$A \rightarrow P$ is a first order reaction. At 300 K this reaction was started with $[A]=0.5 \mathrm{~mol} \mathrm{~L}^{-1}$.

The rate constant of reaction was $0.125 \mathrm{~min}^{-1}$. The same reaction was started separately with $[A]=1 \mathrm{molL}^{-1}$ at 300 K . The rate constant (in $\mathrm{min}^{-1}$ ) now is

$R \rightarrow P$ is a first order reaction. For this reaction a graph of $\ln [R]$ (on $y$-axis) and time (on x -axis) gave a straight line with negative slope. The intercept on $y$-axis is equal to ( $k=$ rate constant)

The half-life of a zero order reaction $A \rightarrow$ products, is 0.5 hour. The initial concentration of $A$ is $4 \mathrm{molL}^{-1}$.

How much time (in hr ) does it take for its concentration to come from $2.0 \mathrm{~mol} \mathrm{~L}^{-1}$ to $1.0 \mathrm{~mol} \mathrm{~L}^{-1}$ ?

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

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