90
Langmuir 1986, 2, 90-96
Vapor-Liquid Equilibria of Nonelectrolyte Solutions in Small Capillaries. 1. Experimental Determination of Equilibrium Compositions G. C. Yeh,* M. S. Shah,? and B. V. Yeh* Department of Chemical Engineering, Villanova University, Villanova, Pennsylvania 19085 Received M a y 23, 1985. I n Final Form: October 8, 1985 The vapor-liquid equilibrium of an ethanol-water solution held in small pores (pore size range, 7-27 fim; median pore size, 13.5 Mm) inside a porous sintered stainless steel plate was determined at 50 “C by using a static method. The vapor pressure of ethanol and of water held in these small pores was found to differ greatly from the values obtained from the Antoine equation. By a treatment of the experimental data, it was shown that the ratio of the vapor pressure of pure ethanol to that of pure water in the capillary plate is 3.7876. The ratio of the vapor pressure of pure ethanol and water as predicted from the Antoine equation is 2.3092. Thus, the relative volatility of ethanol and water held in the capillary plate is about 1.58 times the normal relative volatility in the bulk phase. Under the normal vapor-liquid equilibrium in the bulk phase, the value of the relative volatility of the ethanol-water system is unity at X1 = 0.9060 at 50 “C. In the experimental study of the same system in the capillary plate, the relative volatility does not become unity when X Iis less than 0.99. A further treatment of the experimental data by a method suggested by Hirata confirmed the absence of the formation of any azeotrope at XI 5 0.99. The consistency test and thermodynamic test were performed on the experimental data, showing that the data are very consistent and satisfy the rigorous thermodynamic relationships. These tests also displayed the absence of systematic errors in the experiment. In view of the experimental findings made in this study, it is strongly recommended that further experimental studies be conducted on the vapor-liquid equilibrium in small capillaries, for both ideal and nonideal liquid solutions. With the advent of capillary distillation,”1° these data will be important for the understanding and implementation of the new technique to separate nonideal azeotropic mixtures,
Introduction Many physical properties such as the latent heat of vaporization, density, surface tension, viscosity, and vapor pressures of liquids held in small capillaries are known to be different from those in bulk solution. At present, the Kelvin equation is used to predict the vapor pressure of liquids held in a small capillary. In his equation, Kelvin considered only the effect of the curvature of the meniscus on the vapor pressure of a pure, nonpolar liquid held inside a capillary. The early works of Shereshefsky, however, suggested that the Kelvin equation cannot be used to accurately predict the vapor pressure of a polar liquid held in a capillary.’ Shereshefsky experimented with water held in uniform capillaries and found the lowering of the vapor pressure to be about 23 times greater than that predicted by the Kelvin equation. Folman and Shereshefsky investigated the vapor pressures of toluene and of isopropyl alcohol held in capillaries and found that the vapor pressures of these liquids were much lower than the vapor pressures obtained under normal conditions. They attributed the abnormal lowering of the vapor pressures to the polarities of the two liquids.2 The degree to which the vapor pressure of each component of a liquid solution will differ from that obtained under normal conditions will depend on the polarity of the liquid. Thus, the relative volatility of two liquids in a solution held in a capillary may be altered if the extent of the lowering of vapor pressures differs among the component liquids in the solution. Accordingly, the vaporliquid equilibrium of a liquid solution held in a capillary may be different from that in the bulk phase due to a change in the relative volatility. The only published work attempting to explain the cause and effect of the change in relative volatility on the vapor-liquid equilibria of liquid solutions held in capillaries -‘Present address: Monsanto Co., Nitro, WV. Present address: Cargill, Inc., Gainesville, GA 30501.
