If the rate of reaction is given by $Rate = K [A]^{3/2} [B]^{-1/2}$,then find the order of the reaction.

The following graph shows the relationship between $(a-x)^{-1}$ and time $t$ for a second-order reaction. If $\theta = \tan^{-1}(1/2)$ and $OA = 2 \ L \ mol^{-1}$,then the rate at the start of the reaction will be (in $mol \ L^{-1} \ min^{-1}$):

The mechanism of the decomposition of nitramide $(NH_2NO_2)$ in aqueous solution is given below:
$NH_2NO_2(aq) + OH^-(aq) \to NHNO_2^-(aq) + H_2O(l)$
$NHNO_2^-(aq) \to N_2O(aq) + OH^-(aq)$
Identify the catalyst for this reaction.

For a reaction,$A + B \rightarrow$ products,the rate of the reaction at various concentrations is given below. The rate law for the above reaction is:

Expt. no.	$[A]$	$[B]$	Rate $(\text{mol} \ \text{dm}^{-3} \ \text{s}^{-1})$
$1$	$0.2$	$0.2$	$2$
$2$	$0.2$	$0.4$	$4$
$3$	$0.6$	$0.4$	$36$

The hydrolysis of ethyl acetate is a reaction of $.........$ order.
$CH_3COOEt + H_2O \xrightarrow{H^{+}} CH_3COOH + EtOH$

For the reaction between $A$ and $B$,the initial rate of reaction $(r_0)$ was measured for different initial concentrations of $A$ and $B$ as given below. Determine the order of the reaction with respect to $A$ and $B$ respectively.

$[A] / mol \ L^{-1}$	$0.2, 0.2, 0.4$
$[B] / mol \ L^{-1}$	$0.3, 0.1, 0.05$
$r_0 / mol \ L^{-1} s^{-1}$	$5.0 \times 10^{-5}, 5.0 \times 10^{-5}, 1.4 \times 10^{-4}$