Dec., 1957
SOLUBILITY OF IODINE IN BENZENE-CARBON TETRACHLORIDE
could be perhaps related to the above-suggested temperature dependence of the intrinsic intensity of the Dz band. My t.hanks are due the University of Illinois for its hospitality, Dr. R. Emerson and the staff a t the
1605
Photosynthesis Laboratory for their assistance in the carrying out of the experiments and Dr. Rabinowitch for valuable discussions and suggestions, as well as for his help in the preparation of this paper.
THE SOLUBILITY OF IODINE IN BENZENE-CARBON TETRACHLORIDE MIXTURES1 BY SCOTTE. WOOD,BURTON D. FINE^ AND LEONARD M. ISAACSON Contribution from the Department of Chemistry, Illinois Institute of Technology, Chicago 16, Illinois Received Maz, 8 0 , 1067
The solubility of iodine in benzene, carbon tetrachloride and mixtures of these solvents has been determined at 25’ and every ten degrees from 20 to 60’. From these data and the vapor pressure of the benzene-carbon tetrachloride system, the changes of the thermodynamic functions on mixing have been calculated for the homogeneous region of the ternary system and also for the two binary systems containing iodine. The excess free energy of mixing is positive for all compositions. For the iodine-carbon tetrachloride system, the excess enthalpy and excess entropy of mixing are both positive and essentially independent of temperature. For the iodine-benzene system, the excess entropy is negative and the excess enthalpy is generally positive; both decrease markedly with temperature. Values of the equilibrium constant for the formation of the 1: 1 complex between iodine and benzene have been obtained which agree qualitatively with those obtained from spectrophotometric measurements.
Solutions of iodine in various liquids have been nary system from solubility measurements alone, extensively studied3 and indeed such studies have ( 2 ) to determine if the thermodynamic properties led in a large measure to our present understanding of the homogeneous phase of the ternary system of non-electrolytic solutions. Recently, the for- could be obtained from those of the three binary mation of complexes between iodine and certain systems, and (3) to determine the thermodynamic solvents, such as aromatic and olefinic compounds, equilibrium constant for the formation of the benhas been studied by means of spectrophotometric zene-iodine complex from the components. No measurement^.^ The determination of the thermo- equation for the excess free energy of mixing based dynamic functions of the benzene-iodine system on the solubility data alone was found which, on and of the thermodynamic equilibrium constant extrapolation to zero iodine concentration, gave for the formation of the complex between iodine the excess free energy of the benzene-carbon tetraand benzene are certainly of interest. However, chloride system. An equation was developed for a binary system, saturated in respect to a solid this quantity in the homogeneous region by inphase a t constant pressure is monovariant and iso- cluding the data for the benzene-carbon tetrathermal thermodynamic functions cannot be de- chloride system. This equation contained no termined from solubility measurements alone. An terms involving the mole fractions of all three comadditional degree of freedom is afforded in a ter- ponents, and thus the data were fitted to an equanary system. Therefore, the solubility of iodine in tion which could be obtained from the properties benzene-carbon tetrachloride mixtures has been of the binary system alone. Finally, values were measured in this research a t 25” and every ten de- obtained for the thermodynamic equilibrium congrees from 20 to 60”. Carbon tetrachloride was stant and its temperature derivative which are chosen as the additional component because the comparable to those obtained from spectroscopic thermodynamic functions of the benzene-carbon measurements. tetrachloride system were known already.5 Experimental Part These measurements were made in order to study Purification of Materials .-The benzene0 and carbon tetrathree problems: (1) to determine if the changes of the thermodynamic functions on mixing could be chloride? were initially purified as described previously. preparing samples for use in the solubility measurements, determined for the homogeneous phase of the ter- In both liquids were further purified by refluxing over calcium (1) Presented before the Division of Physical and Inorganic Chemist r y at the Cincinnati meeting of the American Chemical Society, April, 1955. (2) Taken in part from the thesis of Burton D. Fine submitted to t h e Graduate School. Illinois Institute of Technology, in partial fulfillment of the requirements for the degree of Doctor of Philosophy. The partial support of this work by the Atomic Energy Commission and the National Science Foundation is gratefully acknowledged. (3) J. H. Hildebrand and R. L. Scott, “The Solubility of Nonelectrolytes,” Reinhold Publ. Corp., New York, N. Y . , 1950. (4) (a) H. Benesi and J. H. Hildebrand, J . A m . Chem. Soc., 7 1 , 2703 (1949); (b) T. Cromwell and R. L. Scott, 7 , 3825 (1850); (c) R. M. Keefer and T. Andrews, ibid., 74, 4500 (1952): (d) J. Ketelaar, Rec. tras. chim., 7 1 , 805 (1952). ( 5 ) G. Scatchar i, S. E. Wood and J. M . Mochel, J . A m . Chem. Soc., 62, 712 (1940).
ibk,
hydride and distilling into sealed ampoules. In the course of these preparations three samples of both liquids were obtained for determination of the densities a t different times over a five-month period. The densities were determined in a single arm pycnometer as previously described.* Values at 25” were, for benzene, 0.87371, 0.87367 and 0.87365 g. per cc. in comparison to 0.87366 listed in the “Selected Values of Properties of hydrocarbon^,"^ and for carbon tetrachloride, 1.58428, 1.58424 and 1.58416 g. per cc., com(6) S. E. Wood and A. E. Austin, ibid.,67, 480 (1945). (7) G. Scatchard, S. E. Wood and J. M. Mochel, ibid., 61, 3206 (1939). (8) 6. E. Wood and John A. Grey, 111, ibid., 7 4 , 3729 (1952). (9) “Selected Values of Properties of Hydrocarbons,” Natl. Bur. Standards, Washington, D. C., Circular C461.
