Half life of zero order reaction $A \rightarrow \text{product}$ is $1 \ \text{hour}$,when initial concentration of reactant is $2.0 \ \text{mol L}^{-1}$. The time required to decrease concentration of $A$ from $0.50$ to $0.25 \ \text{mol L}^{-1}$ is:

$A$ zero order reaction has a half-life time of $0.2 \ min$. If the initial concentration of the reactant is $0.2 \ mol \ dm^{-3}$,find the rate constant.

Consider the reaction $aX \to bY$, for which the rate constant at $30^\circ C$ is $1 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}$. Which of the following statements are true?
$A$. When concentration of $X$ is increased to four times, the rate of reaction becomes $16$ times.
$B$. The reaction is a second order reaction.
$C$. The half-life period is independent of the concentration of $X$.
$D$. Decomposition of $N_2O_5$ is an example of the above reaction.
$E$. $\ln \frac{[R]_0}{[R]}$ vs time is valid for the above reaction.

The unit of the velocity constant in case of zero order reaction is

For a reaction,$A \rightarrow B$,the rate equation is $r = K[A]^0$. If the initial concentration of the reactant is $a \ mol \ dm^{-3}$,find the half-life time of the reaction.

In the following reaction $A \to B + C,$ the rate constant is $0.001 \ M \ s^{-1}.$ If we start with $1 \ M$ of $A,$ then the concentrations of $A$ and $B$ after $10 \ minutes$ are respectively: