Give the relation between half-life $(t_{1/2})$ and initial concentration of reactant $([R]_0)$ for an $(n-1)^{th}$ order reaction.

The hypothetical reaction : $2A + B \to C + D$ is catalyzed by $E$ as indicated in the possible mechanism below -
Step-$1$ : $A + E \rightleftharpoons AE$ (fast)
Step-$2$ : $AE + A \to A_2 + E$ (slow)
Step-$3$ : $A_2 + B \to C + D$ (fast)
What rate law best agrees with this mechanism?

The rate of a reaction depends upon the

Consider the following data for the given reaction $2 HI_{(g)} \rightarrow H_{2_{(g)}} + I_{2_{(g)}}$. The order of the reaction is:

Experiment	$1$	$2$	$3$
$[HI] \ (mol \ L^{-1})$	$0.005$	$0.01$	$0.02$
Rate $(mol \ L^{-1} \ s^{-1})$	$7.5 \times 10^{-4}$	$3.0 \times 10^{-3}$	$1.2 \times 10^{-2}$

For the following homogeneous reaction scheme,the rate constant has units for the reaction $A + B \xrightarrow{K} C$:

For a chemical reaction,$2A + 2B \to C + D$,the order of reaction is $1$ with respect to $A$ and $1$ with respect to $B$. The initial rate of the reaction is $4 \times 10^{-2} \ mol \ L^{-1} \ s^{-1}$. When $50\%$ of the reactants are converted into products,the rate of the reaction would become: