J. LAVOREL
1600
probable that hydrolysis occurs by a chain of bimolecular reactions such as (i), (ii) and either (iii) or (iv). In the proposed chain of reactions it is impossible to decide whether (iii) or (iva) describes the situation. Only in the case of (C6H5)28iC12 have indications
OH I
Rate =
Vol. 61 ~
-d(HzO) -d(RSiCls) = dt dt -
where k stands for a forward velocity constant and K stands for an equilibrium constant. If (HCI)/ K i i is appreciably greater than (lriv/kii) (RXiCh), then this reduces to
of stable groups like =Sic1 been found and this implies t,hat for the other chlorosilanes studied, either Rate = ki,Kii(HzO)(RSiC13)2/(HC1) (6) reaction (iii) or (iv) is very fast compared to (ii) and (ii) is the rate-determining step, or that the Equation 6 is consistent with the known facts but equilibrium for (ii) is far to the left. The data can only be established conclusively by further exavailable on the order of reaction with respect to perimentation. A further study of the order of chlorosilane demand that two molecules of chloro- reaction with respect to chlorosilanes, particularly silane be involved in the rate-controlling step, and in difunctional systems, should be made, and the this requires (iii) or (iv) to be slower than (ii). A kinetics of the reactions of R3SiOH and R,Si(OH), reasonable rate equation which fits the observed with R,SiC14-. should be determined. facts for the hydrolysis of trifunctional chlorosiAcknowledgments.-We are indebted to our aslanes can be obtained by assuming that reaction sociates in the newly formed Silicones Division of (iia) is a reversible reaction which is then followed Union Carbide Corporation for permission to pubby (iva), Then for RSiC13compounds lish this paper.
INFLUENCE OF CONCENTRATION ON THE ABSORPTION SPECTRUM AND THE ACTION SPECTRUM OF FLUORESCENCE OF DYE SOLUTIONS BY J. LAVOREL~ Department o j Botany, University of Illinois, Urbana, Illinois Received May 6, 1967
The action spectrum of the fluorescence of fluorescein in solution is concentration-dependent ; in particular, the longknown drop of efficiency on the long-wave side of the absorption band is practically non-existent at low concentrations, and becomes very marked at high concentrations. These variations in the action spectrum of fluorescence are paralleled by changes of the absorption spectrum. Both can be quantitatively explained by the formation of a non-fluorescent dimer, if one assumes that this dimer has two absorption bands-one on each side of the monomer hand. Similar effects are observed -and the same interpretation appears adequate-also for solutions of thionin. Observations on two chlorophyll-a solutions of different concentration suggest the occnrrence of a similar dimerization effect. The results have a bearing on the interpretation of the concentration quenching of fluorescence, and of the decline observed at the long-wave end in the action spectra of photosynthesis and of the fluorescence in green plants.
Introduction for an intrinsic reason why molecules, excited in the The sharp drop in the efficiency of fluorescence frequency range corresponding to the long-wave excitation, found in many dissolved dyes when side of their absorption band, should dissipate their light is absorbed on the long-wave side of the peak electronic excitation more successfully-in comof the absorption band, has been first observed by petition with fluorescence-than molecules excited Valentiner and Roessiger3s4in the case of fluores- by light of higher frequency. Explanations of this type are somewhat difficult cein. Nichols and Merritt5 had shown previously that, throughout the remainder of the absorption to reconcile with the well-supported idea that, in a spectrum, the energy yield of fluorescence does not condensed phase, thermal equilibration of intravary strongly. Vavilov6 found that t>hequantum molecular vibrations takes a very short time comyield of fluorescence of many dyes remains constant pared to the life-time of the fluorescent state; throughout the spectrum-except a t its long-wave and that accordingly, by the ttime the excited molecules emit fluorescence, they are distribut>ed over end. One can follow two lines of argument in order to a spect,rum of vibrational states which does not deaccount for this phenomenon. First, one can look pend on the way in which they had been originally excited. It has been suggested, however, that (1) Work performed in the Photosynthesis Laboratory of the exceptionally “hot” molecules (i.e., molecules in Department of Botany of the University of Illinois, Urbana. Illinois. during the tenure of a Rockefeller Fellowship, with the assistance of high vibrational states) may lose their electronic the U. S. Office of Naval Research. excitation energy by radiationless transition into (2) Laboratoire de Biologie Physico-chimique, Facult6 de8 Sciences, the ground state before thermal equilibration. Universite de Paris, Paris, France. It, should be noted that such “hot” molecules (3) 9. Valentiner and M. Roessiger. Berlin Bar., 16, 210 (1924); Z . Phyaik. 32, 239 (1925). should contribute to absorption not only on the (4) 8. Valentiner and M . Roessiger, ibid., 36, 81 (1926). long-wave side, but also on the short-wave side of ( 5 ) E. L. Nichols and E. Merritt, Phya. R e v . , 31, 381 (1910). the main peak, causing the efficiency curve of (6) S. I. Vavilov, Phil. Mag., 43, 307 (1922).
