Write the differential rate expression for the following reactions and determine their order of reaction:
$1) \ 2 N_2O_5(g) \rightarrow 4 NO_2(g) + O_2(g)$
$2) \ C_4H_9Cl(aq) + OH^-(aq) \rightarrow C_4H_9OH(aq) + Cl^-(aq)$

For reaction $1$: $2 N_2O_5 \rightarrow 4 NO_2 + O_2$
The differential rate expression is: $Rate = -\frac{1}{2} \frac{d[N_2O_5]}{dt} = \frac{1}{4} \frac{d[NO_2]}{dt} = \frac{d[O_2]}{dt}$.
This is a first-order reaction with respect to $N_2O_5$,so the overall order of reaction is $1$.
For reaction $2$: $C_4H_9Cl + OH^- \rightarrow C_4H_9OH + Cl^-$
The differential rate expression is: $Rate = -\frac{d[C_4H_9Cl]}{dt} = -\frac{d[OH^-]}{dt} = \frac{d[C_4H_9OH]}{dt} = \frac{d[Cl^-]}{dt}$.
This is a nucleophilic substitution reaction (specifically $S_N2$ mechanism),which is a second-order reaction (first order with respect to both $C_4H_9Cl$ and $OH^-$),so the overall order of reaction is $2$.