The rate of a first order reaction is $1.5 \times 10^{-2} \ mol \ L^{-1} \ \min^{-1}$ at $0.5 \ M$ concentration of the reactant. The half life of the reaction is ....... $\min$

$A$ reactant undergoes $90\%$ decomposition in $366 \text{ minutes}$. What is the half-life of this first-order reaction?

Consider the following first-order gas-phase reaction: $A_{(g)} \to B_{(g)} + C_{(g)}$. At time $t$,the total pressure is $p_t \ atm$. Derive the integrated rate equation for this reaction.

For a first order gas phase elementary reaction $A_{(g)} \xrightarrow{k} 2B_{(g)}$,which of the following is $INCORRECT$?

$t_{1/4}$ can be taken as the time taken for the concentration of a reactant to drop to $3/4$ of its initial value. If the rate constant for a first order reaction is $K$,the $t_{1/4}$ can be written as (in $/K$)

Consider the following two first order reactions occurring at $298 \ K$ with same initial concentration of $A$: $(1)$ $A \rightarrow B$; rate constant, $k=0.693 \ min^{-1}$ $(2)$ $A \rightarrow C$; half-life, $t_{1/2}=0.693 \ min$. Choose the correct option.