The pressure dependence of rates of homolytic fission of metal-ligand bonds in aqueous solution

KOJI ISHIHARA AND THOMAS WILSON SWADDLE Department o f chern i~ tn , The Un~ver~z t ) of C a l g a ~ , Calgcrn, Alta., Canada T2N IN4

Received May 13, 1986

KOJI I~HIHARA and THOMAS WILSON SWADDLE. Can. J . Chem. 64, 2168 (1986). The volume of activation for the exclusively homolytic decomposition of protonated 4-pyridylmethylchromium(II1) ion in

aqueous HClO, at 63.4"C is + 19 cm3 molp' , with negligible dependence on pressure up to 350 MPa at least. The origins of the strongly positive volumes of activation that characterize homolysis of complex catlons in aqueous solution are examined.

KOJI ISHIHARA et THOMAS WILSON SWADDLE. Can. J . Chem. 64, 2168 (1986). Le volume d'activation uniquement de la dkcomposition homolytique de l'ion methyl-4 pyridyl chrome(II1) protone, a 63.4"C

et en solution dans du HCIOj aqueux, est Cgal 2 + 19 cm' m o l ' : cette valeur ne varie pratiquement pas avec la pression jusqu'i 350 MPa. On discute des origines des valeurs extrkmement positives des volumes d'activation qui caractkrisent l'homolyse des cations complexes, en solutions aqueuses.

[Traduit par la revue]

Introduction There are relatively few authenticated cases of homo-

lytic fission of metal-ligand bonds in aqueous coordination chemistry, and most of them involve Cr-C u-bonds in organochromium complexes of the type ( H 2 0 ) 5 C r ~ 2 + , the chemistry of which has been reviewed by Espenson (1). There are two primary mechanisms for the decomposition of these complexes in acidic aqueous solution: heterolysis, which would in principle give initially Cr3+ (aq) and the carbanion R- but actually seems to produce RH together with the conjugate base of CrH1(aq):

k~ [I] ( H ~ O ) ~ C ~ R ~ ' + H 2 0 - c ~ ( H ~ o ) ~ o H ~ ' + RH,

and homolysis which gives initially chromium(I1) and the organic free radical R ":

I?] ( H ~ O ) ~ C ~ R ' + + H 2 0 & C r ( ~ ~ 0 ) ~ ~ . + R' + etc k - H

Homolytic decomposition can be suppressed by addition of sufficient chromium(I1) ion, or it can be driven at the limiting rate set by the first-order rate constant kH by adding a scavenger such as Q2 or Cu2+ to eliminate Cr2+(aq) and (or) Re ( 2 , 3). Reaction [I] , however, cannot be suppressed, and turns out to be important in the decompositions of most CrR2+ species in acidic aqueous solution (indeed, it is usually acid-catalyzed).

In two suitable cases (R = CH(CH3)2 and C(CH3)20H) in which kH and the rate constant kA for reaction [ I ] are similar under ambient conditions, it proved to be possible to measure the pressure dependence of the rate constants to obtain the corresponding volumes of activation AVH* and AVA* (Table 1) (4). This is intriguing inasmuch as AVHX and AVA* refer to isomeric transition states (in essence, {(H20)6Cr2+. . . Rm} * and {(H20)5CrOH2+. . . HR} *) for the decomposition of a given species. As Table 1 shows, activation via the homolytic pathway involves a remarkable expansion whereas heterolysis does not, and this was attributed (4) to the necessity of breaking up the solvent cage in homolysis to separate Cr2' from R" if recombination is to be avoided and net reaction observed - a restriction that is irrelevant to heterolysis, which forms the product RH directly and irreversibly.

The measured volume of activation for homolytic decompo- sition of (H20)5~rCH(C~3)22+ , however, decreased significantly

with increasing pressure beyond 100 MPa (4), i .e . , the plot of In kH against pressure was curved. Such curvature is a common phenomenon, and is often associated with solvational change in the activation process (5), which in this case could be related to break-up of the solvent cage (4). Nevertheless, data from the 100-300 MPa region which defined this curvature were susceptible to systematic errors because the fraction kH/(kH + kA) of the total rate constant for decomposition that was due to homolysis became small at high pressures.

We have therefore measured kH over a wide range of pressure - .

for a reaction for which kA is negligible (i.e., for which homolysis is the only detectable reaction pathway), namely, the decomposition of the protonated 4-pyridylmethylchromium(I11) aqua-ion, ( H ~ O ) ~ C ~ C H ~ C ~ H , N H ~ + , in oxygenated aqueous HClO, (2, 3, 6).

