Outer sphere rate constant

The outer-sphere rate constant for the Cr(H20)5+/IrClg reaction can be estimated, using /larcus equation, as =10 M s". A value of this magnitude can obviously be competitive dtb that for the inner-snhere nath. which is more usual with the hiehlv labile CrtH,0)i ... 

How do we obtain kis and kos from such a complicated rate expression As indicated in equations (5.13) and (5.14), we can determine kso experimentally by carrying out the reaction between [Co(ox)2(en)] and [Co(en)3]2+ under pseudo-first-order conditions with varying excess [Co(en)3]2+. A plot of kobs vs [Co(en)3]2+ will give the second-order rate constant (kso) f°r the reaction. Using equation (5.15), and given the value for the inner-sphere rate constant, kis, which has been measured independently, the outer-sphere rate constant, kos, will be determined. In Experiment 5.6, Marcus theory will be used to model this reaction and the calculated vs the observed outer-sphere rate constants will be compared. 

Q5.15 Compare the magnitudes of the inner-sphere and outer-sphere rate constants. Comment. 

EXPERIMENT 5.6 MARCUS THEORY THEORETICAL CALCULATION OF THE OUTER-SPHERE RATE CONSTANT, kos, FOR THE REACTION BETWEEN [Co(ox)2(EN)] AND [Co(en)3]2+11... 

Table 1 lists outer-sphere rate constants of these kinds. Finally, there are outer-sphere reactions in which neither reagent is substitutionally inert on the time scale of oxidation-reduction, but the outer-sphere path is chosen in the absence of a ligand capable of bridging the two reagents. Only indirect comparisons establish examples of this class. Self-exchange between Fe and Fe is such an example. The appearance of the rate law term k[Fe l(Fe ] is remarkable in other reactions of aquated metal ions, the term k [M M ][H ] is so large that the former is buried in experimen-... 

All of the pre-exponential factors and contributions to the overall AG are incorporated into the transition state theory equation to obtain the calculated outer-sphere rate constant as... 

Under these conditions, the formation rate constant, k, can be estimated from the product of the outer sphere stability constant, Kos, and the water loss rate constant, h2o, (equation (28) Table 2). The outer sphere stability constant can be estimated from the free energy of electrostatic interaction between M(H20)q+ and L and the ionic strength of the medium [5,164,172,173]. Consequently, Kos does not depend on the chemical nature of the ligand. A similar mechanism will also apply to a coordination complex with polydentate ligands, if the rate-limiting step is the formation of the first metal-ligand bond [5]. Values for the dissociation rate constants, k, are usually estimated from the thermodynamic equilibrium constant, using calculated values of kf ... 

Rate constants for the formation of complexes from the aquometal ion and various chelating ligands are often predicted from the expected outer-sphere association constant (K ) and... 

The separation of the two stages is easier to discern when the rates of the two processes are so different, but it can also be seen in the ultrasonic spectra of metal-sulfate systems (Sec. 3.4.4). Ultrasonic absorption peaks can be attributed to formation of outer-sphere complexes (at higher frequency, shorter t) and collapse of outer-sphere to inner-sphere complexes (at lower frequency). In addition to uv spectral and ultrasonic detection, polarimetry and nmr methods have also been used to monitor and measure the strength of the interaction. There are difficulties in assessing the value of ATq, the outer-sphere formation constant. The assemblage that registers as an ion pair by conductivity measurements may show a blank spectroscopically. The value of Aq at T" K may be estimated using theoretically deduced expres-... 

A major application of eqn. (47) is to diagnose the presence of catalytic, presumably inner-sphere, electrochemical pathways. This utilizes the availability of a number of homogeneous redox couples, such as Ru(NH3)e+/2+ and Cr(bipyridine) +,2+ that must react via inner-sphere pathways since they lack the ability to coordinate to other species [5]. Provided that at least one of the electrochemical reactions also occurs via a well-defined outer-sphere pathway, the observation of markedly larger electrochemical rate constants for a reaction other than that expected from eqn. (47) indicates that the latter utilizes a more expeditious pathway. This procedure can be used not only to diagnose the presence of inner-sphere pathways, but also to evaluate the extent of inner-sphere electrocatalysis (Sect. 4.6) it enables reliable estimates to be made of the corresponding outer-sphere rate parameters [12a, 116, 120c]. 

