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
Communicationsto the Editor
1444
O't
i
***
I
I
--A 1 0
02
0.6
0.4 PHENOL
0.8
1.0
YOLA1IIV
Figure 1. Phenol monomer concentration as a function of total phenol concentration: 13C curve calculated by using K2 = 0.57 M - l at 27" (C.901 r r - ' from Table I l l , ref 5); Cal. curve calculated by using K3 = 5.6 M-' at 25" from calorimetric data of ref 1; 0 phenol nionomer Concentration at 29.1" from absorbance data of ref 2; X phenol monomer inferred from activity data (this work) using limiting relationship CM(phenoli = a(pheno1)/2.87; 0 phenol nionomer concentration at 20.7 from absorbance data of ref 2. TABLE I: Activity of Phenol in CCL at Several Concentrations at 21.0: Ca
a*
C
a
1 .os0 0.934 0.867 0.743 0.650 0.520 0.462
0.637 0.626 0.602 0.578 0.552 0,526 0.506
0.390 0.297 0.240 0.173 0.095 0.050
0.482 0.435 0.403 0.343 0.227
0.121
a Molar concentration of phenol in CCL. Ratio of vapor concentration of phenol above phenol-CCI solutions (determined spectrally in the vicinity of 2704 nm) Lo vapor concentration above solid phenol a t 21.0'.
Vapor pressure methods have been shown to be uniquely powerful in evaluating alternative models for the association of alcohol^.^^^ Unfortunately, phenol is not volatile enough to permit use of conventional vapor pressure methods in this connection. However, the large absorption of phenol vapor in the ultraviolet region makes it possible to determine activities of phenol from absorbance measurements on phenol vapor above organic solutions of the compound; reliable results can be obtained even at partial pressures of phenol on the order of 100 p or less. Some initial results are reported here for solutions of phenol in CC14. Table I lists values of phenol activity (expressed as a ratio of the partial pressure of phenol to the vapor pressure of pure solid phenol) in CC14 solutions at 21.0'. Values of phenol monomer concentration derived from our measurementsg are plotted in Figure 1 along with the concentration of phenol monomer inferred from several types of data for phenol-CC14 solutions in the temperature range 20-29". The present activity results are in excellent agreement with the near-infrared results of Whetsel and Lady.2 Both our results and those of Whetsel and Lady are also in reasonable agreement with values derived from partition-water solubility datalo and with phenol activities derived from total vapor pressure measurements on phenol-CCl4 solutions by use of the Gibbs-Duhem equation.ll However, our results cannot be reconciled The Journal of Physicai Chemisfry, Voi. 78. No. 14. 7974
with either the interpretation of Nakashima, et u L . , ~ of 13C nmr measurements on phenol-CC14 solutions or with the 1-3 interpretation of calorimetric measurements1 at phenol concentrations exceeding about 0.15 M . Both the 1-2 and 1-3 interpretations of these latter sets of data lead to calculated phenol monomer concentrations which increase much too rapidly with total phenol concentration to be consistent with activity measurements. We also note that the numerous pmr studies using models which limit phenol association only to trimer ( e . g . , ref 7 and 8) would produce curves similar to that for the calorimetric curve in Figure 1. In view of the relation between thermodynamic activity values and the concentration of phenol monomer in solution it is essential that any association model for phenol solutions be consistent with reliable activity results. This restriction arises from the basic assumption (made in all spectral and classical studies of phenol association) that Henry's law is obeyed by each of the individual phenol species. Under this assumption, values of the concentration of phenol monomer obtained from various association models should vary linearly with the thermodynamic activity. Relatively few types of physical measurements used to date on hydrogen-bonding systems can provide a directly observable quantity related to the activity of the monomeric species. Two methods which have been used are measurements of absorbance a t the monomer hydroxyl stretching frequency12 and vapor pressure measurements on alcohol-hexadecane solution^.^.