*
0~43-7463/86/2402-0090~01.50 /O
is that of Yeh et al.3 Yeh et al. reported the results of experimental studies made by distilling various liquid mixtures including some azeotropic mixtures by the use of fractionating plates having capillary-type passages, which were found to have altered the vapor-liquid equilibria of these liquid mixtures and resulted in abnormally high separation efficiencies. The primary objective of the experimental investigation is to attempt to study the effect of capillary pores on the relative volatility of liquid solutions held in these small capillaries inside a capillary plate. The liquid solution considered for the study is that of ethanol and water. The capillary plate is a sintered porous stainless steel plate manufactured by the Brunswick technetics Corporation and identified by them as product FM1104SS, which is one of the types of fractionating plates used by Yeh et al., in capillary distillation mentioned above.3
Experimental Section The determination of the vapor-liquid equilibrium composition of ethanol-water mixtures was made by an isothermal static method. This method is deceptively simple in principle but quite difficult in practice. The time required for equilibrium is very long and the withdrawal of a sample can further increase the time required to obtain equilibrium. The apparatus (static still) is similar to the one reported by Yeh et al.? with an improved design for better control of the liquid height during the run. It is comprised of three sections, A, B, and C, all made of Pyrex glass with ground-glassjoints, as shown in Figure 1. Section C is the solution receiver with a provision for introducing the solution into it through a glass tube (1)and stopcock (2). Section B is the capillary plate retainer with a provision for extracting liquid samples or excess liquid through a glass tube (31, to which a Teflon capillary tube and valve are (1)Shereshefsky, J. L. J. Am. Chem. SOC.1928,50, 3966. (2) Folman, M.; Shereshesky, J. L. J. Phys. Chem. 1955, 59, 607. (3) Yeh, G. C.; et al. ‘Capillary Distillation”; Paper presented at National Meeting of A.I.Ch.E.,Denver, CO, Aug 29, 1983.
0 1986 American
Chemical Societv
Langmuir, Vol. 2, No. 1, 1986 91
Vapor-Liquid Equilibria
Table I. Relation between XIand Y , Section A
4
Section B
Section C
Figure 1. Three sections of the apparatus (A, B, and C).
c
3
Figure 2. Assembled apparatus in the air bath. attached (not shown). A ring shelf (4) is also built into Section B for mounting a capillary plate (5). Section A is the top (or cover) to the static still and has an outlet (6), attached with a Teflon capillary tube and valve (not shown), for vapor sampling and pressure measurement (if necessary). The still is placed inside a constant-temperature air bath (see Figure 2). The air bath is brought to a constant temperature of 50 O C , and the thermometer (7) is used to monitor the temperature throughout the experimental run. A predetermined volume of feed solution consisting of ethanol and water at a desired concentration is heated to about 55 "C and introduced into the apparatus from the spout (1). Care must be taken to ensure that the feed is stopped just as it touches the capillary plate-so that there is no liquid droplet or pool of liquid present on top of the plate. During the experimental run any adjustments in the liquid height can be made through the spout (2). It is imperative that the bulk liquid is a t all times in contact with the lower side of the plate.
XI
Yl
0.0172 0.0260 0.0420 0.2123 0.3101 0.3104
0.3916 0.4963 0.6254 0.6840 0.7069 0.7090
X,
Yl
0.3768 0.3799 0.6288 0.8656 0.9868
0.7240 0.7246 0.7472 0.8770 0.9879
Care must also be exercised to make certain that the entire apparatus is well within the air bath in order to avoid any local cooling. A direct effect of such local cooling would have the adverse effect of condensation in the local vapor-phase region. Any required adjustments can be made using the screw/nut arrangements (4-6) by lowering and leveling the still. Due to the absence of a stirrer in the bulk liquid and of circulation in the vapor phase, it takes at least 24 h to reach a steady-state equilibrium. A t equilibrium, 1.0 mL of vapor (out of a total volume of nearly 130 mL) is withdrawn by using a gas sampling syringe. The vapor sample is analyzed on a gas chromatograph. The composition of the bulk liquid at the end of each run is also determined by gas chromatography and the values recorded. The properties and specifications of the capillary plate employed are as follows: manufacturer, Brunswick Technetics, DeLand, FL 32720; series number, 347 SS; product number, FM 1104SS; percent density, 40% by volume; thickness, 0.062 in. (0.1575 cm); median pore size, 13.50 pm; pore size range, 7-27 pm; surface area, 3900 in.'