The kinetic data for the given reaction $\mathrm{A}\left(\mathrm{g}\right)+2 \mathrm{B}( \mathrm{g})⟶\mathrm{C}\left(\mathrm{g}\right)$ is provided in the following table for three experiments at $300 \mathrm{K}.$

Ex. No.	$[\mathrm{A}/\mathrm{M}]$	$[\mathrm{B}/\mathrm{M}]$	[Initial rate $\left({\mathrm{Msec}}^{-1}\right)$]
1	$0.01$	$0.01$	$6.930\times {10}^{-6}$
2	$0.02$	$0.01$	$1.386\times {10}^{-5}$
3	$0.02$	$0.02$	$1.386\times {10}^{-5}$

In another experiment starting with initial concentration of $0.5$ and $1\mathrm{M}$ respectively for $\mathrm{A}$ and $\mathrm{B}$ at $300 \mathrm{K}.$ Find the rate of reaction after $50$ minutes from start of experiment (in $\mathrm{M}/\sec$)?

In three different reactions, involving a single reactant in each case, a plot of the rate of the reaction on the $\mathrm{y}$-axis, versus the concentration of the reactant on the $\mathrm{x}$-axis, yields three different curves are shown below.

$\left(\mathrm{I}\right)$ 

$\left(\mathrm{II}\right)$ 

$\left(\mathrm{III}\right)$ 

What are the possible orders of the reactions $\left(\mathrm{I}\right),\left(\mathrm{II}\right),\left(\mathrm{III}\right)$?

Which integrated equation is correct for the following $1^{\mathrm{st} }$ order reaction started with only $\mathrm{A}\left(\mathrm{g}\right)$ in a closed rigid vessel?

$\mathrm{A}\left(\mathrm{g}\right)⟶\mathrm{B}\left(\mathrm{g}\right)+\mathrm{C}\left(\mathrm{g}\right)+\mathrm{D}\left(\mathrm{g}\right)$

${\mathrm{P}}_{\mathrm{i}}=$ initial pressure, ${\mathrm{P}}_{\mathrm{t}}=$ total pressure at time $\mathrm{t}$.

The following data were obtained in an experiment on inversion of cane sugar; (a first order kinetics)

The rate constant (in ${\mathrm{second}}^{-1}$) is $[\ln 2=0.693]$

The decomposition of $N_2{O}_5$in chloroform was followed by measuring the volume of O₂ gas evolved : $2N_2{O}_5$($CC{1}_{4 }$)$\to$$2N_2{O}_4$($CC{1}_{4 }$) + $O_2 \left(g\right)$. The maximum volume of $O_{2 }$gasobtained was$100c{m}^3$. In 500 minutes, $90c{m}^3$of $O_{2 }$were evolved. The first order rate constant $\left(in mi{n}^{-1}\right)$ for the disappearance of $N_2{O}_5$is :