Question #44814

The aminolysis of phenyl acetate ($E$) by a primary amine ($A$) in an aprotic solvent at 298 K proceeds via a zwitterionic tetrahedral intermediate ($T^{\pm}$). The proposed mechanism involves the following elementary steps:

Step 1: $E + A \rightleftharpoons T^{\pm}$ (forward rate constant $k_1$, reverse $k_{-1}$)

Step 2: $T^{\pm} \xrightarrow{k_2} \text{Amide} + \text{Phenol}$

Step 3: $T^{\pm} + A \xrightarrow{k_3} \text{Amide} + \text{Phenol} + A$

The experimental initial rate of amide formation is expressed as $v_0 = k_{app}[E][A]$. Applying the steady-state approximation to $T^{\pm}$, what are the limiting values of the apparent second-order rate constant $k_{app}$ at very low amine concentration ($[A] \to 0$) and very high amine concentration ($[A] \to \infty$), respectively?