/lb (55471.0 cm2/kg). The capillary plates used in this study and similar sintered porous metallic plates are commercially produced by several manufacturers through a process of forming a thin, uniform layer of metal powder and sintering the same by applying heat and pressure. The porosity, pore size, and thickness of the plate can be varied by varying the powder particle size, the initial layer thickness, and the temperature and time of sintering. In order to assure the cleanliness of the experimentalapparatus, the following procedures were adhered. Twenty capillary plates were cut by a machine from a large sheet of the same material. These capillary plates were air-blown to remove dust on their surfaces and then washed thoroughly in a tank containingacetone for 24 h. After the acetone washing, they were dried in a vacuum and then placed in boiling distilled, deionized water for 8 h twice, using fresh water each time. The plates were then tested for perfect cleanliness by using fresh distilled, deionized water by observing their ability to be wetted completely and instantly by the water. All the glass parts and plastic parts were first thoroughly cleaned with a commercially available, special formulation detergent, e.g., "Decon go", and rinsed with water. After the rinsing, they were placed in a mixture (solution) containing 30 g of sodium hydroxide, 4 g of sodium hexametaphosphate, 8 g of trisodium phosphate, and 1L of water for 24 h. The parts were then placed in boiling distilled, deionized water for 8 h twice, each time using fresh water. After this, the parts were tested for perfect cleanliness by using fresh distilled, deionized water to confirm that only an unbroken film of water remains on the surfaces when they are withdrawn from the water. The already cleaned parts and capillary plate were dried and kept in a dust-free drier at 50 OC. Clean plastic gloves were worn whenever a part (or parts) of the apparatus was handled. Note. The apparatus was designed and constructed for the sole objective of obtaining equilibrium compositions of solutions and not vapor pressures of the component liquids in solutions. Therefore no data of vapor pressure were obtained by using the apparatus. (A separate experimental study is being conducted to test the capabilities of several experimentalsetups for obtaining the total pressure of the vapor phase and vapor pressures of the liquid components in solutions, separately. The data will be published when they become available.)
Results and Discussion T h e vapor-phase equilibrium composition Yl (mole fraction of ethanol) determined by t h e static method are presented with the corresponding liquid-phase equilibrium composition X1 in T a b l e I. As t h e system studied is a
Yeh et al.
92 Langmuir, Vol. 2, No. 1, 1986 Table 11. Azeotropic Pressure, Temperature, and ComDosition Data for Ethyl Alcohol-Water System’ pressure, lb/in2 abs. comp, mol % alcohol temp, O C 14.7 50 100 200 300
89.4 88.2 87.4 86.2 85.2
40tf
78.3 112.6 136.7 164.2 182.6
CapiIIar y
binary solution, its vapor-liquid equilibrium may be described readily in terms of relative ~ o l a t i l i t y . ~ The relative volatility a12of component 1with respect to component 2 in a binary system is defined as
where y1 = activity coefficient of ethanol, y2 = activity coefficient of water, P,O = vapor pressure of pure ethanol, Pzo= vapor pressure of pure water, and X1 = 1- X 2 and Yl = 1 - Y2 for a binary system; therefore
Since relative volatility a varies greatly with composition in nonideal solutions, it might have values greater than unity at some concentrations and less than unity a t some other concentrations. As a is continuous with compositions X1 it will equal unity a t a particular value of XI. The system studied is a typical example of a “low-boiling” azeotropic system; i.e., its values of a are greater than unity at lower concentrations and less than unity a t high concentrations. The azeotropic point of this system changes when the total pressure of the system is changed, as may be seen from Table 11. A. Effect of a Capillary Plate on Vapor Pressure. The liquid-phase activity coefficients for a system are well described by the Margules two-suffix equation In y1 = A ( l (3) In y2 = A ( l - X2)2
(4)
where A is the binary parameter. Hence we may say that y1/y2 = exp(A(1- 2X1)) (5) and the expression for the relative volatility a12becomes a12= (P?/P2O) exp(A(1 - 2x1)) (6) where Ploand P20 are the vapor pressures of the pure components 1and 2. If eq 6 is expressed in terms of the natural logarithm of cyl2, we obtain In aI2= In (Pl0/P2O) + A ( l - 2x1) (7) which is a linear equation. With the aid of eq 7 and with the experimentally obtained values of a12and X1we find that A = slope = 1.9433 = 1.3317 In (P,10/Pc20)
therefore
Pc10/Pc20= 3.7876 Thus the ratio of the vapor pressure of pure ethanol to (4) Null, H. R. “Phase Equilibrium in Process Design”;Wiley-Interscience: New York, 1970. (5)Outski; Williams, C. E. Chern. Eng. B o g . , Syrnp. Ser. 1953, No. 49, 55. (6)Hirata, M.Jpn. Sci. Reu. Ser 1952, 12 (3), 265. (7)Prausnitz, J. M. “Molecular Thermodynamics of Fluid-Phase Equilibria”;Prentice-Hall: Englewood Clifff, NJ, 1969. (8)Gilmont, R.Ind. Eng. Chern. 1950,42, 1607.
