March 5, 1957
VAPOR-LIQUID EQUILIBRIA IN BINARY SYSTEMS
1037
According to the foregoing discussion of the absorption, the excited state of the 231 mp band of mesityl oxide is more polar than the normal state. I n other words, the oxygen atom is more negatively charged in the former state than in the latter. Then it is reasonable to consider that the attachAccording to an earlier explanation based on the ment of a proton to oxygen results in larger energy MO theory,22this can be replaced by the interac- stabilization in the upper state than in the lower tion between the highest occupied orbital of the state and therefore in a large red shift of the absorpC=C bond (Hc-c) and the lowest vacant one of tion band. Furthermore, the solvation energy in the carbonyl group (V+O) as shown in Fig. 4a.22 polar medium, which is conceivably larger in the As the result of the interaction between these two excited state than in the normal one, should also help orbitals, we can expect the appearance of two new the red shift. Thus, the large red shift seems to be One of them explained qualitatively on the basis of the conceporbitals +n and $e for mesityl which is filled with two electrons in the normal tion of charge transfer absorption. state W, can be represented by a linear combinaExperimental tion of wave functions for orbitals Hc-c and Vc=o, C.P. acetone was treated with an aqueous alkaline solunamely, +n = aJlc-c b+c-o. The value of b, tion of AgNOs, distilled, dried with anhydrous KlCOz and which represents a measure of the electron migra- finally fractionally distilled before use. White label Easttion from the C=C bond to the C=O bond in the man mesityl oxide and. mesitylene were fractionally disnormal state, or in other words the degree of the tilled. Commercial phorone was four times recrystallized methanol. n-Heptane was stirred with concentrated contribution of the polar structure to the resonance from sulfuric acid for one or two days, washed with water and in that state, is usually small. On the other hand, aqueous alkaline solution, dried with CaClg and finally the wave function of the excited level We, which is fractionally distilled with sodium metal. Water treated by orthogonal to that of W,, contains one electron in ion exchange resin was distilled with KMnOd. C.P. consulfuric acid was used without further purificafin and the second in the orbital +e of the form +e = centrated tion. bfic-c - u+c=o (a > b). Then in the We state, The absorption spectra were measured with a Beckman the R electron on the C=C bond migrates to the spectrophotometer model DU, using the quartz absorption C=O bond to a large extent. Thus it may be ex- cell with 10 mm. light path. The temperature of the cell pected that the transition from W, to W e can be compartment was kept a t 25' by the use of the thermospacer. Acknowledgments.-The authors wish to exaccompanied by a large electron transfer and therefore by a strong absorption. This absorption may press their sincere thanks to Professor Mulliken be called an intramolecular charge transfer absorp- for his kindness in reading this manuscript and tion in analogy to the intermolecular charge trans- in giving them some valuable advice. One of the authors (S. N.) is also indebted to Professor Mullifer absorption discussed by Mulliken.* ken and Professor Platt and other members of the (22) S. Nagakura and J. Tanaka, J . C h e w Phys., 22, 236 (1954): Laboratory for the hospitality shown during his S. Nagakura, ibid., 23, 1441 (1955). stay a t Chicago. (23) A more accurate treatment will be published shortly.
and the polar structure
0I H
+
[ CONTRIBUTION FROM THE RESEARCH DEPARTMENT, PLASTICS DIVISION, MONSANTO CHEMICAL COMPANY]
Vapor-Liquid Equilibria in Binary Systems BY W. F. YATES RECEIVED OCTOBER5, 1956 An equation containing two parameters has been derived from kinetic considerations which relates instantaneous vaporliquid equilibria in binary systems. The two constants appearing in the equation have been described in terms of the thermodynamic properties of the mixtures concerned. The validity of the assumptions involved has been tested by applying them to data selected from the literature. Until recently the only adequate means of representing vapor-liquid equilibrium data involved the use of activity coefficients and rely on various integrations of the Gibbs-Duhem equation. The relationships existing, however, do not greatly contribute to the understanding of the phenomena involved in evaporation or condensation.
