Imaginary equivalent pathway

None the less, a set of rules can be given for catalyst systems with a macs. As shown in the previous section, the rate equation for a catalytic reaction with a macs is the same as that for an imaginary (linear) simple pathway that "starts" and "ends" with the macs. Think of the catalytic cycle as being "cut" at the macs to give a linear pathway with the macs at both end (see Figure 8.5). That imaginary equivalent pathway has the same rate equation as the actual catalytic cycle. With this principle, the rules for reaction orders deduced in Section 7.3.1 can be reformulated for catalytic cycles with a macs (as in the earlier section, the rules are for the forward rate if the reaction is reversible). 

The forward step consuming the macs corresponds to the first step in the equivalent imaginary linear pathway. This correspondence immediately yields the following rules regarding reaction orders from the rules 7.13 to 7.16 in Section 7.3.1 ... 

If significant fractions of the catalyst material may be bound in the form of reaction intermediates, the rules for reaction orders in noncatalytic simple pathways no longer apply. However, if one of the cycle members—the free catalyst or an intermediate—is a macs (most abundant catalyst-containing species, containing practically all of the catalyst material), the rules for noncatalytic pathways can be adapted The rate equation and reaction orders for the cycle are the same as for an imaginary equivalent linear pathway that starts and ends with macs. A cycle member that contains only an insignificant fraction of catalyst material is a lacs (low-abundance catalyst containing species), and the denominator terms it contributes can be dropped. 

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