^ The results of our work provide a direct measurement of phenol activity in anhydrous phenol-CCl4 solutions in the concentration 1.0 M . At phenol pressures not exceeding about range 0 300 p it is highly improbable that significant quantities of associated phenol are present in the vapor and thus we expect the concentration of phenol vapor over phenolCC14 solutions to be directly proportional to the monomer concentration of dissolved phenol. All association models which have been used to describe phenol polymerization must be reducible, directly or indirectly, to monomer us. total concentration curves. It is obvious that a common curve (at fixed temperature and solvent) should be obtained from reliable physical data of all types if a realistic model has been applied to fit the data. The marked discrepancies among the curves in Figure 1 clearly indicate that not all of the interpretations represented are meaningful. The directness of our measurements and the close agreement of our data with those of Whetsel and Lady2 lead us to conclude that the concentrations of phenol monomer derived from our measurements and those of Whetsel and Lady are upper limiting values. Phenol association models which are limited to dimerizations and/or trimerizationl97 8 can be rejected as being physically unrealistic. More generally, we think that no single associated species model ( e g , monomer-trimer or monomer-tetramer) is useful except in quite restricted ranges of phenol concentration. A careful numerical analysis of the infrared data of Whetsel and Lady and consideration of our activity results convinces us that no model yet proposed for representing the association of phenol in CCl4 is as satisfactory as the monomer-trimer-sequential polymer model discussed p r e v i ~ u s l y . ~ J ~
-
Acknowledgment. We wish to express our appreciation for support of this work by the National Science Foundation through Grants No. GP-33519X and 6P-43307.
Communicationsto the Editor
1445
References and Notes (1) E. N. Woolley, J G . Travers, 5 . P. Erno, and L. G . Hepler, J. Phys. Chem., 75,3591 (1971). (2) K. 5 . Whetsel and J. H. Lady, "Spectrometry of Fuels," Plenum Press, New York, N. Y.,1970, pp 259-279. (3) E. E. Tucker, S. e. Farnham, and S. D. Christian, J. Phys. Chem., 73,3820 (1969). 14) E. E.Tucker and E. D. Becker. J. Phys. Chem., 77, 1783 (1973) (5) T. T. Nakashima, B. D. Traficante. and G. E. Maciel, J. Phys. Chem., 78, 124 (1974). (6) E. M. Woolleyand I.., G. Hepler, J. Phys. Chem.. 76, 3059 (1972). (7) A. J. Dale and T. Gramstad, Spectrochim. Acta, Sect. A , 28, 639 (1972). (8) Y. S. Bogachev, L K . Vasianian, N. N. Shapetko, and T. L. Alexeeva, Org. Magn. Resonance, 4, 453 (1972). (9) Monomer concentrations were derived from our activities from the slope of a plot of activity vs. monomer concentration from Whetsel and Lady's data at 20.7". The reason for this procedure is that we have few low concentration data and thus considerabie error would be involved in determining the intercept of a plot of activity/concentration vs. phenol concentration. Plots of our activity vs. monomer concentrations derived from 13C and calorimetric measurements are markedly nonlinear. (10) J. R, Johnson, S. D. Christian, and t i E. Affsprung, J. Chem. Soc., 1 (1965). J. R . Johnson, Ph.0. Dissertatlon. University of Oklahoma, 1966. (11) J Chevalley, BuliSoc. Chim. Fr., 510 (1961). (12) It is probable, as has been suggested.'3 that there is at least a small degree of overlap at the monomer frequency from end hydroxyl groups of a polymer(s). Consequently, infrared results might be expected to lead to values of monomer concentration which are somewhat too large, particularly at the higher phenol concentrations.* In any case, monomer concentrations derived from infrared data on phenol soititions should represent upper limiting values; other spectra! and thermodynamic results should be expected to yield monomer concentrations no larger than these. (13) F. A. Smith and E. C. Creitz, J. Res. Naf. Bur, Sfand., 46, 145 (1951). (14) E. E. Tucker and E. Lippert, "High Resolution NMR Studies of Hydrogen Bonding." in Recent Advances in Hydrogen Bonding. P. Schuster, G. Zundel and C. Sandorfy, Ed., North-Holland Publishing Co , Amsterdam, in press.