..
:Dee., 1957
ACTIONSPECTRUM OF FLUORESCENCE OF DYESOLUTIONS
1601
fluorescence excitation to drop on both sides of this except that it now appeared to be strongly concenpeak (as observed by Neporent, et al.,’ in some or- tration-dependent. As for the decline on the ganic vapors, where this decline can be attenuated short wave side, this variation has apparently been by the addition of incrt gases, which accelerate overlooked in the past, due to its smaller amplitude. The important fact for us was the concentration thermal equilibration). An alternative “intrinsic” hypothesis is that of dependence of the phenomenon, which seemed to Jablonski,8 who suggested that the drop in quan- rule out explanations of the first of the two abovetum yield is caused by the existence of a “forbid- mentioned types; whereas it could easily be exden” electronic transition leading to a metastable plained if-as suggested by Forster-a non-fluoresstate, which contributes to light absorption on the cent dimer was in equilibrium with a fluorescent long-wave side of the main band. More re- monomer. The following analysis of the expericently, Russian authors (Levshin, Neporent and mental data confirms this hypothesis. Borisevichg) proposed, as a third alternative, the Methods existence-in the same region-of a broad purely General.-Testing the hypothesis of the “screening” vibrational band. I n cases where the drop be- effect of a non-fluorescent dimer requires the comparison, comes marked in a region where absorption is still a t any given concentration, of two quantities: (1) A,, the relative absorption of the monomer, i.e., its contribution toquite strong, explanations of the last two kinds ward the total absorption, as function of wave length. seem insufficient. All three “intrinsic” hypotheses (2) +, the quantum yield of fluorescence, also as function of predict that the action spectrum of fluorescence wave length. A , is readily given by the expression excitation should be independent of concentration. X Ern A, = (1) An alternative is to look for extrinsic reasons for xem 1/*(1 - X ) € d the phenomenon-ie., for a competition for the exE, and Ed are the molar extinction coefficients of the citing photons by molecules other than the ones where monomer and dimer, respectively; x is the molar fraction of which produce fluorescence. Forster,’O on the basis the monomer of the results of Rabinowitch and Epstein” on the [monomer] = xc dimerization of certain dyes, thought that dimeric (c = total concentration of the dye, calculated if it were molecules could play that role, if these molecules all in the monomeric form); z further obeys the relation are non-fluorescent-which is generally the case. _ x_2 = _ 2K (A similar explanation of the concentration quench1-x c ing of fluorescence was proposed much earlier by K being the constant of the dissociation equilibrium Walter. 12) dimer 2 monomer The results presented in this paper support Forster’s hypothesis. We have described in anOne can easily see, that +, too, must be proportional to (other paperl3 a new method for measuring the ex- (I), if we assume that only the light absorbed by the montent of energy migration by resonance transfer, omer can reappear as fluorescence. In practice, we were able to determine the quantities A , lbased on the observation of slight changes in the and +only in arbitrary units, L e . , multiplied by unknown;shape of the fluorescence band and in the action but If our hypothesis is correct, plotconstant-factors. ;spectrum of fluorescence, caused by increased con- ting the two sets of data as a function of wave length on centration of a fluorescent dye. I n certain regions semi-log paper should give two curves of identical shape, (of the spectrum, these concentration effects were which could be brought to coincidence by a translation to the axis of ordinates. relatively small, and could be satisfactorily inter- parallel Action Spectra of Fluorescence.-The experiments were preted by energy migration (in conjunction with made as described in our previous paper.ls The following secondary fluorescence). I n other regions, how- filters were used in front of the photomultiplier tube: ,ever, the variations were much wider, and had to be for fluorescein, Corning no. 3484; for thionin, Corning no. 2030, in order to record only the non re-absorbable part of the in-terpreted in a different way. Specifically, the fluorescence band, and to prevent exciting stray light from efficiency of excitation declined more or less reaching the photomultiplier tube. sharply, on both sides of the absorption peak; For any given concentration of the dye, the relative efthis decline, negligible a t very low concentrations, ficiency of excitation as a function of wave length was calculated, using the known intensity of the monochromatic became more pronounced as concentration in- exciting beam, expressed in numbers of incident quanta per creased. unit time and unit area. Absorption Spectra.-In the case of fluorescein, one has to The longwave side drop was obviously the same go to very high concentrations in order to see any change in phenomenon as described by earlier investigatorsthe absorption spectrum. Thus, the conventional 1 cm.
+
(7) B. S. Neporent and B. S. Stepanov, Uspekhi fiz. nauk, 4 3 , 380 (1957). (8) A. Jablonski, Nature. 181, 839 (1933); Acta phys. U.S.S.R.. 2, 97 (1933). (9) C/. B. S. Neporent and N. A. Borisevich, Compt. rend. (Doklady), Acad. Sci. U S S R , 94, 447 (1954). (10) Th. Forster. “Fluoreszenz Organischer Verbindungen,” Vandenhoeck & Ruprecht, Gottingen, 1951,p. 245. (11) E . Rabinowitch and L. F. Epstein, J . A m . Chem. Soc.. 63, 09 (1941) (12) B. Walter, Ann. P h y s i k , 36, 502, 518 (1889). (1%) NOTEA D D E D IN PROoF.-While this paper was in press, E study by Farster and Konig appeared [Z. Bleklrochem., 61, 344 (1957)) dealing with the absorption spectra of concentrated dye solutions (fluorescein, eosin, rhodamin B) with results qualitatively similar to $hose shown in Figs. 3 and 0, below. 113) J. Laswrel, THIBJOURNAL,61, 8134 (1957).
thick cells could not be used for this purpose, and a special technique was necessary. Two rectangular pieces of ordinary glass, about 0.5 cm. thick, were cut so that, when pressed together, they would fit into the cuvette holder of a Beckman spectrophotometer. Mica spacers, in shape of rectangular frames, were split to different thicknesses; with reasonable care, spacers as thin as about 5 could be used. A few drops of the solution were deposited between the two pieces of glass, which were then pressed together as closely as allowed by the spacer. Care was taken to exclude air bubbles. The four non-optical sides of the bloc were cemented with melted paraffin, and the optical density was measured with a Beckman DU spectrophotometer. We assumed that the most diluted solution (about M ) was free of the dimer, and took its absorption spectrum as that of the monomer. We will call its optical density
J. LAVOREL
1602
Vol. 61
Chlorophyll-a, prepared according to the method . of Jacobs, Vatter and Holt14 was used in liquid paraffin solution (Stanolind oil). All experiments were carried out at room temperature (ca. 24”).
