For a first order decomposition of a certain reaction, rate constant is given by the equation. $\log k\left(s^{-1}\right)=7.14-\frac{1 \times 10^4 \mathrm{~K}}{T}$. The activation energy of the reaction ( in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) is

$$ \left(R=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right) $$

Consider a general first order reaction,

$$ A(g) \longrightarrow B(g)+C(g) $$

If the initial pressure is 200 mm and after 20 minutes it is 250 mm , then the half-life period of the reaction (in minutes) is ( $\log 2=0.30, \log 3=0.48, \log 4=0.60$ )

For the reaction $R \rightarrow P$, half life is independent of initial concentration of the reactant, $R$. Which one of the following graphs is not correct for the reaction?

For the gaseous reaction, $\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}$

the rate can be expressed as

$ \begin{array}{l} -\frac{d\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]}{d t}=K_{1}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] \\\\ +\frac{d\left[\mathrm{NO}_{2}\right]}{d t}=K_{2}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] \\\\ +\frac{d\left[\mathrm{O}_{2}\right]}{d t}=K_{3}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] \end{array} $

The correct relation between $K_{1}, K_{2}$ and $K_{3}$