Edwin E. Tucker" Sherril D. Christian Lung-Nan Lin
D e p a r t m e n t of Chemistry O k l a h o m a University Norman, O k l a h o m a 73069 Received March I I , 1974
per, "A Study of the Formation itric Oxide and the Interaction
Parkes and S ~ g d e n using ,~ a drift tube, measured both the attachment rate in NO e + 2 N 0 --+ NO- + NO (6) and its' reverse and from detailed balancing they deduce EA(N0) = 0.028 eV, in agreement with the Siegel, et al., value. The detachment rate constant of Parkes and Sugden agreed closely with that of McFarland, e t al , using a completely different experimental technique. Additionally, using endothermic reaction thresholds, Hughes, et aL.,5 have recently shown that EA(N0) < 0.1 eV, Berkowitz, et a1.,6 t h a t ' E A ( N 0 ) < 0.5 eV, and Lecmann and 0. It has been known for Herschbach7 that EA(N0) some time from the demonstrated exothermicity of the charge-transfer reaction
-
+
NO-
+
02 --+ 0 2 -
NO
(1) that EA(NO) < EA(02) = 0.46 eV.8 The few earlier experiments which gave large NO electron affinities have now been fully discredited. Thus there is no doubt that reaction 7 is in fact very endothermic and cannot occur a t thermal energies. Moreover, the reaction of 1%- with NO has been studied directly and found not to charge transfer but rather to associatively detach
-
H- + NO HNO + e + 1.4 eV (2) with a rate constant hz = 4.6 x ~ m ~ / s eThe c . ~concluding statement in ref 1 that "NO reacts with H- to produce H atoms and is thus a source of free radicals" is therefore erroneous and should not be propagated in radiation chemistry. The second point we make concerns the manner of formation of NO-. Gupta and Melton propose the termolecular collision (6). Although not noted by them this rate constant has been measured by a number of workers ,as discussed in ref 3), the most reliable measurement b&,g that of Parkes and Sugden* who obtained a value k6 = 8 f 2 x cm6/sec at 300°K. Very little N O - could have been made this way in the 360°K ion source of Gupta and Melton because of the rapid collisional detachment of NO- by NO. The maximum possible NO- production by attachment would be the equilibrium value
- from Water," by S. K. Gupta
and C. E. Melton Pubiication costs assisted b y the U S Department of Commerce Nationai Oceanic and Atmospheric Administration
Sv: We wish to point out that a recent paper by Gupta and Meltonl con*a i m very serious errors concerning the negative ion NO- and its chemistry. The first point concerns the reaction (with the original equation numbering)
+
(7 1 which Gupta and Melton find to have the extremely large rate constant 4 x 10F9 cm3 molecule-i sec-l and which they therefore assume to be exothermic, from which they deduce that the electron affinity of NO exceeds that of atomic hydrogen which is 0.75 eV. The electron affinity of NO Is now very well established by several methods to be less than 0.1 eV. The most precise determination is that of Siegel, et a l , 2 in which a value E A ( N 0 ) = 0.024 0.010 or -0.005 eV was determined by photodetachment electron spectroscopy. McFarland, et al , studied the collisional detachment of NO- in eight gases in a temperature variable flowing afterglow system. The detachment rate in CO established that E A ( N 0 ) < 0.046 eV and for each of the eight gases it was established that EA(N0) < 0.11 eV. 14- -t NO
4
NO-
H
+
At 360"K, the equilibrium constant is 7.7 x cm3 and a t Torr NO pressure that maximum NO- density would be 2.6 X 10-5[e] where [e] refers to themal electrons. Presumably the energetic beam electrons would undergo three-body attachment to a much Less extent. It seems likely that the NO- is produced in the wellknown reaction 0-
+
NzO
3
NO-
+
NO
(5)
which has a rate constant of 2.5 x cm3/sec at 300"K.I0 Gupta and Melton's statement that they had purified the NO to impurity levels no greater than a few ppm is not convincing. Our experience is that the NzO cannot be removed from NO to this extent by the distillation described and that substantially improved purification techniques only remove N20 to about the part per thousand level.li We are aware that others have experienced the same difficulty. The third point we raise concerns Gupta and Melton's reaction 0-
+
2N0
for which they deduce
k4
--+
NO
= 7.6
x
+
NOz-
(4 1
cm6/sec. This is
The Journal of Physical Chemistry, Voi. 78. No 14 1974
