1121
Communications to the Editor
we find Cpo(H+)still large and positive. This situation implies that Cpo of common cations and anions are vastly different; for example, Cpo of alkali and halide ions would be of opposite signs. From the preliminary results, the approach followed here suffers no obvious inconsistency and appears promising in supplying independent estimates of ionic partial molar volumes and heat capacities. The hypothesis is being further investigated with other analogous pairs of ionic and neutral compounds, with particular attention to two limiting aspects. In a first part, we should elucidate how the residual charge on the -ROH substituent of the cation will affect the derived ionic values. On the other hand, since it is known that V” of quaternary ions depends on the nature of the central atoms (differences in bond len@hs13),we should establish the dependence of the ionic scales on this parameter.
Acknowledgment. The authors gratefully acknowledge financial assistance from the National Research Council of Canada through an operation grant and a scholarship to one of us (J.C.M.). References and Notes (1) D. R. Rosseinsky, Cbem. Rev., 65, 467 (1965). (2) J. E. Desnoyers and C. Jollcoeur in “Modern Aspects of Electrochemistry”, B. E. Conway and J. O’M. Bockris, Ed., Plenum Press, New York, N.Y., 1969, Chapter 1. (3) C. M. Criss and J. W. Cobble, J. Am. Chem. Soc., 86, 5390 (1964). (4) R. M. Noyes, J . Am. Cbem. Soc., 86, 941 (1964). (5) B. E. Conway, R. E. Verrall, and J. E. Desnoyers, Trans. Faraday Soc., 62, 2738 (1966). (6) C. Jolicoeur, P. R. Philip, G. Perron, P. A. Leduc, and J. E. Desnoyers, Can. J. Cbem., 50, 3167 (1972). (7) C. Shun, I. Worsley, and C. M. Criss, private communication. (8) C. Jolicoeur and G . Lacroix, Can. J. Cbem., 54, 624 (1976). (9) P. Picker, E. Tremblay, and C. Jolicoeur, J . Solution Cbem., 3, 377 (1974). (10) P. Picker, P. A. Leduc, P. R. Philip, and J. E. Desnoyers, J. Cbem. Tbermodyn.,3 , 631 (1971). (1 1) Reference 2, p 26. (12) J. L. Fortier, P. A. Leduc, and J. E. Desnoyers, J. Solution Cbem., 3, 323 (1974). (13) F. J. Millero, J. Pbys. Cbem., 75, 280 (1971). Department of Chemistry Universitg de Sherbrooke Sherbrooke, Quebec J 1K 2R I, Canada
Carmel Jollcoeur’ Jean-Claude Mercier
Received December 20, 1976
Termolecular Complexes of Trinitrobenrene and 5-Methoxyindole
Sir: It has been suggested that some of the observed anomalies concerning the calculated values of association constants for the formation of 1:l complexes between .rr electron donors (D) and acceptors (A) are due to the presence in solution of termolecular complexes as well as AD2 is the the more familiar bimolecular c~mplexes.l-~ termolecular complex reported since in the solutions usually studied the total concentration of donor ([D],) is greater than the total concentration of acceptor ([A],). In this paper we shall describe a study of the interaction of 5-methoxyindole with trinitrobenzene (TNB) in 1,2-dichloroethane that was performed using a variety of ratios of [A], to [D], in order to be able to observe different species of complexes. Thus when [D], [A], AD should be the only complex present in solution if the solutions are dilute and the association constants for formation of the termolecular complexes are less than that for the bimolecular complex, while if the ratio is [A], >> [D], AD and
A2D will be the predominant species and if [Dlo >> [A], the major species present will be AD and AD2. The equations for the formation of these complexes are A + D=AD AD + D = AD, AD + A = A,D
(excess D) (excess A)
