For reaction $\mathrm{RX}+{\mathrm{OH}}^{-}\to \mathrm{ROH}+{\mathrm{X}}^{-}$, rate expression is 

$\mathrm{R}=4.7\times {10}^{-5}\left[\mathrm{RX}\right]\left[{\mathrm{OH}}^{-}\right]+2.4\times {10}^{-5}\left[\mathrm{RX}\right]$.

What % of reactant react by ${\mathrm{S}}_{\mathrm{N}}2$ mechanism when $\left[{\mathrm{OH}}^{-}\right]=0.001$ molar? 

$$\begin{gathered} {\mathrm{r}}_{\left({\mathrm{SN}}^1\right)}=\mathrm{K}{\left[\mathrm{R}-\mathrm{X}\right]}^1 \\ {\mathrm{r}}_{\left({\mathrm{SN}}^2\right)}=\mathrm{K}{\left[\mathrm{R}-\mathrm{X}\right]}^1{\left[{\mathrm{OH}}^{-}\right]}^1 \\ {\mathrm{r}}_{{\mathrm{SN}}^2}=4.7\times {10}^{-5}\left[\mathrm{R}-\mathrm{X}\right]\left[{10}^{-3}\right] \\ {\mathrm{r}}_{{\mathrm{SN}}^1}=2.4\times {10}^{-5}\left[\mathrm{R}-\mathrm{X}\right] \end{gathered}$$

Fraction of reactant Reacted by ${\mathrm{S}}_{\mathrm{N}}2$ mechanism 

            $=\frac{4.7\times {10}^{-5}\left[\mathrm{RX}\right]\left[{\mathrm{OH}}^{-}\right]}{4.7\times {10}^{-5}\left[\mathrm{RX}\right]\left[{\mathrm{OH}}^{-}\right]+2.4\times {10}^{-5}\left[\mathrm{RX}\right]}$

$=\frac{4.7\times {10}^{-5}\times {10}^{-3}\left[\mathrm{R}-\mathrm{X}\right]}{4.7\times {10}^{-5}\times {10}^{-3}\left[\mathrm{R}-\mathrm{X}\right]+2.4\times {10}^{-5}\left[\mathrm{R}-\mathrm{X}\right]}\times 100$

             =  1.9