Kinetics of multi-step reactions

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We consider a reaction of the type

$\text{A }+2\,\text{B}\longrightarrow \text{AB}_2$ Suppose that this reaction proceeds via the following reaction mechanism:

$\begin{aligned}\text{A }+\text{B} &\longrightarrow \text{AB}\quad\,\text{ slow reaction}\\ \text{AB }+\text{B} &\longrightarrow \text{AB}_2\quad\text{very fast reaction}\end{aligned}$ Which formula can we use for the reaction rate $r$ of the overall reaction (with rate constant $k$ )?

Chemical reaction kinetics: Kinetics of multi-step reactions

Kinetics of multi-step reactions