3945
THERMAL AND PHOTOCHEMICAL RACEMIZATION OF Cr(C204)sa- ION of excitation cross sections are not inconsistent with theoretical calculation^.^^^^^ Thus Massey and Moisei~ i t s c hhave ~ ~ calculated . ~ ~ values of -2 X lo-'* cm2for ~ ( 2 3 s )and ~ ( 2 % and ) 1.3 X cm2 for U ( ~ ~aPt ) value of 1.5 X cm2 for ~ ( 2 % ) 23 ey. Their24,26 u(2aP) is to be compared with our value of 4.2 X 10-17 cm2 for the sum, which may have to be taken over
+
all triplet states in view of the width of our electron beam. Acknowledgment. This work was supported by Grant GP-8065 from The National Science Foundation. We also wish to thank The National Science Foundation for supplying funds to assist in the original purchase of the mass spectrometers.
Preferential Solvation and the Thermal and Photochemical Racemization of Tris (oxalato) chromate(II1) Ion1 by V. S. Sastri and C. H. Langfordz Department of Chemistm, Carletan Univers&i, Ottawa 1, Canada
(Received May 19, 1970)
The nmr method for determining the composition of the solvation shell of a paramagnetic solute introduced by Frankel, Stengle, and Langford has been applied to the [Cr(C204)3]8complex in H20-DMSO mixtures. Thermal and photochemical racemization rates of d-[Cr(C20*)al8-have been determined as a function of the solvation shell composition. Both thermal and photochemical rates were found to be acid-catalyzed with the former showing a first-order dependence on H+ ion concentration in the pH range 1 to 3. The results could be explained in terms of a cooperative effect of the solvent molecules in the aquodechelation of the complex through hydrogen bonding. Quantum yields obtained at 4200 A (4T1,) and their solvent dependence may be explained in terms of relaxation of the initial excited state t o an intermediate which is substitution labile. The solvent dependence of quantum yields is regarded as arising in the relaxation process.
Introduction Spees and Adamsona have proposed a substitutional mechanism for the thermal and photochemical racemization of Cr(Cz04)38-ion based on the mechanism for aquation and oxalate exchange proposed by Harris and coworker^.^ The crucial step is an aquo-dechelation step [Cr(Cz04)ala-
+ HzO E [Cr(C@~)~(OCOCO2) (OK) la-
Although wavelength dependence, temperature dependence, and solvent dependence in alcohol-water mixtures can be consistently interpreted with this proposal, Spees and Adamson noted3 that: ". . . I n the absence of some independent means of determining the solvent cage composition, it is difficult to make any detailed treatment of our data. . . . " An independent nmr method for the determination of relative solvent shell composition in mixed solvents has been proposed by Frankel, Stengle, and L a n g f ~ r d . ~ It has been possible to establish the correlation suggested by Adamson with respect to thermal substitution reactions of [Cr(NHa)2(SCN)4 1- in acetone-water
mixturesj6 acetonitrile-water mixtures,' and for [Cr(NCS)aI3- in acetonitrile-water mixtures.8 However, the photochemical substitution reactions in acetonitrile-water mixtures7s8display a different solvent dependence. The results indicate that the entering water ligand need not be in encounter with the Cr complex in advance of excitation. I n this paper, a somewhat different kind of mixed solvent system is examined. The dechelation step which is assumed to be crucial for racemization of [Cr(C204),ls- is a substitution reaction, but unlike acet(1) Presented at the 157th National Meeting of the American Chemical Society, Minneapolis, Minn., April 13-18, 1969. (2) All correspondence should be addressed to this author; Alfred P. Sloan Fellow, 1968-1970. (3) S. T. Spees and A. W. Adamson, Inorg. Chem., 1, 531 (1962). (4) K. V. Krishnamurty and G. M. Harris, J . Phys. Chem., 64, 346 (1960). ( 5 ) L. S. Frankel, T. R. Stengle, and C. H. Langford, Chem. Commum, 373 (1966). (6) C. H. Langford and J. F. White, Can. J . Chem., 45, 3049 (1967). (7) V. S. Sastri, S. Behrendt, R. Henwood, and C. H. Langford, to be published. (8) S. Behrendt, C. H. Langford, and L. S. Frankel, J . Amer. Chem. Soc., 91, 2236 (1969).