Spinner, Lu and Graydon' have observed the similarity between representations of vapor-liquid equilibrium data and copolymer-monomer composition plots and have applied the Alfrey-Price2 relationship to predict vapor-liquid equilibria. The remarkable success of these investigations has prompted closer study to see if there is any basis in theorv for the use of the eauations thev DroDose. Cons;dered from the stindpoint of a' b h a r y (1) 1. H. Suinner. B. C.-Y. Lu and W. F. Graydon. . I n d . E%?. Chem.. 48,' 147 (1956). (2) T. Alfrey and C . C . Price, J . Polymer Sci., 2, 101 (1947).
liquid mixture containing components A and B in the process of evaporating, four possible processes are occurring kii
-A
- A(l) + -A(1)
-B
- il(1) + -B(1)
-B
- B(1) + -B(l)
k21
k22
kiz
'
-A
- B(1) --+
-A(1)
+ A(g) + A(g) + B(g) + B(g)
(1) (2)
(3)
(4)
W F.YATES
1038
syatrm
1 , OC.
Benzene-cyclohexane
W E
71.5 1240 1277 1242 1340 328 337 - 550 50.5 - 500
283 241.5 61.3 54.8 76.1 72.5 1597 1557 1652 1681 504 476 - 636 169 - 500
42.9 56.0 138, 1 511 579
32.4 - 7.6 - 51.4 1326 1426
711 40
Curhoii tetrachloritie--l,er~~etie
’ir I 40 ‘iir
Methanol-benzene
35 55 35 55 25 35 35 35 50 60 - 198 - 178 - 148 50 60
Methanol-carbon tetrachloride Methyl acetate-benzene Dimethoxqmethane-chloroform Dimethoxymethane-benzene Acetone-chloroformQ
Nitrogen-oxygen
Ethanol-water
where k11, etc., are the rate constants for the respective processes. The rate of change in liquid composition for each component is then given by -d N A
~-
dt
-
kll(
-A - A)
+
k21(
-B - -4) (5a)
=
kZ1(-B -B )
+
kl?(
-A - B)
and ~-d’B
dt
(5b)
By setting up steady-state conditions for equations l through 4 it can be seen that
’(--‘I -~
dt
-0
=
klz( -.4 - B) -
k21(
ki?( --I - B)
-B - A) or
=
kii(
PZlE
306.5 261 G ,5 , 3 61 .o ”i u-. 5
40
Carbon tetrachloride-cyclohexa~~e
Vol. 79
-B - A) (6)
By dividing equation 5a by 5b and substituting equation 6 into the result (7)
Since A and B must each distribute themselves in the liquid by attaching to molecules according to the ratio of their mole fractions and
ri
P,O/PZO
0.9895 1,0129 1.1559 1,1351 1.1682 1.1207 1.1147 1.5781 1.2014 1.3820 2.2615 2.2296 1.9383 3.9782 1.1646 1.1636 5.2273 3.3061 2.3652 2.4029 2.3621
.1580
(1946). (8) J . C. Chu, “Distillation Equilibrium Data,” Reinhold Pub]. Corp., New York, N. Y . , 1950. (9) YI and 1%values a t 60’ calcd. nsing equation 14 with H n m = - 1800 a n d Hzlm= - 1760. (IO) C. A . Jones, E . 11.Schoenborn a n d A . P. Colburn, I ~ i d . EX^. Chem., 35, 606 (1943).
,0561
,1765 1.3000 1 ,2858 4.7585 3,6635 2.5381 2.3311 3.9200 3.4574 1.3572 1.084 0.985
dLh7h _ -diVB
Krf.
3
4 3
0
7
.0549 ,1889 ,2061 1.4580 0.1908 1,5714 1.7257 0.1539 ,2905 ,5200
8 8
,053
10
8
S
8
,0491
+ xz)
YI(TIXI
+ xi)
(9)
L~(T?x~
The change in liquid composition, dNA/dNB, must define the vapor composition. If the vapor composition is expressed in terms of mole fractions equation 9 becomes =
y?
