The hypothetical reaction : $2A + B \to C + D$ is catalyzed by $E$ as indicated in the possible mechanism below -
Step-$1$ : $A + E \rightleftharpoons AE$ (fast)
Step-$2$ : $AE + A \to A_2 + E$ (slow)
Step-$3$ : $A_2 + B \to C + D$ (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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$Run$ $[A] / mol \ L^{-1}$ $[B] / mol \ L^{-1}$ Initial rate of formation of $D / mol \ L^{-1} \ min^{-1}$
$I.$ $0.1$ $0.1$ $6.0 \times 10^{-3}$
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$III.$ $0.3$ $0.4$ $2.88 \times 10^{-1}$
$IV.$ $0.4$ $0.1$ $2.40 \times 10^{-2}$

Based on the above data,which one of the following is correct?

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