The initial concentration of ${\mathrm{N}}_2{\mathrm{O}}_5$ in the following first order reaction, ${\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)⟶2{\mathrm{NO}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)$
was $1.24\times {10}^{-2} \mathrm{mol}{ \mathrm{L}}^{-1}$ at $318 \mathrm{K}$. The concentration of ${\mathrm{N}}_2{\mathrm{O}}_5$ after $60$ minutes was $0.20\times {10}^{-2} \mathrm{mol}{ \mathrm{L}}^{-1}.$ Calculate the rate constant of the reaction at $318 \mathrm{K}.$

For the thermal decomposition of azomethane, ${\mathrm{CH}}_3{ \mathrm{N}}_2{\mathrm{CH}}_3$ at $600 \mathrm{K}$ to ${\mathrm{N}}_2$ and ${\mathrm{C}}_2{\mathrm{H}}_6$

$\begin{array}{lccl}\mathrm{t}\left(\sec \right)& 0& 1000& 2000\\ {\mathrm{P}}_{\mathrm{A}}\left({10}^{-2}\mathrm{torr}\right)& 8.20& 5.72& 3.99\end{array}$ $\begin{array}{lll}& 3000& 4000\\ & 2.78& 1.94\end{array}$

where ${\mathrm{P}}_{\mathrm{A}}$ is the partial pressure of azomethane. Show that the decomposition is a first order reaction and find the rate constant.

The following data were obtained during the first order thermal decomposition of ${\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)$ at constant volume: $2{ \mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)⟶2{ \mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$

Calculate rate constant.

Hydrolysis of methyl acetate in aqueous solution has been studied by titrating the liberated acetic acid against sodium hydroxide. The concentration of the ester at different times is given below:

Show that it follows a pseudo first order reaction, as the concentration of water remains nearly constant $\left(55 \mathrm{mol}{ \mathrm{L}}^{-1}\right)$ during the course of the reaction. What is the value of ${\mathrm{k}}^{\text{'}}$ in this equation? Rate $={\mathrm{k}}^{\text{'}}\left[{\mathrm{CH}}_3{\mathrm{COOCH}}_3\right]\left[{\mathrm{H}}_2\mathrm{O}\right]$

[Hint. $\mathrm{k}=\mathrm{k}\text{'}\left[{\mathrm{H}}_2\mathrm{O}\right]=\frac{2.303}{\mathrm{t}}\log \frac{{\mathrm{C}}_0}{{\mathrm{C}}_{\mathrm{t}}}$]

The kinetics of hydrolysis of methyl acetate in excess of hydrochloric acid solution at $298 \mathrm{K}$ were followed by withdrawing $2 \mathrm{mL}$ of the reaction mixture at intervals of time (t), adding $50 \mathrm{mL}$ of water and titrating against baryta-water. The following results were obtained:

Determine the velocity constant of the hydrolysis.

[Hint. Substitute $\mathrm{a}=34.8-18.5=16.3$, and $\mathrm{a}-\mathrm{x}=(34.8-19.1)$, $\left(34.8-20.1\right),\left(34.8-21.6\right),\left(34.8-24.6\right)$ at$\mathrm{t}=10, 28, 58$ and $115$ respectively in $\mathrm{k}=2.303/t \log a/a-\mathrm{x}$ and get $\mathrm{k}]$

At a certain temperature, the half-life period for the decomposition for the substance A is as follows:

$\mathrm{P}\left(\mathrm{mm}\right)$                        $500$            $700$           $900\mathrm{mm}$

Half-life period              $18$             $17.9$              $18$

What is order of reaction ?

Following data were obtained for the catalytic decomposition of ammonia:

Find the order of reaction.