1606
SCOTT L. WOOD,BURTON D. FINEAND LEONARD M. TSAACSON
pared t o a range of values of 1.5841 to 1.5848 reported in the literature. The average of these t,hree values was used in determining the molar volumes of the two components. Resublimed iodine mas again sublimed; approsirnately the middle third was retained. Apparatus and Procedure.lO-Solutions of benzene and carbon tetrachloride of known composit>ionwere preparccl from the weighed samples contained i n the ampoules. The ampoules were made with break-seals for transferring the liquids into the solubility tubes. The solubility tube was made from a Corning straight sealing tube with a coarse fritted disc of about 20 mm. diameter. One end of the tube had a test-tube end and a side arm for transferring the iodine and the two liquids. A small thin-walled bulb of about 5-ml. capacity was sealed on the other end. Transfer of the substances was carried out under vacuum. During the evacuation considerable iodine was sublimed to ensure a dry sample of iodine. Equilibrium was attained by rotating the solubility tubes on a specially designed drum in an oil t,hermostat for about three hours. After equilibrium was attained, the axis of the drum was rotated so that the saturated solution filtered into the thin walled bulb. Enough solution for analysis filtered through the disc in about one-half hour. The tube was then removed from the thermostat and the bulb was quickly sealed off. The filtering was never complete and seemed to stop while the tube was still in the thermostat. When the tube was removed from the thermostat, filtering commenced again either because of the differences of rates of cooling on the t'wo sides of the disc or because of the changes in or on the surface of the disc due to handling or change of t.emperature. It was, therefore, necessary to work rapidly in sealing off the bulb. The after-drainage was more pronounced a t the higher temperatures. Also some charring occurred on the glass surface on sealing the bulb when mixtures of benzene and carbon tetrachloride were used but not when the pure solvents were used. The bulbs were weighed and then broken under a concentrated solution of potassium iodide. The iodine was titrated with sodium thiosulfate in a weight buret,; starch was used as the indicator. Several samples were titrated at a time, a freshly standardized solution being used for each series. After the titration, the glass fragments were collected in a sint.ered glass filtering crucible, thoroughly washed, dried and weighed. All weighings were done with enough care to give mole fractions accurate in the fourth decimal place. Where it was a t all feasible, an identical tare was used in order to minimize surface effects. In order to obtain accurate compositions from the various observed masses, many corrections were found necessary. Such corrections were the buoyancy of the moist air in the balance case, the weight of dry or moist air inside the piece of apparatus, and the masses of each substance in the vapor phase in the pycnometers, the solubility tubes, and in the small bulbs. Errors caused by the additional drainage and by the charring a t the time of sealing the bulb could not be estimated. All temperatures were measured to and maintained within f0.01'. This variation gives a negligible variation of the solubility of iodine. In the calculations the pressure has been assumed to be one atmosphere while the pressure in the solubility tubes was the vapor pressure of the saturated ternary system. This difference in pressure has a negligible effect on the solubility of iodine. The effect of pressure on the melting point of pure iodine is just within the variation of the temperature itself and consequently is not considered. Composition of the Solid Phase.-For thermodynamic calculations, the nature of the solid phase must be known. Benzene and a small excess of iodine were placed in three tubes which were then sealed under vacuum. The tubes were heated to dissolve all t#heiodine and cooled to room temperature. After several weeks, the tubes were opened and a small sample of the solid phase removed, dried in air and analyzed. The results were 99.9 f 0.2% iodine. This indicated that the solid phase was pure iodine in agreement with Hildebrand and Jenks." Since the solubility curves were smooth over the whole range of the mixed sol(10) The complete description of the apparatus and experimental procedure is given in the thesis written b y Burton D. Fine, which is on file in the library of Illinois Institute of Technology. (11) J. H. Hildebrand and C. W. Jcnks, J . A m . Chem. Soc., 42, 2180 (1920).
Vol. 61
vent, it was assumed that the solid phase was always pure iodine.