0
02
04
06
08
10
X
Figure 3. Correlation of aI2vs. XI for normal and capillary conditions.
water PClO/Pc2O held inside the capillary plate is found to be 3.7876. The ratio of the vapor pressure of pure ethanol and water in bulk places as predicted by the Antoine equation is 2.3902. Hence, the effect of the capillary plate is an increase in the ratio of the vapor pressures by a factor of nearly 1.58. A comparison of the relative volatilities a12of the ethanol and water system under normal circumstances (in bulk phases) and those obtained under the effect of the capillary plate is presented in Figure 3. As seen from Figure 3, a t low concentrations the value of relative volatility a12 changes substantially with changes in XI when the solution is held in a capillary. This may be attributed to the very strong polar interactions between water molecules and the surfaces of the capillary plate used at low concentrations of ethanol (i.e., high concentrations of water). Yeh3 has studied the vapor-liquid equilibrium in small capillaries and developed a theory to account for changes in the vapor pressures of pure liquids as well as the liquid components of a solution held in such capillaries. The following three types of molecular interactions were considered to affect the vapor pressure of a liquid held in capillaries: (a) the London force dispersion interactions; (b) the induction force polar interactions; (c) the effects of the curvature of meniscus. Yeh has found the effect of the curvature of meniscus on the vapor pressure is generally negligible compared to those of the dispersion interactions and of the polar interactions. The effect of the curvature of meniscus is predicted by the well-known Kelvin equation. Both the dispersion interactions and the polar interactions which originate a t the solid-liquid interface will propagate into the depth of the liquid in contact with the solid although their magnitudes diminish rapidly with the distance from the solid-liquid interface. The length or distance of their propagations are believed to reach as much as several micrometers, in some instances. B. Correlation of the Vapor-Liquid Equilibrium Data. Clarks and Gilmont* have proposed empirical methods which algebraically express the mutual dependence of equilibrium composition and relative volatility. These empirical equations fulfii a number of fundamental and practical requirements for the analysis of vapor-liquid equilibrium data. These requirements are the following: (1) they are in agreement with the physicochemical laws; (9) Clark, w. s. Science (WU8hhgtOn, D.C.) 1946,103, 145. (10)Yeh, G.C.U.S. Patent 4 118285,1978.
Langmuir, Vol. 2, No. 1, 1986 93
Vapor-Liquid Equilibria Table 111. Analysis of X - Y Relationship Using Clark's Equation' exptl XI Yl Yl(calcd) Y,(calcd) - Yl 0.017 0.026 0.042 0.212 0.310 0.310 0.376 0.379 0.628 0.865 0.986
0.391 0.496 0.625 0.684 0.706 0.709 0.724 0.722 0.747 0.877 0.987
0.408 0.483 0.561 0.709 0.724 0.724 0.729 0.740 0.714 0.884 0.988
0.010 -0.013 -0.064 0.025 0.017 0.015 0.004 0.018 -0.033 -0.007 -0.0001
Clark's Equation
/
'Error = (sum of deviation)/(total no. of data points) = -0.002.
