Kinetics of the A → B→ С Mechanism: Full Analytical Derivation
The kinetics of consecutive first-order reactions $$\ce{ A->B->C }$$ provides a classic example of a system that leads to an elegant analytical solution. In this article, I derive the full expression for the time dependence of the product concentration $$\ce{ C(t) }$$, starting directly from the reaction mechanism.
Reaction scheme and basic assumptions
The reaction sequence $$\ce{ A -> [k_1]B -> C }$$ represents a standard consecutive first-order mechanism in which the reactant A first converts into the intermediate $\ce{ B }$, and $\ce{ B }$ subsequently transforms into the final product $\ce{ C }$. To construct an analytical expression for the time dependence of each species, we begin by stating the initial conditions and establishing the material balance for the system.
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