Results Fluorescein.-The optical density of the dye solution, and the relative efficiency of fluorescence, were measured between 450 and 510 mp-a range 5 . 3 X IO” comprising the long-wave absorption band. No changes in the efficiency curve or the absorption spectrum were found up to M . Above this concentration, and up to the highest one investiIC 1.1x102 gated (5.3 X lov2,)[ti changes of 6 and A , were found to follow a parallel course. Figure 1 shows how closely the curves for 4 and -4, can be made to coincide. It would be of primary importance to know the value of K . This would permit calculation of the 2.6x absorption spectrum of the dimer. As pointed out previously, the thickness of the micro-cuvettes could be measured only with a very poor accuracy; this precluded precise determination of 2 as a function of c. However, we arrived a t a crude esti5.3XIU2 mate of K by a procedure which rests on the following assumptions. L (1) There are portions of the curves D(o)/D(c) 4 50 500 h y ) which are nearly horizontal, with small fluctuaFig. 1.-Comparison of 6- and Am-dependence on X for tions about an average straight line (Fig. 2). fluorescein in 1 M NaOH aqueous solution, at different This means that in this range, the shapes of the abconcentrations. +values are represented by circles, Ansorption spectra of the two forms are nearly the values by dots. same. We can assume, in this case, that Ed 2 e,. Calling A the average value of D(o)/D(c) in this range of wave lengths, we get 1.
I
1
A-
x
+ 1/2(1 - x) 2
= 1
,
(2) The curves D(o)/D(c)-for sufficiently high c’s-have a maximum a t the peak of the absorption band of the monomer. This obviously means that, a t that particular wave length, em Ed. Assuming that em >> t d and calling B the value of D(o)/D(c), one sees from (2) that a>
’Of0
I
\
Noting that the coefficient of proportionality between D(o)/D(c) and em/[ZEm f ‘/z(1 - z) ea] (cf. 2) is the same in both cases, we can further write A
Ll
,
400
,
,
,
;
,
,
,
4 50
,
,
!
X ( ,m p )
,
500
M solution, Fig. 2.-Am-curve of fluorescein in 5 X showing a n almost horizontal portion a t A and a maximum at B . D(o). For each given concentration c, we calculated the ratio D(o)/D(c), D(c) being the optical density of the corresponding solution. As the thickness of the microcuvette could not be measured accurately, this ratio was not equal, but only proportional to A , em
-
D ( 0 ) = const x A m (2) $ern ‘/2(1 - x ) € d D(c) Dyes.-Fluorescein (Eastman Kodak Co.) was used in alkaline (NaOH, 1 M ) aqueous solution. Thionin (Hartman and Leddon) was used in aqueous solutions. ~
+
B=” The values of K , calculated with the aid of this formula for the three highest concentrations used, agree rather well, as shown in the table C
(mole/l.)
1.1 x 10-2 2.6 X
5.3 x 10-2
K
(mole/l.)
0.130 .194 .136 Av. 0.15
We have calculated, with this average value of K , a tentative absorption spectrum of the dimer, (14) E. E. Jacobs. A. E. Vatter and A. S. Holt, Arch. Biochsm. Biophys., 58, 228 (1954).
I
~
357
ACTION SPECTRUM OF FLUORESCENCE OF DYESOLUTIONS
OPTICAL DENSITY
6
I
EXlo-4
1G03
M
\
\ ,
400
,
500
600
Fig. 5.-Absorption bands of the monomer (M), and of the dinier ( D1and Dz) of thionin, calculated from Rabinowitch and Epstein's data."
Xpr)
OPTICAL DENSITY
5 00
Fig. 3.-Absorption bands of the monomer (M), and the dimer (D1 and D2), of fluorescein (in arbitrary units).
630
L Fig. 4.--Comparison of 4- and &-dependence on X for thionin in aqueous solution, calculated from Rabinowitch and Epstein's data in (11). +values are represented by circles, &-values by dots.
shown-along with that of the monomer-in Fig. 3. The presence of two absorption bands in the spectrum of the dimeric form is noteworthy. (Somewhat similar results-although interpreted differently-were obtained, for the same dye, as well as for eosin, by Soderborg.16)
Fig. 6.-Absorption curves of chlorophyll a in liquid paraffin a t low and high concentration: A , calculated from these curves.
