Write the differential rate expression for the following reactions and determine their order of reaction:
$1. CHCl_3 + Cl_2 \rightarrow CCl_4 + HCl$
$2. CH_3COOC_2H_5 + H_2O \rightarrow CH_3COOH + C_2H_5OH$

(N/A) For reaction $1$: $CHCl_3 + Cl_2 \rightarrow CCl_4 + HCl$
The experimental rate law is $Rate = k[CHCl_3][Cl_2]^{1/2}$.
The differential rate expression is: $-\frac{d[CHCl_3]}{dt} = -\frac{d[Cl_2]}{dt} = \frac{d[CCl_4]}{dt} = \frac{d[HCl]}{dt} = k[CHCl_3][Cl_2]^{1/2}$.
The order of reaction is $1 + 1/2 = 1.5$.
For reaction $2$: $CH_3COOC_2H_5 + H_2O \rightarrow CH_3COOH + C_2H_5OH$
This is a pseudo-first-order reaction because water is in large excess.
The experimental rate law is $Rate = k'[CH_3COOC_2H_5]$.
The differential rate expression is: $-\frac{d[CH_3COOC_2H_5]}{dt} = k'[CH_3COOC_2H_5]$.
The order of reaction is $1$.