Turnover frequency and active site

In more fundamental studies, the reaction rate should not refer to the mass of catalyst or metal, but to the active site. As the total number of the active sites is not known, it is common practice, as recently discussed by the author et to substitute it with the total number of surface metal atoms, which can be correctly calculated by Eq. (7.71). The reaction rate expressed as the number of reacting molecules transformed per surface metal atom per second is often called as trunover frequency (TOF) and is expressed as sec . TOF is currently used to draw fundamental conclusions about the intrinsic activity of metals and the mechanism of the reaction. Unfortunately, many TOF values have been so frequently affected by large errors in dav, at least for supported metal catalysts, that they require a substantial revision. It is rather obvious that the number of active sites will always be lower than that of surface metal atoms, because either the latter one is not energetically equal in the reaction conditions or the active sites consist of nanoensembles of metal atoms (this point should be taken into account for any comparison with homogeneous or enzymatic catalysis). Hence, it is convenient to introduce the concept of real turnover frequency, given by the TOFr = TOF/fAs, where /as is the fraction of surface atoms working as active sites. 

When /as does not depend on dav the reaction is called structure-insensitive and the reaction rate is inversely proportional to dav In fact the reaction rate rm, (Eq. (7.26)), expressed as moles of reactant transformed per catalyst gram per second, is related to TOFr by the equation  

Therefore, when the reaction rate is plotted versus reciprocal dav, for structural insensitive reactions a straight line is obtained, from whose slope the product /as x TOFr can be calculated. Unfortunately there is presently no way to separate the two factors. 

Accordingly, a wide range of experiments about the metal particle nanoradius depending on the reaction rate for evaluating the performance of the catalyst and the active site will bring some impetus. Needless to say, such experimentation absolutely 

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