(2) they are capable of expressing the behavior of both ideal and nonideal systems; (3) they are simple to use but produce new information from a minimum amount of experimental data. It may be shown that all of the empirical equations relating relative volatility a12to liquid compositions X1 and X2 are special cases of the general equation ff12
=
a0112(1 + a12X2) 1 + a1pX, + az1X12
(8)
where aol12,a12,and a21are constants. Clark's equations have the forms
A=aX+b A = a'X b'
+
(9) (10)
X,
Figure 4. Experimental Yl-Xl data and Clark's equation.
X1 0.0172 0.0260 0.0420 0.2123 0.3101 0.3104 0.3768 0.3799 0.6288 0.8056 0.9868
Table IV. Analysis of a,,Using XI' a12 a12(cald) a12- a12(cald) ~~
36.7889 36.9140 38.0800 8.0334 5.3038 5.4140 4.3540 4.2494 1.7451 1.1077 0.9923
~~
36.6152 37.3211 37.8467 8.2391 5.2991 5.2875 4.1619 4.1189 2.0530 1.1904 0.9091
~~
~~
-0.1738 0.4071 -0.2333 0.2057 -0.0687 -0.1265 -0.1921 -0.1205 0.3070 0.0826 -0.0833
'Error = (sum of deviations)/(total no. of dati points) = 0.0004.
where A = Y1/Y2
x = x,/x2 and the constants a, a', b, and b'are related by
f(aa9°.5f (bb9°.5= 1 Equation 9 applies for large values of X1, and eq 10 applies for small values of XI. Analysis of the experimental data gave the following values for the constants a and b: a = 1.083; a' = 0.0195; b = 0.658; b' = 0.3387. Hence we can now compute constants ~ ~ 1 1 a12, 2 , and a21 to calculate a12using the general eq 8 as follows:
ao12= 39.846 ff12
a12= 0.287 a21=35.793 1 + 0.287X2 = 39m846135.793x1
+
The estimate of the equilibrium composition using Clark's equation is presented in Table 111. From Table 111, it can be seen that the values of the vapor-liquid equilibrium composition calculated from Clark's equation are in excellent agreement with the experimental values. From the liquid concentrations X1, the error of the estimation of Yl is -0.002. Figure 4 shows the vapor-liquid equilibrium relationship (Y-X curve) comparing Clark's equation with the experimental data. The prediction of the vapor-liquid equilibrium compositions by correlating the relative volatility a12with the composition of the liquid phase yields results that are comparable to those obtained from Clark's equations. Figure 3 shows the correlation between a12obtained experimentally with X,. It can be seen from Figure 3 that for X1I0.13 there is a linear relationship between a12and X1. It can be shown by simple numerical analysis that the
remaining portion of the curve (viz., X1 > 0.13) is well represented by the equation ( ~ 1 2= A B/X1
+
Using the values of a12and X1 in Table IV we get, for X1 50.15, ff12 = o.a67a/x1 + 38.7007 (11) and, for X1 > 0.15, ff12
= i.9a27/x1 - 1.002
(12)
The correlation factors for eq 11 and 12 are 0.9 and 1.0, respectively. As shown in Table IV, eq 11 and 12 do predict a12quite well. The error between the predicted values and the experimental values of a12is 0.0004. With the predicted value of a12a t a given X,, the value of Yl can be calculated readily by using the definition of ff12 as
The calculated Yl values are compared to the experimental values in Table V, and the error of prediction of Y, by this method has a magnitude of 0.003. In Figure 5 , the calculated Yl values (circles) are shown with the experimental Yl values (curve) in a X-Y correlation in which the normal X-Y curve is also included for reference. From Figure 5, it may be said that the above method of predicting a X-Y curve is very accurate. C. Effect of Capillary Plate on Azeotropic Compositions. Outski and Williams5 reported the relation between the azeotropic composition and the temperature for the system of ethanol and water as follows log X1= 1.967 - (1.971 X 10-4)t
Yeh et al.
94 Langmuir, Vol. 2, No. 1, 1986 Table V. Y , Calculated from a,,Correlation" exptl
Y, 0.39167 0.496 32 0.62540 0.684 06 0.706 90 0.709 05 0.724 69 0.722 01 0.747 28 0.877 07 0.987 90
XI 0.0172 0.0260 0.0420 0.2123 0.3101 0.3104 0.3768 0.3799 0.6288 0.8656 0.9868
Y 1(calcd) 0.3905 0.4991 0.6240 0.6900 0.7045 0.7041 0.7156 0.7162 0.7767 0.8846 0.9855
Yl (calcd) - Yl -0.0012 0.0028 -0.0014 0.0059 -0.0024 -0.0050 -0.0091 0.0058 0.0294 0.0075 -0.0024
"Error = (sum of deviations)/'(no. of data points) = 0.003.
1
0.1 0.01
0.1
100
10
1.0 x 1
x
Figure 6. log (YJ(1- Yl)) vs. log (Xl/(l- XJ); Hirata's method of analysis.
0
02
04
0.6
08
1.0
x
Figure 5. Y1-XI data at 50 "C for normal and capillary con-
ditions.
where XI is the axeotropic liquid concentration of ethanol and t is the temperature in degrees Centigrade. By their equation, a t 50 "C the value of X1 in the ethanol-water system is 0.9060. Experimentally the value of a12was found to be 0.992 38 at X , = 0.9868 for the capillary plate used. Hence a definite effect of the capillary plate was to alter the vapor pressures so that a is not unity at XI = 0.906 but a t Xl = 0.990 a t the same temperature and pressure. Thus the azeotropic point has been elevated from 90.6045 to 99.0 mol % ethanol when the ethanolwater system is placed in the capillary plate. The effect of the capillary plate on the equilibrium composition can also be examined by Hirata's method of analysk6 Hirata suggested that the equilibrium curve Y vs. X may be replaced by three straight lines on a log-log plot in which the ordinate is given by Yl
A =1 - Yl
and the abscissa is given by
x = - XI 1- x 1 Hirata used this technique of analysis and studied a large amount of data published in the literature. He then made the following conclusive observations: (1) A A - X plot consists of three straight line segments. The equation for each of these line segments is given by log A = n log X + log C where C is the intercept and is equal to the relative volatility in case of ideal solutions and n is the slope. (2) The middle line segment has a slope between zero and one, which is the characteristic of nonazeotropic systems.
0
02
04
0.6
08
10
X
Figure 7. Consistency test; ( Yl
- XI) vs. XI.
(3) For azeotropic systems condition 2 will not hold. Instead the middle line segment should have a slope greater than one. By use of the experimental results (Table I), a plot constructured from Hirata's method of analysis is shown in Figure 6. From Figure 6 it can be shown that the slope of the middle segment is approximately 0.40. This clearly suggests that no azeotrope was formed at any concentrations of ethanol when the capillary plate was used. Hirata's technique of analysis further indicates that if an azeotrope were formed it must have been formed at some X 1 values close to 1.0. This conclusion agrees with the experimentally determined X - Y curve, which also indicates that if an azeotrope were formed it must have been formed a t some X 1 value greater than 0.99. Yeh et aL3 reported a partial result of their studies on the capillary distillation of the ethanol-water system including the azeotropic mixture and mixtures having ethanol concentrations above the axeotropic point. The unusual results of their experimental studies can be readily understood with the knowledge of the effect of a capillary on the relative volatility of the solution described above. D. Consistency and Thermodynamic Tests. The experimental data obtained (Table 111) for the ethanolwater system show little or no sign of the presence of large random errors as may be seen in Figure 7, a plot of ( Y X ) vs. X . However, the smoothness of a curve is not a guarantee of the absence of systematic errors. The consistency of the data should thus be subjected to a test using an exact thermodynamic relationship. For pressures up to 1 atm the Duheum-Margules equation in the following form may be used for a ther-
Langmuir, Vol. 2, No. 1, 1986 95
Vapor-Liquid Equilibria modynamic consistency test. XI dP1 PI dX1
dP2 =O PZ dX2
x 2
0.9
t\
A more straightforward method of testing isothermal data is by using the Gibbs-Duheum equation
&’ In
dX1 = 0.5
In most cases the data required to evaluate the integral on the right-hand side of the above equation are not available. Prausnitz7 suggests that for isothermal data a good approximation is to set the value of the right-hand side integral in the Gibbs-Duheum equation equal to zero. In the absence of the experimental capillary vapor pressures of both ethanol and water, the activity coefficients y1and yzcan be obtained from a method suggested by Gilmont.e From Raoult’s law we have for nonideal systems
0.4
0.