Results The solubility of iodine in benzenecarbon tetrachloride mixtures expressed in mole fr,zct8ions is given in the first two columns of Table I. The first column gives the mole fraction of carbon tetrachloride (subscript 1) and the second, the mole fraction of iodine (subscript 3). The other columns will be discussed later. Hildebrand and Jenks report smooth values for the benzene-iodine system of 0.0420 a t 20°, 0.0182 a t 25", 0.0718 a t 40' and 0.0953 a t 50" and for the carbon tetrachloride-iodine system of 0.0092 a t 20°, 0.0110 at 2 5 O , 0.01G9 a t 40" and 0.0268 a t 50". All calculations have been made in terms of volume fractions, Zk, defined as n k pko/ niVia, where i
each n represents the number of moles of each component and VO the molar volume of the pure component. The values of the molar volumes of the components a t 25" are 97.107 cc. for carbon tetrachloride, 89.401 cc. for benzene and 59.593 cc. for iodine. This latt,er value was obtained by extrapolating the density of liquid iodine to 25" by means of the equationl2 ,
d = 3.94916
+ 0.003267(120 - t )
(1)
The volume fractions are thus taken to be independent of temperature, and can be considered only as a composition variable. However, the volume fractions using the molar volumes a t GO" differ from those at 25' only in the fourth place, about the observed experimental error. The solubility of iodine in pure benzene a t 20°, given in Table I, is not the experimentally determined value. In treating t,he data an anomaly was discovered a t 20" which indicated that the experimental value was about 2% high. Extrapolation of the observed solubility in the mixed solvents to pure benzene a t 20" gave a volume fraction of 0.02832 while a temperature-wise interpolation of the solubilities in pure benzene except a t 20' and the additional point a t 16.3' given by A r c t o ~ s k igave ~ ~ a value of 0.02830. The value reported in the table is obtained from the average of these two values.
Discussion Thermodynamic Treatment.-The the solution has been expressed as F =
RT In zi i
+
APE
free energy of
+
niwio
(2)
i
where A F Z E may be called the excess free energy of the solution on a volume fraction basis. The standard state of all three substances is taken as the pure liquids at the experimental temperature and one atmosphere pressure. The chemical potential of iodine in solution is then expressed as
t (12) T. Nayder, C. A . , 29, 97G (1935). (13) H.Arctowski, 2. anow. Chem., 11, 276 (189G).
I
SOLUBILITY OF IODINE IN BENZENE-CARBON TETRACHLORIDE
Dee., 1957 THES O L U B I L I T Y 51
TABLE I BENZENE-CARBON TETRACHLORIDE MIXTURES Apaze/ pan, cal./cc. 23 Obsd. Calcd. A Z ~x 105 20
O
0.00939 ,00943 .01231 ,01450 .01483 ,01760 .01997 ,02526 ,02809 .e2835 ,03177 .03570 .03941 ( ,04188)
0.98876 ,98874 ,85559 .8680G .76520 ,46378 .44441 ,28321 .22966 .16471 .loll5 .00000 .00000
0.01124 .0 112G .01495 ,01512 .01740 .02820 ,02883 ,03543 .03755 .0409 1 ,04352 .04814 .04812
25 ' 32.19 32.20 29.31 29.20 27. 78 22.87 22.65 20.54 19.95 19.07 18.44 17.40 17.41
0.01332 .01339 .O1026 ,02322 .02431 .03011 .03317 .03532 ,03878 ,04109 ,04467 ,04957 .05483
30" 31.96 31.90 28.16 26,24 25.76 23.54 22,54 21.88 20.91 20.31 19.43 18.36 17.30
31.77 31.77 28.43 26. 35 25.55 23.22 22.35 21 .GO 20.76 20.30 19.27 18,39 17.18
4-30 30 -20 10 +36 57 +39 +65 $38 + 2 +30 - 15 +23
0,01907 ,01935 ,02506 ,02515 ,03716 ,04004 ,04622 ,05007 ,05931 ,06021 . 06720 .07280 .07265 ,07307
40" 31.05 30.90 28.14 28.10 23.93 23.14 21 .GO 20.73 18.81 18,75 17.56 16.69 16.72 16.67
30.97 30.97 28,13 27.94 23,75 23.09 21.47 20.52 18.89 18.64 17.MI 16.69 16.69 16.69
0 0 + 2 +23 +38 15 37 +34 + 8
0.98GG8 ,98661 .82508 .70930 ,66008 .50748 ,44611 ,38795 ,32167 ,28463 ,19360 ,112G2 . 00000
0.98098 .98065 ,83566 ,82384 ,57992 .53672 ,41947 ,34513 ,20907 ,18445 ,07416 ,00000 .00000 .00000
50
01" I O D I N E I N
0.99061 ,99057 .87257 .78684 .77787 ,67971 .59993 .44011 .35753 ,34311 .25741 .14817 ,06183 .00000
32.50 32.45 29.81 28.10 27.96 26.26 24.99 22.65 21.58 21.48 20.34 19.16 18.17 17.5G
32.48 32.48 29.95 28.29 28.12 26.39 25.10 22.79 21.72 21.55 20.50 19.24 18.27 17.58
32.13 32.13 29.33
... 27.62 22.85 22.59 20.55 19.92 19.18 18.47 17,38 17.38
'
0 0 -11 - 9 -15 - 14 -13 -23 -22 - 10 -30 - 18 -21 - 5
+. . +16 + 4 +170 + 5
+ 5 f 5
+ + +
+ +
+40 + 18 +29 +29 4- 29
0.97314 .97303 ,81473 .53411 ,50290 ,43099 ,34295 .21310 ,11635 ,11112 ,10738 .06202 .00000 . 00000
0.02686 .02607 .03529 ,05356 .05473 .05997 .06711 ,07690 ,08571 ,08584 ,08571 ,09082 ,09627 .09587
0.96291 ,96254 ,84089 ,74160 ,56252 .49559 .39998 ,26054 ,16064 .07505 . 00000 . 00000
