Early stages of the hydrolysis of chromium(III) in aqueous solution—7. Kinetics of cleavage of the hydrolytic dimer in acidic solution

Polyhedron Vol. Printed in Great

IO, No. Britain

16, pp.

18654872,

0277-5387/91 %3.00+.00 Pergamon Press plc

1991

EARLY STAGES OF THE HYDROLYSIS OF CHROMIUM(II1) IN AQUEOUS SOLUTION-7. KINETICS OF CLEAVAGE OF THE HYDROLYTIC DIMER IN ACIDIC SOLUTION? LEONE

SPICCIA

Department of Chemistry, Monash University, Clayton, Victoria 3 168, Australia (Received 26 February 1991; accepted 4 June 1991)

Abstract-The kinetics of cleavage of the hydrolytic dimer of chromium(II1) have been studied in acidic solution and at elevated t~peratures using spectrophotometric methods. The slightly curved dependence of kobson [H+] has been attributed to equilibration between a doubly-bridged dimer (DBD) and two singly-bridged dimer forms (fully protonated, SBD and monodeprotonated SBD-H), which are related by a protonation equilibrium that gives rise to the acid dependence of kobs. Two pathways for cleavage of SBD forms into Cr3+ are proposed involving SBD and SBD-H and the actual bridge cleavage reactions are concluded to be acid independent. The calculated rate constants and activation parameters at 25°C were as follows : kseo+, = 3.9( +0.4) x lo- 7 s- ’ [AH* = 98( + 3) kJ mol- ’ and AS* = 2O(rt:ll) JK-’ mol-‘1; ksBD= 2.7(+0.2)x10e6 s-’ [AZ%*= 112(f2) kJ mol-’ and AS* = 83( k 5) JK- ’ mol- ‘3.The significance of these results is discussed and a comparison with existing information on the oxo-bridged hydrolytic dimer of chromium(II1) is made. The rate of the dimerization reaction between Cr3+ and CrOH’+ has been estimated and found to be about 1000 times slower than the dimerization of two CrOH*+ ions.

Hydroxy- (or oxo-) bridged binuclear complexes, dimers, are the first products of the hydrolytic polymerization of many metal ions in aqueous solution. Consequently, there is continuing interest in the properties of these complexes. 2,3 However, most work has focussed on complexes in which the metal centre is bound to several N-donor ligands3 and in comparison very few hydrolytic dimers, in which the ligands are derived entirely from the solvent (H,O), have been studied in detail.2-7 Thus, comparisons of the behaviour and properties of binuclear complexes containing, for example, Ndonor ligands, with those of purely hydrolytic dimers are generally lacking and there is some uncertainty as to whether the information obtained for the former is directly relevant to the hydrolytic behaviour of aqueous metal ions. The hydrolytic dimer of chromium(II1) is one oligomer which has been the subject of extensive characterization studies3,“9 as well as comprehensive kinetic and ther-

modynamic investigations 1,6,9-1 3and is particularly well-suited for making such an assessment. Thompson and Connick6 have demonstrated that the hydrolytic dimer can exist in both singly-bridged (SBD) and doubly-bridged (DBD) forms. Subsequently, the structure of DBD has been determined,’ and its magnetic and spectroscopic properties investigated.‘* Thompson6*g further showed that the acid cleavage of DBD into Cr3+ involves two consecutive, clearly separable processes [eq. (l)]. The order of these processes is believed to bc reversed in the dimerization of Cr3+. ” The overall rate of acid cleavage is much slower for SBD than for DBD which means that each of these processes can be studied with little interference from the other. As a result, measurements of the rate of interconversion’*9 and equilibrium’ 3 between SBD and DBD have been possible. In addition, estimates of the overall rate of acid cleavage to give Cr3+ are also available but were obtained at variable ionic strength.’ DBD e

t Part VI : Ref. 1. 1865

SBD ;--‘Cr3+

(1)

