Read the following industrial methods for the preparation of ${\mathrm{H}}_2{\mathrm{SO}}_4$ and answer the question at the end. Professor Molina of the Massachusetts Institute of Technology won the 1995 Noble prize in Chemistry for his work on atmospheric chemistry. One reaction that he studied in detail is the acid rain reaction which produces ${\mathrm{H}}_2{\mathrm{SO}}_4$ in the atmosphere. He proposed two possible stoichiometric reactions:

Proposal A: ${\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{SO}}_3\left(\mathrm{g}\right)⟶{\mathrm{H}}_2{\mathrm{SO}}_4\left(\mathrm{g}\right)$

Proposal B:  $2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{SO}}_3\left(\mathrm{g}\right)⟶{\mathrm{H}}_2{\mathrm{SO}}_4\left(g\right)+{\mathrm{H}}_2\mathrm{O}\left(g\right)$

Using the simple collision theory, what reaction orders would be expected for proposal B? Proposal B is thought to proceed by the following two-step process :

${\mathrm{SO}}_3+2{\mathrm{H}}_2\mathrm{O}\underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons }}{\mathrm{SO}}_3\cdot 2{\mathrm{H}}_2\mathrm{O}$               (fast)

${\mathrm{SO}}_3\cdot {2\mathrm{H}}_2\mathrm{O}\stackrel{{\mathrm{K}}_2}{⟶}{\mathrm{H}}_2{\mathrm{SO}}_4+{\mathrm{H}}_2\mathrm{O}$                     (slow)

$\left({\mathrm{SO}}_9\cdot 2{\mathrm{H}}_2\mathrm{O}\right.$ is a complex which is stabilized by hydrogen bonds and $k_2\ll k_1$ or $\left.k_{-1}\right)$