3040
2.A, SCHELLY,D. J. HARWARD, P. HEMMES, AND E. M, EYEING
those of Rogers, may have affected the course of the decomposition either by selective catalysis or through gross properties of the reaction medium. Further observations which suggest that the properties of the medium and the nature of the coproducts play important roles by both increasing and decreasing reactivities of the various species are as follows. A 4-g sample of pure 2 was found to ignite spontaneously in less than 30 min at 200”; the amounts recovered from our residues require, however, that this aldehyde survives appreciably longer in the presence of its coproducts, On the other hand, 2 does seem to catalyze reactions of other species; 0.5 g of 2, when admixed
with 2 g of TNT, caused extensive decomposition of the latter after only 1 hr a t 200”. Any one of the phenomena mentioned above could markedly influence relative times-to-explosion or gas evolution rates. Taken in combination, they provide strong reinforcement to our views regarding the discrepancies and uncertainties in published activation parameters.
Aclcnowledgnzents. The authors are indebted to Dr. Darrell V. Sickman for useful discussions. The work was carried out under U. S. Naval Ordnance Laboratory Foundational Research Task FR-44.
Bonding in Dye Aggregates. Energetics of the Dimerization of Aqueous Cobalt(II)-4,4’,4’’,4’’’-TetrasulfophthalooyanineIon by Z. A. Schelly, D. J. Harward, P. Hemmes, and E. M. Eyring Department of Chemistry, University of Utah, Salt Lake City, Utah 84119
(Received April 8, 1970)
The thermodynamic functions 4H0, AGO, and 4S”, as well as the activation parameters of the dimerization oki
2S4 J _ D of aqueous Co(II)4,4’,4’’,4’~’-tetrasulfophthalocyanine ion (Co(I1)-TSPC) were calculated using Qk- 1
concentration-jump relaxation kinetic and equilibrium photometric data obtained at 38, 48, and 58”. The radius of the activated complex r and the binding energy between the constituents in the dimer were calculated. The nature of binding forces and effect of the dielectric constant of the medium are discussed.
*
Introduction I n a recent paper’ we reported on the kinetics of the dimerization of Co(I1)-TSPC in aqueous solution at 58”. I n the present work we focus on the energetics of this association equilibrium thus elucidating the reaction mechanism and the nature of binding forces between the constituents in the dimer. This kinetic-thermodynamic approach should supplement the substantial spectroscopic-thermodynamic effort2 which has been made to explain the forces in aggregates of charged or neutral dye molecules in general. The results show again the abilities of relaxation kinetic techniques to reveal intimate details of fast association processes. * Based on the temperature dependence of the thermodynamic equilibrium constant K and the forward and reverse ionic strength independent rate constants ok~ and oJc-1, respectively, we show below the results of a calculation of the standard molar reaction enthalpy AH’, molar free energy change and entropy of The Journal of Physical Chemistry, Vol. 74, No. 16,1970
aggregation AS”aa1 of the reaction as well as the activaoki
2 M s D Ok-1
tion parameters AHAI*, AG~A*, and A&*, for the forward (1) and reverse (- 1) reactions, respectively. The important effect of the dielectric constant of the solvent on the rate constants and the nature of the bonding in the dimer are discussed.
Experimental Section We have supplemented our previous concentrationjump relaxation kinetic and equilibrium photometric (1) Z.A. Schelly, R. D. Farina, and E. M. Eyring, J. Phys. Chem., 74, 617 (1970). (2) On the nature of bonding in dye aggregates, cf. K. K. Rohatgi and G . S. Singhal, J. Phys. Chem., 70, 1695 (1966), and references cited therein. (3) M: Eigen and L. DeMaeyer in A . Weissberger’s “Techniques of Organic Chemistry,” Vol. VIII, Part 11, Interscience Publishers, New York, N . Y., 1963, p 895 ff; E.F. Caldin, “Fast Reactions in Solution,” Wiley, New York, N. Y.,1964.