The Journal of Physical Chemistry, Vol. 74, No. $8, 1970
3946
V. S. SASTRIAND C. H. LANGFORD
onitrile, dimethyl sulfoxide (DMSO) which is here mixed with water is a good ligand for attack on CrIII.9 Despite this property the reaction in DMSO is much slower than the reaction in water. The reason for such a solvent effect on rates must be sought in a factor other than the ability of one solvent to function as a n entering ligand in a substitution reaction. This point is clearly made in what follows by the fact that the rates are much more sensitive to bulk solvent composition than is the probability of occupancy of a particular site in the solvation shell (or "solvent cage" or "encounter complex"). In contrast to earlier examples,6J the quantum yield for photochemical racemization is shown to be quite solvent sensitive. The discussion in this paper will attempt to rationalize the solvent dependence of the thermal racemiza] ~ - then proceed to a discussion tion of [ C r ( C ~ 0 4 ) ~and of solvent effects in photochemical reactions by development of a "plausible" model (for photochemical substitution of CrI'I that lends itself to analysis in the framework for discussion of mechanistic photochemistry recently proposed by Hammond.lo
ried out for 2 t o 3 half-lives and good linear plots were obtained. An aliquot (15 ml) was transferred into a 5-cm cell and irradiated for a definite period of time and the optical activity was determined after irradiation. Chemical actinometry before and after irradiation of the complex confirmed the constancy of the light intensity. A parallel dark run was conducted for correcting the photochemical rate of racemization. Solvation Studies. Preferential solvation studies by nmr were carried out by recording solvent proton signals at 25.0" on a JEOL C-60 nmr spectrometer. Confirmation was obtained by observation of the solvent dependence of the ligand field bands of the complex recorded on a Cary 14 spectrophotometer.
Results Preferential Solvation. The nmr studies were analyzed according to the previously described These are summarized in an Appendix to the present paper. Typical line broadenings are collected in Table I. These reflect two factors: (a) the probability
Experimental Section
~
-
Materials. Crystalline K3Cr(C204)33Mz0 was prepared according to the published procedure" and resolved according to the procedure given in the literature,12 and the resulting complex d-K3Cr(CzO& had a molar rotation of 7600". Crystalline K3Fe(C204)3 3Hz0 was prepared according to the standard procedure. l 3 Reinecke's salt obtained from Alfa Inorganics was purified by recrystallization. Reagent grade strychnine sulfate (Rlann Research Laboratory, New York, N. Y.) and Fisher certified buffer solutions were used as such. Spectranalyzed DMSO (Fisher Scientific Co.) and distilled water were used to make solvent mix tures. Apparatus. (i) A 1000-W xenon-mercury source (Oriel Optics) was used as the light source and the beam collimated with the help of lenses of 7.5- and 5-cm focal length, and passed through a Jarrell-Ash monochromator (Model 82-410) for selecting the appropriate wavelength. A circular spectrophotometric cell of 5-cm path length thermostated at 25.0 0.1" was used for irradiation. The light source was calibrated using Reinecke's saltI4 as well as potassium ferrioxalateI6 as standards for chemical actinometry. (ii) Optical activity was measured with a Perkin-Elmer speotropolarimeter (Model 141) to an accuracy of =tO.OOl". (iii) Absorbance measurements in the course of chemical actinometric procedures were made with a Gilford spectrophotometer Model 240. Reaction Studies. A weighed amount of the optically active complex was dissolved in the solvent mixture and thermostated at 25". An aliquot of the solution was transferred into a cell and the optical rotation was recorded as a function of time. Thermal runs were carThe Journal of Physical Chemistry, Vol. 74, No. 9% 1970