0.03709 ,03746 ,04572 .05295 ,06771 .07439 ,08341 ,09745 ,10825 ,11681 ,12557 .12587
30.15 30.10 27.14 22.53 22.29 21.78 20.02 18.51 17.30 17.30 17.29 1G.65 16.00 1G.04
30.12 30.12 27.10 22.51 22.08 21.08 19.92 18.37 17.28 17.23 17.20 16.68 16.04 16,04
29.17 29.06 26.79 25.12 22.31 21.23 19.92 18.13 16.92 16.04 15.20 15.17
29.18 29.18 26.93 25.21 22.36 21.45 20.02 18.27 17.00 16.06 15.18 15.18
+2 + 2 10 + 7 47 $54 +39 45
+ + +
+ 7 $37 46 - 14 -11 -11
+
60'
- 1 - 1 12
+- 249
1GO7
- 15 - 15 -29 -20 -20 - 80 - 46 -75 -49 - 13 - 8 - 8
The condition of equilibrium, that the chemical potential of the iodine in solution is equal to the chemical potential of the pure solid iodine, permits the calculation of A p ~ by 3 ~the ~ relations &aZE
= p3O(s)
- paO(l)- RT RTz, (1 -
In z3 -
2;)
- RTzz (1
-
2;)
(4)
and
Here A g is the difference of the enthalpy of the liquid and solid iodine a t one atmosphere pressure and is a function of the temperature (T = 273.16 t ) and T,, is the melting point of iodine a t one atmosphere pressure. To evaluate the integral, the molar heat of fusion at the melting point'* is taken as 3740 cal. per mole, the molar heat capacity of the liquid phase as 19.5 cal. per deg. mole and that of the solid phase as
+
E,,
=
13.07
+ 0.000321 ( t - 25)2
(6)
The values of A p 3 E Z / V ~ othus calculated are given in the third column of Table I. They are given to four figures for purposes of calculation but are only accurate to three. I n order t o obtain values of the thermodynamic functions for the homogeneous region of the ternary system, an expression for the exess chemical potential of the iodine consistent with an expression for the excess free energy of the solution is necessary. The most general expression for this latter quantity, in terms of volume fractions, is (14) K. J. Frederick and J. H. Hildebrand, J. A m . Chem. Soc., 60, 1436 (1938).
SCOTT L. WOOD,BURTON D. FINEAND LEONARD M. ISAACSON
1608
+ d z ~ +~ ze a~a 2 4+ hz2'Za + + f ka3zz + + + nzlz33 + + + + + + +
AFZE/Vo = U Z I Z Z 4- b w 3
Vol. 61
equation to express the thermodynamic functions as a function of the composition could not be obL 2 1 2 ~ ~ WL21323 tained and an arbitrary decision had to be made. 022aZ3 P22Z33 q21'2z2 ~Z12X32 52z22a2 t21Z2z23 The use of the pair p' W p"X was not considered ~ ~ 1 z 2 f 2 ~ ~3 ~ I z 2 ~ (3 72 ) because then the deviations from ideality of the through the quartic terms. In this equation V ois carbon tetrachloride-iodine system would be expressed by a quadratic, cubic and quartic term c n i V i o . All attempts to fit the data using the while those of the benzene-iodine system would rei square and cubic terms alone failed in that ex- quire only a quadratic term. The values of the cotremely large and apparently meaningless coeffi- efficients of the two remaining equations, one using cients were obtained. It, therefore, became neces- p"X y'Y and the other using p"X yHZ, sary to include the quartic terms. Equation 7 was were then determined a t each temperature except first transformed into the equation of Redlich and 30" and finally the temperature dependence of the Kister16 in order to reduce the number of coeffi- coefficients was determined.l* cients, so that16 The values of a, a' and a" are a = 0.89566 0.00146271, a' = 0.02986 - 0.0000510t, '10 = 0. AFzE/Vo = (YZIZZ c t ' ~ ~ ~ z (21 ZZ) ~ " Z I Z Z ( Z I - 22)' The values of the other coefficients of equation 8 Pziza P ' ~ a ( 2 i - 23) 6"2123(21 - 23)' WZZ~ are, in the one case (equation 11) p = 28.625, P' = Y ' Z Z Z ~ ( Z ~- 23) y"~a(22 - 23)' (8) 0, PI' = 5.471 - 0.0514t1 = 20.577 - 0.10706t The assumption thus is made that the thermo0.0007990t2, 7' = 0, 7'' = -1.789 0.0806t1 dynamic functions of the ternary system can be and, in the other case (equation 12) p = 27.707 expressed in terms of those of the three binary sys- 0.6911t 0.0003758t2, p' = 0, /3" = 6.179 tems. The excess chemical potential of iodine per 0.103t1 y = 26.769 - 0.36456t 0.0020182t2, 7' cc. of pure liquid iodine is obtained readily from eq. = 7.259 0.2771, y" = 0. 