9 (YlX1 x2
(TZXZ
+ +
Xi)
(10)
XI)
Equation 10 is seen to be identical with the vaporliquid equilibrium equation proposed by Spinner, Lu and Graydon.‘ The derivation of equation 10 is valid only for systems a t constant temperature. Spinner has presented a number of calculations of 71 and r l values for systems a t constant pressure and has demonstrated that the equation describes the data in most cases. Calculation of Binary Constants.-In order to predict vapor-liquid equilibria for binary systems i t is necessary to have an independent means of computing values of rl and r?. Spinner used the empirical relationship Ti = 4 e-B1(B, - a?) (1la) 4 2
=
i12 e-Bz(Bz .-1l
(1946). (7) G. Scatchard, S. E . IVood and J. M , Mochel, i b i d . , 66, 1960
0.6411 ,6927 ,7839 ,8129 ,7574 ,8019 ,0521 , 0381
Substituting equations Sa and 8b into 7 and by defining rl = k11/kp2 and YZ = k??/k?l
y1
(3) G. Scatchard, S.E Wood a n d J . M . Mochel, J. Phys. Chcm., 43, 119 (1939). (4) G. Scatchard, S E R’ood and J. M. Mochel, Tnxs JOURNAL, 61, 3206 (1939). ( 5 ) G. Scatchard, S. E . Wood and J. M. Mochel, i b i d . , 62,712 (1940). (6) G. Scatchard, S. E. Wood and J . M. Mochel, i b i d . , 68, 1957
T
0.6045 0.6906 1.0407 1.0379 1.0347 1 ,oo9i 0.1867 ,2224
-~
i
)
(Ilb)
and evaluated the constants A and B from x-y data. It would be advantageous to be able to predict r1 and r2 values from thermodynamic properties of each system. The rate of evaporation of a pure compound k11, should be given by the Arrhenius equation when it is considered that the energy barrier to evaporation is equal to the heat of vaporization, LU kll =
Slle-Lii/RT
(12a)
Similarly, for molecules of B evaporating from molecules of X klz = s l s r - L d R ? ‘
121, J
I n order t o evaluate LlZone can consider i t t o be equal to the heat required t o unmix a mole of B from an infinitely dilute solution in A (where no B-B bonds are to be found), and vaporize it Liz = -HZ
+ Lm
0 . 3 1 1 0.519 0.631 0.797 0 . 9 2 0 .493 ,534 ,561 ,631 .758 ,530 ,557 ,579 .642 .769
Methanol-benzene ( 5 5 ' )
where HE is equal to x2 o (bE)/(bxz) and H," is the heat of mixing to form a mole of solution of specified composition, From these relationships sll/slze(- Li1
Methanol-benzene (35') 0.024 0.130 y i (calcd.) ,245 .432 y i (obsd.) ,273 ,486 XI
0.030 0.103 yi (calcd.) .405 ,261 yi (obsd.) ,484 .302
XI
limit
y1 =
1039
VAPOR-LIQUID EQUILIBRIA I N BINARY SYSTEMS
March 5 , 1957
+ L22 - H;",)/RT
Methanol-carbon tetrachloride (35") Xl
yl (calcd.)
yi (obsd.)
(13)
By differentiating equation 13, and combining the results with the differential form of the Clapeyron equation it can be seen that
0.330 0 . 4 9 8 0.608 0.790 0.901 ,498 .536 .564 ,644 .751 ,554 .586 ,608 ,672 .770
0.135 ,430 .463
0.356 ,497 .492
0.478 ,519 .503
0 . 4 9 4 0.656 0.791 ,522 ,558 .612 ,506 ,530 ,579
0.912 .724 .702
Methanol-carbon tetrachloride ( 5 5 " ) 0.790 .622 ,619
0.909 ,733 .734
0.100 0.200 0.400 0.500 0.600 0.800 yi (calcd.) ,430 .593 .298 .659 .724 .856 yi (obsd.) ,466 .621 ,323 .681 .738 .864
0.900 ,926 .931
XI
(calcd.) yi (obsd.) YI
0.058 .348 ,364
0.149 .440 .498
0.365 0.495 ,501 ,526 ,528 ,544
0.645 .562 ,569
Methyl acetate-benzene (25') x1
where PI" and Pzo are the vapor pressures of the pure components. By regarding the constant ~1 PZo/P1" as analogous to an equilibrium constant, i t should be possible to evaluate it from the excess chemical potential of component B in an infinitely dilute solution in A
Methyl-acetate-benzene (35') 0.100
Xi
yi (calcd.) yi
(obsd.)