2. Thionin.-In this case, we have only measured the 4 curves between 520 and (330 mp and compared them with the A , curves as calculated from the data of Rabinowitch and Epstein.ll As shown in Fig. 4, the fit is nearly as satisfactory as with fluorescein, particularly if one considers that the two sets of data come from two independent investigations. (15)
B. Soderborg, Ann. Physik, 41, 381 (1913).
1604
J. LAVOREL
Vol. 61
We have also calculated, from the absorption of the absorption band of the monomer is very spectra and the K-value given by the above-cited steep, so that even a relatively weak band of a nonauthors, the absorption spectrum of the thionin fluorescent dimer, located on the “red side” of the dimer (Fig. 5). It is interesting to note here again monomer band, could make a large enough contrithe apparition of a second dimer band on the long- bution to the total absorption in this region to acwave side of the band of the monomer-in addition count for the observed effect. to that on the short-wave side, described by the In order to explain Soderborg’s results on fluoresearlier authors. ceinls-now confirmed by our own observations3. Chlorophyll a.-Although we do not have FOrster1’ did admit that, in some cases, the dispersystematic, exact data for this compound, we sion forces, which, in his theory, are held responthought it desirable, in view of the possible bearing sible for dimerization, are not strong enough to of the results on some problems in photosynthesis, impose a strictly anti-parallel orientation of the dito include here the curves (Fig. 6) showing the poles, so that the total transition dipole correabsorption spectra of two chlorophyll solutions in sponding to the D2 band of the dimer needs not to be liquid paraffin at two widely different concentra- zero. One might perhaps visualize this deviation from antiparallelism as the result of thermal fluctions, and the A,-curve derived from them. The similarity of the A, curve in Fig. 6 to those tuations about an equilibrium position, in which for fluorescein and thionin is suggestive. Duy- case the intensity of the D2 band should increase gave a curve for 4 of chlorophyll in vivo with increasing temperatures. Steric factors, or which exhibits similar features-a minimum on the electrostatic repulsion between two dye ions of the short-wave side, a maximum at the absorption same sign, also could favor a not strictly antipeak, and a large drop on the long-wave side of this parallel orientation of the two components in the dimeric molecule. peak. (2) The D2 band may be of importance in the explanation of the phenomenon of concentration Discussion We do not need here to be concerned with the quenching. Its position on the long-wave side of theoretical reasons why dimerization leads t o the the absorption band of the monomer leads to strong appearance of two new absorption bands-one on overlapping with the fluorescence band of the latter. each side of the monomer band. These reasons Therefore, a transfer of electronic excitation by have been given by Forster.17 We would like to resonance from an excited monomer molecule to a non-excited molecule of the dimer should be, ceteris add only a few remarks. (1) Let us call the two dimer bands D1 and D2,in paribus, more probable than its transfer to another the order of increasing wave lengths. I n the orig- monomer molecule. Thus, not only should the exinal work of Rabinowitch and Epstein,ll D2 was citation energy be lost for fluorescence whenever it not noticed. Later, Forster, l7 discussing the rela- happens to reach a dimer molecule-whether by tive orientation of the components of the transition direct absorption or by resonance transfer-but dipole moment in the two molecules forming the di- there should be a definite preference for the transfer mer, pointed out that these components could be of the excitation energy to such an “energyeither parallel or antiparallel, leading to two ab- trapping” dimer molecule. The suggestion that concentration quenching is sorption bands; but that the one of lower freassociated with energy transfer was already made quency, D2, corresponding to an anti-parallel orientation of the two dipoles, should be very small. by Vavilov,l* Francklg and Forster”; the latter Forster noted that, in the spectral curves of Rabino- also proposed, more specifically, that the excitation witch and Epstein, a certain increase in the absorp- is quenched when it reaches a dimer molecule. (3) Emerson, et U ~ . , ~ Ohave lately re-investigated tion a t high concentrations was noticeable also on the long-wave side of the monomer bands of thionin the long-known, formally similar phenomenon of and methylene blue, but he attributed this t o the the long-wave limit of efficiency of photosynthesis. great width of the D1-band of the dimer, rather than .They have found that the wave length at which the drop starts, can be pushed toward the red by lowerto the existence of a second band, Dz. We believe that, a t least in the case of the two ing the temperature; in some cases, a t least, also by dyes we have investigated quantitatively, and prob- supplying accessory light in other parts of the specably also in that of chlorophyll, the Dz-band does trum. In view of the analogy between this photochemappear in the absorption spectrum with significant ical phenomenon and the one we have examined, intensity.’’