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L. SPICCIA

We report here the result of a variable temperature and [H+] (I = 1.OM) study of the cleavage of the dimer into Cr 3+ from which two reaction pathways have been established. EXPERIMENTAL Materials Solutions

of

the

hydrolytic dimer [Cr,(pOHh(OH,hIWOJ,, were prepared using a recently published method, ’ 5 the only modification being that HC104 rather than aromatic sulphonic acids was used to oxidize chromium metal to Cr2+ . The resulting crude dimer solutions were purified and standardized as described previously. ’ OWhen stored at - 18°C stock dimer solutions showed no change in composition after several months. Analytical grade reagents were used throughout. Water was deionized and doubly distilled prior to use. NaClO, and LiC104 solutions of known concentration were prepared by neutralization of standardized solutions of either NaOH or LiOH with HC104. All solutions were filtered through 0.22 pm Sartorius SM 11307 cellulose nitrate membrane filters prior to use in kinetic experiments. Instruments The instruments and techniques used to measure the pH of the solutions and to carry out kinetic measurements have been described previously. ’ Kinetic experiments Reaction mixtures were prepared at the desired temperature (62.391.5”C) by mixing equal volumes of a dimer solution ([Cr,(p0H),(OH,)J4+ = 4.28 x lo- 3 M, [HClO,] = 9.3 x lo- 3 M and [NaClO,] = 0.122 M, determined at room temperature, ca 22°C according to published methods) with a series of solutions containing varying proportions of HClO, and NaClO, (or LiC104 in some cases) but whose ionic strength was constant (1.83 M at room temperature). The final reaction conditions were [Dimer] = 2.14 x lop3 M, [HClO,] = 0.0271-0.919 M and I = 1.0 M (NaC104 or LiClO,). In the analysis of the kinetic data these acid concentrations were corrected for the temperature-dependent expansion of the solvent. The reaction was monitored in the UV region (A c 300 nm) where the absorbance was found to decrease as the dimer is converted into Cr3+. The data were analysed at 250 nm where this decrease was between 0.5 and 0.7 units. Pseudo-first order

rate constants, kobs, were calculated at this wavelength from the change in absorbance, A,, with time, t, by means of linear least-squares fitting of the data to the expression A, = (Ao-A,)eeko~‘+A,. In most cases Ao, A, and kobswere determined from the A, vs t data. However, as a check on the suitability of the procedure A, was measured experimentally for several runs and used in the calculation of kobs. The values of kobs obtained from the two treatments were within experimental error. Furthermore, experimental and fitted A, values were in excellent agreement. RESULTS The overall rate of cleavage of the hydrolytic dimer of chromium(II1) was measured in the temperature range 62.3-915°C and [H+] range 0.026 0.90 M, but at constant ionic strength (1.0 M). High temperatures were chosen because this gave reaction rates which could be measured using conventional spectrophotometric methods. Chromatographic analysis was used to show tha.t Cr’+ is the only species present at the completion of the reaction. That is, the reaction is irreversible under the conditions used. The spectrophotometric data could be fitted accurately with a single exponential function (O.O02k,,,,< ok,,, < O.Olk,,,J, which indicates that the process being followed is first order with respect to the dimer. Table 1 summarizes the [H+] and temperature dependence of the observed rate constants (kobs). The dependence of kobson [H+] is almost linear (slight curvature becomes apparent at high [H+]) with a non-zero intercept at all temperatures (see Fig. 1). Thus, the cleavage of the dimer involves at

Table 1. Observed rate constants (kobs)for the cleavage of the hydrolytic dimer into Cr’+ in acidic solution at various temperatures and I = 1.wh T (“C)

lH+l’ (M)

10’ kobs(s- ‘)

62.3

0.905 0.905 0.725 0.725 0.545 0.545 0.545 0.365 0.185 0.0945 0.0495 0.0270

5.33 5.23 4.39 4.42 3.45 3.34 3.37 2.47 1.55 0.984 0.786 0.650

Early stages of the hydrolysis of chromium(II1) in aqueous solution-7 Table 1.-continued

T (“Cl

[H+]‘(M)

lo5 kobs(s- ‘)