If this model is correct and proper account is taken of the termolecular species, experimental values of the association constants determined for AD ( K A D ) should be the same when separately evaluated for each of the different ranges of concentration since AD is the complex species common to all the solutions. The TNB 5-methoxyindole complex was chosen for this work because of a study on it and other substituted indole TNB complexes by Sung and Parker in which they assumed that only AD was presents5 The values of K m that they gave differ considerably when results obtained for [D], >> [A], are compared with those obtained for [A], >> [D],. Further indication that these compounds may form termolecular complexes can also be seen from the almost 100% variation in K A D values obtained using the NMR spectral lines of different protons in the same complex. A recent review by Foster has discussed the methods used to obtain the association constant from either the optical density (OD) at the peak of the charge transfer band or the upfield shift of a NMR line in one component caused by the other component (A).’ In solutions where the ratio [D],/[A], = n is close to one and [AD] > [D], or [D], >> [A], and only 1:l complexes are assumed to be present the scatchard equation (eq 2) can be used to
OD
OD - -KAD [AI o[DIo [A10 + K A D ~ A Dfor [Dl0 >> [A10 OD OD -KAD [AI OLD1 0 [Dl0 + K A D ~ A Dfor [ A I , > > [Dlo
(2a)
(2b 1 evaluate KADand CAD. Both eq 2a and 2b are linear equations, so K A D and CAD can be determined from the least-squares values of the slopes and intercepts of plots of OD/[Al~[Dl~ vs. OD/[A], or OD/[D],. When the formation of termolecular complexes (either AD2 or A2D) is taken into account eq 3 is applicable. Kmzand K A a are
-
the formation constants for the reaction of AD with excess D or excess A. These last equations unlike eq 2a and 2b The Journal of Physical Chemistry, Vu/. 81, No. 1 1 , 1977
1122
Communications to the Editor
TABLE 1: Association Constants, A b s o r p t i o n Coefficients, a n d Chemical Shifts for 5 - M e t h o x y i n d o l e - T N B Complexes in CH,ClCH,Cl a t 33 ’C
Concn ratio
[AI,- [Dl0 Dl,> [AI, [AI,> [Dlo [DI,> [A10 [AI,> [Dl, [D],> [A], [D],> [A],
Equation used M e t h o d
1 2 2 3
3 2 3
uv uv uv uv uv NMR NMR
K A q (kg of solution/mol)
4.8 r 0.8 1.62 f 0.06 2.02?: 0.13 4.3 * 0.6 4.5 r 0.6 1.43 i. 0.04 4.6f 0.6
€AD
910 r 180 2040 f 20 1580 r 40 800f 100 6 7 0 r 100 A A D = 1.20r 0.02 ppm A A D = 0.4 k 0.1 ppm
are not linear. In order to obtain values of the four parameters a least-squares procedure adapted from Wolberg‘ was used. For NMR data eq 2 and 3 can be used with A replacing OD/[A], when [Dlo >> [A], or OD/[D], when [A], >> [D]@The differences between the chemical shift of a given proton in the complexes and the same proton or AAD,) replace the in the free component (AAD, AA~D, appropriate values of 6 . The charge transfer peak of the complex is at 415 nm and it does not appear to vary in wavelength as the ratio of [A], to [D], changes over a very wide range. Therefore all the absorption readings were taken at this wavelength. Since the curvature predicted by eq 3 is not very pronounced, it is necessary to have values of OD for many solutions that cover a wide range of concentrations. Thus 16 solutions with a ratio of [A], to [D], ranging from 8 to 180 were used for one set of data while 23 solutions with a ratio of [D], to [A], from 4.5 to 150 were used for the other set. At first glance it appears that the data fits eq 2a or 2b well, with only a small curvature in the linear plots. The regression coefficients for linear plots using all the data points are 0.955 for [D], >> [A], and 0.967 for [A], >> [D]@ The values of KAD and CAD obtained from the two plots (Table I, lines 2 and 3) do not agree with each other. More importantly, neither sets of K m and tm values agree with the values obtained using eq 1on data from solutions with [A], [D], (Table I, line 1). When the data for the solutions with an excess of one component are treated by eq 3a or 3b the parameters obtained have larger standard deviations than those obtained from eq 2a or 2b (Table I, lines 4 and 5 ) . This increase in standard deviation is understandable since the regression coefficients indicate that