For a first order reaction $A \to B$,the reaction rate at reactant concentration of $0.01 \ M$ is found to be $2.0 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$. The half-life period of the reaction is .......... $sec$.

Time required for completion of $90 \%$ of a first order reaction is '$t$'. What is the time required for completion of $99.9 \%$ of the reaction?

For a first-order reaction $A \to B$,what will be the slope of the graph of $t$ versus $\log(a - x)$?

For a first order reaction $A_5 \rightarrow 5 B_2$,the concentration vs time plot is as shown. The half-life of the reaction is

The rate constant and half-life of a first-order reaction are related to each other as -

The reaction $A + B \xrightarrow{k}$ product is first order with respect to $A$ and zero order with respect to $B$. If $a_0$ and $a_t$ are the concentrations of $A$ at $t = 0$ and after time $t \, sec$ respectively,then select the correct relationship -