Experimental The general preparative and kinetic procedures have been described

elsewhere (2, 3, 6). Rate constants were measured in situ with a Cary Model 17H spectrophotometer at 308 nm and 63.4"C; the light beam was allowed to pass through the sample only long enough to make intermittent absorbance measurements, so as to avoid possible photolysis of the organochromium complex (although there was no indication that this was ever significant). Samples were saturated with pure oxygen gas at O"C before each kinetic run. For runs at high pressure, the samples were contained in a le Noble-Schlott cell (7) and pressurized with water in an Aminco high-pressure optical cell.

Because the reactions were slow, especially at the higher pressures, the first-order rate constants k H were calculated by the Kedzy- Swinboume method (8) from optical absorbance data collected over the first four half-lives; standard deviations were typically about 0.3%, and values of kH obtained at atmospheric pressure were in excellent agreement with published data (2. 3).

Results Two to four measurements of k H were made at each of ten

pressures P ranging from 0.1 to 350 MPa. The results are summarized in the semilogarithmic plot (Fig. 1) in which the error bars show the range in In kH values. Clearly, In kt, is quite adequately represented by the linear relationship

which gives AVH* = + 18.9 5 0.3 cm3 mol-' and the zero- pressure rate constant kHO = 1.50 X lop4 s- ' (* 1.6%). with a

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ISHIHARA AND SWADDLE

TABLE 1. Volumes of activation for heterolytic and homolytic decomposition of (H20)5CrR(2+'Jt in aqueous HC104

"Reference 4; [HClO,] = 1 .O-1.1 mol L 1 ; 25.0°C except as stated. bLow-pressure asymptotic value from quadratic fit (eq. [4]). '15.0°C. "This work: [Cr] = 5.2 X rnol L 1 ; [HCIO,] = 0.026 rnol L-.'; 63.4"C

FIG. 1. Pressure dependence of In k H for the decomposition of 4-pyridylmethylchromium(III) ion in aqueous HC104 (0.026 mol L-I at ambient conditions) at 63.4OC. Line represents linear fit of data (eq. PI) .

residual sum of squares of 0.0954. Only a minor improvement in fit (residual sum of squares = 0.0905) is achieved by going to a quadratic in pressure

in which the zero-pressure volume of activation AvHO* =

+20.0 2 0.9 em3 mol-' and the mean compressibility coeffi- cient of activation APH* = -(dAVH*/dp)T for this pressure range is (6.8 2 5.6) x em3 molp ' MPap ' . These uncer- tainty limits are standard deviations, so APH* is not really significant at the 9570 confidence level. but in any event it is only about one-tenth of that reported (4) for the 2-propyl- chromium(II1) ion ( + (5.9 ? 1.4) x lo-' cm3 m o l l MPa- ' ).

Discussion Table 1 shows that a large, positive volume of activation

is characteristic of the homolytic pathway for decomposition of aqueous organochromium(111) complexes, regardless of the charge on the leaving organic radical, R'.

The ApH* data, however, raise the question as to whether AVH" is, in the general case, significantly pressure-dependent.

When 'CH(CH3)2 is the leaving group, the measured ApHV is large, but is derived from rate data at the higher pressures where kH makes only a minor contribution and may therefore be subject to large systematic errors. For cationic 'CH2C5H4NHC as the leaving-group, kH values at the higher pressures are more reliable than for the 2-propyl analogue because heterolysis is absent, and here APH* is negligible. It is likely, however, that the marked curvature of the plot of In kH vs. P for the 2-propylchromium(III) case is real, and originates in a desolvation effect associated with neutral hydrocarbon radical release that may be minimized when both of the separating fragments (cr2+ and R") are cations. In other words, solvent cage break-up need not imply desolvation, at least not when the escaping fragments are both cationic.

It is not feasible at present to attempt to account in a quantitative, absolute way for the large, positive values that are found for AVH*, but a crude estimate of AAV* = (AVH* - AV4*), i.e., the volume of activation for homolysis relative to heterolysis for the decomposition of a given aqueous organo- chromium(II1) complex, can be made. A model introduced previously (9, 10) allows us to estimate that the (presently unmeasured) absolute molar volume of ~ r ( H , o ) ~ ~ ' ( a ~ ) is 20.7 em3 molp' larger than that of C ~ ( H ~ O ) ~ ~ + (aq), and so, from the known volume of hydrolysis of the latter ion (1 I) , 19.1 cm3 mol-' larger than that of C r ( ~ ~ 0 ) ~ 0 H ~ + ( a ~ ) . The contribution of a covalent hydrogen atom to the molar volume of an alkyl group is about 5.5 em3 mol-' (12), and so, solvation apart, the radical R' should occupy that much less volume than RH. Thus, if the activation processes of heterolysis and homolysis can be approximated to the generation of the intermediates shown in reactions [ I ] and [2], AAV* should be about 14 cm3 mol-' if solvation of R and RH is ignored (solvation of the chromium ions is already taken into account). Table 1 indicates that this is a reasonable estimate; the excess in the experimental AAV* values probably reflects contributions from desolvation, and indeed is largest where ApH* is signi- ficant.

