Chapter 20, Problem 20.77E

The nitration of methanol, ${\text{CH}}_{\text{3}}\text{OH}$, by nitrous acid is thought to proceed via the following mechanism:

$\begin{array}{c}{\text{CH}}_{\text{3}}\text{OH}+{\text{H}}^{+}\to {\text{CH}}_{\text{3}}{\text{OH}}_{\text{2}}{}^{+}\\ {\text{CH}}_{\text{3}}{\text{OH}}_{\text{2}}{}^{+}\to {\text{CH}}_{\text{3}}{}^{+}+{\text{H}}_{\text{2}}\text{O}\\ {\text{CH}}_{\text{3}}{}^{+}+{\text{NO}}_{\text{2}}{}^{-}\to {\text{CH}}_{\text{3}}{\text{NO}}_{\text{2}}\end{array}$

Suppose the first step is the RDS. What is the expected rate law in terms of the original reactants?