April, 1963
DIFF USION C OE FFIC IE N T, CM?/SEC.
to5
AGAR CONCENTRATION % ,
0
93s
XOTEH
0.5
I .o
Fig. I.---Diffusion coefficient of tritiated water in agar gel a t different concentrations. The assumption of a semi-infinite column was validated in that tracer artivity was not present in thr untreated end within the 3-8-hr. exposure prriod. An average diiiusiun Coefficient vias taken from the calruiation for the first five 1-cm. sections of rach column.
Results The diffusion coefficients of H3H1OI6measured a t four agar gel concentrations are presented in Fig. 1. A linear regression equation was calculated for this relation from which a value D = 2.41 f 0.055 X cm.? sec.-’ was determined for the diffusion coeficieiit of tritiated water in ordinary water. This value compares favorably with the results of Wang, et aL2 THERMODYX AMIC PROPERTIES O F T H E ATiMOSPHERIC GASES I X AQUEOUS SOLUTIONS‘ BY CORNELIUS E. NLOTSAND BRUCEB. BEXSON
qualitative solubility data.4 h precision of 0.1% in the solubility measurements permittrd the graphical evaluation of these data with an estimated error of 1% for the enthalpies and entropies and 10% for the heat capacities Relative values for different solutes are, however, considcrahly niow accwnl c. ‘I‘hiis, for r\nniplr, the identical d u e s of the partial molal heat capaci t ics reflect a relationship revealed in this work and exhibited in Fig. 1 and 2 . Plots of ln[K(S2)/K(Ar,02)1 = In [ai(Ar,Oz)/a(Nz)] us. l/T, where the K’s are the Henry’s law constants and the ai’s are the Bunsen solubility coefficients, give excellent straight lines. The standard deviations are 0.16% in the case of oxygen and 0.10% for argon. The nitrogen solubility coefficients employed for this purpose mere the result of thirty-two absolute measurements throughout the full temperature range. Discussion The observed entropies of solution and the enormous partial molal heat capacities give substance to the iceberg picture of aqueous solutions3 which envisages this heat capacity as arising largely from the melting of an ice-like structure surrounding each solute molecule. This 17iew has proved a useful one5 and has been extended to larger molecules of biological importance.6 Recent 3.m.r. investigations reveal, however, that the situation is not so simple.89 The present results therefore are of interest as they suggest an approach to this intriguing and important problem of the structural modifications in aqueous solution. The slopes of Fig. 1 and 2 are related to A(AH) = AH(Sz),,lu - AH(Oe,Ar),,ln and imply that these quantities are constant throughout the temperature range studied despite the fact that the individual enthalpies of solution display a pronounced temperature dependence. This suggests that the “icebergs”
’
TAnLE
Department of Phystcs, Amherst College, Amherst, Massachusetts Kecezved A p r d 18, 1961
Recent precision determinations of the solubility coefficients of nitrogen, oxygen, and argon in distilled water2 permit straightforward evaluations of certain thermodynamic properties of these solutions. Their magnitudes are of interest as an indication of the “iceberg” structures surrounding the solute molecules in water.3 A previously unreported relationship among these properties has now been obtained which supports previous ideas and offers a means of testing detailed models of these structures. Experimental The solubility measurements covered the temperature range 2-27”. Both manometric determinations of the absolute solubilities and mass spectrometric measurements of solubility rattos for a pair of gases were made, the two techniques giving identical results. These methods and the solubility coefficients are reported elsewhere.2
Results The derived partial molal enthalpies and entropies of solution and the partial molal heat capacities in solution are given in Table I. They are in good agreement with previously reported values based upon more (1) This work was supported by t h e National Science roundatlon under Grant NSF-G9437. (2) C. E. Klots and B. B. Benson, J. Marine Res., 21, 48 (1983). (3) (a) H. 6. Frank and M. W. Evans, J . Chem. Phys., 13, 507 (1945); (b) W. F. Clausseri and M. F. Polglase, J . Am. Cfiem. Soc., 74, 4817 (1952).