67.6

0.902 0.902 0.722 0.722 0.543 0.543 0.363 0.184 0.0942 0.0494 0.0269

8.68 8.56d 7.08 7.24d 5.71 5.56d 4.08 2.37 1.75 1.38 1.18

76.9

0.897 0.897 0.716 0.716 0.540 0.540 0.361 0.183 0.183 0.0937 0.0937 0.0491 0.0491

20.0d 20.1 16.7d 16.6 13.4 13.4d 9.75 6.28 5.92 4.29d 4.23 3.50 3.39

83.5

0.894 0.716 0.538 0.360 0.182 0.0933 0.0489 0.0266

36.2 30.7 24.6 18.5 11.6 8.62 7.28 6.52

91.5

0.712 0.535 0.535 0.358 0.358 0.181 0.0928 0.0928 0.0486 0.0486 0.0486 0.0265 0.0265

53.8d 43.7 44.1” 34.7d 33.6 23.9 16.9 17.2d 15.2 14.5 15.0d 13.2 13.6

“Except where otherwise indicated NaCIO, was used as supporting electrolyte. ‘A comprehensive table listing 17~~~values and the weighting factors used in fitting the data to eq. (4) can be obtained from the author on request. ’ [H ‘1 corrected for the temperature dependent expansion of the solvent. dLiC1O, used as supporting electrolyte.

1867

least two pathways, one of which is dependent on [H+]. In contrast, Thompson’ observed no systematic variation of kobs with w+] in the concentration range l-8 M but in this case no attempt was made to maintain constant ionic strength. The simplest reaction mechanism which will accommodate the almost linear dependence of kobs on [H+], and existing information on the interconversion between SBD and DBD forms’,9 is that given in Scheme I. The overall process involves several pathways which can be subdivided into two types: cleavage of DBD to give SBD forms (top half of Scheme I) followed by cleavage of SBD forms into Cr3+. Thompson’ has shown that there are substantial differences in the rates at which these processes occur, interconversion between SBD and DBD being ca 200 times faster than cleavage to Cr3+. In fact, measurements of the equilibrium between SBD forms and DBD have been possible without interference from the cleavage of SBD forms to Cr3+.13 This suggests that the overall cleavage of the dimer is rate-determined by the cleavage of SBD forms. In Scheme I, the rate constants of importance are ksBn and kSBD_H,which represent the rate of bridge cleavage within SBD and SBD-H, respectively. Note that the actual bridge cleavage processes are proposed to be acid independent and that the acid dependence of kobs arises from the protonation equilibrium between SBD-H and SBD. If the actual bridge cleavage processes were acid catalysed, a dependence of kobs on [H+]’ might be expected. The rate law for the

HDBD

SBD

bBD

ho

L. SPICCIA

1868

42.0

7J

30.0

3

24.0

P

18.0 12.0 6.0

IH+lC-4

Fig. 1. Acid concentration and temperature dependence of the observed rate constant for cleavage of the hydrolytic dimer of ehromium(II1) at Z = 1.O M. Full lines represent the calculated values of kobsdetermined from eq. (4). (a) 62.3”C; (m) 67.6”C; (m) 76.9”C; (0) 83.5”C; (+) 915°C.

cleavage of the dimer may be written

as :

d[Cr3+] ~ = ksrn,_n[SBD-H] +ks&BD], dt

(2)

for where kSBD_Hand ksBD are the rate constants cleavage of SBD-H and SBD, respectively. Use of the expressions K1 = [SBD-H]/[DBD], K,, = [SBD-H][H+]/[SBD] and [DIM], = {[DBD] + [SBD-H] + [SBD]} = (1 + l/K, + [H+]/IY,K,,}[DBD] followed by simplification gives eq. (3). [k,, + k,[H ‘II [l + l/K, + [H+]/e,K,,]

d[Cr3+] -= dt

[D1M1T = k,bs[DIM]T

(3)

[In eq. (3) k,, = kSBD+,/KI and kc = kSBD/KIKal.l In the case where both K, and K,K,, are large and the denominator in eq. (3) is ca 1, a linear dependence of kobs on [H+] would result. Taking into account the temperature dependence of each parameter gives the following expression for kobs : kT [i( h

AH& - TASfmc exp

RT

>

>)I -AH;, AH; - TASg

+[H+] exp

RT

+ TAS;,

(4)

(f 2.7) kJ mall ’ and AS” = - 15.0( f 8.9) JK-’ mol- ‘) and KIKl (AH” = 29.5( f 1.1) kJ mol- ’ and AS” = 104.4( k3.7) JK- ’ mol- ‘) were used to reduce the number of parameters in eq. (4). The activation parameters for k, and k, (Table 2) were determined from weighted nonlinear least squares fitting of the temperature and [H+] dependence of kobs to eq. (4). The procedure involved minimization of Ei FV~(k~b,,i-ka&2 where W, = li~i~,~ and kobs,iykcaic,iy W and okobi are the observed rate constants, calculated rate constants, weighting factors and standard error in each kobs value, respectively. An excellent fit of the data is indicated by the small standard errors associated with each parameter (Table 2). The activation parameters for each cleavage process have been used to calculate kc and k,, at 25”C, which is outside the range of temperature used in this study. From these values, published values of K, and K,K,,, (respectively, 10.1 and 1.83 at 25”C)‘3 and using the expressions kSBD_H= K,k,, and k SBD= kcK,Ka,, kCSBD_H and ksBD have been estimated. Activation parameters for ksBD_Hand ksBD were determined from those of k,, and k, and the thermodynamic constants of K, and K,K,, given above. All of this information is listed in Table 2 and will be used in the discussion to follow.

RT

+B+lexp In analysing thermodynamic

-AfG,,, + TAS;,,, RT

the data, previously determined13 constants for K1 (AH” = - 10.4

DISCUSSION The kinetic data for cleavage of the hydrolytic dimer of chromium(II1) can be interpreted in terms of two bridge-cleavage processes (Scheme I), cleav-

Early stages of the hydrolysis of chromium(II1) in aqueous solution-7

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Table 2. Activation parameters and calculated rate constants for cleavage of the hydrolytic dimer of chromium(II1) lo6 k (s- ‘)

Parameter k, k, ksrwd &n-He

0.038( +0.002) 1.46( f O.OSp 0.39( + 0.04) 2.7( kO.2)

k_(

22(f

k-,&j k-0

52(&-l) 520 (est)g

1)

AH* (kJ mol- ‘) 108.7( f0.8)b 82.7( +0.6)b 98(+3) 112(f2) llO(k5) 59(f2) 104 (est)*

AS (JK- ’ mol- ‘)

35( +2)b - 22( f 2)b 20(fll) 83(+5) 35(* 16) -130(f8) 0 (est)h

“Rate constants at 25°C calculated from the activation parameters. ‘Determined by fitting the data to eq. (4). ‘Units are M-’ s-l. dActivation parameters for kSBD_H determined assuming kseD_H= K,k, and using data for k, given above and published values of K,, AH”(K,) and AS”(K,) (ref. 13). ‘Activation parameters for k,,, determined assuming k,,, = k,K,K,, using data for kc given above and published values of K,K,,, AH”(K,K,,) and AS”(K,K,,) (ref. 13). ‘Data from ref. 1. gEstimated from k_,K,, assuming Kp3 N 0.1 Mm’. hActivation parameters for km, estimated from parameters for km,K,, and assuming AH” (K,,) N -45 kJ mall’ and AS” (Kp3) = - 130 JK-’ mall’.