Xl YI
limit
y2
=
P~o/P~~~-~%RT
(15b)
,306
0 . 2 0 0 0.400 .420 ,587 ,448 ,616
(calcd.) (obsd.)
0.100 0.200 0.400 0.500 0.600 ,098 ,243 ,567 ,701 .SO5 ,092 ,222 .534 ,675 ,788
TABLE I1 CALCULATION OF VAPOR-LIQUID EQUILIBRIA System Benzene-cyclohexane (40') X.
yl (calcd.) yi (obsd.)
0 , 1 2 8 0.235 .278 .169 ,277 ,166
0.369 .392 .391
0.493 .489 .495
0.614 0.743 0.866 ,583 ,692 .817 ,591 ,698 .821
Benzene-cyclohexane (70") 0.119 0 . 2 4 1 0.376 .397 .151 ,277 y i (calcd.) ,398 ,149 ,281 yi (obsd.) XI
0.495 .495 .498
0.618 .597 .603
0.725 0.866 ,691 .831 ,696 .831
Carbon tetrachloride-cyclohexane (40') X:
yi (calcd ) yi (obsd )
0.126 0.245 ,282 ,152 .152 .282
0.367 0.515 0.606 ,548 .633 ,405 ,407 ,547 .634
0.754 .770 ,770
0.876 ,882 ,882
Carbon tetrachloride-cyclohexane (70') Xl
yi (calcd.) yi
(obsd.)
0.125 0 . 2 4 7 0.364 0 . 5 1 5 0.607 ,397 .544 .631 ,146 ,278 .398 ,547 .632 .146 .279
0.754 0.876 .767 .882 ,768 ,882
Carbon tetrachloride-benzene (40') 0.140 0 . 2 3 8 0.374 yi (calcd.) 416 171 .279 yi (obsd.) .170 .277 .416 XI
0.492 0.620 0.759 0.872 ,529 .648 .879 .774 ,530 .648 ,878 ,774
Carbon tetrachloride-benzene (70") xi
(calcd) y i (obsd.) yl
0.143 0.239 0.379 0.493 0 . 6 2 2 ,271 ,411 ,167 ,521 ,642 ,270 ,411 .520 .641 ,167
0.762 ,772 .772
0.875 ,879
,878
0.900 .925 .935
0.800 0.900 .936 .974 ,933 ,972
Dimethoxymethane-benzene (35' ) 0.100 y i (calcd.) ,341 yi (obsd.) .342 x1
0.200 .521 ,520
0.400 ,728 ,720
0.500 ,797 ,788
0.600
,852 ,845
0.800 .937 ,936
0.900 ,971 ,971
Acetone-chloroform (760 mm.) 0.138 0.211 y i (calcd.) ,104 ,179 yi (obsd.) ,100 ,176 Xl
I n order to test the validity of equations 15a and 15b a few systems have been selected from the literature for study. Table I is a compilation of the results of the calculations of YI and rz values therefrom and Table I1 shows the results obtained when the calculated rl and r2 values are applied to equation 10.