~
~~
Table I: Nmr Data on Excess Line Width of 'H Signal of Water (KaCr(CLh)a 0.025 M ; Temp 25') Mole fraotion of DMSO
Exoess line width,
0.0 0.02 0.04 0.07 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
3.48 5.06 4.73 5.38 5.85 S. 63 10.23 9.94 9.69 8.86 9.12 8.97 8.96
Aviiz,
HZ
Relative viscosity 16
n/no
1.00 1.03
1.00 1.10 0.83 0.70 0.59 0.38 0.27 0.20 0.16 0.12 0.09 0.06 0.04
1.14 1.20 2.00 3.25 3 95 3.80 3.40 3.04 2.67 2.40 2.20
that a solvent molecule is in the paramagnetic environment (solvation shell of CrlI1 complexes) and (b) the relaxation time characteristic of that environment. Since the latter cannot be obtained absolutely, we evaluate relative solvation in the mixed solvent compared to pure solvent. The parameter reported is (9) L. S. Frankel, T. R. Stengle, and C. H. Langford, Can. J . Chem.? 46, 3183 (1968). (10) G.S. Hammond, Advan. Photochem., 7, 373 (1969). (11) G.Croft, Phil. Mag., 21, 197 (1842). (12) G.K.Schweitzer and J. L. Rose, J . Phys. Chem., 56,428(1952). (13) J. C. Bailar, Jr., and E. M. Jones, Inorg. Sun., 1, 36 (1939). (14) E.E.Wegner and A. W. Adamson, J. Amer. Chem. Soc., 88,394 (1966). (16) C.G.Hatchard and C. A. Parker, Proc. Roy. Xoc., Ser. A , 235, 518 (1956).
3947
THERMAL AND PHOTOCHEMICAL RACEMIZATION OF Cr(C204)aa- ION
1
X DMSO Figure 1. Activity of water ( p / p ~and ) nmr wlvation data @/no)us. mole fraction of DMSO: A, n/nofor DMSO; A, nlno for HzO; 0, p/po for HqO; 0 , p / p o for DMSO; T = 25".
0.5
1.0
n / n a b o
Figure 2. Position of Cr(CzO4)P- visible ligand field absorption band maxima (nm) us. n/nofor water; T = 25".
n/n, which represents the number of a particular type
of solvent molecules solvating the complex in a mixed solvent compared to the number of the same solvent solvating in the pure solvent. The important assumption is that the relaxation time in the paramagnetic environment is either constant or varies only as a linear function of bulk viscosity as the composition of the solvent is ~ h a n g e d . ~The validity of the assumptions is checked by agreement between values obtained from analysis of protons of water and DMSO. The results are shown in Figure 1. The relaxation time in the paramagnetic environment has been assumed to be proportional to bulk solvent viscosity and the viscosity correction has been applied using Kruus' datalR on DN;ISO-H20 viscosities. A further check on the v* lidity is supplied by the parallelism shown in Figure 2 between the nmr derived n/no values and the (small) solvent dependence of ligand field bands of the CrlI1 chromophore. Table I1 gives the thermal rates and the photochemical quantum yields for racemization of d-K&r(CzO& in DMSO-H20 mixtures. Table I11 records the data on the hydrogen ion dependence of the thermal rates and quantum yields for the racemization reaction, and the n/novalues derived from the nmr data as a function of the mole fraction of DMSO are presented in Figure 3.