age of SBD-H (kSBD_n)and SBD (RSBDj.The actual bridge-cleavage reactions are proposed to be acid independent and the acid dependence of kobs attributed to equilibration between DBD and SBD forms. This is much faster than cleavage of SBD forms and involves a protonation equilibrium for SBD-H, which accounts for the acid dependence. Existing data on the cleavage of DBD into SBD suggests that this is not unreasonable (Table 2). In this case, acid-catalysed cleavage becomes apparent at the highest [H+],‘,9 but the rate for this pathway (k_,K,,) in 1 M H+ at 25°C is only twice as fast as the corresponding uncatalysed process (k- ,). The value of Kp3 has been estimated3 as < 0.1 M-‘. Protonation of the bridging OHin SBD is expected to be more difficult than for DBD because of the higher overall charge while for SBD-H protonation is more likely at the terminal OH-, giving SBD (at 298.15 K, pKa,(SBD) determined from equilibrium studies ’ 3 and kinetic measurements’ were 0.74 and 1.00, respectively). It is important to note that decreases in protonation constants of 100 fold (or even higher) per unit charge increase are not uncommon for terminal OH- groups coordinated to Cr3+ or chromium(II1) oligomers. lo Assuming similar variations in the case of bridging

OH- groups the protonation constant for the bridging OH- group in SBD is likely to be << 0.001 M-‘. Thus, under the conditions of the current study ([H+] N 0.02-l M) acid-catalysed bridge cleavage of SBD forms would become apparent if the rate of cleavage of the protonated form, i.e. Cr-OH,Cr, is faster than the uncatalysed pathway by at least 1000 fold. To the author’s knowledge there are no examples of singly-bridged binuclear complexes of chromium(II1) for which such accelerations in bridge cleavage rate are found (see ref. 3 for a recent review). In the case of rhodium(III), however, acid-catalysed cleavage processes are not uncommon for both singly- and doubly-bridged complexes. 3 An excellent example highlighting this behaviour is the A,A-[(en), Rh(OH),Rh(en),14+ complex.‘6 Holwerda and co-workers” claim to have isolated an oxo-bridged aquo dimer (H,O)&rO Cr(OH & 4+, as a product of the oxidation of Cr2+ with 1,Cbenzoquinone. This species cannot be obtained by deprotonation of SBD because this occurs at the more acidic terminal HZ0 groups. Indeed the kinetics of conversion of SBD into DBD have been followed over several deprotonations of SBD but no evidence for bridge deprotonation was

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L. SPICCIA

obtained.’ This would be apparent in the UV-vis spectrum where the appearance of intense absorptions characteristic of oxo-bridges would occur, as is the case for (NH,)SCrOHCr(NH3),5+.3,‘8 Furthermore, deprotonation of DBD results in the formation of the “active” dimer hydroxide Cr& 0H),(OH),(OH2)4 - 2Hz0 and not an oxo-bridged binuclear species. Cleavage of Holwerda’s 0x0 dimer’7b in acidic solution (1 M HC104) is much faster than cleavage of SBD forms, found in this study (difference in rate ca 1300 fold) and previously by Thompson.’ This is a surprising observation given that the oxo-bridged dimer would be expected to be protonated in acidic solution [note that pKa for (NH,),CrOHCr(NH,),‘+ is 7.6]19 and there are no obvious steric factors which would hinder this protonation process. Thus, it would be expected that an oxo-bridged hydrolytic dimer of this type would be protonated in acidic solution and its cleavage behaviour should parallel that observed for SBD forms. The rate of bridge cleavage in acidic solution is generally faster for DBD than for SBD forms (Table 2), i.e. k_ , and k_ ,, are larger than kSBD+,and kSBD. This cannot be attributed to a change in nucleophile because an important feature of these bridge-cleavage reactions is that they involve attack by a common nucleophile, H,O from the solvent. Note that this is not the case for bridge-formation reactions where coordinated OH -, H20 and OzP (in some cases) can all act as nucleophiles. Although the commonality of nucleophiles reduces the complexity of bridge-cleavage processes, cf. bridge formation, there are nevertheless several other factors that could influence the rate of these processes. These include : (i) electrostatic attraction between the differently charged dimer forms and the incoming nucleophile ; (ii) the relative lability of the chromium(II1) coordination spheres which is known to be influenced by the degree of deprotonation on each chromium(III) centre ; ‘3’ ’ (iii) geometrical differences between dimer forms which may influence the ease of nuclephilic attack ; (iv) hydrogenbond stabilization of deprotonated forms3 In the case of SBD-H, intramolecular hydrogen-bond stabilization is believed to be important ~~3’~ and is likely to influence the rate of both bridge formation and cleavage reactions. This means that kSBD+,is probably not a true measure of the rate of cleavage of SBD-H and furthermore, the form undergoing bridge cleavage is uncertain. From the well-established accelerations in substitution rates with degree of deprotonation of reactants”,*’ it would seem that cleavage of SBD-H should be faster than cleavage of SBD, but the opposite is true in practice (Table 2). The most likely explanation is that the

