1396
NOTES
using 408,8 15gj8 and 1109 atm-' cm-l as decadic extinction coefficients (measured at 25') for cyclohexane, benzene, and N20, respectively. The solid line in Figure 1 indicates the behavior expected of cp(H2) in the absence of any kind of interaction between the mixture components. Values of 4(H2) for c-C&t12-C6H6 mixtures fall below the straight line expected for no interaction between the components. The broken curve in Figure 1 is based on the assumption that energy transfer from cd6H12* to C6H6 is solely responsible for the deviac tion from linearity. The curve was calculated by use of T = 4.7 x sec in eq 1
4 = 4OFc/(l
+ 27)
(1)
in which r$o represents the quantum yield for pure cyclohexane (Fc = 1) and 2 the frequency of collision of c-C6H12*with the energy acceptor,1° in this case C6H6. The value 7 = 4.7 X 10-l' sec is necessarily an upper limit because (1) the collision diameters are probably a lower limit for excitation-transfer diameters" and (2) H-atom scavenging by CsH6, in competition with abstraction from c-c~H12, is expected to contribute to deviation of 4(H2) from linear it^.^ Indeed, with the assumption that H atoms contribute -20% to 4O((H2)I2 and with a reasonable estimate of the specific rate of scavenging relative to that of abstraction at 95') a curve can be calculated (for no energy transfer) that fits the data about as well as the broken curve in Figure 1. As noted in the earlier complications associated with H-atom reactions should be absent in the c-C&l12-N20 mixtures because all H are expected to react with c-ci"~ over the range of mixture compositions used. The results presented in Figure 1 for such mixtures at 750 Torr and 95" show no evidence of energy transfer from c - C ~ H ~to~the * potential acceptor N20.2 An upper limit for 7 can be estimated with the reasonable assumption that a deviation from linearity corresponding to 4/cp°Fc < 0.9 at Fc = 0.4 should have been manifest (ie., not obscured by experimental errors) in a plot such as that of Figure 1. Thus, from eq 1 with 4/4OFc > 0.9 and 2 = 5.1 X lo9 sec-' at FC = 0.4, T = 2 X lo-" sec is obtained as an upper limit. We conclude from the results shown in Figure 1 that absorption of a 1470 - A photon by cyclohexane in the gas phase produces an excited state with a lifetime that is certainly less than 4.7 x lo-" sec and probably less than 2 X lo-" sec. It is clear from present results that Hz formation cannot occur from the same excited state of cyclohexane in both the gas and liquid photolyses at 1470 8. For example, if the results in Figure 1 are attributable to energy transfer alone, then the excited state involved must transfer energy more efficiently to benzene than to N2O; however, such behavior is contrary to that observed in the liquid phase.2 Furthermore, even for T = 4.7 X lo-" sec, T h e Journal of Physical Chemistry
the results of Holroyd and coworkers2 require specific rates of transfer from c-C6&* in the liquid to CBHG and N2O of 6.8 X 1OO ' M-' sec-l and 14.5 X 1Olo M-' sec-l, respectively. The simplest interpretation of present results is that (1) Hz formation in the gas phase occurs from that state of cyclohexane produced by absorption of a 14708 photon and (2) Hz formation in the liquid phase occurs from a lower, longer-lived state of excitation. Such an interpretation is consistent with recent conclusions of Hirayama and Lipskyla from their observations on the fluorescence of saturated hydrocarbons. Fluorescence was observed from alkanes, including cyclohexane, when excited as neat liquids at wavelengths in the range 1470-1720 A. With excitation in the liquid at 1470 8, sensitization of benzene fluorescence was shown to accompany quenching of cyclohexane fluorescence. However, no fluorescence was observed on excitation of alkane vapors at 1470 A. Excitatitn of the vapor at wavelengths longer than -1600 A produced an emission which, except for a slight blue shift, was identical with the liquid fluorescence. The authors conclude that both liquid and vapor emissions are of molecular origin with the upper state being strongly predissociated in the vapor above -7.7 eV . (8) Values for cyclohexane and benzepe were obtained by S. Lipsky with a high-pressure Ar lamp at 1467 A and were privately communicated. (9) M.Zelikoff, K.Watanabe, and E. C. Y. Inn, J . Chem. Phys., 21, 1643 (1953). (10) Collision frequencies were calculated using 6.1, 5.3, and 3.9 k as the collision diameters of c-CeH~z,C&, and NzO, respectively; cf., J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids," John Wiley & Sons, Inc., New York, N. Y., 1954, p 1111. (11) T.Watanabe, Advances in Chemistry Series No. 82, American Chemical Society, Washington, D. C., 1968, p 176. (12) Hentz and Rzad (ref 4) have made a rough estimate of -10% for the H-atom contribution. (13) F. Hirayama and S. Lipsky, J . Chem. Phys., 51,3616 (1969).