Discussion Thermal Reaction. Although DMSO is probably a better ligand for coordination at a vacated position of CIII in a dechelation step than any of the several solvents in which racemization of Cr(C204)p was examined by Schweitzer and Rose, l 2 it retards racemization more effectivelythan any other solvent considered. The first interesting point is that this effect does not
Table 11: Thermal Rate Constants and Quantum Yields of Racemization of d-Ka[Cr(C204)~] at 25 =k 0.1' Mole fraction of DMSO
0.00 0.02 0.04 0.07 0.10 0.20 0.30 0.40 0.50 1.00
4,
k,
4200
meo-1
5.55 x 3.79 x 2.72 x 1.36 x 8.62 x 8.37 X 7.73 x 2.91 x 2.17 x 1.44 x
10-4 10-4 10-4 10-4 10-5 10-6 10-7 10-7
10-7 10-7
A
0.110 0.103 0.076 0.069 0.036 0,0087 0.0018 0.0004 ( 1 ) 0.0009 ( 1 ) 0.0005 ( 1 )
arise from changes in thermodynamic activity of water in the solvent mixtures. As the vapor pressure curve for water" in Figure 1 indicates, mixing of water with DMSO does not lead to lowering of water activity that differs significantly from the other solvents methanol, ethanol, propanol, dioxane, or acetone, which affect reactivity of this complex less ~ t r i k i n g l y . ~ *We ' ~ must look to something involving the metal complex itself and its immediate environment. Comparison of the vapor pressure curve (p/pO)" in Figure 1 with the n/no (HzO) and measures of reactivity shown in Figure 3 is suggestive. We see that reactivity changes more rapidly than water activity and that n/n, decreases (16) P. Kruus, private communication. (17) B. G . Cox and P. T. McTigue, Aust. J . Chem., 20, 1816 (1967).
The Journal of Physical Chemistry, Val. 74, No. $8, 1970
3948
V. S. SASTRIAND C. H. LANGFORD
Table 111: pH Dependence of Racemization Rate Constants and Quantum Yield of d-KsCr(C204)a a t 25.0 k 0.1”
3.93 x 1.i o x 4.56 x 1.38 x 1.80 x 1.67 x 8.37 X
0.00 1.05 1.35 2.05 2.52 3.00 6.00 a
10-3 10-3 10-4 10-4 10-6 10-6 10-8
0.0206 0.0248 0.0087
In 0.2 M DMSO.
I n water.
1.0
t
0
Y
\ Y
z0 \
% DMSO Figure 3. Relative thermal rates ( 0 )and quantum yields (A) for racemization of Cr(Cn04)33-in DMSO-H20, and n/no for water (0)us. mole fraction of DMSO; T = 25’.
rapidly as DR!tSO is introduced. That is, DNSO replaces water in the solvation shell of Cr(Cz04)Z3-preferentially. However, the relationship of reactivity to n/nois not simple. If the reaction rate were simply related to the probability of encounter between Cr(C204)33- and a water molecule in a suitable solvation site, one would predict proportionality of rate to n/noas has been elsewhere observed.* That behavior would be what might be expected if water were simply functioning as a nucleophile in the dechelation step, but we have said that DAIS0 is a good nucleophile so we need to identify other roles for water. In fact, there is a simple and plausible account of the role of water. It can solvate the dissociating oxalate of the transition state of the dechelation step by hydrogen bonding. Although DMSO appears to be a good competitor for solvation of Cr(Cz0&3- in the ground state, it is not so in the transition state. The transition state The Journal of Phygical Chemistry, Vol. 74, N o . 91,1970
with a weakened Cr-0 bond has a requirement for hydrogen bonding that may be imagined to involve all of the oxygens on the oxalate group which is undergoing dechelation. This will require several water molecules playing nonequivalent hydrogen bonding roles. Thus the rate is expected to depend on n/no to a high and not necessarily integral power. It would seem that this explanation of the solvent dependence of racemization rate is supported by the existence of an H + dependent term in the rate law. If hydrogen bonding can stabilize the transition state, protonation of the complex should also stabilize the transition state relative to the ground state. The two paths, one H + dependent and the other HzO dependent, are probably mechanistically similar. Photochemical Reactions. To make suggestions concerning the photochemistry of Cr(Cz04)3a-,it is useful to compare the results t o those obtained for CI(NCS)~~and Cr(NH&(NCS)*-, but first, some general suggestions must be recorded. Adamsonla has emphasized that the wavelength dependence of a number of reactions of CrIII complexes may be understood if reactions occur from the quartet excited states. He has also pointed out that these states are likely to be subject to substantial distortion from octahedral symmetry. In