When the value of rate constant $(k)$ is $2.0 \text{ min}^{-1}$, then what will be the half-life of the reaction $(t_{1/2})$ in seconds?

Azo isopropane decomposes according to the equation:
$((CH_3)_2CHN)_2N_{2(g)} \xrightarrow{250 - 290 \ ^oC} N_{2(g)} + C_6H_{14(g)}$
It is found to be a first order reaction. If the initial pressure is $P_o$ and the total pressure of the mixture at time $t$ is $P_t$,then the rate constant $K$ is given by:

Which of the following is correct regarding $t_{1/2}$ of a reaction if we double the initial concentration of a reactant in a first-order reaction?

Consider the first order reaction $R \to P$. The fraction of molecules decomposed in the given first order reaction can be expressed as:

For a reaction,$r = k[A]$. If $50 \%$ of $A$ is decomposed in $120 \ \text{minutes}$,the time taken for $90 \%$ decomposition of $A$ is $............ \ \text{minutes}$.

Slope of the graph between $\log \frac{[A]_0}{[A]_t}$ ($y$-axis) and time ($x$-axis) for a first-order reaction is equal to: