Free catalyst concentration

As has already been pointed out, any rate equation containing the concentration of the free catalyst is of little practical use if that concentration is unknown, is difficult or impossible to measure, and may vary with conversion, as is the case if a significant fraction of the total catalyst material is present in the form of intermediates of the reaction. This is often true in catalysis by enzymes or other trace-level catalysts. To be sure, the equations in terms of free-catalyst concentration remain correct. However, unless practically all the catalyst material is present as free catalyst, they no longer reflect the actual reaction orders. This is because the concentrations of the participants affect the rate not only directly as expressed explicitly in those equations, but also indirectly and implicitly through their effect on the free-catalyst concentration As the reactant concentration decreases, so do those of the intermediates in turn, this produces an increase in the free-catalyst concentration that boost the rate and, thereby, decreases the apparent reaction order. To reflect this facet correctly, what is needed are rate equations in terms of the total amount of catalyst material, a quantity that is constant and known. 

Equation 8.23 derived in the present section differs by having the total instead of the free catalyst concentration in the numerator, as well as two additional terms in the denominator. The equivalence of the two equations can be shown as follows Replacement of Ccat in eqn 8.25 with use of eqn 8.16 and subsequent replacement of Cx with the Bodenstein approximation (eqn 8.20 with additional term kvxC Cr) yields eqn 8.23. Equation 8.25 is simpler and therefore preferable if one can be sure that all but an insignificant fraction of catalyst is in free form. Equation 8.23 is not subject to this restriction, an advantage one must pay for with the inconvenience of having to handle two more denominator terms. 

In this matrix the sum of the elements of each row is proportional to the concentration of one of the members in the catalyts cycle. In other words, if we start the cycle with the free catalyst concentration taking part in the first step, then the first row is proportional to the free catalyst conentration (coverage of vacant sites in heterogeneous catalysis) - which we will consider as first intermediate and the second row is proportional to the concentration of the second intermediate, i.e. intermediate which is bound to the free catalyst, etc. From these mechanistic considerations we arrive at eq. (4.123), presented in the previous chapter. The ratio of the concentration of the intermediate to the total catalyst concentration is... 

Since for the kinetic measurements a large excess of catalyst is used, the concentration of free catalyst [M" ]/ essentially equals the total concentration of catalyst. Moreover, since ko k jt and under the conditions of the measurements the concentration of free 2.4 is small, the contribution of the uncatalysed reaction can be neglected and equation 7 simplifies to ... 

The effects of manganese on the cobalt/bromide-catalyzed autoxidation of alkylaromatics are summarized in Figure 17. The use of the Mn/Co/Br system allows for higher reaction temperatures and lower catalyst concentrations than the bromide-free processes. The only disavantage is the corrosive nature of the bromide-containing system which necessitates the use of titanium-lined reactors. 

HIGHER REACTION TEMPERATURE (190-210°C) AND LOWER CATALYST CONCENTRATION THAN WITH BROMIDE-FREE PROCESSES (< 140 C)... 

In all cases a transicis selectivity of around 7/3 is obtained Numbers separated by dashes indicate results in successive reuses Bromine-free ionic liquid Catalyst concentration 25 mM... 

Rhodium,3 osmium4 and ruthenium5 based catalyst systems are affected by nitrile in a similar way. This arises from the relatively high affinity of complexes of these metals towards nitrile group coordination.11 The resulting equilibrium between free catalyst and catalyst with bound nitrile reduces the effective catalyst concentration and hence reaction rate for a given set of conditions. 

The Michaelis constant has the dimension of a concentration and characterizes - independently of the method of approximation - the substrate concentration at which the ratio of free catalyst to catalyst-substrate complex equals unity. At this point, exactly one-half of the catalyst is complexed by the substrate. Likewise, one finds that at a value of [S = 10 Kki, the ratio of [E]/[ES]... 

It was shown by means of conductivity measurements that (Xxr)0 = c0, the initial catalyst concentration, and that initiation is almost instantaneous, but the question to what extent free ions and ion-pairs are involved is not yet entirely clear, though it seems probable that free ions are dominant because of this uncertainty we will denote these propagation constants by k. For rapid and completely efficient initiation, and termination by reaction with polymer... 

Type 2. Where a homogeneous catalyst of initial concentration Cq is present in two forms, either as free catalyst C or combined in an appreciable extent to form intermediate X, an accounting for the catalyst gives... 

Extending the definition of n-type and p-type reactions, as defined by Vol kenshtein (21) to the electron transfer step, it would seem that the only reaction given by Equation 1 is a p-type reaction. This reaction would be accelerated by the increase in the value of free hole concentration. On the other hand, all other reactions besides the one given by Equation 1 are n-type and would be accelerated by the increase in free electron concentration. Hydrocarbon oxidation reactions catalyzed by solid oxides are accompanied by oxidation and reduction of the catalyst and the degree of the stoichiometric disturbance in the semiconductor changes. The catalytic process in the oxidation of 2-methylpropene over copper oxide catalyst in the presence of Se02 can be visualized as ... 

The result of this approach was a 100-fold increase in the hydrolytic activity of the imprinted polymer compared with the background at pH = 7.6. As a control, another polymer was made using a complex between amidine and benzoate, showing a surprisingly 20-fold increase in the hydrolysis of the substrate. The authors also reported a kinetic investigation of the TSA-imprinted and the benzoate-imprinted polymers, in addition to the free catalyst in solution. Although the ratio substrate/catalyst is not specified, and therefore the steady-state conditions could not be verified, the authors claimed for the two polymers a Michaelis-Menten kinetic behaviour, with a higher profile for the TSA-imprinted polymer. On the other hand, the free catalyst in solution showed, as expected, a linear dependence of the rate from the substrate concentration. The TSA also showed a moderate selectivity towards its own substrate. 

---