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 reaction $3ClO^{-} \rightarrow ClO_{3}^{-} + 2Cl^{-}$ occurs in the following two steps:
$(i)$ $ClO^{-} + ClO^{-} \xrightarrow{K_{1}} ClO_{2}^{-} + Cl^{-}$ (Slow step)
$(ii)$ $ClO_{2}^{-} + ClO^{-} \xrightarrow{K_{2}} ClO_{3}^{-} + Cl^{-}$ (Fast step)
Then the rate of the given reaction is equal to . . . . . . .

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

The mechanism of the reaction $2NO_{(g)} + Br_{2(g)} \rightarrow 2NOBr_{(g)}$ is given by:
$1) NO_{(g)} + Br_{2(g)} \rightleftharpoons NOBr_{2(g)}$ (fast)
$2) NOBr_{2(g)} + NO_{(g)} \rightarrow 2NOBr_{(g)}$ (slow)
If the second step is the rate-determining step,what is the order of the reaction with respect to $NO_{(g)}$?

The reaction $2N_2O_5 \rightleftharpoons 4NO_2 + O_2$ follows first order kinetics. Hence,the molecularity of the reaction is

From the rate expression for the following reaction,determine its order of reaction and the dimensions of the rate constant: $(iv) \ C_{2}H_{5}Cl_{(g)} \rightarrow C_{2}H_{4(g)} + HCl_{(g)} \quad \text{Rate} = k[C_{2}H_{5}Cl]$