8. I n order to reduce the number of coefficients A comparison of these two equations is givsn in still further, the values of a, a' and a" were deter- Table I1 where the limiting values of A ~ C L ~ ~ Eas/ V ~ O mined from the data of Scatchard, Wood and Moc- x3 goes to zero for the two binary systems are listed hel.5 Thus the attempt to obtain the thermo- a t the various temperatures. This comparison dynamic functions for the homogeneous region of involves the extrapolation to infinite dilution of a the ternary system from solubility data alone was function whose coefficients have been determined abandoned. Also p and y were eJaluated in terms along the saturated line, and is probably the most of the average values of Ap3ZE/V30a t x 2 = 0 and critical one that can be made. The agreement of x1 = 0, respectively. This step is based on the as- the two equations is good up to 30" but above 30°, sumption that the points for the two binary sys- the values diverge, the difference being greater for tems are less susceptible to error than the points the benzene-iodine system than for the carbon for the ternary system. A deviation function tetrachloride-iodine system. The comparison for A ( A p 3 Z E / r 3 0 )was , then written as the ternary systems should be intermediate betyeen the two binary systems. Values of Ap3zE/ A(Ap32E/v30) = p'w p"x y " z (9) V30,calculated by the use of equation 11, are given where in the fourth column of Table I. The root mean w = 42i3 6212~2- 321' - 22122 22122' square deviations a t each temperature are 0.11 a t ('h* - 3)(2i2 f WZ) 20°, 0.07 a t 25", 0.19 a t 30°, 0.11 a t 40°, 0.10 a t and 50" and 0.11 a t 60". The differences between the observed values of 23 and those calculated by use of x = 1521'22' 1221~- 2021~22- 1 6 2 1 ~ 2421~22 equations 3, 5 , 9 and 11 are given in the last column 32122~- 6 ~ 1 ~ 232122 ~ 521' of Table I. The root mean square deviations of (12212* - l621* 5) (21' Z ~ Z Z ) (IO) these values are 0.00016 a t 20°, 0.00010 at 25", Y and 2 are similar to W and X, respectively, the 0.00034 a t 30°, 0.00027 a t 40°, 0.00029 a t 50" and difference being the interchange of the subscripts. 0.00040 a t 60". These detailed calculations were I n these equations zl*is the value of x1 a t x z = 0 not done with equation 12. and x2* the value of x2 a t x1 = 0. Thermodynamic Functions.-Tables 111, IV and The deviation function given by equation 9 is al- V ~ Q give, respectively, values of AFZE, TASZE, ways positive over the whole range of composition. and &E calculated by use of equation 11. In each At 20" it is asymmetric with the maximum occurmated by p"X and consequently the three equations involving (3"X ring a t about x z = 0.35 while at 60" it is much more should fit the deviation function. The two equations symmetric. Attempts to fit the data by equations involvingreasonably (3'W + y"Z and y ' Y + y"Z should be less satisfactory be9 and 10 showed that solutions involving the pairs cause the individual terms have opposite asymmetry. The decision as to suitable fitting was based on the magnitude of the coefficients of terms, P'W p " X , p"X y'Y and p"X and the consistency of the limiting values of A w Z E / ~ 3 0as +a goes to y"Z were about equally satisfactory.'7 A unique zero at E L = 0 and also at zz = 0. f21zz3
+
CZZZ3
i2223'
gZlZ3'
jZlZ223
+
+
+
+
+
+
+ +
+
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+
+ +
+
+
+
+
+
(15) 0. Redlicli and A. T . Kister, Ind. Eng. Chem., 40, 341 (1948). (16) The following conditions must be assumed for this transformation (I = a,(I' = d = - e , (I" = ]c = 1 = -qj2f p = b , p' = j = - g , @ J f = rn = n = -r/2, y = c , y ) = h = -q', yf' 0 = p = -8j2andj = t = u = 0 = 0. (17) No equation involving one, three or four terms was satisfactory. Of the six possible equations containing two terms, the equation using B'W y ' Y involves only ternary terms and therefore was not considered. The asymmetry of the deviation function is approxi-
+
(18) The deviations of the values of A ~ 3 ~ ~ / b d ~ farsmootli om function were larger a t 30° than a t any other temperature. The uncertainties increase with increase in temperature but decrease with an increase in solubility. A maximization of the uncertainties is thus possible. This maximum apparently occurs at about 30". (19) The standard state of iodine is the supercooled, liquid iodine a t one atmosphere pressure and the designated temperature. Thus the values of A H E are the changes of enthalpy on mixing liquid iodine and the two solvents to form the solution.
I
I
b I
SOLUBILITY OF IODINE IN BENZENE-CARBON TETRACHLORIDE
Dec., 1957
TABLE I1 COMPARISON OF
LIMITINGVALUESOF ApaZE/P$ FOR T w o BINARY SYSTEMS
THE
THE CEHE-11
20 25 30 40 50 60
Eq. 11
Eq. 12
CCl4-1~ Eq. 12 Eq. 11
18.58 18.63 18.71 19.01 19.46 20.08
18.55 18.57 18.68 19.22 20.16 21.49
33.07 32.82 32.56 32.04 31.53 30.91
33.06 32.81 32.54 31.95 31.27 30.15
table the temperatures listed are 20 and 60". The first column gives the volume fraction of iodine for each line of the table. The other columns give the thermodynamic values for the different compositions of the solvent given at the top of each column.
ture according to equation 12. The agreement between the two values in each case is good up t o about 30" but the differences increase as the temperature increases. For the benzene-iodine system, the variation of T A S Z E and A g E with the temperature is very much larger with equation 12 than with equation 11 and the agreement is generally poorer a t the larger volume fractions of iodine. The differences for the ternary systems would presumably be intermediate between these values for the two binary systems. Because of its simpler temperature dependence, equation 11 will be used in the remainder of this paper. TABLE V THEEXCESS CHANGEOF ENTHALPY IN CAL. PER MOLE, A H E , CALCULATED BY USE OF EQUATION I1
TABLE I11 THEEXCESS CHANGE OF FREEENERGY I N CAL.PER MOLE,
23
AfiZE, CALCULATED BY USE OF EQUATION 11
0.005 .01 .02 .04
23.0 45.2 85.9 157.7
41.0 59.2 92.5 156.3
0.005 .01 .02 .04
23.0 45.2 85.9 157.7
38.6 54.7 83.7 137.8
zz
za = 0
0.005 .Ol .02 .04
15.9 31.4 60.3 113.1
20° 31.1 28.2 40.9 41.7 65.1 62.5 112.1 101.4
24.3 33.4 50.9 83.8
8.2 16.2 31.6 60.1
0.005 .01 .02 .04
14.9 29.5 56.8 107.3
60 O 26.6 38.9 62.6 107.3
23.3 32.4 49.9 82.7
8.8 17.4 33.7 63.4
0.25
= 0.50 ze = 0.75
=0
23
ZP
29.4 39.8 59.9 97.6
ZI
ze = 0
ze = 0.25
za =
0.50
21
0.005 .Ol .02 .04
7.1 13.8 25.6 44.6
12.8 18.3 27.4 44.2
20" 14.5 18.9 27.5 44.4
10.4 13.5 19.8 33.5
12.0 15.8 21.1 30.5
60 O 11.5 11.6 11.7 11.7
4.6 0.8 - 6.3 -18.9
0.005 .Ol .02 .04
'
za = 0.75
ze = 0.25
8.1 15.7 29.1 50.7
ZP
= 0.50
ZI = 0
-
0.5 - 0.6 - 0.4 6.5
+
-10.0 -19.4 -35.8 -61.4
Table VI gives a comparison of the values of the thermodynamic functions calculated by the use of e uations 11 and 12 for the binary systems only. T Ie first column gives the temperature, the second column gives the value of 23 for the three different sections of the table, and the other columns, taken painvise, give, in order, the values of AFZE, TASZE, and A R E obtained by the use of the two different equations. The agreement of APZE is rather good although the differences begin to be important for the benzene-iodine system a t the higher temperatures and larger values of 23. The agreement of T A s z E and A R E is much better for the carbon tetrachloride-iodine system than for the benzene-iodine sys_tem. For the former system both ASzE and AHE are independent of the temperature according to equation 11 but are functions of the tempera-
ZI =
0
45.6 60.6 90.0 145.8
34.7 46.9 70.7 117.3
40.9 51.4 71.6 109.3
27.9 33.2 43.6 63.8
7.7 15.6 32.0 66.6
60 "
COMPARISON OF
40 60
-1.2 -2.0 -2.1 +2.0
TABLE VI THERMODYNAMIC FUNCTIONS CALCUUSE OF EQUATIONS 11 A N D 12
THE
LATED BY
zz = 0
= 0.75
20"
TABLE IV t 23 A ~ E TAW Eq. 11 Eq. 12 Eq. 11 Eq. 12 THE PRODUCT OF THE EXCESS CHANGEOF ENTROPY AND cc14-I2 THE TEMPERATURE IN CAL.PER MOLE,TABZE,CALCULATED BY USE OF EQUATION 11 20 0.005 15.9 15.9 7.1 7.6 28
1609
15.4 15.4 14.9 14.7
7.6 8.1
9.3 12.4
ATP Eq. 11 Eq. 12
23.0 23.0 23.0
22.5 24.6 27.1
CeHsL 0.9 7.7 9.1 20 0.005 8 . 2 8 . 2 - 0 . 5 40 8 . 4 8.5 - 5.0 - 9.8 3.4 - 1.3 60 8.8 9 . 5 -10.0 - 22.3 -1.2 -12.8 20 0.06 85.7 86.3 17.1 54.7 102.8 141.0 40 86.0 86.3 -27.8 - 57.9 * 58.2 28.4 60 89.2 9 3 . 8 -78.6 -185.4 10.6 -91.7
The excess free energy is always positive for the homogeneous system. For solutions rich in carbon tetrachloride, the excess entropy of mixing is also positive. However, for the benzene-iodine system, it is essentially zero or negative; only a t xs = 0.04 does it become positive. The values of A B E are generally positive and become slightly negative only a t 60" for the more dilute solutions of iodine in benzene. The decrease of both ASZE and A R E with increase of temperature for the benzene-iodine system seems to be very large. It represents a value of -0.48z2x;1 for AZ',E/Vo. The uncertainty of this dependence on temperature is difficult to estimate and could be quite large because it involves the second derivative of the original data. However the negative excess entropy of mixing is consistent with the concept of the formation of a complex between iodine and benzene.