fact, the distortion is required if the lifetimes implied by the photochemical kinetics are to be understood.l9 An increase in the excited-state distortion can be expected to favor “relaxation” of that state to photochemical product rather than to the initial ground state if the distortion tends to make the excited state resemble product more than reactant. This point is cogently discussed by Hammond.lo Now the role of solvent may be considered. There is a parallel (but not an exact correspondence) between the solvent sensitivities in thermal and photochemical reactions for the three complexes we discuss. For both reaction types solvent sensitivity decreases in the order ) ~ Cr(NCS)t-. In Cr(Cz04)33- > C I - ( S H ~ ) ~ ( N C S> the thermal reaction, this is to be understood in terms of the degree to which the hydrogen bonding of solvent waters aids the distortion of the complex required for heterolytic fission of a metal to ligand bond. Photochemically, it is to be understood in terms of the degree to TThich hydrogen bonding to water favors distortion of the excited state so that it resembles the primary photoproduct. Now an interesting difference arises between thermal and photochemical pathways. The photochemical pathways are consistently less solvent sensitive. I n the case of Cr(NCS)e3- and Cr(NH3)2(NCS)4-, this difference is indicated to be one water molecule by the n/no correlation. It is certainly tempting to suggest that the primary photochemical product is a reactive inter(18) A. W. Adamson, J. Phgs. Chem., 71, 798 (1867). (19) S. Chen and G. B. Porter, J . Amer. Chem. Soc., 9 2 , 2189 (1970).
3949
THERMAL AND PHOTOCHEMICAL RACEMIZATION OF Cr(C,04),+ ION mediate with one ligand removed so that one water molecule which is present in the thermal transition state is not required. Of course, there are alternate accounts of the present limited information.
1 / T 2 may ~ be measured from study of solvents free of paramagnetic solute. Consequently, P M / T ~isMexperimentally accessible. It is related to the excess line width at half-height of the nmr absorption signal (Av)
Acknowledgments. We thank the National Research Council of Canada for financial support.
TAU = -
Appendix. Solvation Analysis by Nmr6-e The transverse relaxation time, T2, of the proton on a solvent molecule will be greatly reduced by a paramagnetic solute. In cases of solvation in the outer coordination sphere, this effect depends on dipolar coupling between the paramagnetic elections and the proton under observation. This coupling enters relaxation time equations with an r-6 distance dependence. As a result of the short-range character of the interactions, it is a good approximation to partition the solution into a paramagnetic environment (solvation shell) and a diamagnetic environment (bulk solvent). Exchange between these environments is fast and McConnell’s equation applies -1--_P_f -P
Tz
TZD
7’2~
T2 is the observed relaxation time, PDis the probability that a solvent molecule is in the diamagnetic environment (bulk), and PMis the probability that a proton is in the paramagnetic environment (solvation shell). T ~ and D T ~ are M the relaxation times characteristic of the two environments, respectively. I n a dilute solution of the paramagnetic solute, PO N l and the term
PM TZM
T ~ isMdifficult to evaluate accurately by either experi= TZMO ment or theory. If we may hope that T ~ M where T ~ is Mthe paramagnetic environment relaxation time for protons of a particular component of a mixed solvent (say, DMSO) and TZMO is the relaxation time in the paramagnetic environment for protons of the same component in pure solvent (e.g., pure DMSO), we may write AV
Avo
- PM
T 2 ~ o- PM TZM PMO PMO
where the subscript 0 designates pure solvent and unsubscripted variables denote mixtures. If the bulk composition of the solvent mixture is known, it is a straightforward matter to convert PM/PMO data into the fraction of the particular solvent (e.g., DMSO) in the solvation shell of the complex in a mixed solvent. This fraction is called n/no. Now, the “hope” that T ~ M = TZMOis not always realized. One major reason for a failure is that T 2 ~ may be dependent upon “tumbling” times which are proportional to solvent viscosity. Such a failure is easily corrected by normalizing all line width values to the same bulk v i s c ~ s i t y . ~
The Journal of Physical Chemistry, Vol. 74, No. 88, 1970