3041
ENERGETICS OF THE DIMERIZATION OF Co (11)-TSPC Table I : Rate Constants, Equilibrium Constants, and the Dielectric Constant of Water a t Different Temperatures
M-1 see-1 o k ~ sec-' , Kopt,ahf-1 Kkin = oki/ok-1, MA' Temp, OK
DE*O D H ~X O T, "K a
38'
480
16.0 rt 0 . 5 X lo2 2.6 0 . 1 x 10-3 8 - 0 A 0.5 X lo6 6.17 rt 0.43 X lo6 311.15 73.96 2.3 x 1 0 4
13.3 z t 0.3 X lo2 3.0 0.1 x 10-3 4.7 =t0.1 x 106 4.55 rf 0.25 x 106 321.15 70.68 2.27 x 104
68O
5.36 f 0.15 X l o 2 2.8 0.1x 10-3 2.05 i: 0.05 X lo6 1.92 rt 0.12 x 105 331.15 67 38 2.23 x 104
*
I
Photometrically determined thermodynamic equilibrium constant.
Table 11: Thermodynamic Functions and Activation Parameters for Forward (1) and Reverse ( - 1) Reaction, Respectively.
(Energies Are Given in kcal/mol, and Entropies in eu) i E a = -12.6 f 0.63
AH"
-14 rf 0.9 -8 f 0.02 ASoaai = -18 k 3 AGO331
AH1* = -13.3 f. 0.63 = 1 5 . 3 f. 1 . 3 A81 *a31 = 86.2 A 2 AG1*331
-1Ea = 0 i 0.66
AH-1* = -0.66 f 0.66 = 23.3 =k 1.3 A8-1*$81 = -72.4 f. 2 AG-1*3ai
work' done a t 58" with new data obtained at 48 and 38". An extension of the temperature to a range significantly above 58" is not possible because of formation of bubbles within the stopped-flow apparatus as well as in the spectrophotometer cell. Below 58", on the other hand, further polymerization (beyond the dimer stage) starts a t a lower total concentration CT = CM 2CD than a t 58". Since we had to restrict our investigations to the monomer-dimer equilibrium, the experiments a t 48 and 38" were performed with solutions of CT 5 3 X lo-' M . The experimental uncertainty increases, of course, at such high dilution and this is reflected in the lower precision of the data obtained a t 48 and 38". The experimental procedure' and the interpretation of the kinetic data4 have already been described.
+
Results and Discussion All experimental data and calculated results are collected in Tables I and 11. Uncertainties associated with numerical values are given as average deviations from the mean. The kinetically determined equilibrium constants K k i n = okl/&-l are presented as the mean of the extreme values of the quotients. I n the calculation of the thermodynamic quantities the standard state of the components is considered to be the state of the pure components in an ideal dilute solution, I n this case, if CT --t 0, then the activities ai -+ ci, and the change of the standard molar enthalpy of the reaction AH" becomes equal to AHm(change of the molar enthalpy at infinite dilution) which can be calculated from d In K / d T = AHo/RT2. Similarly, AGO = AGm = -RT In K , and AG" = AH" - TAS" The Arrhenius activation energy klE, for the forward or reverse reaction was obtained from the leastos. T-l. Since square corrected linear plot of In
='=
AH1* - AH-1* = -12.64 1.29 AG1* - AG-1* = -8 f 2.6 A&+ - As-1* = -13.8 f.4
+
E,
= AH* RT, the entropy of activation can be calculated from the equation
=
kT
exp( - AHk1*/RT) exp(A& h
* / R ) (1)
as given by the transition-state theory. Obviously, , AH" = AH1* - AH-,*, and since K = o k l / ~ k - ~then AG" = AGl* - AG-,*a nd AS" = A&* - AS-1 The dimerization reaction is exothermic (AH = - 14 kcal), and in spite of a decrease in entropy (-18 eu), formation of dimer is favored from an energetic point of view (AG = -8 kcal). Since the change in enthalpy includes also the heat of solution of the monomer and dimer, which are not known, AH" cannot be interpreted in terms of bond energy or heat of dissociation, The zero activation energy for the dissociation reaction is noteworthy. It indicates that in the course of separation of the constituents of the dimer to a distance corresponding to that in the activated complex, the repelling and binding forces are approximately in balance. Based on a simple electrostatic picture, viewing two point charges of the same sign ( x = -4) in a continuous medium, the electrical work W,I of bringing them together from an infinite distance to a distance of 2r+ by which they are separated in the activated complex is given by Coulomb's law
*.