lGl0
SCOTTL. WOOD,BURTON D. FINEAKD LEONARD 111. ISAACSON
The agreement between our values of the excess change of enthalpy and the excess change of entropy, calculated from equation 11, with other reported values a t 25” is rather good. Hartley and Skinnerz0report a value of 5.8 f 0.2 kcal. per mole of iodine for the change of enthalpy on dissolving solid iodine in carbon tetrachloride in comparison to our value of 6.1. This value is essentially independent of the concentration. Hildebrand and Scott2’have calculated a value of 3.49 cal. per mole deg. for the excess partial molal entropy a t saturation and a t constant pressure in comparison to our value of 2.9. Hartley and Skinner20 report a value of 4.25 f 0.5 kcal. per mole of iodine for the change of enthalpy on dissolving solid iodine in benzene in comparison to 4.17. The Equilibrium Constant for the BenzeneIodine Complex.-The thermodynamic functions given in the first part of this paper have all been obtained in terms of the components of the system. When species other than the components are assumed to be present in the solution, it is possible to determine from the same data the equilibrium constants for the formation of the new species from the components. In the present system the components have been assumed to be molecular iodine, benzene and carbon tetrachloride and the only new species the 1:l complex between iodine and benzene. The equilibrium constant for the formation of this complex from the compoiients in benzene alone and in the mixed solvent has been estimated at several temperatures. The uncertainty of the values is quite large and difficult to estimate. The chemical potential of iodine must be the same whether it is expressed in terms of components or species. If the chemical potentials are obtained from equation 2, this condition becomes
Vol. 61
respect to the species. T h u s , the values of the equilibrizcm constant f o r the formation of the benxeneiodine complex are wholely dependent u p o n the assumptions made concerning Ap3zEf. The approximation of Ap3zEf has been obtained through the use of the equation * AFZE’/VO/
- 61)2~1’zZ’ + ( 6 3 - 61)2zl’z3’+ - 62)222‘23‘ $. (64 - 61)2zl’z4’ f (64 - 62)22z’2h’ + (64 - 63)223’2r’
= (62
(63
(15)
for the excess free energy per unit volume of solution referred to equation 2 and based on the species present. This equation is formally the Hildebrand-Scatchard equation for a four component system and is in the simplest possible form. The value of 82 - 61a t each temperature was determined by equating equation 15 to equation 8 (with equation 11) under the conditions that x1 equals x 2 and x3 is equal to zero. This assumes that A F Z E / V ofor the benzene-carbon tetrachloride system is symmetric rather than asymmetric but is probably the best assumption that can be made. Similarly (63 - &) was determined by equating the same equations with 21 equal to 0.995 and zz equal to zero. Again this assumes a symmetric relation for A F z E / V o for the carbon tetrachloride-iodine system rather than asymmetric, but this is justified in that the evaluation is made in the same region of concentrations that is used for the calculation of the equilibrium constant. The value of ( 6 3 - a2) was determined by difference. At 25” when 6 3 is taken as 14.1, 61 becomes 8.4 and a2 9.3, compared with 8.6 and 9.15 given by Hildebrand and Scott.22 Finally, both 64 and V440 must be approximated. If 6 2 is interpreted as A E / V , where A E is the energy of evaporation to an ideal gas, then 6 and V are not independent and must be chosen to give reasonable values for A E . The molar volume of the pure liquid complex might be given values intermediate between the molar volume of benzene, 89 cc., and the sum of the molar volumes of benzene and liquid iodine, 149 cc. Hildebrand and Benesi4a estimated the value of J4 to be the arithmetical mean where the primed quantities refer to species rather of the 6’s for benzene and iodine, which would be than comp_onents,the subscript 4 refers to the com- 11.6. However, this value gives values of A E beplex, and V40’isthe molar volume of the pure liquid tween 11,500 and 20,000 cal. per mole for the sugcomplex. The standard states of the species are gested range of volumes and thus it seems to be too all taken as the pure liquid species a t one atmos- large. When 64 is chosen to be 8, AE ranges from phere pressure and the temperature T . This 5,800 to 9,600 cal. per mole. This value might be too small except for the larger volumes. Th_e interequation can be approximated by mediate values of 9.5 for 8 4 and 100 cc. for V4O were RT 1n(z3/z3’) = ApSzE’ - A I43 Z E (14) finally chosen arbitrarily. Then A E is 9000 cal. because the sum of the other terms is negligible. per mole. This value of 6 4 has been assumed to be The problem then reduces to finding by approxi- independent of temperature because of the lack of any other information. Fortunately since zq/ is mation methods values of K,,defined as xql/z,’x:, which satisfy equation 14 for chosen values of x,’ ~’ quite small and a4 - a2 is very small, A p ~ 3 ~and thus K , are not largely dependent on 64. The and x: . Values of ApsZE were determined from equation value-of K. is sensitive however to th_e value chosen 11. These values are always positive. But x 3 for V40, an increase of 1Oyo in VdOcausing an should be greater than x i on the assumption of the increase of 5 to 10% in ICz. The thermodynamic formation of a complex between iodine and ben- equilibrium constant, IC,, can be calculated easily zene. Consequently ApLaZE’cannot be zero,, i.e., from REby the relation the solution cannot be considered to be ideal with In K , = In K , ZZ’( p30 - if,O)/TZ’ z3’( vzo- t740)/1730 f 24’[( r3’ $. pZ0)/F4’ - 21 zl’[( v3’ $. vZo - p4’) (20) H. Hartley and H. A. Skinner, T r a n s . Faraday Soc., 46, G21 (1950). / p l 0 - 11 -/- (AprZE’ - AplZE’ - A,d”‘)/RT ( l G )
+
(21) J. H. Hildebrand and R. L. Scott, J . C h e n . Phys., 20, 1520 (1952).
