The hypothetical reaction : $2A + B \to C + D$ is catalyzed by $E$ as indicated in the possible mechanism below -

Step$-1$ : ${\text{A  +  E }} \rightleftharpoons AE$ (fast)

Step$-2$ :${\text{AE  +  A }} \to {A_2} + E$ (slow)

Step$-3$ :${{\text{A}}_2}{\text{ +  B }} \to {\text{D}}$ (fast)

what rate law best agrees with this mechanism

  • A

    $r = k[A] [B]$

  • B

    $r = k[A] [E]$

  • C

    $r = k[A]^2 [E]$

  • D

    $r = k[A]^2 [B]$

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  • [AIPMT 2012]