= Catalytic cycle
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A <catalytic cycle> follows the changing forms of a <catalyst> through a <reaction mechanism> until its starting form is regenerated. The schematic binding cycle in <catalyst> illustrates the bookkeeping: C is consumed and recovered, whereas AC is a <reaction intermediate> formed and consumed. Cancelling both gives the net A-to-B <chemical equation>. Regeneration concerns the completed cycle; it does not imply that C avoids forming <chemical bonds> or exchanging <Electrons>. An alternative <reaction mechanism> may have more <elementary reactions> than the uncatalysed route and still be faster.<Chemistry 2e by Paul Flowers and others>[§12.7, Figure 12.19 and Homogeneous Catalysts: alternative steps, intermediate formation and catalyst regeneration]{ref}
For that reversible binding cycle, ideal <thermodynamic activities> give step <equilibrium constants> $K_1=a_{\mathrm{AC}}/(a_{\mathrm A}a_{\mathrm C})$ and $K_2=a_{\mathrm B}a_{\mathrm C}/a_{\mathrm{AC}}$. Their <product> is $K_1K_2=a_{\mathrm B}/a_{\mathrm A}=K$: the same cancellations occur in the equilibrium bookkeeping. Choose consistent <standard states> for the species. A proposed cycle with $K_1K_2\ne K$ for the same net conversion at the same <temperature> would contradict its specified <thermodynamics>. This statement concerns free-species <thermodynamic activities>. Appreciable binding in AC can change how the conserved total amount is partitioned among free A, free B and bound AC. An assay counting bound and free material together therefore needs that additional balance; unchanged $a_{\mathrm B}/a_{\mathrm A}$ does not by itself guarantee identical analytical totals when the amount of C changes.
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