing t.he iipparent radius by the refractive indes of the glass. capillai~yand its v:tpor ft,oni :L I>rilk solution of thc liquid Eight suitnl)le capillaries were at,tached t o the inner wall of n Pgi,es tube 14 mm. in diameter which served as the cnl)ill:iry ch:tmber. They were arranged in four pairs and placed on different levels 30 mni. apart. The attachment of the capillaries was carried out by heating carefully, with a microburner from the outside, the point of the tube opposite the capillary's closed end, until the glass melted slightly. This prevented any possible damage to the capillary. A 100-cc. bulb attached to the lower end of the capillary chamber served as tlie solution vessel. The thermostat, was of 250-liters capacity. It included a toluene-mercury thernioi,egulator, it 400 watt heating element wit,h a variable resistance in series, u n e1ect)ronic relay, a. copper coil connect,ed to a refrigerating unit with a circulating pump, and a powerful electrical stirrer. The
M. FoLMAN AND J. L. SHERESHEFSKY
608
Vol. 59
TABLE I TOLUENE DATAAT 20" Kelvin
Mol.
radius, a
frac. 0 .00466b .00611" ,0061l b , 00'7Mb .007G3" . oo900b .01080b .01174b .01174" .01375b Evaporation.
b
Cap.
Cap.
7
16
0.51 .41 1 .41 ... .34 ... .34 ... .28 .23 ... * 21 * 21 .18 ... Condensation.
1.55 1.80 1.20 1.15 1.30
...
... ...
...
Capillary radii at level of meniscus at equilibrium, p Cap. Cap. Cap. Cap. Cap. 14 5 17 1 18
1.GO 1.30 1.30 1.30 1.35 1.30 1.25 1.10 1.20 1.05
1.70 full 1.30 1.30 1.30 1.35 1.30 1.25 1.30 1.20
2.35 2.10 2.20 1.65 2.00 2.05 2.00 1.90 1.90 1.85
1.50 1.20 1.00 0.95 1.00 1.10 1.00 0.90 0.95 0.90
1.45 1.20 1.35 1.20 1.10 1.05 1.00 0.95 1.00 0.90
Obsd.
Cap. 2
Calcd.
1.50 1.30 1.30 1.25 1.25 1.10 1.00 0.95 0.95 0.85
2.9 3.5 3.0 3.5 3.G 4.2 4.8 4.9 5.1 5,4
TABLE I1 ISOPROPYL ALCOHOLDATAAT 20' Kelvin radius,
Ilol. frar.
a
0 . 00342a1c .00342"sc .00342bfc . 00342b9C 00411a .00471a .00471a ,00552" .00552" ,00663" . U0923" , 0 122Gb .0 1226" .01578" ,01578" Evaporation.
P
b
Cap. 14
Capillary radii a t level of meniscus at equilibrium, a Cap. cap. Cap. Cap. 5 17 1 18
0.39 1.90 2.15 .39 2.00 2 25 .39 I . 80 2.10 .39 1.80 2.10 1.70 1.70 .33 .29 1.60 1.30 ,29 1.50 1.40 .25 1.55 1.20 .25 1.60 1.30 .20 1.40 1.20 .15 1.30 1.00 .ll 0.95 0.95 .11 1.oo 1.00 .086 0.95 1 .IO ,086 0 95 1.00 Condensation. e Measurements a t 25 '.
temperature was maintained constant within 0.001 to 0.002' for 24 hours. The weighing vessel was a glass bulb of 60 cc. with a stopcock. It was connected t o the vacuum system by means of a ground glass joint and a three-way stopcock. The vessel for storing pure liquid consisted of two conjugated bulbs attached t o the system through a stopcock. The position of the meiiiscus was measured by a Gaertner cathetometer that permitted adjustment t o 0.01 mm. A fluorescent lamp placed out,side the thermostat served as a source of diffuse light. Dibutyl phthalate was used as the non-volntile solute. It was prepared from an analytical grade sampk by double vacuum distillntion and collection of the middle fractions. The toluene \vith which the first series of measurements was carried out was purified from an analytical grade sample by shaking with concentrated sulfuric acid until no brown color appeared, washing with dilute NaOH solut'ion and distilled water, drying over metallic sodium by refluxing for 24 hours and distilling. The isopropyl alcohol, of analytical grade, was twice distilled and dried over calcium oxide under reflux for 24 hours and distilled. 3 . Procedure.--A weighed quant>ity of the solute was introduced into the solution vessel which was then pumped for 24 hours and left under high vacuum for several days. The purified solvent was inti,oduced into the storage vessel, and was freed of dissolved air by vacuum distillation from one bulb t o the other and subsequent pumping off of the freed air. The s?lve?t was tjhen ti.ansferred to tho weighing bulb by distillation zn vacuo. The hull) was removed and weighed, and after its re-attachment to the system the solvent was t,ransferred by evaporation to t,he solution vessel. Equilibrium was approached from two directions, by evaporation from full capillnrie.: and by condensation into empty or partially filled capillaries. The positions of the meniscws were measured a t intervals of 15 t o XO minutes.
...
... ... ...
...
... 1.90 1.90 1.70
1.80 1.55 1.65 1.65 1.75
2.30 2.35 2.20 2.20 1.50 1.30 1.40 1.35 1.30 1.20 1.25 1.00 1.05 1.10 1.00
2.50 2.55 2.50 2.60 1.60 1.35 1.30 1.20 1.25 1.20 1.20 1 .oo 1.10 1.10 1.05
Obsd.
