Reaction rate unit conversion: how to convert from molarity to ppm
We can do it in two ways:

1) For dilute solutions, ppm and mg/L is equivalent. So, for dilute solutions, the straightforward conversion scheme should look like::
$$ppm=\frac{mol}{L}\times MW\times 1000$$  

2) with no assumption::  

first, remember that $ppm=y_i \times 10^{-6}$

$$ppm=\frac{mol}{L} \times \frac{x gm}{mol} \times \frac{1 L}{10^{-3} m^3} \times \frac{m^3}{y~gm} \times 10^{-6}$$  

here, x is the MW of solute and y is the density of the solvent (for dilute solutions) or solution in $\frac{gm}{m^3}$