Nuclear Magnetic Resonance Study of Solvent Effects on Hydrogen Bonding in Methanol1
by William B. Dixon2 Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received October 26,1989)
For the past decade or more, nmr techniques have been very fruitfully applied to the study of hydrogenbonded systems in solution.3~4 This success is due to (1) Based on work performed under the auspices of the U. S. Atomic Energy Commission. (2) Resident Research Associate from Wheaton College, Wheaton, Ill. Department of Chemistry, State University College, Oneonta, N.Y. 13820.
1397
NOTES the large chemical shifts experienced by protons when they become involved in hydrogen bonds and to the accuracy with which these shifts may be measured. The method has been applied to the determination of such thermodynamic quantities as equilibrium constants for hydrogen bond formation and hydrogen bond energies as well as to the investigation of the structures of hydrogen-bonded species. I n much of this work solvent effects have been largely ignored, and more recently it has become evident that some of the so-called inert solvents may interact appreciably with the systems under in~estigation,~ thus casting doubt on some of the quantitative conclusions that have been reached. Also, it is quite probable that infrared studies of hydrogen bonding in solution have been similarly influenced. The present work is a study of the effects that several different solvents have on the extent of self-associatidn in methanol through hydrogen bonding. Experimental Section Spectra were recorded with a Varian HA-60 60-Me spectrometer and frequency measurements made by the side-band technique. For some of the weaker lines signal-to-noise ratios were improved by accumulating repeated scans using a Varian C-1024 time averaging computer. All spectra were recorded at 25 f 0.5’. Reagent grade solvents were dried over Linde molecular sieve pellets and used without further purification. All solutions were prepared volumetrically and in most cases contained 0.5% by volume cyclopentane as an internal reference. The hydroxyl proton peak of methanol was often split into a quartet through spin-spin interaction with the methyl group, and it was sometimes convenient to collapse and sharpen this peak by adding 0.5% by volume concentrated hydrochloric acid solution or dry HC1 gas to the otherwise pure methanol used in preparing the solutions. Observations in a number of instances both with and without the added HC1 showed no significant difference in the chemical shift. Results and Discussion The chemical shifts of the hydroxyl proton of methanol at 25’ as a function of concentration in cyclohexane, cyclopentane, benzene, carbon tetrachloride, and acetonitrile are shown in Figure 1. I n all cases the shifts are given relative to cyclopentane, which was used as the internal reference. However, in the cyclohexane solution the solvent itself was used as the internal reference and a correction of +3.5 cps made in the measured shifts to account for the shift between cyclohexane and cyclopentane. The use of an internal reference eliminates the influence of solvent bulk susceptibility on the observed shifts and, in principle, virtually cancels out other nonspecific solvent eff ects,6 in particular, that due to the van der Waals interaction between the solute and solvent and that due to the anisotropy of the magnetic susceptibility of the solvent molecules.
1001
I
1
0
4
8
I
I
I
I
I
12 16 20 24 28 Mole Fraction Methanol ( x I 0 3 )
I
32
Figure 1. Chemical shift of the methanol hydroxyl proton (relative to cyclopentane as internal reference) as i function of concentration at 25”. Solvents: 0, cyclohexane; A, cyclopentane; W, benzene; +, carbon tetrachloride; V, acetonitrile. The curve drawn through the cyclohexane points is a calculated one while the others are experimental curves.
For the nonpolar solvents, cyclohexane, cyclopentane, benzene, and carbon tetrachloride, the reaction field effects, too, should be small and not contribute significantly t o the shift. Thus, in these four solvents at least, differences in the hydroxyl shift should be due almost entirely to specific interactions of the solutesolvent or solute-solute type or both. For the four nonpolar solvents the dilution curves show the expected downfield shift of the hydroxyl proton resonance with increasing concentration, as more of the protons become involved in hydrogen bonds between solute molecules. This tendency toward selfassociation would depend mainly on the dielectric constant of the solvent if other factors were the same, since hydrogen bonding is largely an electrostatic effect. However, the marked variation ip the slopes of the dilution curves, in spite of the similarity in solvent dielectric constants, indicates an inhibiting effect by (3) G. C. Pimentel and A. L. McClellan, “The Hydrogen Bond,” W. H. Freeman and Co., San Francisco, Calif., 1960. (4) P. Laszlo in “Progress in Nuclear Magnetic Resonance Spectroscopy,” Vol. 3, J. W. Emsley, J. Feeney, and L.H. Sutcliffe, Ed., Pergamon Press, Oxford, 1967,pp 279-310. (6) A. D.Buckingham, T. Sohaefer, and W. G. Schneider, J. Chem. Phys., 32,1227 (1960).
Volume 74,Number 6 Maroh 19, 1970
NOTES
1398
benzene and carbon tetrachloride on self-association of the solute. These two solvents are evidently involved in solute-solvent interactions which are serious enough to discourage their use in any quantitative study of self-association by hy drogen-bonding solutes. The behavior of methanol in the two relatively inert solvents, cyclohexane, and cyclopentane, deserves particular attention. The only previously reported nmr investigation6 of an alcohol in an aliphatic hydrocarbon solvent did not include dilute solutions, and only fairly recently have any such infrared studies been made.'38 Because of the rapid exchange that takes place between the monomer and the various possible dimeric and polymeric species of methanol in solution, the hydroxyl protons show only a single resonance whose shift is the weighted average of the shifts attributed to the individual species. Thesame observation is true of the methyl proton resonance as well. Infrared spectra of alcohols, on the other hand, show the presence of individual species but their interpretation is not completely straightforward, and the estimation of concentrations from band intensities is hazardous. Therefore, in the present work, no special restrictions from this source were placed on the choice of a model for the structure of methanol in solution. Of the various simple models, monomer-dimer, monomer-trimer, and monomer-tetramer, normally considered for the structure of hydroxylic compounds in solution, the monomer-tetramer model gave by far the best fit to the hydroxyl proton shift data for methanol in cyclohexane. The excellent agreement is shown in Figure 1, where the calculated curve for this model is drawn through the experimental points for methanol in cyclohexane. The experimental points for the solvent cyclopentane lie very close to the same theoretical curve. I n carrying out the calculations from which this curve was derived, the observed shift was assumed to be given by bobad
= (nM/nO)aM
f
~(%T/~OI~T
where nois the total number of moles of methanol added to the solution and n~ and n~ are the number of moles of monomer and tetramer, respectively, present a t equilibrium; 6M and 8~ are the shifts attributed to the monomer and tetramer alone. Substituting nM
= no
-4
n ~
(1)
into the above equation yields $bed
=
6M
+
-
~ ( ~ T / ~ o ) ( J T 6M)
= 6M
+
and the corresponding equilibrium constant is given by
x T/XM
(3) where X Mand XTare the mole fractions of monomer and tetramer in the solution. This can be further expressed , ne, the number of moles of in terms of no, n ~ and solvent, as K4
=
+
K4 = (n~/n~)[(ns/no)1
3(n~/no)1 3 ~ 1- 4(n~/no)14
For any assumed value of Kq, ~ T / % omay be calculated for each solution from its known ns/no value. This computation was readily accomplished by an iterative procedure using a Wang 360 programmable desk calculator. After elimination of 6~ from eq 2, yielding bobad2
- bobsdl
= 4[(nT/'%)2
- (nT/no)l].hT
pairs of n ~ / l tvalues ~ together with the corresponding values of bobad were used t o calculate AT. The best value of Kd was the one which resulted in the most nearly equal values of AT obtained in this way for various pairs of experimental points. The value of K 4 so obtained at 25' and the corresponding values of the other parameters are
*
K4 = 3 . 1 ( 0.2) X 105 (mole fraction units) AT = -305 3 CPS GM = 73 cps
*
The hydrogen bond shift for the tetramer, AT, is seen to lie in the vicinity of the hydroxyl proton shift, -277 cps, for pure methanol relative t o that of the monomer. The latter value was found by subtracting 8~ from the hydroxyl shift, -203.5 cps, of pure methanol relative to cyclopentane as internal reference, which was measured in this work. The rough agreement tends to support the monomer-tetramer model as opposed t o the monomer-dimer and monomer-trimer models, for which unrealistically large hydrogen bond shifts were calculated. The "best" value for the hydrogen bond shift as calculated from the monomer-dimer model, for example, was in the neighborhood of - 1000 cps. The present value of K 4 may be compared with that of Saunders and Hyne,g who obtained a result of 3.1 X lo4 (after conversion from units of liter3 per mol3 to mole fraction) based on a monomer-tetramer model for methanol in carbon tetrachloride. The tenfold difference between the two values may be attributed to the inhibiting effect of the solute-solvent interaction upon hydrogen bonding between methanol molecules in carbon tetrachloride.