I
HEATSAKD ENTROPIES O B SOLUTION AS FUNCTIOXS OF TEVPERATURE (BASEDOK A HYPOTI-ZETICAL STAND.4RD S T A T E I N SOLUTION OF UNITMOLEFRACTION) AC, = Cp(M)so1n. - C,(M)gas T,‘(2. Nz
-AH (cal./mole)
0 2
Ar Kz
-AS
(cal./mole-deg.) 02 4r
ACp(oal./mole-der:)
2 5 10 20 25 15 4190 3650 3260 2950 2698 2520 4560 4020 3630 3320 3065 2890 4510 3970 3580 3018 2840 3270 36 9 34 9 31 6 31.0 33 5 32 5 36 8 34 8 33 4 32 4 31 5 30 9 36 4 34 4 33 0 32 0 31 1 30 5
:: 0 2
161
120
76
59
46
33
for these solutes are virtually identical at any given temperature. Small differences in the enthalpies (and entropies) of solution are then due solely to the process of introducing the solute molecule into its ice-like cage. Thus one may write: AH(M)soln. = AH(iceberg) AH(R4),,,ity. Here the first term on the right represents the heat of formation of the iceberg and is strongly temperature dependent; the second term arises from the introduction of the solute molecule (AI)
+
(4) D. M. Himmelblau, J. Phys. Chem , 6S, 1803 (1959). (5) (a) H. 8. Frank and W. Y . Wen, Dzseussions Faraday Soc., 24, 133 (1957); (b) H S Frank, Proc. R o y . SOC.(London), 8247, 481 (1958). (6) I. &I Klots, Sczence. 128, 875 (1955). (7) I. AI Klots and S.W. Luborsky, J Am. Chem. Soc., 81, 5119 (1959). (S) E. A. Balazs, A. A. Bothner-By, and J. Gergely, J , M o J , BzoJ,, 1, 147 (1959). (9) F. A. Bovey, Nature, 192, 324 (1961).
934
XOTES
Vol. 67
A detailed iceberg model should permit evaluation of these terms independently. The small differences in the solute-dependent term will then serve as a sensitive test of the model. It has been suggestedlO that a cell theory approach should be useful for this purpose. Solubility isotope effects with oxygen and nitrogen, for example, indicate a slightly larger free volume for the oxygen molecule, properly reflecting its smaller “hardsphere” diameter and consistent with the entropies of solution reported here. A further correlation between solute force constants and thermodynamic data of the present type has been noted previ~usly.~ The present data also illustrate unambiguously that a previous notion1’ of a unique water-oxygen complex is untenable. A recent communication12 suggesting a more general interaction of the contact charge transfer type is reasonable. The existence of a shifting equilibrium among more than one “kind” of iceberg is, however, not excluded and may be indicated by LIir temperature-dependent absorption spectrum.l1 (10) C. E. Klots and B. B. Benson, J . Chem. Phue., in press. (11) L. J. Heidt and A. 31.Johnson, J . Am. Chern. Soc., 79, 5587 (1957). (12) J. Jortner and U. Sokolov, J . Phus. Chem., 65, 1633 (1961).
IP
I 3.30
I
335
I
3.40
I
I
3.45
3.50
I
355
I
3.60
SOLUTIOK STRUCTURE IN CONCENTRI1IIED SON-IONIC SURFACTSST SYSTEMS BY J. M. CORKILL
L 36
( V T ) x IO3.
Fig. 1.-Experimental determinations of the ratio of the solubility coefficients cf argon and nitrogen as a function of temperature: open circles, mass spectrometric ratio measurements: closed circles, manometric measurements.
Baszc Research Dept., Procter &. Gamble Ltd., Newcastle-upon-Tune, England AND
K. W , HERRMANN
Miami T’alley Laboratories, The Procter & Gamble Companu, Cincinnati, Ohio
Received August $1, 1068
.310
The X-ray diffraction patterns obtained from moderately concentrated anionic surfactant solutions led Mattoon, Stearns, and Harkins’ to suggest that in addition to micelle formation, a second structural transition took place in these solutions. The existence of this change has also been demonstrated by other techniques, notably viscosity and diffusion coefficient2C3 measurements. The interpretation of the X-ray patterns is still a matter of discussion4; however, it is generally agreed that an increase in order in the solution takes place above the second transition yegion. I n this paper, the results of light scattering and X-ray measurements on aqueous solutions of the dimethyloctyl and dimethyldodecylamine oxides (GAO and C12AO) are described. These results are discussed in terms of the structural changes that occur above the critical micelle concentration (c.m.c.), but below the concentration at which a mesomorphic (middle) phase separates. Although the amine oxides can show cationic character below pH 7, the surfactant is completely non-ionic under the conditions e m p l ~ y e d . ~ ,287-
/
I
I
I
I
I
5
Experimental Light Scattering Measurements .-Turbidities were determined with a commercial apparatus (Phoenix Precision Instrument Company) similar t o that described by Brice, et ~ 1 . 8 The narrow
I/T x IO’
Fig. 2.-Experimental determinations of the ratio of the sohbility coefficients of oxygen and nitrogen as a function of temperature: open circles, mass spectrometric ratio measurements; closed circlos, manometric measurements.
into its cavity and is probably relatively insensitive to temperature.
(1) R. W. Mattoon, R. S. Stearns, and W. D. Harkins, J . Chem. Phys., 15, 209 (1947). (2) R . J. Vetter, J . Phus. Chem., 51, 262 (1947). (3) X. Tyuzyo, Koll. Z., 176, 40 (1961). (4) G. W. Brady, J . Chem. Phus., 12,1547 (1951). ( 5 ) K. VC’. Herrmann. J . PAys. Chem., 66, 295 (1962). (6) B. A. Brice, M. Halwer, and R. Speiser, J. Opt. SOC.Am., 40, 788
(1950).