hydrogen-bonded form does not participate in bridge cleavage and retards the process. Alternatively, the higher charge on SBD (5 +), cf. SBDH (4+), suggests a greater attraction of SBD for H,O and this might be responsible for the observed faster rate of cleavage of SBD. However, previous work on the rate of H,O exchange on Cr3+ and CrOH*+ ” and intramolecular ring closure within SBD forms’ has shown that labilization of the coordination sphere of chromium(III), induced by deprotonation, has a much greater effect on reactivity than these electrostatic effects. The faster rate of bridge cleavage for DBD (k_ , = 2.7 x lop5 ss ‘) when compared with SBD (kst’n = 2 x lo- 6 s- ‘) is probably reflecting a higher lability of DBD (OH/Cr = 1.O) which overall has a higher degree of deprotonation than SBD (OH/Cr = 0.5). In addition, the double-bridging moiety in DBD (bridging 0-Cr-0 angle of 78”) introduces constraints which effectively enlarge some adjacent angles in the chromium(II1) sphere and expand some of the faces of the chromium octahedron. For an associative substitution this might facilitate nucleophilic attack. The actual rate of bridge cleavage within protonated DBD, Cr(p--OH)&-0H,)Cr5+ (Scheme I) has been estimated as 5 x 1O-4 s- ’ (assuming KP3 = 0.1 M- ‘). A somewhat faster rate of cleavage of protonated DBD, cf. DBD and SBD, would not be unexpected since bridging H20 would be held less tightly than bridging OH-, but this difference may not be that large. The activation enthalpies for bridge cleavage are concentrated in the range 98-l 12 kJ mol- ’ while the activation entropies cover a wider range, & 80 JK- ’ mall ’ (Table 2). In the case of SBD-H, hydrogen-bond stabilization would affect AH* and furthermore, it is not known whether the form undergoing cleavage is the hydrogen-bonded form or not. Apart from this, the remarkably constant values of AH* for dimer bridge cleavage correspond closely with those determined for (NH3)5Cr and c&- and trans-[(NH3)5Cr (OH)Cr(NH3L5+ (OH)Cr(NH3)4(OH2)]5+ which range between 105-113 kJ moll’3,2’ and more importantly with AH* for H,O exchange on Cr3+ and CrOH*+ (respectively, 109 and 111 kJ mol- I).*’ On the basis of these comparisons it could be argued that these reactions all involve a similar mechanism @OSsibly I,) and that there are no dramatic differences in the lability of the chromium(II1) coordination sphere for each form of the hydrolytic dimer. However, the data for HZ0 exchange on Cr3+ and CrOH’+ has firmly established that changes in mechanism, from I, to Id, and lability derived solely from AS* are possible. *’ Indeed, sub-

1871

Early stages of the hydrolysis of chromium(II1) in aqueous solution-7 stantial variations in AS* are found for the bridgecleavage reactions but their interpretation is not straightforward. The results of this study together with measurements of the SBD-DBD equilibrium’3 and of the equilibrium distribution of polynuclear species in partially neutralized solutions of Cr3+ I2 allow prediction of dimerization rates for mononuclear chromium(II1) species. For example, from the reaction sequence for the formation of DBD from Cr3+ (Scheme I) it can be shown that k, ,, the rate of dimerization of CrOH2+, is given by eq. (6) k', =

P&,ksm-dk,K,2

= ,%AclKa2;

