Communications to t h e Editor
1442
have been reported in the pulse radiolysis2 and the flash photolysis3 of mercaptoethanol in aqueous solution at high pH. In the flash photolysis case, we have explicitly stated that we consider the 300-nm transient absorption as arising from the RS. radical. Our assignment has recently been verified by pulse radiolytic ~ t u d i e s . ~ Only the RS. transient which is rather insensitive toward oxygen is observed in nonpolar solvents such as cyclohexane. In polar solvents such as water the radical anion, R$SR-, is observed as a n additional transient. In the case of aliphatic thiols the absorption of the radical anion occurs around 420 mn, while for thiophenol the maximum is at 470 nm. The transient radical anions have a rather high extinction coefficient and are therefore readily observed, provided the solution is properly deoxygenated and the pH is adjusted to provide a sufficient concentration of RS- anions. Thyrion states in his paper: “The assignment of the absorption bands to a phenylsulfur radical is in contradiction with that postulated by Caspari and Granzow who observed a transient spectrum with maximum at -420 nm identified as arising from the RSSR- radical anion upon photolyzing aqueous solutions of thiophenol.” Since none of the transient spectra reported by Thyrion was obtained in aqueous solution, it is obviously not possible to compare the two studies, A minor flaw is the incorrect quotation of an absorption maximum for the thiophenol transient a t 420 nm instead of 470 nm. eferences and Notes ( I ) F. C. Thyrion, J . Phys Chem . 7 7 . 1478 (1973). ( 2 ) VI. Karmann, A. Granzow, G . Meissner, and A. Henglein. Int. J . Radiar Phys Chem 1 , 395 (1969) (3) G Caspari and A Granzow J Phys Chem 74, 836 (1970) (4) M 2 H o f f m m a n d E Hayon J Phys Chem 77,990 (1973)
C h e m i c a l R e s e a r c h Division American Cyanamid Company B o u n d Brook Ale w Jerse y 08805
Albrecht Granzow
Received September 73. 7973
Reply to Comments on the Paper, “Flash Photolysis of Aromatic Sulfur Molecules,” by A. Granzow Sir: We thank Caspari and Granzowl for correcting the absorption maximum they observed in aqueous solutions of thiophenol a t 470 nm and not a t 420 nm as reported in our work. We wish to make some further comments. (1) Thiophenol has been photolyzed in H20-EtOH (2:l) solutions at various pH’s and in all cases the short and long wavelength bands were observed. The only difference observed in increasing the pH was an increase of the optical density. This can be explained by a higher absorption of flash light by the parent compound. (2) It was first thought that a radical ion produced the long wavelength band but this hypothesis was ruled out when considering the decay curves and the decrease of transient concentrations with an increase of parent compound concentrations. (3) The longer flash duration in the experiment of Caspari and Granzow may be responsible of the discrepancy between the results. (4) The comparison between flash photolysis and pulse radiolysis results can be made only with great care since the primary processes are likely different. The Journai of Physical Chemistry. Vol. 78, No. 14, 1974
References and Notes (1) G. Caspari and A. Granzow, J. Phys. Chem., 74,836 (1970).
Laboratoire de cinetique chimique 8-1348 Louvain-La-Neuve, Belgium
F. C. Thyrion
Received March 19, 1974
On the Use of the van’t Hoff Relation in Determinations of the Enthalpy of Micelle Formation‘ Publication costs assisted by the National Institutes of Health
Sir: There is considerable interest today in hydrophobic bonds. Since the outstanding thermodynamic characteristic of such bonds is the sizable temperature dependence of the enthalpy change that accompanies their formation, interest has grown in the determination of this enthalpy. One possible route to this goal is through study of detergent micelles. Unfortunately, although a quite general thermodynamic analysis of micellar solutions has been made,2,3implementation of the equations is not possible because they involve various quantities that are unmeasurable a t the present time. There is a particular property of micellar solutions, the critical micelle concentration (cmc), that can be very readily and precisely measured. Consequently, there is a need for methods of interpretation of that quantity in terms of the thermodynamic properties of the micellar solution. Various viewpoints are available that make such an interpretation possible,4 includingone described earlier by US^-^ that comes under the rubric of “quasistatistical mechanical” methods.2 In that method, attention is focused upon the reaction Ai
+
A;
A$+i
(1)
wherein AI is a detergent monomer and A N is a micelle containing fir monomers, N being the number of detergent monomers in the micelle of size most probable a t the concentration, temperature, and pressure of the cmc measurement; and it is shown that the standard free-energy change (infinitely dilute reference state) of reaction I may be estimated by
Experimental determination of the temperature dependence of the cmc is customarily then interpreted in the usual way, Le., through the van’t Hoff relation, to provide the standard enthalpy of reaction LS However, since the more general thermodynamic analyses show that macroscopic, operational van’t Hoff relations fail in this system if the micelle number is temperature d e ~ e n d e n tthe , ~ question arises whether the quasistatistical mechanical method under scrutiny is consistent with that result. We are thus driven to analyze closely the temperature dependence of Acfi“‘. In the following, we demonstrate that the two approaches are consistent and therefore that such use of the van’t Hoff relation is in principle incorrect. We also show that in practice numerical values of enthalpies so obtained may be very wrong. Consider a micelle containing N monomers. In the ab-