0.500 0 . 6 0 0 0.800 ,655 ,720 .854 ,679 ,741 ,866
Dimethoxymethane-chloroform (25") yl
I n this case p& is equal t o xz ___) o (bFxE)/ (bxz), or is the change in excess free energy accompanying the solution of a mole of B into an infinite amount of A. It can further be shown that
,286
0.477 ,520 ,517
0.663 0.739 0.859 0 , 9 1 5 ,749 .825 ,922 .957 ,751 ,824 ,917 ,952
Nitrogen-oxygen ( -198") 0.100 yi (calcd.) .376 yi (obsd.) ,417 Xi
0.200 ,551 ,601
0.400 ,746 ,779
0.500 0.600 .810 .862 .833 ,877
0.800
.941 ,945
0,900 .973 .974
Nitrogen-oxygen ( - 178') 0.100 0 . 2 0 0 0 . 4 0 0 0.500 0 . 6 0 0 0.800 0.900 YI (calcd.) ,261 ,428 ,648 ,728 .797 .910 ,957 yi (obsd.) ,271 ,445 ,666 ,743 .SO8 ,913 .958
x1
Nitrogen-oxygen ( - 148') 0.100 0 . 2 0 0 0.400 yi (calcd.) ,169 ,303 ,519 yi (obsd.) ,173 ,315 ,534 Xl
0.500 ,608 ,622
0.600 0.800 0,900 ,693 ,851 ,926 ,702 ,851 ,924
Ethanol-water (50") 0.093 YL (calcd.) ,423 y i (obsd.) ,424 xi
0.123 ,455 ,482
0.158 .484 ,507
0.343 ,587 ,586
0.513 ,671 ,649
0.824 ,857 ,845
0.908
0.860
0.972 .972 ,972
,921 ,910
Ethanol-water (60") XI
yi (calcd.) YI (obsd.)
0.197 0.375 ,418 ,508 ,589 ,393 ,517 .596
0.086
0.527 ,668 .660
0.808 ,835 ,826
,875 ,867
Discussion By far the most reliable data used in these studies are those published by Scatchard and coworkers on benzene-cyclohexane, carbon tetrachloride-benzene, carbon tetrachloride-cyclohexane, methanol-benzene, and methanol-carbon tetrachloride. It is quite apparent that the agreement between calculated and observed values for yl in Table I1 is much poorer in the cases of sys-
1040
RAYMOND Q. WILLEAND MARYL. GOOD
tems containing polar materials such as methanol. The very good agreement in the set of systems containing benzene, cyclohexane and carbon tetrachloride makes it appear that the theory is sound for non-polar materials. The validity of equations l l a and l l b as proposed by Spinner may find some justification in the expression derived from equations 12a and 12b [A CONTRIBUTION FROM
THE
yl =:
VOl. 79
sl! e(-Lii
+ Lia)/RT
s1z
and r2 =
* 321
e(-Lar
+L ~ ~ ) / R T
but any such justification involves a number of unwarranted assumptions. TEXAS CITY,TEXAS
COATES CHEMICAL LABORATORY, IdOUISIANA STATE UNIVERSITY]
The Distribution of Iodine between Carbon Tetrachloride and Water and a Proposed Mechanism for Dilute, Aqueous Iodine Reactions1 BY RAYMOND G. WILLE AND MARYL. GOOD RECEIVED AUGUST20, 1956 The distribution of iodine between carbon tetrachloride and mater a t 25’ has been studied as a function of the totaliodine concentration (lo-’ to lo-’ M ) ; the PH of the aqueous phase (1.0 to 7.0); and the time of mixing. Both tracer techniques and spectrophotometric methods were used. Discrepancies between calculated and experimental distribution coefficientsfor low iodine concentrations are reported. Some information on the chemical behavior of the iodine species in the water phase is presented along with a mechanism to explain the anomalous behavior of dilute aqueous iodine solutions.
