$R \rightarrow P$ 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

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

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 ( $\log 2=0.30, \log 3=0.48, \log 4=0.60$ )