Cap. 2
Calcd.
2.60 2.65 2.55 2.60 1.80 1.60 1.50 1.30 1.40 1.30 1.30 1.10 1.20 1.10 1.00
5.8 5.7 6.0 5.9 5.1 4.9 5.0 5.3 5.4 6.3 8.0 9.0 9.6 12.6 11.6
The level a t which the meniscus remained unchanged for one or two hours was accepted as the equilibrium point.
Results The contact angles of toluene and isopropyl alcohol as determined macroscopically on glass are zero. To determine the angle in microscopic capillaries a series of microphotographs were taken of capillaries of approximately 10 j~ radius and partially filled with the liquid. The menisci were clearly seen and showed that the contact angle was not appreciably different from zero. Figure 1 shows the variation of the radii of the capillaries with the distance from the open end. The measurements on toluene were carried out at 20". They were made a t seveii different concentrations of the solution. Three of the determinations mere made both by evaporation and condensation. The results are given in Table I. In column 1 is given the concentration of the solutions in mole fractions, in column 2 the theoretical Kelvin radius, in the remaining columns except the last are given the observed radii of the capillaries a t the level of the meniscus a t equilibrium, and in the last column is given the ratio of the average observed radius to the calculated one. The results in capillary 17 are not included in the averages. Good agreement can be observed between the
L~uuru-l'.~rwn EQUILIBRIUAI IN R~ICROSCOPIC CAPILLARIW
July, 1955 14
12
I:!
4
.-e5 .--
s
5? 10 X
5:
3
c
v
(j
\
=i
4 2
4
0 0 8 10 12 14 Lctigtli, niiii. Fig. 1.-Variation of capiilwy IXJI~C: ( ! ; t p . I , 0 ; cap. 2 M; cap. 5,O; cap. 7 , A; cap. 14, 0;cap. lG, A ; cap. 17, @; cap. 18, 0 . 0
2
4
results in different capillaries with the exception of capillary 17 which for yet unknown reasons always gave higher results, as compared with the others. There is also good agreement between the values obtained by evaporation and condensation procedures, except for capillaries 7 and 16 a t the mole fraction 0.00Gll. At this concentration the capillaries 7 and 1 G gave values which were higher than the average, perhaps, because being the largest capillaries they required a long time t o reach equilibrium a t this low concentration. These two capillaries were calibrated to 1.7 and 1.1 ,u, respectively, and therefore show no data for radii below these. I t can be seen from the last column that the ratio r(obs.)/r(calctl.) increases from 2.9 for the lower concentration to 5.4 for the highest concentration. All measurements on isopropyl alcohol were carried out a t 20", except for the mole fraction 0.00342. For technical reasons, the latter had to be made a t 25". Table I1 contains the results obtained for ten different concentrations. Here also, good agreement exists between the values for the several capillaries. An exception is capillary 17 which again gave higher values. At low concentrations the spread in the results for the different capillai+ies is rather great, although the agreement between capillaries on the same level in the capillary vessel is remarkably good. The ratio r(obs.)/r(calcd.) for all capillaries, except no. 17, varies from 4.9 to 12.G. Discussion The results of these measurements show that t,he Ilelviii equation cannot be applied in est,imating vapor pressure lowering over concave surfaces in microscopic capillaries. Nor can it be applied in estimating pore mdii a t given vapor pressures as it is done in adsorption analysis. The observed Io\veriiig is many t8imes greatlev t8ha,ii t,he valiie
2 1
0 0.2
0.0
1.0 1.4 1.8 2.2 Radius, p. Fig. 2.-Relatmive vitpor pressure lowering. Isoprop,~,l alcohol: Kelvin 1, nieasurements 0 ; toluene: Kelvin 2, measurements H.
calculated with this equation. Moreover, t.he effect differs in magnitude with the nature of the liquid. The lowering for isopropyl alcohol was found to be much greater than for toluene, and the results for water reported in the preceding paperg show that the effect for the latter is still greater. This effect seems to change with the polarity of the liquid, and increases with increasing dipole moment of the molecule. It is well known that many physical properties of capillary held liquids are different from t'hose for the bulk liquid. To the literature references given in the preceding paper, describing these anomalies, can be added the observations on t,he freezing point of capillary condensates, 10-12 the increase in the heat of vaporization,'3 the rise in the critical temperature,14 and the increase in specific p~larizatioii.'~In so far as d e r ~ s i t y ~ ~ ~ ~ ~ and surface tension'* are concerned, experimental data show values which are very near those of the bulk liquid. Theoretical considerations bj7 T01maii'~ and Hillz0 require that the effect of curvature on surface tension be slight a t the curvatures prevailing in these experiments, and hecome (10) 8 . Briinaiier, "The Adsorption of Gnhes and Liqiiid," Princeton Lniversity Press, I'rinceton, N. J.. 1048, p. 411. (11) J. P. Jones and R . A . Gortner. T H I R J O U R N A L36, , 387 (1932). (12) RI. Sliitniau a n d I . Higuti, ibid., 56, 1'38 (1062). (13) L. F. Cleysteen a n d \'. R. Deits, J . Research A ' d . Bur. SL~MLni,ds, 35, 283 (1935). Patrick, I\'. C . Prrston stid .4. E. Owens, T H I SJ O L . R N A L , 29, 431 (1925). (15) S. KiirosaLi, (bid.,58, 320 (1954). (16) E. 0. W i i g s n d A. J. Juliola, J . .4m.Chem. SO