In a previous paper2 an extensive study of the distribution of iodine between carbon disulfide and aqueous solutions was reported. In this study i t was found that more iodine (in various chemical forms) appeared in the water phase than could be accounted for by considering the well-known iodine equilibrium reactions. The discrepancies became more pronounced as the total iodine concentration in the system was decreased. Attention was called to the fact that similar results were obtained by Kahn3 in a study of the distribution of iodine between benzene and water. Also other investigators have found anomalous behavior in dilute iodine solutions. Examples are (1) the studies made by Reid and Mulliken4 on dilute solutions of iodine in pyridine where excess triiodide appeared as the iodine concentration was decreased; and (2) the investigation of the ionization constant of iodine by KatzinKwhere the value obtained for the constant increased as the iodine concentration decreased. No definite conclusions were made to account for results reported in these cases. However, it was generally agreed that either impurities were playing an important role in these studies or there was some unknown reaction occurring a t low iodine concentrations between iodine and the solvent in its “brown” solutions. The results of the carbon disulfide-water distribution study2 indicated that the anomalous behavior was quite reproducible. This is not generally a characteristic of impurity reactions. Thus i t seems the most likely explanation is that some iodine reaction, heretofore not taken into account, becomes important a t low iodine concentrations. (1) This work was supported in part by a Frederick Gardner Cottrell Grant from the Research Corporation, Abstracted from a portion of the thesis submitted by Raymond G. Wille to the Graduate School of the Louisiana State University, Baton Rouge, in partial fulfillment of the requirements for the degree of Master of Science. (2) M. L. Good and R. R. Edwards, J. Inorg. N r c l . Ckcm., 2, I96 (1956). (3) M . Kahn, Thesis submitted for degree of Doctor of Philosophy, Washington University, St. Louis, Mo., 1950. (4) C . Reid and R. S. Mulliken, THISJOURNAL, 76, 3869 (1954). ( 5 ) 1,. I . Katzin, J. Ckcm. Phyr.. 81, 490 (1953).
To further study this interesting iodine behavior, a distribution study of iodine between carbon tetrachloride and aqueous solutions was carried out. Tracer techniques were employed to follow the distribution so that the lowest possible iodine concentrations could be used.
Experimental The experimental procedure described previously* for the distribution study of iodine in the carbon disulfide-water system was essentially repeated. Reagent grade carbon tetrachloride was purified further by a method described by Edwards and Davies.6 Buffers a t PH 6.98, 5.01 and 2.98 were prepared using 0.1 M citric acid and 0.2 M disodium phosphate. A dilute solution of sulfuric acid was used for PH 1.02. All buffer systems were made up with conductivity water. A Beckman Model G $H meter was used to determine the $H of the buffer solutions. U. S. P. iodine (resublimed) was used to prepare carrier solutions of iodine in carbon tetrachloride. All carrier solutions were diluted obtained from from a 0.1 M stock solution. Eight day the Oak Ridge Xational Laboratory in a “carrier-free” state, in a sodium sulfite solution, was used as a tracer. The radioactive solutions to be used in the distributions were obtained by shaking the carbon tetrachloride solutions of carrier iodine with diluted solutions of the Oak Ridge P1. The two phases were separated leaving the iodine in the carbon tetrachloride phase tagged with IlS1due t o the exchange between the active iodide ions and the I p molecules. Radioactivity measurements were made on liquid samples using a well type NaI (thallium activated) scintillation counter. A Dumont 6292 photomultiplier tube; a Nuclear Corporation Power supply, Model 1090A; a Radiation Counter Laboratories linear amplifier, Model 2206; and a Nuclear Corporation scaling unit, Model 161, were used. The distributions were made by adding 20 ml. of carbon tetrachloride containing radioactive iodine to an equal volume of buffered water in a 100-ml. glass-stoppered flask. The flask was immersed in a water-bath controlled a t 25 f 1O . The flask was mechanically shaken a t a constant rate. The solutions were shaken for varying lengths of time from two minutes to several hours. After each period of mixing the layers were allowed to separate and equal volumes of solution were removed from each phase and counted. To obtain the reproducibility a second series of distributions were made. Results of the two separate runs agreed within experimental error (approximately 10%). (6) R. R . Edwards and T . H . Davies, “Piational Nuclear Energy Series, Book 1, Radiochemical Studies; The Fission Products,” Paper 23, McGraw-Hill Book Co., Inc., New York, N. Y.,1951.
