In a first order reaction $A \to B,$ if $k$ is the rate constant and the initial concentration of the reactant $A$ is $0.5 \ M,$ then the half-life is:

For the reaction $A \rightarrow B$,the following graph was obtained. The time required (in seconds) for the concentration of $A$ to reduce to $2.5 \ g \ L^{-1}$ (if the initial concentration of $A$ was $50 \ g \ L^{-1}$) is $........$ (Nearest integer). Given: $\log 2 = 0.3010$.

The reaction $2N_2O_5 \,(g) \to 4NO_2 \,(g) + O_2 \,(g)$ follows first order kinetics. The pressure of a vessel containing only $N_2O_5$ was found to increase from $50 \, mmHg$ to $87.5 \, mmHg$ in $30 \, min$. The pressure exerted by the gases after $60 \, min$ will be .......... $mmHg$ (assume temperature remains constant).

Calculate the half-life period of a first-order reaction if the rate constant of the reaction is $0.02 \ min^{-1}$. (in $min$)

The plot of $t_{1/2}$ versus $[R]_0$ for a reaction is a straight line parallel to the $x$-axis. The unit for the rate constant of this reaction is:

The rate constant for a first-order reaction is $0.02232 \ min^{-1}$. Calculate the time required for $75 \%$ completion of the reaction. (in $min$)