Write the rate equation for the following reactions:
$1.$ $5 Br^{-}_{(aq)} + BrO^{-}_{3_{(aq)}} + 6 H^{+}_{(aq)} \rightarrow 3 Br_{2_{(aq)}} + 3 H_2O_{(l)}$
$2.$ $R \rightarrow P$
$3.$ $C_4H_9Cl + H_2O \rightarrow C_4H_9OH + HCl$

The rate of reaction is expressed in terms of the change in concentration of reactants and products over time,divided by their respective stoichiometric coefficients.
$1.$ $\text{Rate} = -\frac{1}{5} \frac{d[Br^{-}]}{dt} = -\frac{d[BrO_3^{-}]}{dt} = -\frac{1}{6} \frac{d[H^{+}]}{dt} = \frac{1}{3} \frac{d[Br_2]}{dt} = \frac{1}{3} \frac{d[H_2O]}{dt}$
$2.$ $\text{Rate} = -\frac{d[R]}{dt} = \frac{d[P]}{dt}$
$3.$ $\text{Rate} = -\frac{d[C_4H_9Cl]}{dt} = -\frac{d[H_2O]}{dt} = \frac{d[C_4H_9OH]}{dt} = \frac{d[HCl]}{dt}$