D is the dielectric constant of the medium and
ri is the radius of the activated complex in eq 2. A value (4) 2. A . Sohelly, R. D. Farina, and E. M. Eyring, Monatsh. Chem.,
101, 493 (1970).
The Journal of Physical Chemhtry, VoL 74, No. 16, 1070
Z . A. SCHELLY, D. J. HARWARD, P. HEMMEB, AND E, M. EYRING
3042 for r* can be obtained from the slope of the In 1/DT plot based on the equation5 In
=
In k‘ -
Xi2 jeo2 __
r+lcDT
vs.
(3)
where IC” is the forward rate constant at D = T = m, and 1E,’ is the activation energy of the association at D m a Infinite dielectric constant, however, means that charges do not “see” one another; consequently there is no repulsion between the similarly charged reacting ions. I n this case the activation energy lEat is presumably zero or negligibly small and so the dependence of 0k1 on D and T is determined by the last term on the right side of eq 4. In water with increasing temperature D goes down faster than T goes up so that the product DT decreases (Table I), resulting in a smaller &I. Thus the plot of In us. 1/T gives an apparently negative activation energy for the association process. The effect of the dielectric constant of the medium on the kinetics of the association may partially explain earlier equilibrium observations* that in alcohol or glycerol solution dye aggregation is much weaker than in water. 9
where k‘ symbolizes the ionic strength independent rate constant in a mediup with D = m . The calculated value foror+ is 2.51 A representing a charge separation of 4 A in the activated complex. Since we are dealing with large planar ions, this distance is equal to the separation of the two parallel monomer planes. Comparing this with values obtained from X-ray measurements on phthalocyanine6 and Ni-phthalocyanine’ crystals as well as on graphite, where the distances between the planes of the parallel molecules (staggered stacking) are 3.38, 3.38, and 3.41 k, respectively, one may expect that the separation within the dimer in solution is between 5 and 3.38 A. I n other words, the structure of the dimer in solution resembles that in the crystalline state, and the bonding is accomplished by the overlapping of the extended r-electron clouds of two conjugated systems. Thus, the possibility of hydrogen bonding or “sandwich structure” can be excluded. The bond energy, as indicated earlier, can be calculated from eq 2. Multiplying W,1 by N we obtained 16.5kcal/mol. The fact that the experimentally determined activation energy for the forward reaction is negative is striking. This, however, can be understood in the following way. Noting that L’ in eq 3 is temperature dependent, we may rewrite this equation as
The Journal of Physical Chemistry, Vol. 74,No. 16, 1970
Acknowledgment. This work has been sponsored by AFOSR (SRC)-OAR, USAF, Grant No. 69-1717-D. (5) A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,” 2nd ed, Wiley, New York, N. Y.,1965,p 145. (6) J. M. Robertson, J. Chem. SOC.,1195 (1936). (7) J. M. Robertson and L. Woodward, ibid., 219 (1937). (8) E. Rabinowitoh and L. F. Epstein, J. Amer. Chem. Soc., 63, 69 (1941); V. L. Levschin and L. V. Krotova, Opt. Spektrosk., 1 3 , 457 (1962); V. L. Levsohin and E. G. Baranova, J . Chim. Phvs. Physicochim. Bid., 55, 869 (1958); K. Bernauer and S. Fallab, Xelu. Chim. Acta, 44, 1287 (1961).