Propose a three-step reaction mechanism (involving K3 for [Co(en)3]2+ and the outer- and inner-sphere rate constants, fcos and kis, respectively) that is consistent with the stoichiometry information. 

Few standard rate constants are available for simple one-electron redox reactions known to follow inner-sphere pathways. One reason is that reactions are required that are free from coupled chemical steps (i.e., are chemically reversible) so that values of E, and hence k can be obtained. Such redox couples [e.g., Ru(III)/(II)] exhibit rapid electrode kinetics even for outer-sphere pathways, so that the inner-sphere rate constants commonly are immeasurably large. 

Clearly, there are some very intriguing results that any theory must be able to explain. For example, the two ligands 17 and 18 afford complexes which are either extremely active or inactive. Further the Mn(II) complex of the pentamethyl ligand 10 has no pH dependence to its catalytic rate, even though it has the highest pH-dependent rate measured in this class of complexes, with k = 3.90 x 10 M" s . Thus, any theory which attempts to rationalize the observed reaction rate constants for catalytic dismutation of superoxide must predict why the Mn(II) complex of ligand 10 has no pH-dependent outer-sphere rate. 

Stopped-flow studies of the base hydrolysis of aminocarboxylato-complexes of (as well as Mo and have been reported. The 1 1 complexes are involved with edda , nta , and edta, and a 1 2 (V ligand) complex with ida . The observed pseudo-first-order rate constant varies with OH according to the equation /robs=(A i+A 2J os[OH"] )/(l-l-Aos[OH ]") where =2 for and = 1 for and Koa is the outer-sphere formation constant between complex and OH ion, and and are rate constants for attack by H2O and OH ion respectively. The non-bonded carboxylate arms of the ligands increase values of k and k by factors of 10 —10 . 

The pseudo-first-order rate constant (/robs) for the base hydrolysis of amino-carboxylato-complexes of Mo, and vary with [OH ] according to the general equation /robs=(/ri-l-/r2i ro[OH-]")/(l-l-J5 o[OH ] ) with n=2 for and n=l for Mo i and W i, where Ko is the outer-sphere association constant and k and k are the rate constants for reaction of the rapidly formed ion-pair with HgO and OH ion respectively. Complexes with ida , edda , nta , and edta ions were investigated, and non-bonded carboxylate arms were found to increase values of k and k by factors of 10 —10 . An analytic procedure has been proposed, based on these reactions, which allows concentrations of Mo, and to be estimated to an accuracy of ca. 5 % at molarities in the region of 10 M. ... 

The reaction of Mg + with pyrophosphate is about twice as slow in D2O as in H2O (at 15 °C). This difference is attributed to a change in the outer-sphere association constant rather than to a change in the interchange rate constant. Kinetics of solvolysis of [Fe(bipy)3] + in D2O lend support to the mechanism of dissociation via a unidentate-bipyridyl transient intermediate postulated, for aqueous solution, many years ago. ... 

The dependence of rate constant on ionic strength is still widely used, often in conjunction with the dependence of rate constant on dielectric constant, as an indicator of substitution mechanism. Recent instances of this classical approach include the reaction of /ra j-[Co(dmgH)2(SCN)(tu)] with thiourea (tu), aquation of trans-[Rh(dmgH)2Cl(tu)], aquation of the [Co(02CCHaCl)(NH3)6]"+ cation, and substitution at the [Fe(CN)6(OH2)] anion by nitrite, thiocyanate, sulphite, or nitrosobenzene. Salt effects on observed rate constants for the reaction of nickel(n) with pyrophosphate operate via the outer-sphere association constant rather than via the interchange rate constant. ... 

From an analysis of the polarographic behaviour of [Ni(edrate constant for Ni(OH)+ + Hedda was estimated to be 6.9 x 10 1 mol s. Since this is numerically close to the water-exchange rate constant at Ni 5, and the outer-sphere formation constant is expected to be ca. llmol the author suggests that the normal mechanism applies in this case. Measurement of the dissociation rate of the nickel complex of (6) has also been used to estimate kt the results are discussed... 

Ru(NH3)5SalH]. An inner-sphere complex is formed with a second-order rate constant of 6.3 x 10 M s and the electron transfer rate is in excess of 10 s much greater than the calculated outer-sphere rate of 60s due to the favorable t2g/t2g overlap. 

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