* Furthermore, from the apparently very general occurrence of the long-wave drop in the we would like to suggest that an explanation in efficiency of fluorescence, we surmise that the Dz- terms of the presence of a photosynthetically inband is present in all dyes which show this drop. active, as well as non-fluorescent, dimer could be Its intensity does not need to be nearly as high as attempted. A change in the absorption spectrum that of the band Dl in order to account for the rapid of chlorophyll in vitro a t high concentrations, which drop of efficiency, for, as a rule, the long-wave side suggests the existence of a dimer band on the longwave side of the monomer band, was noted above. (16) L. N. M. Duysens, “Transfer of Excitation Energy in PhotoThe temperature effect observed by Emerson synthesis,” Thesis, University of Utreoht. 1952, p. 45. (17) Th. Forster, ref. 10, p. 250, et asq. (17a) NOTEADDED I N PROOF.-FSrster and Konig (12a) found two bands (DIand Dz) for the dimers of fluoreseein, eosin and rhodamin B, but etill believed that only one appears in the spectrum of dimeric thionin.
(18) 8. I. Vavilov, 2. Phyaik, 81, 750 (1925). (19) J. Franok and R. Livingston, Rev. Modein Phys., 21, 505 (1949). (20) R. Emerson, R. Chalmers and C. Cederstrand, PPOC. Natl. Acad. Sci., 43, 133 (1957).
I
,
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 extensively studied3 and indeed such studies have led in a large measure to our present understanding of non-electrolytic solutions. Recently, the formation of complexes between iodine and certain solvents, such as aromatic and olefinic compounds, has been studied by means of spectrophotometric measurement^.^ The determination of the thermodynamic functions of the benzene-iodine system and of the thermodynamic equilibrium constant for the formation of the complex between iodine and benzene are certainly of interest. However, a binary system, saturated in respect to a solid phase a t constant pressure is monovariant and isothermal thermodynamic functions cannot be determined from solubility measurements alone. An additional degree of freedom is afforded in a ternary system. Therefore, the solubility of iodine in benzene-carbon tetrachloride mixtures has been measured in this research a t 25” and every ten degrees from 20 to 60”. Carbon tetrachloride was chosen as the additional component because the thermodynamic functions of the benzene-carbon tetrachloride system were known already.5 These measurements were made in order to study three problems: (1) to determine if the changes of the thermodynamic functions on mixing could be determined for the homogeneous phase of the ter(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,
nary system from solubility measurements alone, ( 2 ) to determine if the thermodynamic properties of the homogeneous phase of the ternary system could be obtained from those of the three binary systems, and (3) to determine the thermodynamic equilibrium constant for the formation of the benzene-iodine complex from the components. No equation for the excess free energy of mixing based on the solubility data alone was found which, on extrapolation to zero iodine concentration, gave the excess free energy of the benzene-carbon tetrachloride system. An equation was developed for this quantity in the homogeneous region by including the data for the benzene-carbon tetrachloride system. This equation contained no terms involving the mole fractions of all three components, and thus the data were fitted to an equation which could be obtained from the properties of the binary system alone. Finally, values were obtained for the thermodynamic equilibrium constant and its temperature derivative which are comparable to those obtained from spectroscopic measurements.
Experimental Part Purification of Materials .-The benzene0 and carbon tetrachloride? were initially purified as described previously. In preparing samples for use in the solubility measurements, both liquids were further purified by refluxing over calcium 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 a t 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.