Finally, we consider other possible homolyses involving inorganic complexes in aqueous solution for which volumes of activation are available. It has been proposed (13) that the internal redox decomposition of the 0-bonded sulfitopenta- amminecobalt(II1) ion in water involves a rate-determining initial step in which the SO3"- radical is created along with cobalt(I1) - i.e., that the Co-OSO2 bond undergoes homo- lysis:

slow [5] C O ( N H ~ ) ~ O S O ~ + --+ C O ( N H ~ ) ~ ' + + SOs'- + etc

Our present study lends support to this interpretation, since the volume of activation is strongly positive ( + 35 cm' mol-' (13);

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2170 CAN J CHEM VOL 64. 1986

the pressure range w a s only 100 MPa, so experimental uncer- tainty may have obscured any curvature of the In k vs. P plot). This volume of activation is unusually large by the standards set by Table 1, and may reflect homolysis with a change of spin state on going from cobalt(II1) (singlet) to cobalt(I1) (quartet), as this would be accompanied by substantial changes in metal- ligand bond lengths (14).

It might be thought that the markedly positive and pressure- dependent volume of activation (A v'* = + 16.0 em3 mol- ', A @ * = $2.1 X em3 mol-' M P ~ - ' ) for the acid-indepen- dent pathway for hydrolysis of azidopentaamminecobalt(I1I) ion (15) is indicative of a very plausible homolytic mechanism producing initially C O ( N I I ~ ) ~ ~ + and the familiar N,' radical, with co2+(aq) and gaseous nitrogen among the final products. The products of hydrolysis in dilute aqueous acid, however, appear to be exclusively C O ( N H ~ ) ~ O H ~ ~ + and HN3 (16), and certainly the reverse reaction in azide/hydrazoic acid buffer goes to at least 99% completion with very little reduction of cobalt(II1) (17). The heterolytic interpretation advanced previously (1 5, 17) therefore remains appropriate.

We therefore conclude that a strongly positive volume of activation provides a valuable piece of confirmatory evidence in the assignment of homolytic mechanisms of decomposition of metal complexes in aqueous solution. Caution, however, must be exercised in the use of AVx as a prima facie criterion of a homolysis mechanism, however plausible such a process may seem, unless there is supporting chemical evidence.

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(1970). 3. R. G. COOMBES and M. D. JOHNSON. J . Chem. Soc. A, 177

(1966). 4. M. J. SISLEY, W. RINDERMANN, R . VAN ELDIK, and T. W.

SWADDLE. J. Am. Chem. Soc. 406, 7432 (1984). 5. T. W. SWADDLE. In Mechanistic aspects of inorganic reactions.

Edited by D. B. Rorabacher and J . F. Endicott. Am. Chem. Soc. Symp. Ser. 198, 39 (1982).

6. A. R . SCHMIDT. M. Sc. Thesis, The University of Calgary. 1970. 7. W. LE NOBLE and R. SCHLOTT. Rev. Sci. Instrum. 47, 770

(1976). 8. J. H. ESPENSON. Chemical kinetics and reaction mechanisms.

McGraw-Hill, New York, 1981. p. 25. 9. T. W. SWADDLE and M. K. S. MAK. Can. J. Chem. 61, 473

(1983). 10. T. W. SWADDLE. Inorg. Chem. 22, 2663 (1983). 11. T. W. SWADDLE and P.-C. KONG. Can. J. Chem. 48, 3223

(1 970). 12. B. E. CONWAY and J. C. CURRIE. J . Chem. Soc. Faraday Trans.

I , 74, 1390 (1978). 13. R . VAN ELDIK. Inorg. Chem. 22. 353 (1983). 14. H. C. STYNES and J . A. IBERS. Inorg. Chem. 10. 2304 (1971). 15. W. E. JONES, L. R. CAREY, and T. W. SWADDLE. Can. J. Chem.

50, 2739 (1972). 16. G. C. LALOR and E. A. MOELWYN-HUGHES. J. Chem. Soc. 1560

(1 963). 17. T. W. SWADDLE and G. GUASTALLA. Inorg. Chem. 8, 1604

(1969).

Acknowledgement We thank the Natural Sciences and Engineering Research

Council of Canada for financial support.

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