Question #44839

The formation of an oxime from hydroxylamine (\ce{NH2OH}) and acetone proceeds via a carbinolamine intermediate ($I$) in an aqueous buffer at 298 K:

Step 1: \ce{NH2OH + (CH3)2CO <=>[k_1][k_{-1}] I}

Step 2: \ce{I + H+ ->[k_2] Oxime + H2O + H+}

Given the following kinetic and thermodynamic parameters: $k_1 = 1.0 \times 10^2 \, \text{M}^{-1}\text{s}^{-1}$ $k_{-1} = 1.0 \times 10^{-2} \, \text{s}^{-1}$ $k_2 = 1.0 \times 10^4 \, \text{M}^{-1}\text{s}^{-1}$ Acid dissociation constant of \ce{NH3+OH}, $K_a = 1.0 \times 10^{-6} \, \text{M}$

Assuming the intermediate $I$ is in a steady state, and the total concentration of hydroxylamine ($[\ce{NH2OH}]_{\text{total}} = [\ce{NH2OH}] + [\ce{NH3+OH}]$) is much greater than $[I]$, at what pH will the initial rate of oxime formation be maximized?