the data fit the linear equations very well and using the termolecular model decreases the ratio of data to parameters by a half. Thus we cannot state that eq 3 gives a better fit of the data. However, within these limits the values of KAD and CAD from eq 3a are in agreement with those given by eq 3b. Significantly,both sets of values are also in agreement with the data obtained from [AI, [Dlo. From these results it is clear that both termolecular complexes exist in these solutions at different conditions. Further evidence for the presence of AD2 in solutions with [D], >> [A], was obtained from measurements of the chemical shifts of the protons in TNB. A linear plot of A vs. A/[D], has only a slight curvature with a high regression coefficient (0.981, 16 points), however, the value of KAD obtained from eq 2 with these data (Table I, line 6) does not agree with the Km values obtained using the UV measurements. When these data are treated with eq 3 (Table I, line 7) the values of K m and K m Zobtained are in reasonable agreement with the values obtained from the UV data on the basis of termolecular species being present. Due to the limited sensitivity of NMR measurements, [D]o could not be data for solutions in which [A], obtained. Also, attempts to follow the NMR spectra of
-
K A D , = 1.0 f 0.3 K A , D 0.9f. 0.3
CAD, = 1800 r
K A D , = 0.7
AAD, =
f
0.2
~
A =~ 2230 D f
200 200
1.4 f. 0.2 ppm
the donor protons in solutions with [A], >> [D], were unsuccessful because the donor has a complex multiplet spectra. Addition of A caused the multiplets due to various donor protons to widen as well as move upfield. Thus it was impossible to obtain accurate values of A since changes in [A], would cause one multiplet to overlap another. The only clear cut observation that can be made from the NMR data for [A], >> [D], is that the protons at the 2 and 3 positions in D were the ones most affected by the acceptor. This could indicate that there is a greater interaction at these position, in agreement with previous theoretical’ and experimental suggestion^."^ Acknowledgment. This work was partially supported by an NSF undergraduate research participation program, Grant No. SM176-03971. References and Notes (1) R. Foster in “Molecular Complexes”, Vol. 2, R. Foster, Ed., Crane, Russak & Co., New York, N.Y., 1974, Chapter 3. (2) C. C. Thompson, Jr., and Y. E. Ho,J. Chem. Soc.,Chem. Commun., 609 (1973). (3) B. Dodson, R. Foster, A. A. S.Bright, M. I. Foreman, and J. Gorton, J. Chem. SOC.B, 1283 (1971). (4) A. A. S.Bright, J. A. Chudek, and R. Foster, J. Chem. Soc., Perkin Trans. 2 , 1256 (1975). (5) M. T. Sung and J. A. Parker, Proc. Natl. Acad. Sci., U . S . A . , 69, 1196 (1972). (6) J. R. Wolberg, “Prediction Analysis”, Van Nostrand, Princeton, N.J., 1976, Chapters 3 and 4. (7) (a) A. SzentOjiorgyi and I. Isenberg, Roc. Natl. Acad. Sci., U.S.A., 46, 1334 (1960); (b) A. Szent-Gyorgi, I.Isenberg, and J. Mclaughlin, ibid., 47, 1089 (1961). (8) (a) R. Foster and P. Hanson, Trans. Faraday SOC.,80, 2189 (1964); (b) R. Foster and C. A. Fyfe, J. Chem. SOC.B, 926 (1966). Chemistry Department University of North Dakota Grand Forks, North Dakota 58201
Norman Kulevsky’ Shella Specker
Received November 22, 1976
-
N
The Journal of Physical Chemistry, Vol. 8 1 , No. 1 1 , 1977
Vibratlonal Relaxation of Water at High Temperatures’ Publication costs assisted by the U S . Air Force Office of Scientiflc Research
Sir: Several years ago we carried out a theoretical study of the v 2 deexcitation of H 2 0 based on a model of vibration-to-rotation (VR) energy transfer.’ The model is based on the rapid rotational motion of colliding molecules and is expected to describe the relaxation process at higher temperatures, but no experimental data were available at such temperatures for a rigorous test of the model. However, Kung and Center3 recently reported the high temperature shock-tube measurements on the relaxation