~ ( ~ T / ~ o )(2) AT
where AT is the hydrogen bond shift between monomer and tetramer alone. The chemical equilibrium is expressed by the equation 4CHsOH The Journal of Physical Chemistry
(CH3OH)d
(6) A. B.Littlewood and F. W. Willmot, Trans. Faraday Soc., 62, 3287 (1966). (7) H . C.Van Ness, J . Van Winkle, H . H . Richtol, and H. B. Hollinger, J.Phys. Chem., 71,1483 (1967). (8) A.N . Fletcher and C. A . Heller, ibid., 71,3742(1967). (9) M.Saunders and J. B.Hyne, J. Chem. Physu2Q, 1319 (1968).
COMMUNICATIONS TO THE EDITOR
It should be emphasized that even though the simple monomer-tetramer model provides an excellent fit to the experimental data, the existence of significant though smaller concentrations of dimer or trimer is by no means ruled out. It is possible, for example, t o include a small amount of dimer contribution in a predominantly monomer-tetramer model by making appropriate choices for the monomer-dimer equilibrium constant and the dimer hydrogen bond shift and still obtain a reasonably good fit to the data. Such a modification of the model is in fact necessary in order to secure consistency with infrared results, which provide strong evidence for the presence of dimers as well as polymers in dilute solutions of methanol and other aliphatic alc0hols.~~7J' Because of the presence of dimers, moreover, the dilution curve for methanol would not be expected to have a slope of zero a t infinite dilution like that of the theoretical curve in Figure 1. It should have a more negative slope at the very lowest concentrations, which were not accessible for study, and intersect the 6 axis at a point somewhat farther upfield. Thus, the value of tiu, the monomer shift for
1399
methanol, might be more correctly estimated as 80 5cps. It is interesting to note the large percentage of methanol molecules present as tetramer, even at the low concentrations studied. At a methanol mole fraction of 0.02, for example, the model indicates that 5201, of the methanol exists as tetramer. As seen from Figure 1, the infinite dilution shift for methanol in carbon tetrachloride lies downfield from the shift in cyclohexane. This observation is consistent with a hydrogen bonding type of interaction between methanol and carbon tetrachloride. The upfield infinite dilution shift for methanol in benzene may be interpreted in terms of the type of model proposed by Schneider,1° involving a directed solute-solvent interaction and the magnetic anisotropy of the benzene ring.
Acknowledgment. The author expresses his appreciation to Dr. J. C. Hindman for his interest and suggestions during the course of this work. (10) W. G. Schneider, J.Pkys. Chem., 66,2653 (1962).
COMMUNICATIONS T O THE E D I T O R
Multiple Equilibria in Donor-Acceptor Complexing Studied by Ultracentrifugation
molecular weight uw for a single ideal species a t equilibrium a t the radius r is given by7
Sir: There are serious difficulties in attempting t o measure unambiguously the formation and properties of donor-acceptor (D-A) complexes in s ~ l u t i o n . ~ - ~where C = concentration of the solute species a t radius r, M = molecular weight (g/mol) of the solute, V = The influence of s ~ l v a t i o nand ~ ~component ~ activities' partial specific volume (cm/g) of the solute, p = soluhas been discussed. Recently the possible presence of tion density (g/cm)3, w = angular velocity (radians/ significant contributions from 2 : l and 1:2 D plus A complexes, in addition to the commonly assumed 1:1 see), R = gas constant, T = abs temperature (OK). stoichiometry, has been considered as a potential source (1) R. L. Scott, Rec. Trav. Chim. Pays-Bas, 71, 1104 (1952); 75, of error in spectral and nmr determination^.^-^ How787 (1956). ever, no direct evidence for such higher aggregates has (2) P.J. Trotter and M. W. Hanna, J. Amer. Chem. SOC., 88, 3724 (1966),and references therein. been offered as yet. (3) S. Carter, J. Chem. Soc., A, 404 (1968). I n order to examine states of aggregation in D-A (4) D.A. Deranleau, J . Amer. Chem. Soo., 91, 4060 (1969). solutions we have employed equilibrium ultracentri@ - S aD.Ross and M. M. Labes, ibid., 79, 76 (1957). fugation?with the optical absorption scanner.8 Charge(6) G.D.Johnson and R. E. Bowen, ibid., 87, 1665 (1965). transfer (CT) absorption can be measured as a function (7) (a) J. W. Williams, K. E. Van Holde, R. L. Baldwin, and H. of radius in the spinning sample (36,000 to 56,000 rpm) Fujita, Chem. Rev., 5 8 , 715 (1958); (b) K.E.Van Holde and R. L. Baldwin, J. Phys. Chem., 62, 734 (1958); (c) D.A. Yphantis, Bioto obtain information on D plus A aggregates by equichemistry, 3 , 297 (1964). librium sedimentation analyses. The effective reduced (8) H. K. Schachman and 5. J. Edelstein, ibid., 5, 2681 (1966). Volume 74, Number 6 March 19, 1970