(22) Ref. 3, page 435.
+
+
Dee., 1957
TRANSFER OF MONOLAYERS THROUGH SURFACE CHANNELS : MECHANISM
The results of such calculations for two concentrations of iodine in the mixed solvents as well as pure benzene at 25, 40 and 60" are given in Table VII. The first column gives the volume fraction of benzene as a species (the last line of each section gives values for pure benzene). The next three columns give values for 231 equal to 0.005 and the last two columns give values for zJ' z: equal to 0.01. The values of K , are given in the second and fifth columns and the values of K , in the third and sixth columns. For comparison, the values of K,, which have been calculated with 8, equal to 11.6, are given in the fourth column. The values for Ka for B4 equal to 9.5 are essentially constant at 25'. At 40", they are about the same for the two concentrations of iodine but there is an apparent trend to lower values as the concentration of the solvent approaches pure benzene. At 60' these changes are more marked than at 40". I n contrast to these, no constant values are obtained when a4 is taken as 11.6. It seems that the values of K, for a4 equal t o 9.5 may have some realistic meaning. More constant values might be obtained by adjusting the values of S4 or VE or by allowing 84 t o vary with temperature. But the approximations which are necessary to even make such calculations do not warrant such detailed study. The values of the equilibrium constant determined by spectrophotometric methods are given in terms of mole fractions, K,. Comparison of K . with K , is obtained by multiplying K , by Vd0. is the molar volume of the VO/17poV34,where solution. Using pure benzene as the solvent, the molar volume of the solution has been taken as 88.6 cc. per mole. Then the K , of Benesi and Hildebrandb is 2.87 based on measurements in carbon tetrachloride solutions and 2.00 based on measurements in n-heptane solutions, that of Cromwell and Scott4bis 3.62, and that of KetelaaP
+
(23)
+
J. Ketelaar, J . Phys. Radium,16, 197 (1954).
1611
is 2.01 in contrast to 0.86 given in Table VII. A crude estimate of the change of enthalpy for the formation of one mole of the pure liquid complex from pure liquid benzene and pure liquid iodine can be obtained from the quantities given in TABLE VI1 THE EQUILIBRIUM CONBTANT
FOR T H E
BENZENE-IODINE
COMPLEX
ti'
ta'
+84 = 9.50.005 +4'
Ka
K.
0.25 .50 .75 11'
=0
0.25 .50 .75 21'
=0
0.25 .50 .75 ZIJ
=0
1.86 1.50 1.17 0.86
1.80 1.44 1.00 0.70 1.45 1.05 0.63 .35
6r =
11.6
K.
t = 25" 0.058 0.211 .178 .060 .156 .063 .059 .123 t = 40" 0.067 0.229 .068 .190 .060 .142 .052 .lo5 t = 60" 0.068 0.215 .063 .166 .046 .lo6 .032 .062 '
za' '
+64 = 9.5 = 0.01 14'
K.
K.
1.87 1.66 1.14 0.86
0.059 .066 .061 .062
1.67 1.46
0.061
1 .oo
.70
.060 .051
1.30 1.14 0.60 .33
0.063 .068 ,045 .033
.060
Table VII. For the sol.utions in which xz' is less than 0.50 the value of Ka is essentially constant and hence AH0 appears to be zero. When benzene itself is the solvent, AHo is -3.5 kcal. per mole. .When all the values listed a t each temperature are averaged and the temperature dependence of the three values determined, AHo becomes about -0.9 kcal. per mole. These values are consistent within the large uncertainties involved with the value of -1.3 kcal. per mole reported by Cromwell and Scott and by Ketelaar.
THE TRANSFER OF MONOLAYERS THROUGH SURFACE CHANNELS. 11. MECHANISM BYMARTINBLANKAND VICTORK. LA MER Department of Chemistry, Columbia University, New York 27, New York Received June 10, 1967
.
The process of selective transfer is discussed and the assumptions made in deriving rate expressions are examined. The contact angle for the transferred film on the walls confining the surface channel is then calculated. A specific rate constant, also calculated from the transfer rate data, is compared to the surface fluidity for cetyl alcohol. It is shown that in the process of transfer, the monolayer drags a very much thicker layer of sub-phase (water) with it, even against a counter hydrostatic flow of sub-phase.
I n a previous communication,' a process for continuously transferring monolayers through surface channels was described, and a mechanism to account for the rate of transfer was proposed and tested. I n this paper some of the assumptions made for the mechanism of transfer will be reexamined. An attempt to ascertain the physical meaning of the monolayer flow property determined from the transfer rate will also be made. (1) V. K. La Mer and M. Blank, J . Coll. Sei., 11, 608 (1956).
The procedure consists in depositing a surfactant on a water surface (surface 1) which is connected to another water surface (surface 2) by a brass ring with a machined groove on its upper face (which is wet with water). The process involves the transfer of the monolayer over the layer of water residing in the groove from surface 1 t o surface 2. The monolayer is continuously washed away on the second surface. Various methods of cleaning the groove were tried. Polishing with Shamva Metal-
