Question #44822

In aqueous phase kinetics, the protonation of a highly sterically hindered amine, $\ce{B(aq)}$, is gated by the shedding of its primary hydration shell before an effective collision with $\ce{H+}$ can occur. The reaction proceeds via the following mechanism:

Step 1: $\ce{B(aq) <=>[k_1][k_{-1}] B^*(aq)}$ (Formation of reactive desolvated intermediate) Step 2: $\ce{B^*(aq) + H+(aq) ->[k_2] BH+(aq)}$

At $298\text{ K}$, the rate constants are $k_1 = 2.0 \times 10^3 \text{ s}^{-1}$, $k_{-1} = 1.0 \times 10^8 \text{ s}^{-1}$, and $k_2 = 4.0 \times 10^9 \text{ M}^{-1}\text{s}^{-1}$.

Calculate the initial rate of formation of $\ce{BH+(aq)}$ when the initial concentration of the amine is $[\ce{B}]_0 = 5.0 \times 10^{-4} \text{ M}$ and the solution is buffered at $\text{pH} = 1.125$ (Assume $[\ce{H+}] = 0.075 \text{ M}$).