Textbook $3\mathrm{.}36$

Ammonia $($NH$3)$ is a common constituent of many natural waters and wastewaters. When water$-$containing ammonia is treated at a water treatment plant,the ammonia reacts with the disinfectant hypochlorous acid $(HOCl)$ in solution to form monochloramine $(NH2Cl)$ as follows:

The rate law for this reaction is

$($a$)$ What is the reaction order with respect to $NH3?$

$($b$)$ What order is this reaction overall?

$($c$)$ If the HOCl concentration is held constant and equals ${10}^{-4}M,$ and the rate constant equals ${5\mathrm{.}1}^{**}{10}^6\frac{L}{m}$ole$-s,$ calculate the time required to reduce the concentration of $NH3$ to one$-$half its original value.