Communicationsto the Editor
1443
sence of external fields, its change in standard (infinitely diiute reference state) partial molal Gibbs free energy is described by
wherein the last term accounts for possible gain or loss of monomers, since the most probable micelle may change with temperature. A similar relation holds for the micelle containing I^v i- I monomers, while for monomer itself -
GI" =
6-dP
-
ilm dTi
(4)
For reaction 1,then -
d(AG.cm) = Aq,?-
dP
-
As,"
dT
+
from which we see that the temperature coefficient of A?2=,tmis
Substituting -Asxi- = (A(?" 6 we find
- AH")/T and eq 2 into eq
300"K, e = 4.8 X esu, 6 N 80, b = 2 nm, and converting to calories, we find for this term (6.3 X lO4)(a&'/aT),. The only relevant measurements we have been able to find of the temperature dependence of micelle number are those of Debye? which give a magnitude of -0.4 far (afirlaT)p. Thus, the magnitude of the electrical part of the last term of eq 7 is -2.5 X lo4 cal. For ionic micelles, experiments show that the left-hand side of eq 7 is nearly zero at room temperature, so that AH" as determined from the van't Hoff relation ( i e . , by neglecting the last term of eq 7) may be grossly in error even if the total free energy is only a few per cent of the electrical part. I t is unfortunately not really possible to take the offending term into account since the result is so sensitive to its value and experimental errors in measuring I^v are such that a value of 0.4 for (aN/aT), is barely distinguishable from zero over the accessible temperature range. It would seem that the only valid way of assessing micellar enthalpies lies in the use of calorimetry. .Referencesand Notes (1) This investigation was supported by Research Grant No. GM-20064 from the Division of General Medical Sciences, U.S. Public Health Service. (2) T . Hill, "Thermodynamics of Small Systems," Vol. 2, W. A. Benjamin, New York, N.Y., 1964. (3) D. Hall and 5. Pethica in "Nonionic Surfactants," M. Schick. Ed., Marcel Dekker, New York, N.Y., 1967. (4) E. Anacker in "Cationic Surfactants," E. Jungermann, Ed., Marcel Dekker, New York, N.Y., 1970. (5) M. Emerson and A. Holtzer, J. Phys. Chem., 69, 3718 (1965). (6) M. Emerson and A. Holtzer, J" Phys. Chem., 71, 1898 (1967). (7) M. Emerson and A. Holtzer, J. Phys. Chem., 71, 3320 (1967). (8) Numerous references by a variety of authors could be given here as the procedure is commonplace, but we prefer to point an accusing finger only at ourselves: see ref 7, then, as a typical exaniple. (9) P. Debye, Ann. N. Y. Acad. Sci., 51, 575 (1949).
Department of Chemistry Washington University St. Louis, Missouri 63 130
The left-hand side of eq 7 is the experimental quantity, and, as eq '7 shows, gives AH" by a van't Hoff relation only if (aI^v/aT),is zero, Le., only if the most probable micelle number is independent of temperature. In general, we do not expect this to be the case, so the temperature coefficient of the cmc cannot be used to obtain heats of micelle formation. The physical reason why the van't Hoff relation fails hwe is perfectly plain. If we measure a cmc a t two different temperatures, and use eq 2 to calculate the two free-energy changes, those free-energy changes refer to two different chemical reactions, A1 A;hl'(~t,f r = A N ( T+~1 in one case, and A1 AN(T~,= NIT^, + 1 in the other. These two reactions are only the same if &' is temperature independent. The question remaining is whether the last term of eq 7 is numerically very significant. Sufficient information does not exist to decide the question unequivocally, but we can make the following rough computation as an enlightening estimate. Although no good theoretical expression exists for the total standard Gibbs free-energy change of reaction eq 1, the electrical part of the standard free-energy change for an ionic micelle in the absence of added salt is4
+
+
wherein NAis Avogadro's number, e the protonic charge, t the solvent dielectric constant, and b the micellar radius. Assuming constant radius, the last term of eq 7 thus becomes, in magnitude (NATe2/tb)(aN/aT),. Using T =
Alfred Holtzer'
ma^^^^^ F. Holtzer
Received March 8. 1974
Hydrogen Bonding of Phenol in Carbon Tetrachloride. The Use of Activity Data to Evaluate Association Models Publication costs assisted by the National Science Foundarior
Szr: In spite of numerous studies which have been made of the self-association of phenol, there is still considerable disagreement regarding the nature of molecular aggregates of phenol which exist in organic so1vents.l In the case of the volatile aliphatic alcohols methanol and tert-butyl alcohol, a combination of infrared and nmr spectral data and vapor pressure results provides evidence that trimers and larger polymers are present in solutions in CC14 and hydrocarbon solvents, even a t concentrations well below unit m ~ l a r i t y,4. ~On the other hand, recent measurements of the physical properties of solutions of phenol in cC14 and cyclohexane a t concentrations up to or exceeding 1 M have been interpreted in terms of association models limited to dimerization and/or trimerization l95-8 In the present communication we provide thermodynamic evidence which can be used to discriminate among various classes of association models purported to represent the state of phenol aggregation in organic solvents. The Journal of Physical Chemistry. Vol. 78. No. 14. 1974