(6)

where /?22 is the stability constant for the dimer [5.6(+0.5)x 10e6M-’ at 25”C],‘2 K,is the first acid dissociation constant of Cr’+ [5.13( f 0.4) x lo- 5 M at 25”C],” K, = (k,/k_ ,) is the equilibrium constant for interconversion between SBD-H and DBD, kSBD_”is the rate of cleavage of SBD-H and k,, is the overall rate for the uncatalysed cleavage of the dimer (Table 2). This calculation gave k,, = 8(+2)x10P5MP’sP’whichisinreasonable agreement with the directly determined value of 2.0( + 0.4) x 1O- 4 M ~ ’ s- ‘. ’ ’ Similarly for the reaction of Cr3+ with CrOH2+, the rate of dimerization k,, is given by eq. (7) k,o =

B22k-,ksmlk,&Ka

=

lL&clK;

(7)

where K,, is the first acid dissociation constant of SBD,13 ksBDis the rate of cleavage of SBD and k, is the overall rate of acid-catalysed cleavage of dimer (Table 2). The value of klo [1.6(-10.3)x 10e7 MP’ sP ‘1 obtained in this way is much lower than that given previously in ref. 11 where a calculation error was made. The reaction of Cr3’ with CrOH2+ is ca 1000 times slower than dimerization of CrOH2+, further demonstrating the dramatic effect of deprotonation on reactivity. The predicted rate of the reaction between CrOH2+ and Cr3+ is only slightly faster than the rate of H20 substitution on Cr3+ (4.3 x lo-* M- ’ s- ’ when corrected for [H,O]). This indicates that the difference in nucleophilic character between coordinated OH- and H20 from the solvent is small, assuming of course, that the coordinated OH- is the attacking nucleophile in the dimerization reaction. Indirect evidence exists suggesting that this is the case.3,22 The constant for the 2CrOH2+ it SBD-H equilibrium is K, , = k, ,/kseD.,, N 500 M- ’ and is much greater than that for the Cr3+ fCrOH2+ F? SBD equilibrium, where K, o = k, O/kSBD1: 0.6 M- ‘. This comparison suggests that SBD forms become strongly favoured over mononuclear chrom-

ium(II1) tonation

species as the overall increases.

degree

of depro-

CONCLUSION Bridge formation and cleavage processes play important roles in the formation, cleavage and interconversion reactions of hydrolytic oligomers but the information available on these processes is limited. The current and previous’,“3 kinetic investigations of the hydrolytic dimer of chromium(II1) have focussed attention on the factors that determine the rate of these substitution processes. The important factors, some of which also determine the behaviour of A4M(~-OH)2MA44f systems3 include the degree of deprotonation, lability and overall charge on the dimer species undergoing reaction, the nature of the attacking nucleophile,3 the mechanism of substitution and in the case of SBD-H, intramolecular hydrogen-bond stabilization3 However, it has been difficult to disentangle the relative importance of each of these factors. In comparing the information for the hydrolytic dimer with the numerous studies on related systems of the type A4M(p-OH)2MA44f, it is found that the behaviour of the hydrolytic dimer parallels closely that of these tetraammine systems at low pH and (< 2).‘,3*9 This is true of both bridge-cleavage formation processes. At higher pH values, such as those found in natural systems, the behaviour of the hydrolytic dimer becomes vastly different from that of the tetraammines. ‘s3In the case of the hydrolytic dimer, many coordinated H,O ligands are present which when deprotonated allow bridge formation processes, in particular, to occur at greatly enhanced rates. For example, double deprotonation of SBD (pK,, = 4.30)’ has a much greater effect on the rate of ring closure than monodeprotonation (pK,, = 1.OO).’ In addition, the dimerization of DBD to give the tetramer occurs at measurable rates at pH > 3 [pK,,(DBD) = 3.681 and is followed by further polymerization.23 This is in complete contrast to the tetraammine complexes, where once diol formation (DBD forms) is complete further reaction (except for bridge deprotonation) is prevented by the presence of four nitrogen-donor ligands. 3

Acknowledgements-Part of this work was carried out at the Institut de Chimie, UniversitC de Neuchdtel, Neuchbtel, Switzerland under support from the Swiss National Foundation. Financial support was also received from the Australian Research Council.

L. SPICCIA

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