1.o
0
2.0
3.0
low,,
Figure 8. XI vs. log q2used in determining activity coefficients. y2
= xczY2pc2°
Hence 71 P C l 0 -YlXC2 - - a12 = -
Y2XCl
7 2 PC2O
rearranging in the following form
_ -- a12 71
PC?
72
PC2O
By taking logarithms of the above equation and differentiating we get d log 71 - d log yz = d log
a12
(13)
The Gibbs-Duheum equation may also be given in the form
XI d log 71 + Xz d log 7 2 = 0
(14)
Figure 9. Thermodynamic test; log (y1/y2)vs. X1.
Hence from eq 13 and 14 we get log y2 = - l X I d log a 1 2
(15)
1
log y1 =
J - xd~log a12
::::M -1 0
(16)
Thus if a12is known as a function of XI (or X2) then the values of y1and y2 can be obtained from eq 15 and 16. As suggested by Gilmonts for the ultimate accuracy and rigidity graphical integration should be used. Hence values of y1 and y2can now be obtained by using relative volatility a12(Figure 8). Figure 9 is a plot of log (y1/y2)w. XI used for evaluation of the left-hand side of the above GibbsDuheum equation. Prausnitz7 suggests that the criterion to decide if a set of data “passes” or “fails” may be given as (area above X axis) - (area below X axis) 0.02 > (area above X axis) + (area below X axis) He further adds that the above criterion is arbitrary and the quantity on the left-hand side (0.02) may be raised or lowered, reflecting the rigidity of the consistency test. For the system of ethanol and water the above area test yields a value of 0.0589, which is the same order of magnitude as suggested by Prausnitz, and therefore the data may be
considered thermodynamically consistent.
Conclusions The effect of the capillary plate increases the ratio of the vapor pressures by a factor of nearly 1.58. Since relative volatility is a ratio of the vapor pressures, one may conclude that the relative volatility of the ethanol-water system held in small pores of the capillary plate is about 1.58 times that in the bulk phases at the same temperature of 50 OC. Correlation of the vapor-liquid equilibrium data using Clark’s equations results in excellent agreement with the experimental values. The average deviation between the values predicted by Clark’s equation and the experimental values obtained is in the range of 0.002 (mole fraction). Prediction of the vapor-liquid equilibrium composition using a direct correlation between a12and X1 was also attempted. This method yielded results that are comparable to those obtained by using Clark’s equations. The average deviation between the values predicted by the direct correlation method and the experimental values obtained is in the range of 0.003 (mole fraction). Under the effect of the capillary plate the relative volatility a12attains the value of unity at Xl > 0.99. The
Langmuir 1986, 2, 96-101
96
effect of the capillary plate has shifted the azeotropic point from X, = 0.906 045 to X1 > 0.99. A further treatment of the data by a method suggested by Hirata confirms the absence of the formation of an azeotrope at X1 < 0.99. The experimental data have little or no random errors, as may be seen from Figure 7. The data obtained are thus considered to be consistent. The experimental data also satisfy the Gibbs-Duehem equation, further indicating their thermodynamic consistency.
Remarks The static still used in this experimental investigation consists of three sections, having a bulk liquid capacity of nearly 160 mL. Had a stirrer been used in the liquid phase, the time required to attain equilibrium would have been reduced. A stirrer was not used because it would have created a vortex. The effect of the vortex is that the lower face of the capillary plate would not have been in complete contact with the bulk liquid at all times. In addition, the turbulence generated by the stirrer would cause splashing onto the capillary plate, which is unacceptable. No mechanisms were used to recirculate the vapor phase to ensure the complete mixing. Total removal of the air (inerts) from section A was not achieved prior to each run due to the fact that boiling of the liquid phase would
introduce liquid droplets in the vapor phase, resulting in erroneous equilibrium compositions. In our next paper forthcoming we will report the results of an analytical study made on effects of attractive forces a t solid-liquid interfaces upon vapor-liquid equilibrium and their comparison with the experimental results obtained.
Acknowledgment. We thank Reverend John M. Driscoll, O.S.A., The President, and Dr. Bernard J. Downey, then Director of Research of Villanova University, for the financial support they were able to obtain for this study. Notations vapor pressure of component i Pi0 P partial pressure x Xl/U - Xl) X mole fraction liquid phase A Yl/(l - Y1) Y mole fraction gas phase a relative volatility Y activity coefficients VE excess molar volume of liquid Subscripts 1 ethanol as component 1 2 water as component 2 C capillary plate conditions
FTIR-ATR Studies on Langmuir-Blodgett Films of Stearic Acid with 1-9 Monolayers Fumiko Kimura, Junzo Umemura, and Tohru Takenaka* Institute of Chemical Research, Kyoto University, Uji, Kyoto-fu 611, Japan Received May 31, 1985. I n Final Form: September 26, 1985 Fourier transform infrared (FTIRbattenuated total reflection (ATR) spectra have been recorded of Langmuir-Blodgett (LB) films of stearic acid deposited on a germanium plate with 1, 2, 3, 5, and 9 monolayers. Examination of the CH2 scissoring band suggests that the hydrocarbon chain of stearic acid in the first monolayer is in a hexagonal or pseudohexagonal subcell packing where each hydrocarbon chain is freely rotated around its axis oriented approximately perpendicular to the surface. In the LB films thicker than 2 monolayers, on the other hand, the molecules in the upper monolayers other than the first monolayer crystallize with the monoclinic form where the hydrocarbon chains are packed alternately and are inclined at an angle of about 30' with respect to the surface normal, showing a tendency to align their a crystal axes parallel to the direction of the withdrawal of the germanium plate in the film preparation. It is also concluded from frequencies and intensities of the progression bands due to the CH2 wagging vibrations that stearic acid occurs as the cis configuration for the C=O and C,-C, bonds in the 1-monolayer film but the trans configuration starts to appear in the 3-monolayer film. A striking feature in this study is the absence of the C=O stretching band of stearic acid in the first monolayer on the germanium plate. This phenomenon may be interpreted by the short-range image field model for its oscillating dipole parallel to the germanium surface.
Introduction Ordered monolayer films transferred from a water surface onto a solid substrate by the Langmuir-Blodgett (LB) technique112have drawn growing interest for a recent few years. This is because the LB films have a good possibility to be artificial molecular assemblies with planned structure and properties. Furthermore, they form well-defined molecular organizates which can be externally handled and controlled. (1) Blodgett, K. B. (2)
J. Am. Chem. SOC.1935, 57, 1007.
Blodgett, K. B.; Langmuir, I. Phys. Reu. 1937, 51, 964. 0743-7463/86/2402-0096$01.50/0
I t has been expected that infrared spectra of the LB films could afford an excellent insight into the structurefunction relationship of these molecular systems. However, the sensitivity of the infrared transmission method by usual dispersion-type spectrophotometers was insufficient to record'spectra of very thin films. Infrared measurements of LB films thinner than 30 monolayers became possible only by using novel reflection techniques such as attenuated total reflection (ATR)3-13and grazing incidence (3) Sharpe, L. H. Proc. Chem. SOC.1961, 461. (4) Takenaka, T.; Nogami, K.; Gotoh, H.; Gotoh, R. J. Colloid Interface Sci. 1971, 35, 395.
0 1986 American Chemical Society
